Monografia

Monografia
The Henryk Niewodniczański
INSTITUTE OF NUCLEAR PHYSICS
Polish Academy of Sciences
ul. Radzikowskiego 152, 31-342 Kraków, Poland
www.ifj.edu.pl/publ/hab/
Kraków, January 17, 2013
Measurements of final states with
τ leptons in proton-proton collisions
using the ATLAS detector at the LHC
Anna Kaczmarska
Habilitation Thesis
This work was supported in part by the Polish Ministry of Higher Education
under grant no. NN202127937.
2
Wydrukowano nakładem Instytutu Fizyki Jadrowej
˛
Polskiej Akademii Nauk
Kraków, 2013
Recenzent: Prof. dr hab. Barbara Wosiek
ISBN 978-83-934248-8-7
3
Physics is like sex: sure, it may give some practical
results, but that’s not why we do it.
- Richard Feynman -
4
5
Abstract
This monograph describes first analyses of processes with τ leptons in final state that have been performed with
√
proton-proton collision data at the centre-of-mass energy of s = 7 TeV collected with the ATLAS detector at
the LHC. Described studies are based on early data, recorded in 2010 and corresponding to an integrated luminosity of 35 pb−1 . Presented Higgs boson(s) searches, requiring higher statistics samples, are based on more data,
corresponding to an integrated luminosity of 1.06 fb−1 and collected in 2010 and the first half of 2011.
The reconstruction algorithms and identification methods for hadronically decaying τ leptons in the ATLAS
experiment are described in detail. Validation of those algorithms in data as well as the first attempts to estimate
the rate of the mis-identification of Quantum Chromodynamics jets or electrons as τ candidates are also presented.
A dedicated Chapter is devoted to the first measurements of Z → ττ and W → τν production cross sections. The
use of the latter process for determination of the hadronic τ decay identification efficiency is also reported.
The early analyses of Higgs boson(s) searches with τ leptons in final states, presented in this document, cover
studies of both the Standard Model and Minimal Supersymmetric Standard Model neutral Higgs boson(s) decaying
into the H → ττ final state as well as Minimal Supersymmetric Standard Model charged Higgs boson decays,
H + → τν. No significant excess over the expected background is observed in any of these studies. Nevertheless,
even though performed on limited statistics, they provided improved exclusion limits as compared to those obtained
by previous experiments.
Streszczenie
Niniejsza rozprawa habilitacyjna opisuje pierwsze analizy procesów z leptonami τ w stanach końcowych przeprowadzone na danych zebranych przez detektor ATLAS na akceleratorze LHC. Użyte dane zostały zgromad√
zone przy zderzeniach proton-proton z energia˛ w środku masy s = 7 TeV. Opisane wyniki uzyskano w wi˛ekszości z wykorzystaniem pierwszych danych zebranych w roku 2010, odpowiadajacych
˛
wycałkowanej świetlności
−1
35 pb . Wyjatek
˛ stanowia˛ rezultaty poszukiwań bozonu(ów) Higgsa, gdyż wymagały one wi˛ekszej liczby zarejestrowanych przypadków. Zostały wi˛ec one oparte o dane odpowiadajace
˛ wycałkowanej swietlności 1.06 fb−1 ,
zebrane zarówno w roku 2010 jak i w pierwszej połowie roku 2011.
Praca zawiera szczegółowy opis algorytmów użytych do rekonstrukcji i identyfikacji hadronowych rozpadów
leptonów τ. Przedstawione zostały także testy tych algorytmów na zebranych danych doświadczalnych, oraz
pierwsze próby wyznaczenia cz˛estości mylnej identyfikacji dżetów Chromodynamiki Kwantowej (QCD) lub elektronów jako kandydatów na leptony τ. Osobny rozdział poświ˛econy został pierwszym pomiarom przekrojów
czynnych procesów Z → ττ i W → τν w eksperymencie ATLAS oraz użyciu przypadków W → τν do oszacowania efektywności identyfikacji hadronowych rozpadów τ.
W ostatnich rozdziałach podsumowano pierwsze analizy majace
˛ na celu poszukiwanie bozonu(ów) Higgsa
w rozpadach z leptonami τ w stanach końcowych. Opisano zarówno poszukiwania prowadzone w ramach Modelu Standardowego jak i jego Minimalnego Supersymetrycznego rozszerzenia. W żadnej z opisanych analiz
nie znaleziono znaczacego
˛
sygnału ponad tło. Niemniej, analizy te, nawet przeprowadzone na małej statystyce
dost˛epnych wówczas przypadków, zaw˛eziły limity wykluczeń wyznaczone przez wcześniejsze eksperymenty.
6
Acknowledgments
This monograph is the result of many years of work and effort, and I could not have completed it without the
support of many people. Let me devote this page to all who helped me.
To Elżbieta Richter-Was,
˛ without whose motivation and encouragement I would not have written this monograph. She provided the vision and advise necessary for me to understand how interesting the τ lepton physics
field is. I am thankful to her for always having time for discussions, for sharing her impressive knowledge and
experience and for her criticism always honest and constructive. I will always owe her a debt of gratitude for all
she has done for me.
To Piotr Malecki, without whom I would not have been in the ATLAS experiment and who taught me that a
true experimentalist should not be scared of challenges and should be able to learn everything, even from scratch
(but with a manual).
To Barbara Wosiek, for continuous support of my research and in particular, of preparing this monograph.
To the Tau Working Group of the ATLAS experiment, and its former and present conveners, for creating the
stimulating and pleasant atmosphere to work on our beloved leptons. Special thanks go to Stan Lai who was
always full of laughter, joy, and support for me and to Zofia Czyczula for long discussions about physics and life.
To the Z → ττ Working Group and in particular to Susanne Kuehn, Elias Coniavitis and Matthew Beckingham
for spending countless and sometimes late hours working to understand and solve problems related to the first
Z → ττ process observation and its cross section measurement.
To Paris LPNHE group where I had a privilege to spend a lot of my time thanks to Polish-French IN2P3
collaboration and invitations from University Paris 7. In particular to Frederic Derue for numerous interesting
discussions and showing me how a beautiful country France is.
To my home institute ATLAS group for vibrant coffee discussions and for friendly and motivating place to
work. I will never forget all the experiences I have shared with you guys. I am very happy that, in many cases, our
friendship have extended well beyond working hours.
To Paweł Brückman, with whom I have the pleasure to stay in the same office, for sharing with me joys and
sorrows in the challenging life of a Polish physicist. Thank you for uplifting my soul every time I felt down.
To the ATLAS Collaboration for allowing me to participate in preparation of our experiment and then to share
the excitement of commissioning the ATLAS detector and analysing the first LHC data.
To Mariusz for being the most understanding husband in the world. Thank you for supporting me in everything
that I do. Finally, to my little son Iwo, for being my spark of optimism when I had hard time. I love you both a lot.
7
Statement on author’s contribution
The physics of τ leptons as well as reconstruction and identification of their hadronic decays have been my major
interest since 2006.
In years 2006-2010, I was creating, developing, maintaining and validating algorithms in the tauRec package, the official tool of the ATLAS Collaboration for reconstruction and identification of hadronically decaying τ
leptons. I introduced the track-based algorithm to complement the existing simple, calorimeter-based one. I was
leading the development of both algorithms and finally, their full merge into a single, robust and effective package.
It was used by the collaboration for all the studies with τ leptons in final states in the first ATLAS data. Prior to
the data taking period I was an author of several ATLAS internal notes documenting development and validation
of the tauRec package [1, 2, 3, 4, 5, 6, 7].
In years 2008-2009 when the ATLAS detector, already commissioned in its underground cavern, collected
several hundred million cosmic ray events I was participating in tests of the reconstruction and identification of
fake τ candidates in those data [8, 9]. I was continuing similar studies with the early data coming from protonproton collisions, first at the centre-of-mass energy of 900 GeV [10] and then 7 TeV [11, 12]. Thus I contributed
to all stages of obtaining results presented in Chapter 4 of the presented monograph, not only to the final outcome
but also to the long process of the creation, development and validation of the algorithms needed to obtain it.
In parallel to the development and validation of the reconstruction and identification of hadronically decaying
τ leptons I studied the Z → ττ process. As the first stage I prepared and optimised the cut flow of the analysis
in order to obtain the clear signal over the background. These studies were first performed using Monte Carlo
samples [13, 14]. After collision data taking had started, this analysis led to the first observation of Z → ττ decays
in the ATLAS experiment [15] and then to the cross section measurement of this process [16]. I was playing a
central role in those studies as a convener of the Z → ττ analysis group and co-editor of the observation conference
note and the cross section measurement paper. Thus my contribution both to the final Z → ττ studies described in
Chapter 5 as well as their preparation is a major one.
I was not directly involved in the W → τν studies described in Chapter 5 but I contributed to them by discussions, help and passing experience from my group to the parallel W → τν group doing their analysis after the
Z → ττ cross section had been measured.
I was not involved in the Standard Model and Minimal Supersymmetric Standard Model Higgs boson(s)
searches analyses described in Chapter 6 and Chapter 7 for completeness of the presented monograph. Nevertheless, it should be stressed that those studies would not be possible without the tauRec package developed by
myself in preceding years. Currently, I have started to work on searches for heavy charged Higgs bosons with τ
lepton final states.
Following the rules of the ATLAS Collaboration, only official, public results and plots are included in the
presented monograph, but references to internal notes are given.
8
Contents
1 Introduction
2
11
Physics with τ leptons
2.1 Properties of the τ lepton . . . . . . . . . . . . . . . . .
2.2 Standard Model processes with τ final states . . . . . . .
2.3 Standard Model Higgs boson searches with τ final states
2.4 MSSM Higgs bosons searches with τ final states . . . . .
2.5 Searching for New Physics with τ final states . . . . . .
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3 The ATLAS detector at the Large Hadron Collider
3.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . .
3.2 The ATLAS detector . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Inner Detector . . . . . . . . . . . . . . . . . . . . .
3.2.2 Calorimeters . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Muon spectrometer . . . . . . . . . . . . . . . . . . .
3.2.4 Trigger . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Luminosity detectors . . . . . . . . . . . . . . . . . . . . . .
3.4 Simulation of physics events . . . . . . . . . . . . . . . . . .
3.5 Particle reconstruction and identification . . . . . . . . . . . .
3.6 Data quality and preselection of events for early data analyses
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4 Reconstruction and identification of τ leptons
4.1 Reconstruction of τ decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 Track selection criteria for τ leptons reconstruction . . . . . . . . . . . . . . . . . .
4.1.2 Energy calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.3 π0 reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.4 τ lepton trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 τ leptons identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Rejection of QCD jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Electron and muon vetos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3 τ reconstruction and identification performance in data . . . . . . . . . . . . . . . . . . . .
4.3.1 Estimation of QCD multijets background efficiency as a function of signal efficiency
4.3.2 Measurement of the τ mis-identification probability from QCD jets . . . . . . . . .
4.3.3 Measurement of the mis-identification from electrons . . . . . . . . . . . . . . . . .
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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5 Standard Model processes with τ leptons
5.1 Z → ττ cross section measurement . . .
5.1.1 Data and Monte Carlo samples .
5.1.2 Selection of Z → ττ candidates
5.1.3 Background estimation . . . . .
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CONTENTS
10
5.2
5.3
5.4
5.1.4 Methodology for cross section calculation . . . . . . . . . .
5.1.5 Systematic uncertainties . . . . . . . . . . . . . . . . . . .
5.1.6 Cross section measurement . . . . . . . . . . . . . . . . . .
W → τν cross section measurement . . . . . . . . . . . . . . . . .
5.2.1 Data and Monte Carlo samples . . . . . . . . . . . . . . . .
5.2.2 Selection of W → τhad ν candidates . . . . . . . . . . . . . .
5.2.3 Background estimation . . . . . . . . . . . . . . . . . . . .
5.2.4 Method for cross section calculation . . . . . . . . . . . . .
5.2.5 Systematic uncertainties . . . . . . . . . . . . . . . . . . .
5.2.6 Cross section measurement . . . . . . . . . . . . . . . . . .
Measurement of the τ identification efficiency using W → τν process
5.3.1 Tag-and-probe method . . . . . . . . . . . . . . . . . . . .
5.3.2 Cross section normalisation method . . . . . . . . . . . . .
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Standard Model Higgs boson searches with τ final states
6.1 H → τlep τlep + jets final state . . . . . . . . . . . . .
6.1.1 Data and Monte Carlo samples . . . . . . . .
6.1.2 Objects and event selection . . . . . . . . . .
6.1.3 Background estimation . . . . . . . . . . . .
6.1.4 Systematic uncertainties . . . . . . . . . . .
6.1.5 Results . . . . . . . . . . . . . . . . . . . .
6.2 H → τlep τhad final state . . . . . . . . . . . . . . . .
6.3 Summary . . . . . . . . . . . . . . . . . . . . . . .
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7 MSSM Higgs bosons searches with τ lepton final states
7.1 Neutral MSSM Higgs bosons decaying to ττ pairs . . . . . .
7.1.1 Data sample and Monte Carlo simulations . . . . . .
7.1.2 Object and event selection . . . . . . . . . . . . . .
7.1.3 Background estimation . . . . . . . . . . . . . . . .
7.1.4 Systematic uncertainties . . . . . . . . . . . . . . .
7.1.5 Results for the neutral MSSM Higgs bosons searches
7.2 Search for charged Higgs bosons in tt¯ decays . . . . . . . .
7.2.1 Data sample and Monte Carlo simulations . . . . . .
7.2.2 The τhad +jets final state . . . . . . . . . . . . . . .
7.2.3 The one or two light leptons final state . . . . . . .
7.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . .
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93
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. 94
. 95
. 97
. 98
. 99
. 99
. 100
. 104
. 110
8 Summary
113
A Appendix: τ+ τ− mass reconstruction techniques
115
We were not yet prepared to claim that we had found a new charged lepton,
but we were ready to claim that we had found something new. To accentuate
our uncertainty I denoted the new particle by U for unknown in some of
our 1975-1977 papers. The name τ came later. This name was suggested
by Rapidis, who was then a graduate student and had worked with me in
the early 1970s on the e − µ problem. The letter τ is from the Greek τριτν
for "third" -the third charged lepton.
Martin Perl, The Discovery of the Tau Lepton, in "The Rise of
the Standard Model", Cambridge Univ. Press 1997.
1
Introduction
The history of the τ lepton began 39 years ago when Kobayashi and Maskawa [17] proposed a mechanism for
the CP violation which involved the hypothesis of a third generation of quarks and leptons. At that time there
was no experimental evidence and need for another generation. In early seventies, physicists tried to understand
differences between the muon and the electron. They believed that, perhaps, if other higher mass versions of these
particles exist, then through studying them a new understanding of the origin of lepton differences might emerge.
The first search was performed by two experiments at the ADONE storage ring [18], but its energy was below the
threshold for τ pair production. The next was the Mark I experiment on the SPEAR storage ring at SLAC which
began to take data in 1973. One year later the first anomalous e − µ events, with exactly two oppositely charged
particle tracks, consistent with being an electron and a muon, were observed. However, because of additional
checks and scepticism surrounding the discovery, the first claim of evidence for a new heavy lepton was published
only in late 1975 [19]. The existence of the τ was considered firmly established by the end of 1978 [20, 21].
Since that time, properties of the τ lepton have been extensively studied. Its mass, lifetime, decay modes
and polarisation, have been precisely measured in several experiments using e+ e− collisions, namely the LEP
experiments [22], BaBar [23], Belle [24], BESII [25], CLEO [26] and KEDR [27].
A new era for τ leptons came with hadron colliders, Tevatron [28] and Large Hadron Collider (LHC) [29]. For
those experiments, τ decays themselves are not of primary interest, but rather they are used to measure properties of
τ production processes. τ leptons, and particularly their hadronic decays, play an important role in measurements
of properties of electroweak bosons and top quarks. They are also crucial for discovery physics, like searches
for Higgs boson(s) [30, 31, 32, 33, 34, 35], Supersymmetry (SUSY) [36, 37, 38, 39, 40, 41, 42, 43, 44], or other
unexpected phenomena.
τ leptons are heavy particles with a measurable life-time, undergoing only electroweak interactions. They couple to SUSY particles via Yukawa coupling free from Quantum Chromodynamics (QCD) effects. The production
and decay vertices of τ leptons in typical LHC collisions are well separated in space, providing a potential for
measurements of the polarisation, spin correlations and parity of resonances decaying to τ leptons. The excellent
knowledge of their decay modes from low energy experiments make them an ideal signature for observations of
New Physics.
Despite the strong physics motivation for exploring data with τ leptons in the final state, reconstruction at
hadron colliders remains a very difficult task in terms of distinguishing interesting events from backgrounds dominated by the overwhelming QCD multijet production. Another related challenge is to provide an efficient triggering
for events with hadronic τ decays, while keeping trigger rates at levels manageable by the trigger system.
The LHC started operation in November 2009 and since 30 March 2010 proton-proton (pp) collisions at the
√
centre-of-mass energy of s = 7 TeV have been taking place. In this monograph, the first analyses involving τ
11
12
CHAPTER 1. INTRODUCTION
leptons, using data recorded by the ATLAS detector [45] during 2010 and corresponding to an integrated luminosity of 35 pb−1 , are presented. Only exception are the Higgs boson(s) searches, based on more data (from 2010 and
the first half of 2011) corresponding to an integrated luminosity of 1.06 fb−1 . Both tt¯ and New Physics processes
studied with τ leptons in final state are omitted in the monograph as they require higher statistics of data.
The document is organised as follows.
Chapter 2 gives a short description of τ lepton properties and decays. A review of processes with τ leptons in
final states follows after.
Chapter 3 briefly introduces the ATLAS detector, its subsystems and techniques for particle identification. As
Monte Carlo samples are used in described analyses, their production chain is also presented. For the first data
studies, similar preselection of events, based on detector performance is usually applied. It is described roughly at
the end of this Chapter.
In Chapter 4, the algorithms for the τ lepton reconstruction and identification are presented. Their performance
in terms of identification efficiencies and mis-identification rates is also described.
Chapter 5 focuses on Standard Model processes with τ leptons: W → τν and Z → ττ decays. The first
measurements of their cross sections in ATLAS experiment are described. Finally, an application of those studies
for the measurement of the τ identification efficiency in data using W → τν events is presented
The Higgs boson(s) searches with τ leptons in final state are presented in Chapter 6 for the Standard Model
and in Chapter 7 for the Minimal Supersymmetric Standard Model.
In Appendix A, the τ+ τ− mass reconstruction techniques used in the presented analyses, are described.
Conventions
The ℓ refers to either an electron or a muon. The l symbol refers to an electron or a muon or a τ lepton.
In the following, τ+ , τ− are indicated simply as τ, unless otherwise stated. The same applies to other particles.
The hadronically decaying τ lepton is denoted as τhad , while leptonically decaying as τlep .
Charged Higgs bosons are denoted as H + , with the charge-conjugate H − always implied.
The natural units are used where proton carries a positive unit of charge and the speed of light c= 1.
Is the tau simply a standard model lepton, or will the physics of the tau lead
us outside of the standard model?
Martin Perl
. . . . . . they are ill discoverers that think there is no land when they can
see nothing but sea.
Francis Bacon
2
Physics with τ leptons
The τ lepton together with the τ neutrino forms the third generation of the Standard Model (SM) leptons. Its
properties have been studied in detail in past decades. Now, with the LHC start, a new window opens for physics
with the τ particle. Because of its properties, it is an interesting probe for many processes beyond the Standard
Model. In this Chapter, the main properties of the τ lepton and its role in the ATLAS physics program are presented.
2.1 Properties of the τ lepton
The τ lepton is the first discovered member of the third quark-lepton family. For its discovery in 1975 at the
SLAC [19] Martin Perl was awarded the 1995 Nobel Prize in physics. The measured rest mass of the τ lepton is
1776.82 ± 0.16 MeV [46]. This is almost 3500 times heavier than the equivalent particle of the first generation,
the electron. The τ lepton is unstable, it has a mean lifetime of (290.6 ± 1.0) × 10−15 s, corresponding to a decay
length of 87.11 µm [46].
The τ lepton is the only lepton heavy enough to decay leptonically and hadronically. The coupling of the τ−
current 1 to the W − boson of the weak interaction, shown in Figure 2.1, produces a weakly interacting τ neutrino.
The virtual W − created in this reaction then couples to an additional pair of leptons, e− ν¯e or µ− ν¯µ , or quarks, ūd or
ūs. All other quark pairings, such as c̄d, c̄s, are too massive to be produced. Therefore, to lowest order all decays
of τ leptons are included in these four processes:
τ− → ντ ν¯e e−
−
(2.1)
−
(2.2)
τ → ντ ūd → ντ hadrons
(2.3)
−
τ → ντ ν¯µ µ
−
τ → ντ ūs → ντ hadrons.
(2.4)
Quarks which couple to W − may be from the same generation, as in the ūd case, or from different generations,
as in the ūs case. The relative strengths of these couplings are given by the elements of the Cabibbo-KobayashiMaskawa (CKM) matrix [46]. Couplings to quarks within the same generation are highly favoured over couplings
across generations. Consequently, the ūs decays of the τ have much smaller branching fractions than the analogous
ūd decays.
A list of decays of the τ lepton is given in Table 2.1, along with experimental values for their branching ratios
(BR) [46]. These decays are grouped according to the four possible pairs of particles produced at the W − vertex. In
1
In this Chapter processes with τ− are shown as an example. Charge-conjugate particles and decays are implied.
13
CHAPTER 2. PHYSICS WITH τ LEPTONS
14
ντ
τ−
ν̄e
ν̄µ
ū
ū
e−
µ−
d
s
W−
Figure 2.1: Particle doublets at the W − vertex in τ− lepton decays.
Table 2.1: τ− decays and branching ratios. Decays are classified according to the particles at the W − vertex and
the number of K and π in the final state. Experimental values are current world averages [46].
W − vertex
ν¯e e−
ν¯µ µ−
ūd
ūs
τ lepton decays
channel
final state
e−
µ−
π−
π−
−
ρ
π− π0
−
−
a1
π π+ π−
a−1
π− π0 π0
K−
K ∗−
K ∗−
K1−
K1−
K1−
Branching ratio (%)
17.85 ± 0.05
17.36 ± 0.05
10.91 ± 0.07
25.51 ± 0.09
9.32 ± 0.07
9.29 ± 0.11
π− π+ π− π0
π− π0 π0 π0
4.61 ± 0.06
1.04 ± 0.07
π− π+ π− π+ π−
π− π+ π− π0 π0
π− π0 π0 π0 π0
K−K0
K − K + π−
K − K 0 π0
π− K 0 K¯0
K−
K − π0
K − K¯0
K − π+ π−
K − π0 π0
π− K¯0 π0
K−K+K−
K − K 0 K¯0
0.0839 ± 0.0035
0.495 ± 0.032
0.15 ± 0.04
0.159 ± 0.016
0.140 ± 0.005
0.159 ± 0.020
0.17 ± 0.04
0.696 ± 0.023
0.429 ± 0.015
0.84 ± 0.04
0.287 ± 0.016
0.065 ± 0.023
0.40 ± 0.04
(1.58 ± 0.15) × 10−3
leptonic decays, there is only one decay mode for each of the possible lepton pairs. In hadronic decays, the ūd or
ūs quarks undergo strong interactions in which additional ūu, d̄d, or s̄s quark pairs may be created. The net result
of this process is the production of some number of mesons, predominantly π and K, both charged and neutral.
In 35.2% of the time τ lepton decays leptonically and in 64.8% of the time into one or more hadrons. Considering only hadronically decaying τ leptons, decays with only one charged particle (so called 1-prong) occur in
2.2. STANDARD MODEL PROCESSES WITH τ FINAL STATES
15
t
τ−
τ−
b̄
W
t̄
Z
−
τ−
W−
ν¯τ
(a)
τ+
(b)
ν¯τ
(c)
Figure 2.2: Important Standard Model processes with τ leptons in the final state: W and Z boson production and
top quark decays.
about 72% of the time and with three charged particles (so called 3-prong) in about 23% of the time. The 5-prong
decay has only a fraction of about 0.1%. The hadronic final states are dominated by π± and π0 mesons, but there
is also a small fraction of decays containing K ± and K 0 mesons. As can be seen in Table 2.1, these are dominated
by resonance production.
Leptonic decay modes are well described theoretically. Measurements of leptonic branching ratios of τ decays
and of the lifetime enable precise tests of lepton universality, the fundamental assumption of the Standard Model.
Due to the short-enough lifetime of τ leptons and their parity-violating decays, τ leptons are the only leptons
whose spin information is preserved in kinematics of its decay products recorded by the detector. Especially the
hadronic decay to one charged pion and neutrino final state is sensitive to the spin orientation of the parent τ lepton.
2.2 Standard Model processes with τ final states
The measurement of SM processes was the crucial step in the ATLAS physics program. τ leptons play an important
role in such studies. Decays of Standard Model gauge bosons to τ leptons, W → τν and Z → ττ, are essential to
calibrate τ energy and measure τ lepton detection performance. They are important in the search for New Physics
phenomena as they are dominant background processes in such searches. Thus, their production cross sections
need to be measured precisely. Studies of W → τν and Z → ττ processes at the LHC centre-of-mass energies are
also interesting in their own right, complementing the measurements of the production of the Z boson through its
electron and muon decay modes.
The main source of τ leptons at the LHC is W → τν decay (Figure 2.2(a)) with a cross section times branching
√
ratio of σ × BR = 10.46 ± 0.52 nb [47, 48, 49] at the centre-of-mass energy s = 7 TeV. Having one τ lepton
and a neutrino in the final state, this process requires a good τ identification and missing energy reconstruction due
to the escaping neutrino. This decay channel can be used to measure the leptonic branching ratio of the W boson
and the cross section of W production. In addition, W → τν decays can be used to validate the reconstruction
and identification techniques for τ leptons and the measurement of the missing transverse energy, which are both
fundamental physics objects in a wide spectrum of measurements at the LHC.
The Z → ττ decay (Figure 2.2(b)) has a cross section of an order of magnitude lower than W → τν , but it
has two τ leptons in the final state, with an invariant mass near the Z pole. It provides more robust prospects for
analysis. It is called the golden channel for the detection of τ leptons, since one τ can be used to identify the event,
while the other can probe the performance. This channel can be used to understand the efficiency of τ identification
and τ trigger as well as reconstruction methods for visible 2 and invariant masses of both τ leptons. In addition,
because the visible mass distribution of the τlep -τhad final state is sensitive to the energy scale of the reconstructed
τ candidates, a measurement of the τ lepton energy scale can be made with this sample. Additionally, the ττ
invariant mass is sensitive to ETmiss , hence ETmiss reconstruction properties can be studied with this sample and a
measurement of the ETmiss scale can be made. The measurement of the Z → ττ cross section can provide also a test
2
The invariant mass of visible τ decay products.
16
CHAPTER 2. PHYSICS WITH τ LEPTONS
Figure 2.3: Relevant Standard Model Higgs boson production processes in leading order. (a) gluon fusion, (b)
vector boson fusion, (c) W/Z associated and (d) tt¯ associated production.
of universality, when compared to the Z → ee and Z → µµ counterparts. Finally τ polarisation in W → τν and
Z → ττ decays can be measured. This has not been done previously at hadron colliders.
At the LHC, top quark pairs (tt¯) are produced in abundance due to the high centre-of-mass energy. In that case
one or both W bosons from top quark decays can decay further to τ leptons (Fig. 2.2(c)). This process has more
jets in the event, coming from hadronic W boson decays and b-quarks and gives a different environment compared
to W → τν and Z → ττ. It leads also to a more complex and difficult reconstruction. This final state can provide
an important alternative measurement of the top quark pair production cross section. It can be also further used as
an input in searches of the possible charged Higgs production via top quark decays.
2.3 Standard Model Higgs boson searches with τ final states
Discovering the mechanism responsible for electroweak symmetry breaking and the origin of mass for elementary
particles is one of the fundamental tasks of the LHC. In the Standard Model, this mechanism requires existence of
one scalar particle, the Higgs boson. Direct experimental searches provided only limits on its mass. Indirect limits
on the Higgs boson mass of mH < 185 GeV at 95% confidence level were set using global fits to electroweak
precision data [50]. The experiments at LEP placed the limit at mH > 114.4 GeV [51] and the Tevatron, excluded
the range of 156-177 GeV [52]. During completion of this monograph, both ATLAS and CMS collaborations
claimed observation of a new boson with mass ∼(125-126) GeV [53, 54]. More details and consequences of this
observation for the Higgs boson searches with τ lepton final states are given in Summary of Chapter 6.
At the LHC the dominant Higgs production mechanism is the fusion of two gluons via a heavy-quark loop, as
shown in Figure 2.3 (a). Detection of the Higgs boson produced via gluon fusion, however, is challenging, because
there are large background contributions from QCD multijet production which are hard to suppress if no other
striking signal signatures are present. Only Higgs boson decays to two or more leptons (such as in H → ZZ or
H → WW) or the Higgs decay to two photons will provide sufficient discrimination against backgrounds.
The second largest contribution comes from the fusion of vector bosons radiated from the initial state quarks
(VBF) as shown in Figure 2.3 (b). This process leaves a special signature in the detector. The quarks hadronise
to jets which will be detected in the forward region of the detector (close to the beam pipe). There is no colour
connection between the two quarks, hence between the two forward jets, and so little hadronic activity is expected
in the signal process. This typical VBF signature is used to suppress QCD multijet background.
The third contribution comes from associated production W H, ZH as shown in Figure 2.3 (c). In this process,
the Higgs boson is radiated off a weak vector boson (Higgsstrahlung). This process is important in the intermediate
mass range mH < 2mZ , but its cross section falls rapidly with an increasing value of mH .
17
10
s = 7TeV
1
WW → l± νqq
LHC HIGGS XS WG 2011
σ × BR (pb)
2.4. MSSM HIGGS BOSONS SEARCHES WITH τ FINAL STATES
-
WW → l+νl ν
10-1
-
ZZ → l+l qq
10-2
-
ZZ → l+l νν
τ+τ-
-3
10
WH → l±νbb
ZH → l+l bb
-4
10100
-
l = e, µ
ν = νe,νµ,ντ
q = udscb
γγ
200
-
ZZ → l+l l+l
300
400 500
Higgs boson mass (GeV/c2)
Figure 2.4: The SM Higgs boson production cross sections multiplied by decay branching ratios in pp collisions
√
at s = 7 TeV as a function of Higgs boson mass [55].
The smallest contribution comes from associated production tt¯H presented in Figure 2.3 (d). It is less important
because the cross section is about five times smaller than the one for W H or ZH for mH < 200 GeV.
The branching ratios and cross sections of the Higgs boson production and decay channels are fixed by theory
as soon as the Higgs boson mass is known. The presented Higgs boson decay branching ratios take into account the
recently calculated higher-order QCD and electroweak (EW) corrections in each Higgs boson decay mode [55].
The total SM Higgs boson signal production cross section multiplied by the branching ratio for the final states
analysed currently by the LHC experiments is shown in Figure 2.4. As can be seen, decay of the Higgs into
a pair of τ leptons is an important channel for mH < 140 GeV. It suffers from high background mainly from
Z → ττ decays but the sensitivity can be enhanced by requiring that the Higgs boson is produced in association
with jets. The Higgs boson can be produced in association with jets, at the next-to-leading order (NLO) in the
gluon fusion process and at the leading order in the vector boson fusion process. The presence of jets allows
topological selections which enhance the signal-to-background ratio. In this configuration, the Higgs boson can
acquire a boost in the transverse plane, enhancing the missing transverse energy in the event (due to the undetected
neutrinos from τ decays) which allows for a better discrimination of the signal against some of the background
processes [56, 57, 58, 59]. Also, the measurement of the H → ττ decay rate is a test of the SM prediction for the
τ Yukawa coupling. This decay mode also offers a unique opportunity to study CP violation in the Higgs sector.
Higgs CP properties can be studied in hadronic decays of τ leptons.
2.4 MSSM Higgs bosons searches with τ final states
The Minimal Supersymmetric Standard Model (MSSM) [60, 61, 62, 63, 64] is the minimal extension to the Standard Model that realises supersymmetry. It is minimal in the sense that it contains the smallest number of new
particle states and new interactions consistent with phenomenology.
Two complex Higgs doublets are required in the MSSM - one to generate masses for “up-type” particles, and
the other to generate masses for “down-type” particles. Each Higgs field has a vacuum expectation value, and
the ratio of these is denoted as tanβ (in SM tanβ = 1). Of the eight degrees of freedom provided by the two
doublets, three are absorbed by the longitudinal degrees of freedom of EW bosons. Five physical Higgs bosons
CHAPTER 2. PHYSICS WITH τ LEPTONS
18
g
g
g
q̄
b̄
φ
φ
φ
b
b̄
b̄
φ
g
g
g
(a)
b
(b)
b
b
(c)
φ q
(d)
b
(e)
Figure 2.5: Feynman diagrams contributing to the MSSM Higgs boson production. Diagram a) is called ’direct
production’, diagrams b) to e) contribute to the b quark associated production. In the above diagrams
φ represents either of the neutral Higgs bosons in the MSSM, h, H, or A.
remain: H ± , h (neutral lighter scalar), H (neutral heavier scalar) and A (neutral pseudoscalar). The h and H neutral
Higgs bosons are CP-even, while the A-boson is CP-odd. At the tree level, the Higgs sector of the MSSM can
be completely described in terms of mass of the neutral pseudoscalar, mA , and tanβ. For the H ± studies, those
are usually chosen to be the charged Higgs boson mass and tanβ. Higher order corrections introduce dependence
on another 105 SUSY parameters. Making some general assumptions can reduce this somewhat, as it would be
unfeasible to consider all possible scenarios. Instead, various benchmark models have been defined [65]. The
max scenario
model used in analyses described in this monograph is the maximal mixing scenario, mmax
h . The mh
is designed to give the largest possible mass of the lightest neutral Higgs boson (h), in order to provide the best
agreement with the limits from LEP experiments [51]. In this scenario the upper bound on the mass of the light
Higgs boson h is expected to be around 135 GeV. While the light neutral Higgs boson may be difficult to distinguish
from its Standard Model counterpart, the other heavier Higgs bosons are a distinctive signal of physics beyond the
Standard Model. In the mmax
scenario the h and A boson states are almost degenerate in mass for mA ≤ 130 GeV,
h
the H and the A are approximately degenerate in mass if mA ≥ 130 GeV. The remaining mass difference depends
on tanβ and becomes smaller with increasing tanβ. At mA ∼ 130 GeV, in the intense coupling region, all three
neutral Higgs bosons come close in mass and their separation would be very difficult.
Production of neutral Higgs bosons and their decays are different from those in the Standard Model. While
decays into ZZ or WW are dominant in the Standard Model for Higgs boson masses above mH > 2mW , for high
values of tanβ these decay modes are either suppressed in case of the h and H or even absent in the case of the A
bosons. At lower values of tanβ, the production of neutral Higgs bosons proceeds dominantly via gluon-fusion as
presented in Figure 2.5(a). Its rates are significantly larger than for the Standard Model and for the range of higher
tanβ it is still dominant for low mA . As tanβ increases, production in association with b-jets (Figure 2.5(b)-2.5(e))
gains importance, and (0-2) b-jets can be observed in the final state. For very large values of mA (depending on
tanβ) the cross section of the lightest CP even boson h becomes larger than the cross section for H and A. This is
also called the decoupling region. In fact, if a small value of tanβ is realised in nature, the h will be the only visible
MSSM Higgs over a large range of mA . It will then be indistinguishable from the SM Higgs boson.
The coupling of the Higgs bosons to third generation fermions is strongly enhanced for large regions of the
MSSM parameter space. The dominant decay mode is to bb̄ pairs, accounting for approximately 90% of all decays
(high tanβ region). As with SM Higgs searches, large QCD backgrounds associated with this final state make the
analysis difficult, despite the enhanced production cross section (with respect to a SM Higgs). Approximately 10%
of all MSSM Higgs boson decays are to ττ pairs. In the SM the H → ττ mode is only relevant for a light Higgs
boson masses but in the MSSM this channel is relevant in the whole allowed mass region up to 1 TeV. Previous
results excluding some regions of parameters space come from LEP [66] and Tevatron [67, 68].
The search strategies for charged Higgs bosons depend on the charged Higgs boson mass, which dictates both
the production and the available decay modes. Below the top quark mass, the main production mode is through top
quark decays, t → H + b. The dominant source of top quarks at the LHC is through tt¯ production. The cross section
for charged Higgs boson production from top quark decays in single-top events is much smaller. For tanβ > 3,
2.5. SEARCHING FOR NEW PHYSICS WITH τ FINAL STATES
b
g
t
g
ντ
+
H
τ
f
+
-
t
19
W
g
b
f′
Figure 2.6: Example for a leading-order Feynman diagram for the production of a charged Higgs boson through
gluon fusion in tt¯ decays.
charged Higgs bosons decay mainly via H + → τν [55]. Figure 2.6 presents a leading-order Feynman diagram for
the production of a charged Higgs boson through the gluon fusion in tt¯ decays.
Above the top quark threshold, the production mainly takes place through gb fusion (gb̄ → t¯H + ). For such
high charged Higgs boson masses, the decay into a top and a b quark dominates, H + → tb̄, but H + → τν can still
be sizable and offers a much cleaner signature.
Direct searches at LEP [69] give a lower limit of mH + ∼ 90 GeV for BR(H + → τν)=1. At the Tevatron,
no evidence for charged Higgs boson production has been found. Hence, the Tevatron experiments placed upper
limits on BR(t → H + b) assuming BR(H + → τν) = 1 in the 15-20% range [70, 71].
2.5 Searching for New Physics with τ final states
τ leptons often appear in final states of various supersymmetric scenarios. According to the electroweak symmetry
breaking, a left and right handed sfermion mixing appears in the SUSY breaking, which results in a mixture of left
and right handed components in the mass eigenstates. In certain SUSY models, large mixing between left and right
sfermions, the partners of the left-handed and right-handed SM fermions, implies that the lightest sfermions belong
to the third generation. This leads to a large production rate of τ leptons from decays of τ̃ sleptons and gauginos,
the partners of the SM gauge bosons, in SUSY cascade decays. For example, in the context of Gauge Mediated
SUSY Breaking (GMSB) [72, 73, 74, 75, 76, 77] scenario, the lighter of the two τ̃ sleptons is the next-to-lightest
supersymmetric particle (NLSP) for a large part of the parameter space, and the very light gravitino, G̃, is the LSP.
Hence τ̃ sleptons decay to a τ lepton and a gravitino.
Previous experiments at LEP [78, 79, 80] have placed constraints on τ̃ and ẽ masses and on more generic
GMSB signatures. Among these, the limits from the OPAL experiment [78] were the most stringent, excluding τ̃
NLSPs with masses below 87.4 GeV. The D0 Collaboration performed a search for squark production in events
with hadronically decaying τ leptons, jets, and missing transverse momentum [81], and the CMS Collaboration
performed searches for New Physics in same-sign di-τ events [82] and multi-lepton events [83] including τ pairs,
but the GMSB model was not specifically considered in any of these results.
While writing this monograph, the ATLAS collaboration published recent results on searches for SUSY in
events with large missing transverse momentum, jets, and at least one hadronically decaying τ lepton, with zero
or one additional electron or muon [84]. The studies have been performed using 4.7 fb−1 of pp collision data at
√
s = 7 TeV. No excess above the SM background expectation is observed and a 95% confidence level (CL) limit
for new phenomena is set. In the framework of GMSB model, exclusion limits on the GMSB breaking scale λ
are set at 47 TeV, independently of tanβ. These limits provide the most stringent tests to date of GMSB SUSY
breaking models in a large part of the parameter space considered.
Looking for τ pairs in final states is also valuable for a search for high mass resonances. Heavy gauge bosons
(Z ′ , W ′ ) are predicted in various models [85, 86, 87, 88, 89, 90]. In particular, models with extended weak or
hypercharge gauge groups, predict that such bosons preferentially couple to the third generation fermions. Direct
searches for the τ pair final state have been performed previously by the CDF [91] and CMS [92] collaborations.
The latter sets the most stringent 95% CL limits and excludes Z ′ masses below 468 GeV using 36 pb−1 integrated
20
CHAPTER 2. PHYSICS WITH τ LEPTONS
luminosity. Precision electroweak measurements at LEP [93] indirectly exclude Z ′ masses below 1090 GeV.
Recently, new results on the search for high-mass resonances decaying into τ leptons pairs in the ATLAS
experiment were published [94]. Z ′ bosons of the Sequential Standard Model [95] with masses less than 1.3 TeV
are excluded at 95% CL.
An experiment is a question which science poses to Nature
and a measurement is the recording of Nature’s answer.
Max Planck
3
The ATLAS detector at the Large Hadron Collider
The Large Hadron Collider (LHC) at CERN 1 is actually the largest and highest energy particle accelerator in the
world. It provides collisions of particles allowing to recreate, on a microscale, the state that existed a fraction
of nanosecond after the Big Bang. Under these extreme conditions, never reached before in a laboratory, new
particles may be produced and measured in the detectors providing signs of New Physics. The ATLAS experiment
is one of the four main experiments at the LHC. This Chapter describes briefly details of the ATLAS detector,
luminosity measurement as well as particle reconstruction and identification crucial for the analyses with τ leptons
in final states. Also the data quality and preselection of events for early data analyses are presented.
3.1 The Large Hadron Collider
The LHC is the largest and most energetic particle collider in the world. It is a hadron collider which produces
proton-proton collisions most of the time. Besides proton-proton collisions, lead ions are collided during a short
period of the year, using the same accelerator infrastructure.
The proton beams were successfully circulated at the LHC for the first time in September 2008. Due to a
serious electrical fault between two magnets resulting in a large helium leak into the tunnel, the operations were
interrupted shortly after its opening and restarted in November 2009 at the injection energy of 450 GeV per beam.
√
The first collision at the centre-of-mass energy of s = 7 TeV took place at the end of March 2010 with luminosity
2 × 1027 cm−2 s−1 . In 2011 the luminosity reached 3.65 × 1033 cm−2 s−1 . An integrated luminosity of 45 pb−1 has
been delivered by autumn 2010 and of 5.25 fb−1 until autumn 2011 as shown in Figure 3.1.
In 2012 the LHC has been running with a higher collision energy of 4 TeV per beam in order to enhance
the machine’s discovery potential and open up further possibilities in the searches for New Physics. At the end
of 2012, the LHC will shut down for maintenance for up to two years and then will attempt to reach the design
energy of 14 TeV.
To investigate particle collisions at the LHC, several detectors were built: ATLAS and CMS [96] as detectors
for multi-purpose physics analyses, ALICE [97] for heavy ion collisions, LHCb [98] to investigate CP-violation
and properties of the bottom quark and LHCf [99] and TOTEM [100] to study particle productions, elastic scatterings and total cross sections of pp collisions.
1
Conseil Européen pour la Recherche Nucléaire, European Organization for Nuclear Research.
21
Total Integrated Luminosity [pb-1]
60
ATLAS Online Luminosity
50
s = 7 TeV
LHC Delivered
ATLAS Recorded
40
Total Delivered: 48.1 pb-1
Total Recorded: 45.0 pb-1
30
20
10
0
24/03
Total Integrated Luminosity [fb -1]
CHAPTER 3. THE ATLAS DETECTOR AT THE LARGE HADRON COLLIDER
22
7
6
5
ATLAS Online Luminosity
s = 7 TeV
LHC Delivered
ATLAS Recorded
Total Delivered: 5.61 fb-1
Total Recorded: 5.25 fb-1
4
3
2
1
19/05
14/07
(a)
08/09
03/11
Day in 2010
0
28/02
30/04
30/06
30/08
31/10
Day in 2011
(b)
Figure 3.1: Cumulative luminosity versus day delivered to (green), and recorded by ATLAS (yellow) during stable
beams and for pp collisions at 7 TeV centre-of-mass energy in 2010 (a) and 2011 (b) [101].
3.2 The ATLAS detector
ATLAS (A Toroidal Lhc ApparatuS) is one of the two multi-purpose detectors operating at the LHC, designed to
identify the broadest range of particles and measure their properties. It is 44 m long, with a diameter of 25 m, and
it weighs 7000 tonnes. The goal of ATLAS is to cover the largest possible range of physics, such as searches for
new heavy bosons (in particular the Higgs boson), supersymmetric particles or any other phenomena indicating
New Physics at energies up to a few TeV. Masses of new particles are, in general, unconstrained by theory and their
branching fractions into different final states depend on their masses. The detector has to be, therefore, sensitive
to a large number of possible decay channels. It needs to be capable of measuring four-momentum and position
of particles with high resolution and provide an excellent particle identification. Due to the very high interaction
rate, the detectors require fast and radiation-hard electronics.
Since the QCD multijet production dominates by many orders of magnitude over the production of new particles, ATLAS has to identify efficiently experimental features characteristic to the rare processes. Also, a highly
efficient trigger system is needed to allow for the detection of processes even with very small cross sections providing strong background rejection at the high event rate of the LHC. A typical signature of many New Physics
processes is the presence of non-interacting particles, such as the Standard Model (SM) [102, 103, 104] neutrinos
or supersymmetric neutralinos. Their observation is possible through detection of the momentum imbalance in
the transverse plane often referred to as the missing transverse energy, ETmiss . For the reconstruction of ETmiss it is
important that the ATLAS calorimeter system has a coverage as close to 4π as possible. Many New Physics events,
such as Higgs boson production and decay, are characterised by the presence of b quarks in the final state. The
ATLAS detector was therefore designed to allow for a precise reconstruction of secondary vertices which are of
great importance in identification of b-jets.
To accomplish its tasks, ATLAS consists of several layers of sub-detectors – from the interaction point outwards, the Inner Detector tracking system, the electromagnetic and hadronic calorimeters, and the muon system.
The ATLAS detector is forward-backward symmetric around the interaction point. It is composed of a central
barrel part and two end-caps. A scheme of the detector and of its sub-systems is shown in Figure 3.2.
Coordinate system The nominal interaction point is defined as the origin of the coordinate system, while the
counterclockwise beam direction defines the z-axis and the x-y plane is transverse to the beam direction. The positive x-axis is defined as pointing from the interaction point to the centre of the LHC ring and the positive y-axis
is defined as pointing upwards. The azimuthal angle φ is measured around the beam axis and the polar angle θ is
the angle from the beam axis. The pseudorapidity is defined as η = − ln tan(θ/2). The transverse momentum pT ,
3.2. THE ATLAS DETECTOR
23
Figure 3.2: The ATLAS detector [45].
the transverse energy ET , and the transverse missing energy ETmiss are defined in the x-y plane. The distance ∆R
p
in the η − φ space is defined as ∆R = (∆η)2 + (∆φ)2 .
3.2.1 Inner Detector
The Inner Detector (ID) provides high-precision tracking information for charged particles allowing for reconstruction of tracks and vertices in the event. This information consists of very efficient and accurate position
measurements of particles along their trajectories thus allowing the momentum and charge sign determination and
consequently contributing to their identification. The ID is exposed to a high density particle flux because of its
position closest to the beam line and the interaction point. Thus, a high granularity and a fast readout system is
required.
The Inner Detector is immersed in a 2 T magnetic field generated by the central solenoid. It consists of three
sub-systems, the pixel detector, the SemiConductor Tracker (SCT) and the Transition Radiation Tracker (TRT).
The first two subsystems cover a region of |η| < 2.5 in pseudorapidity, while the TRT reaches up to pseudorapidity
|η| = 2.0. An outline of the ID is shown in Figure 3.3. A track in the ID central region typically produces 11 hits
in the pixel and SCT detectors and 36 hits in the TRT detector.
The innermost component of the ID is a silicon pixel detector with a high degree of segmentation. This is
necessary to cope with the high track density and to reconstruct primary and secondary vertices. The use of silicon
pixel allows also to measure the z coordinate of tracks with sufficient precision to discriminate between tracks from
the primary interaction and tracks from additional pile-up interactions. The pixels are arranged in three layers with
the design requirement to achieve a resolution of 10 µm in the Rφ direction and 115 µm in the beam direction.
The innermost layer, called B-layer, provides the critical vertexing information used to reconstruct the displaced
vertices of short-lived particles.
The next part of the tracking system is the SCT. The reduced charged particle density and radiation level in
that region allow for the use of silicon strips which have a coarser overall granularity while still providing an
excellent measurement accuracy in the Rφ direction. The use of silicon strips rather than pixels allowed to cover a
24
CHAPTER 3. THE ATLAS DETECTOR AT THE LARGE HADRON COLLIDER
Figure 3.3: Overview of the ATLAS Inner Detector [45].
large area at a reasonable cost. In the barrel, the strip detectors are arranged in four layers at different radii. Each
layer is composed of two stereo layers oriented at an angle of 40 mrad relative to each other, which provides a
3-dimensional position measurement. The system contributes to momentum, impact parameter and vertex position
measurements, as well as provides good pattern recognition thanks to high granularity. The spatial resolution is
17 µm in Rφ and 580 µm along the beam direction.
At larger radii the surface area of the detector becomes larger, which would lead to high costs for a silicon
detector. Therefore, a Transition Radiation Tracker is installed there. It consists of 4 mm diameter drift tubes
(straws). In the barrel part the straws are arranged parallel to the beam axis, while in the end-caps a radial arrangement is used. The TRT contributes only with information from the Rφ plane with resolution of 130 µm per straw.
The TRT provides a quasi-continuous tracking with over 30 space-point measurements per track. This leads to an
improvement of the momentum resolution at small pseudorapidities, |η| < 2.0.
The TRT is not only designed for tracking measurements, but also for simple particle identification. The
transition radiation, which occurs when a charged particle with a high velocity crosses a boundary between two
media with different dielectric constants, is also used to discriminate between electrons and pions. There are two
independent thresholds to distinguish between tracking hits and transition radiation (TR) hits. The tracking hits
pass the lower threshold while the TR hits pass the higher one.
3.2.2 Calorimeters
The calorimeter system consists of several components designed to meet the requirements of measuring electrons,
photons and jets with high efficiency as well as excellent spatial and energy resolutions. Figure 3.4 gives an
overview of the ATLAS calorimeter system.
All ATLAS calorimeters are sampling calorimeters providing full solid angle coverage up to |η| < 4.9. The
granularity of the calorimeters varies from a fine grained structure at the region which overlaps with the ID, and a
coarser structure at the rest. Due to high homogeneity and a wide range of acceptance, the calorimeters allow to
reconstruct the missing transverse energy. The smallest units of the calorimeters with a proper signal readout are
3.2. THE ATLAS DETECTOR
25
Figure 3.4: Overview of the ATLAS calorimeter system [45].
called cells.
Electromagnetic Calorimeter The innermost layer is the electromagnetic (EM) calorimeter consisting of a
barrel part reaching up to |η| < 1.475 and two end-caps (EMEC) up to |η| < 3.2. These calorimeters use liquid
argon (LAr) as active medium as it offers stable response over time and good radiation hardness. The use of LAr
forces the operation at low temperatures, and therefore the calorimeter is immersed inside a cryostat. The absorber
material are lead plates in accordion shape which allows for fast signal and uniform response. The EM calorimeter
is longitudinally divided into three segments as shown in Figure 3.5. The first layer is highly segmented in η with
strip-shaped read-out cells. It provides spatial resolution high enough to disentangle two nearby photon showers
from π0 → γγ decays. In the η direction, eight strips of the first layer correspond to one read-out cell in the second
layer. The second layer is segmented into squared cells extending the segmentation in the φ direction. Here the
main part of the electromagnetic shower is measured. The third layer collects the tail of the deposited energy and
has a coarser segmentation in η. The electromagnetic calorimeter is completed with the presampler, a 11 mm thick
LAr calorimeter, which is mounted in front of the first layer. This detector provides first energy sampling in order
to estimate the energy loss by electrons and photons in the material in front of the calorimeter. The transition region
between the barrel and the end-cap EM calorimeters, 1.37 < |η| < 1.52, is expected to have poorer performance
because of more passive material in the front of the calorimeters. The total thickness in terms of radiation lengths,
X0 , in the barrel is at least 24 and at least 26 in the end-caps.
The electromagnetic calorimeter is complemented by two forward electromagnetic calorimeters in the region
up to |η| < 4.9 using copper as an absorber.
Hadronic Calorimeter The EM calorimeters are surrounded by hadronic calorimeters measuring strongly interacting particles forming jets. The hadronic calorimeters consist of a barrel Tile Calorimeter (|η| < 1.0), two
extended barrel Tile Calorimeters (0.8 < |η| < 1.7), two hadronic end-cap calorimeters (1.5 < |η| < 3.2) and the
forward hadron calorimeters (3.2 < |η| < 4.8).
The Tile Calorimeter (TileCal) is the high precision hadronic calorimeter with the absorber made of steel, and
scintillating tiles used as the active material. The TileCal including all the previous systems and support structures,
corresponds at η = 0 to 9.7 interaction lengths, λint .
26
CHAPTER 3. THE ATLAS DETECTOR AT THE LARGE HADRON COLLIDER
Cells in Layer 3
∆ϕ×∆η = 0.0245×0.05
Trigge
r Towe
∆η = 0 r
.1
2X0
47
0m
m
η=0
16X0
Trigge
Tow r
∆ϕ = 0er
.0
982
m
m
4.3X0
15
00
1.7X0
∆ϕ=0.0
245x
36.8m 4
mx
=147.3 4
mm
Square cells in
Layer 2
∆ϕ = 0
.0245
ϕ
37.5m
∆η = 0
.025
m/8 =
4
∆η = 0 .69 mm
.0031
Strip cells in Layer 1
η
Figure 3.5: Drawing of a barrel module of the EM calorimeter, with the accordion shaped absorber plates and
electrodes, consisting of three longitudinal segments with different cell sizes in η and φ [45].
The end-cap calorimeters consists of the Hadronic End-Cap Calorimeter (HEC) and a high-density Forward
Calorimeter (FCal). Due to the high radiation density in the end-cap and forward region a radiation-hard material
is used. The HEC calorimeters use liquid argon as active material. Copper is used as an absorber in the HEC and
in the first part of the FCal, while tungsten in the second and third part of FCal.
A total of at least 10 interaction lengths is provided by the EM and hadronic calorimeters together. It allows
for a good energy resolution of highly energetic jets and minimises punch-through of particles to the muon spectrometer. The large η coverage of the calorimeters ensures a good missing transverse energy measurement, which
is important for many physics studies, such as those involving τ leptons and supersymmetric particles.
3.2.3 Muon spectrometer
The muon spectrometer is the outermost detector system designed for the high precision measurement and identification of muons with transverse momenta above 3 GeV which is the mean energy loss of muons in the calorimeters.
It covers pseudorapidity range of |η| < 2.7. The muon spectrometer has its own magnetic field, allowing measurements of the muon momentum independently of the ID. It is provided by a superconducting air-core toroid magnet
system which minimises multiple-scattering of the muons. The muon spectrometer uses four different chamber
systems: Monitored Drift Tubes (MDT) and Cathode Strip Chambers (CSC) designed for measurements of track
coordinates, Resistive Plate Chambers (RPC) and Thin Gap Chambers (TGC) having fast drift times and used for
triggering. A view of the muon spectrometer is shown in Figure 3.6.
The MDT and the CSC detectors are both designed to provide precise measurement of the muon track segments
and thus the sagitta. The MDT are aluminium tubes of 30 mm diameter, (70 - 630) cm length and filled with an
Ar(93%)CO2 (7%) gas mixture with gold-plated tungsten-rhenium anode wires in the tube centres. The average
spatial resolution of a drift tube is 80 µm. The track position resolution of the MDT chambers is 35 µm. The CSC
are used as precision muon tracking chambers in the innermost layer of the very forward region (2.0 < |η| < 2.7).
They are multi-wire proportional chambers with strip-segmented cathodes having a shorter response time than the
MDT chambers to cope with the high background rates in this detector region. The average spatial resolution of a
CSC chamber in the bending plane is 60 µm.
The RPC and TGC detectors form the muon trigger system. The trigger requires a good resolution not only in
space but also in time to keep the latency time small. Both systems also contribute to the muon track measurement.
3.2. THE ATLAS DETECTOR
27
Figure 3.6: Overview of the ATLAS muon system [45].
The RPC chambers are located on both sides of the MDT middle layer in the barrel. The basic RPC unit is a
narrow gas gap formed by two parallel resistive plates, separated by insulating spacers made of polycarbonate.
The primary ionisation electrons are multiplied into avalanches by a high voltage field. The TGC are used as
trigger detectors in the end-cap region (1.5 < |η| < 2.7). They are multi-wire proportional chambers providing
a high spatial resolution and a good time resolution with a strongly quenching gas mixture. The RPC and TGC
trigger chambers provide bunch crossing identification and measure the coordinate along the drift tubes of the
MDT chambers.
The muon spectrometer provides stand-alone muon momentum measurement. A combination with measurements of the ID and the calorimeters improves the efficiency and resolution, especially for low pT muons.
3.2.4 Trigger
To handle the high interaction rates at the LHC (up to 1 GHz at the design luminosity), an efficient trigger system
is essential. To store interesting physics events the rate must be reduced to ∼ 400 Hz, leading to trigger only on
New Physics and important Standard Model processes.
The ATLAS detector has a three-level trigger system. Each trigger level depends on decisions made by the
previous stage and requires additional criteria, if necessary. The first part of the trigger chain is built by the Level-1
(L1) trigger which uses the information from the muon trigger chambers (RPC and TGC) as well as the reducedgranularity towers from calorimeters. The L1 trigger system is implemented in custom hardware processors and
uses simple algorithms to make fast decisions. While the muon chambers select high pT muons, the calorimeter
objects searched for are high pT electrons, photons, jets and also hadronically decaying τ leptons or large missing
transverse energy and sum of transverse energy. The L1 trigger reduces the data rate to 75 kHz. If an event is
selected, the data is transferred to the Level-2 (L2) trigger and regions of interest (RoI) are defined around the
triggering objects.
The RoIs are used as seeds for the L2 trigger, which has full access to calorimeter information and lowers the
event rate to 3.5 kHz. At this stage also Inner Detector tracks are incorporated into the trigger decision. In case
of muons, the L2 measures the pT more precisely and may increase the pT threshold. It also applies isolation
requirements to the objects. In case of electrons and τ leptons, the L2 requires a match of the calorimeter cluster
with the Inner Detector track and also isolation. Photons do not have a track and hence less rejection power is
gained here. In case of jets, the L2 sets the more precise pT threshold.
28
CHAPTER 3. THE ATLAS DETECTOR AT THE LARGE HADRON COLLIDER
The final trigger decision is carried out by the Event-Filter (EF). At this stage the standard offline reconstruction
software is used to process the complete data from all detector systems. The events are fully reconstructed using
up-to-date calibration and alignment constants and optimised thresholds. The events are finally written to mass
storage devices at a rate of about 400 Hz.
The exact pT thresholds (so called trigger menu) for each object depend on the luminosity. Combinations of
different objects (multi-object triggers) are also possible. In addition, triggers can be prescaled that means that
only 1 in N events passing the trigger is accepted. Details on triggers and the trigger menu used for collecting data
in 2010 can be found in Ref.[105].
3.3 Luminosity detectors
A precise determination of the luminosity is needed for physics measurements. The luminosity is independently
determined using several detectors and multiple algorithms, each having different acceptances, systematic uncertainties and sensitivity to backgrounds [106, 107]. In addition to the main detector, dedicated additional detectors
are used to perform luminosity measurements. These are located at various points along the beam axis (z-direction)
to provide information about the instantaneous and absolute luminosities received at ATLAS.
LUCID (LUminosity measurement using Cerenkov Integrating Detector) [45] detects inelastic proton-proton
scattering on each side of the interaction point at a distance of 17 m. Coverage in the region 5.6 < |η| < 6.0 is
provided. Luminosity is monitored by counting the number of interactions per bunch in the Cherenkov counters.
The primary purpose of the Beam Conditions Monitor (BCM) is to monitor beam losses and provide fast
feedback to the accelerator operations team. The BCM consists of two arms of diamond sensors located at z=
±18.4 m and at radius of 5.5 cm from the beam axis.
The ZDC (Zero Degree Calorimeters) [108, 45] detects forward neutrons and photons with |η| > 8.3 in both pp
and heavy-ion collisions. The ZDC is located ±140 m from the interaction point, at the point where the straight
section of the beam pipe splits back into two separate beam pipes. Eventually, each side of the ZDC will contain
one electromagnetic module (∼ 29 radiation lengths thick) and three hadronic modules (each ∼ 1.14 interaction
lengths thick), but at the time of completing this monograph only the hadronic modules are installed.
The ALFA (Absolute Luminosity For Atlas) sub-detector [109] provides absolute luminosity measurements
via elastic proton-proton scattering at small angles. The optical theorem connects the elastic scattering amplitude
in forward direction with the total cross section, which can be used to determine the absolute luminosity. The
ALFA detector consists of four Roman Pot stations, two on each side of the interaction point at ±240 m. One
station houses two tracking detectors, each equipped with 1500 scintillating fibres.
3.4 Simulation of physics events
To understand the real data seen by the detector and to compare this with theoretical predictions, the simulation of
particle interactions is necessary. The simulated data also enable to study the discovery potential of the detector
and to understand signatures of interesting processes. Monte Carlo simulation and reconstruction of events are
performed within ATHENA [110], the ATLAS offline software framework. The full event simulation is organised
in steps described briefly below. More detailed description of the full ATLAS simulation infrastructure can be
found in Ref. [111].
Event Generation This step is based on Monte Carlo (MC) techniques. Several generators, like PYTHIA [112]
or HERWIG [113], are used to model particle interactions for physics analyses. The generation includes the
simulation of the hard process, the initial and final state radiation, multiple interactions, beam remnants as well
as hadronisation and decays. The τ decays are modelled with TAUOLA library [114, 115] which is taking into
account the effects of the polarisation of the τ leptons. The effect of final state Quantum Electrodynamics (QED)
radiation is simulated by PHOTOS [116]. The result of the event generation are the four-momenta of particles in
3.5. PARTICLE RECONSTRUCTION AND IDENTIFICATION
29
the final state, the so-called Monte Carlo generator level information. The signal and background Monte Carlo
samples used for early data studies are generated with the default ATLAS MC10 tune [117].
Simulation The generated final state particles are subsequently passed through a detector simulation, to track
the way of particles through the detector and simulate the interaction of particles with the detector material and the
magnetic field. Their interaction with traversed material is simulated within the GEANT4 [118, 111] framework.
Detailed information on the detector geometry and the magnetic field is used when simulating propagation of
particles. At this step, the decay of long lived particles is handled. To enable a comparison with the detector
output, the energy deposited in the sensitive regions of the detector is digitised into voltages and currents. Also
detector noise is added as well as cross-talk effects. The output is the raw data format, and at this stage the
simulation output matches the real data detector output format, except for the presence of truth information in the
simulation, containing the generator level information about particles.
Pile-up At high luminosities multiple interaction at a single bunch crossing take place. Most of these collisions
are elastic and inelastic scattering events (minimum bias) but the remnants of these processes are also recorded
together with interesting interactions in the same bunch crossing (pile-up). The additional particles from pile-up
events potentially cause difficulties in the reconstruction of the hard parton collision process. If the pile-up originates from the same bunch crossing as the main interaction, it is called in-time pile-up. In addition, there is also
an out-of-time pile-up contribution, which means that the contribution is from an earlier bunch crossing. Other
pile-up contributions are from the cavern background or from showers induced by particles from cosmic rays.
Hence, an additional step simulating pile-up effects is performed in the physics event simulation.
Reconstruction In this step the digital signals are transformed into tracks and calorimeter clusters to form reconstructed objects like electrons, τ leptons or jets. The input from different detector components is also combined
to reconstruct missing transverse energy. Each object is reconstructed by the use of a dedicated algorithm. In the
next Section the particle reconstruction and identification algorithms for physics objects of interest are explained.
This step is exactly the same for data and simulated events.
3.5 Particle reconstruction and identification
The particle reconstruction and identification is performed usually in two steps. First, information from basic detector units like calorimeter cells or pixels in the tracking system are gathered and evaluated. Then, identification
algorithms make use of the condensed information to perform hypothesis tests and classify the object under investigation. Given a signature in the detector, the identification algorithms can only state a probability that this signature
is caused by a certain particle type. In order to meet the needs of various physics analyses which may benefit from
different identification efficiencies, a couple of working points for object identifications are supported. To avoid
confusion between real physics objects and objects classified by an identification algorithm to be of a certain kind,
the latter are referred to as candidates.
Electrons The reconstruction and identification of electrons [119, 120] starts with the information from the electromagnetic calorimeter. An algorithm searches for spatially grouped calorimeter cells with a significant energy
deposition (cluster). To suppress photons, each cluster has to be matched to a charged particle track of the Inner
Detector. The efficiency of the electron reconstruction is very high (> 90%) and mainly limited by the energy loss
and scattering in the material of the Inner Detector. However, at the LHC, backgrounds of multijets from QCD
processes are large. Also rejection of background electrons, mainly from photon conversions and Dalitz decays is
needed. Hence, several additional requirements are used to further suppress these backgrounds:
• Calorimeter information. Due to the fine granularity of the EM calorimeter, the lateral and longitudinal
shower shape is used to separate electromagnetic from hadronic showers. The showers of QCD multijets are
30
CHAPTER 3. THE ATLAS DETECTOR AT THE LARGE HADRON COLLIDER
more spread compared to electron showers of the same energy. Also the amount of energy deposited in the
hadronic calorimeter, which should be low in the case of electrons, provides a good suppression of jets.
• The Inner Detector information. A minimum number of hits in the pixel and SCT detectors, presence of
the transition radiation in the TRT detector and a transverse impact parameter (minimum distance of the
extrapolated track to the beam axis) are used to identify electrons.
• Cluster-track match criteria. The rejection of jets can be significantly improved by ensuring the consistency
between the EM calorimeter and the ID information. The extrapolation of an electron track into the electromagnetic calorimeter has to match with the barycentre of the corresponding shower. For jets this is usually
not the case since additional charged particles and photons shift the shower position. The electron energy,
E, measured in the EM calorimeter should match the momentum, p, measured in the ID. For jets, larger E/p
values are expected since several tracks can belong to one jet and there is additional energy from neutral
particles in the calorimeter.
The electron reconstruction and identification algorithm is designed to provide various levels of background rejection optimised for high identification efficiencies, over the full acceptance of the ID system, |η| < 2.5. Additionally
up to |η| < 4.9 a dedicated algorithm can reconstruct forward electrons using calorimeter information only. The
electron identification uses a cut-based selection. The cuts are optimised in bins of electron candidate ET and η.
There are three selections defined, with different levels of signal efficiency and purity: loose, medium and tight.
Loose selection includes rough track-cluster matching, a cut on the hadronic leakage and on the shower shapes
calculated in the second sampling of the EM calorimeter. In medium selection in addition to the loose cuts, tighter
cuts on the track-cluster matching are applied and shower shape information calculated in the first sampling is
used. Tight selection includes the same cuts as for the medium set and additionally require a hit in the B-layer of
the pixel detector, TRT information and calorimeter isolation.
All trigger levels are used for triggering electrons. At the hardware-based L1 trigger, objects are selected only
in the EM calorimeter. At the software-based L2 trigger, dedicated fast calorimeter and tracking algorithms are
used. At the EF level, the electron reconstruction and identification, as described above, is applied and leads to
highly efficient triggers.
In many analyses electrons are required to be isolated from the rest of the event. The first isolation variable is
based on the total transverse momentum of charged particles in the Inner Detector in a cone ∆R centered around
∆R , divided by the transverse momentum or transverse energy of the electron
the electron candidate direction, IPT
candidate. A second isolation variable is based on the total transverse energy measured in the calorimeter cells in
∆R , divided by the transverse energy of the electron candidate. In the
a cone ∆R around the electron direction, IET
reconstruction of both isolation variables, ET of the electron candidate is subtracted.
Photons The reconstruction of photons [121] follows in its main aspects that of electrons. Both objects are
treated similarly within an overall reconstruction algorithm. Although the definition of an electron object is rather
straightforward, relying entirely on the presence of a track matching an electromagnetic cluster, that of a photon
is a bit more involved, due to the fact that photons can be classified into two main categories: converted and
unconverted. Photons reconstructed as converted are characterised by the presence of at least one track matching
an electromagnetic cluster originating from a vertex inside the tracker volume, whereas unconverted photons do
not have such a matched track. A dedicated energy calibration is applied to account for upstream energy losses,
lateral leakage and longitudinal leakage, separately for converted and unconverted photon candidates.
Photon identification is based on the lateral and longitudinal energy profiles of the shower in the calorimeter.
The photon candidate is required to deposit only a small fraction of its energy in the hadronic calorimeter. The
transverse shower shape in the second layer of the electromagnetic calorimeter needs to be consistent with that
expected for a single electromagnetic shower. Finally, the high granularity first calorimeter layer (∆η = 0.0031)
is used to discriminate single photons from overlapping photon pairs from neutral meson decays produced in jet
fragmentation, which are the main background source. Based on these criteria, a set of loose and tight identification
3.5. PARTICLE RECONSTRUCTION AND IDENTIFICATION
31
cuts, different for converted and unconverted photon candidates, is applied. The trigger chain for photons is similar
to the one for electrons.
Muons The ATLAS muon identification and reconstruction algorithms take advantage of the multiple subdetector technologies which provide complementary approaches and cover pseudorapidities up to 2.7 over a wide
pT range. The detector components involved in muon reconstruction are the muon spectrometer and the Inner
Detector. However, muons also deposit some energy in calorimeters. The muon system allows the identification
of muons with a pT above 3 GeV. Very low momentum muons are difficult to reconstruct since they do not reach
the spectrometer, lose too much energy in the calorimeter and/or do not leave a significant signal over the noise in
the muon spectrometer.
ATLAS employs a variety of muon reconstruction algorithms [122]. They rely on the muon spectrometer for
standalone muon reconstruction, but in addition they can use the Inner Detector and the calorimeters information.
In majority of physics analyses so called combined muons are used. For their reconstruction, tracks and track
segments found in the muon spectrometer are associated with the corresponding ID track to identify muons at their
production vertex, imposing requirements on track quality and hit multiplicity in muon system. The combination
improves the momentum resolution for muons below 100 GeV and suppresses the mis-identification of particles
that escape the calorimeter and which are not muons. Two reconstruction chains are in use, the MUID [123]
and the STACO [124]. The MUID algorithm globally fits all hits associated to muon tracks. The STACO algorithm determines transverse momentum of muons by a statistical combination of the Inner Detector and the muon
spectrometer tracks. The performance of the two algorithms is very similar [125].
The muon triggers deploy the three level trigger system of ATLAS within the range of |η| < 2.4. At L1, muons
are identified by coincidence signals from the RPC and TGC detectors. Muon candidates with a certain transverse
momentum are taken as seeds for the high level triggers, L2 and EF. At the L2, the information of the MDTs is
used in fast algorithms to reconstruct tracks, which are combined with tracks from the Inner Detector at the EF
level.
The isolation variables for muons are defined in the same way as for electrons.
τ leptons Reconstruction and identification of τ leptons is described in details in Chapter 4.
Jets Quarks and gluons produced in the primary interaction or as initial or final state radiation evolve into collimated jets of hadronic particles. These jets appear in the detector as localised energy deposits (clusters) in
the electromagnetic and hadronic calorimeters. Thus the first step of the jet reconstruction is the clustering of
calorimeter cells including both the electromagnetic and hadronic systems. There are several jet finding algorithms available [126]. In ATLAS the default is the anti-kT algorithm [127] using a distance parameter R = 0.4
or 0.6. Topological clusters [128] are used as an input. They are combined to form particle jets using the anti-kT
algorithm which is both infrared and collinear safe. The quantities di = 1/p2T,i and di, j = min(1/p2T,i , 1/p2T, j )∆R/R
are first calculated for each cluster i and each cluster pair i j, where ∆R is the cone distance between the two
clusters and R is a distance parameter which defines the radius of the jet. The minimum of this set of numbers
is then identified; if it comes from a di, j , the corresponding clusters are merged, whereas if it comes from a di ,
the corresponding cluster is removed from the list of clusters and moved to the list of jets. These two steps are
repeated until all clusters have been combined into jets. The net effect of this algorithm is to sequentially combine
energy depositions around the highest-pT clusters while ensuring that the distance between the resulting jets is always at least of order R. This procedure has a number of advantages when compared with other jet reconstruction
algorithms. In particular, since the priority is given to high-pT clusters, the algorithm is insensitive to collinear
splitting, emission of soft partons, and pile-up.
The jets found by the algorithm are constructed from the raw signals of the calorimeter cells. As the ATLAS
calorimeter is non-compensating for the energy lost in material before the calorimeters, this raw signal has to be
calibrated. This is done by applying Monte Carlo based pT and η dependent correction factors [129]. For the
standard reconstruction of jets, currently two methods are used in ATLAS, a global cell weighting [130, 59] and
32
CHAPTER 3. THE ATLAS DETECTOR AT THE LARGE HADRON COLLIDER
a cluster-level calibration method called local hadronic calibration [131]. In the global cell weighting calibration,
weights are applied after the jet finding to the energies reconstructed in cells that form the jet constituents. The
weights are functions of the cell energy density and the cell position. The dependence of the weights on the energy
density is motivated by the observation that energy deposits with a low energy density are more likely to originate
from the hadronic component of a shower. In the local hadronic calibration, topological clusters are classified
by their shape, position and the structure of the energy deposit as hadronic or electromagnetic clusters. Weights
similar to the weights applied in the global cell weighting calibration are applied to the energies of cells in hadronic
clusters. A correction for energy not included in the cluster is applied. In this method, the calibrated clusters are
used as the input to the jet reconstruction. At the jet level, both methods yield comparable results. After the
calibration, additional corrections are applied at the jet level to correct for particles not reaching the calorimeter
and for inefficiencies of the jet finding algorithm.
The L1 jet trigger is based on a sliding-window algorithm [132] that selects high energy depositions in the
calorimeters. This information is passed to the L2 trigger based on a simplified version of a cone clustering
algorithm, limited to a maximum of three iterations and performed on calorimeter clusters with full granularity. The
EF uses the same reconstruction algorithms as the offline reconstruction, the only difference being the calorimeter
calibration. Further details can be found in Ref. [59].
Missing transverse energy In a collider event the missing transverse energy is defined as the momentum imbalance in the plane transverse to the beam axis. The colliding protons do not have transverse momentum components
and therefore the sum of the transverse momenta of all final state particles has to vanish as well. An imbalance may
signal the presence of unseen particles, such as neutrinos or stable, weakly-interacting supersymmetric particles.
The vector momentum imbalance in the transverse plane is obtained from the negative vector sum of the momenta
of all particles detected in a pp collision and is denoted as missing transverse energy, E~ Tmiss . The symbol ETmiss is
used for its magnitude.
In its simple definition, the ETmiss is built by summation of calorimeter cell energies, addition of all muons and
the estimated energy loss in the inactive material [133]. The calorimeter part is calculated from the energy deposits
of calorimeter cells inside three-dimensional topological clusters [132], calibrated locally to the electromagnetic
or hadronic scale depending on the energy deposit classification. The muon part takes into account the sum of
the combined muon momenta from all isolated combined muons as well as the sum of all non-isolated muons
reconstructed as tracks in the muon spectrometer. A muon is considered isolated if the distance ∆R to the nearest
jet is at least 0.3. To avoid double counting due to the isolated muons, the sum of the energy of the calorimeter
cells crossed by an isolated muon, is subtracted from the calorimeter term.
A more sophisticated method of the ETmiss calculation is called refined calibration [133, 134]. Since the
calorimeter response depends on the particle type, the energy calibration is also different for different objects
like, for example, electrons and jets. Thus, the calibration of all calorimeter cells which can be associated to a
close-by reconstructed object, is replaced by the calibration specific for the type of the identified particle. The idea
hereby is that these identified objects are calibrated with better accuracy than the hadronic energy deposits. The
association follows a defined order: electrons, then photons, τ leptons, jets and finally muons. Energy deposits
in cells which could not be associated are also included and here the global calibration weights are used. The
resultant ETmiss of each object is then added together to form the refined calorimeter term and thus the refined final
ETmiss .
The ETmiss trigger requires that the magnitude of the vector sum of all transverse energies is larger than some
thresholds. Only calorimeter information from the trigger towers is used at L1. At L2, results provided by L1 are
refined by applying corrections taking into account muons reconstructed at L2. Contributions from the electromagnetic and hadronic calorimeters as well as from the muon spectrometers are recomputed with the full granularity of
the detector at the EF. Only positive energy calorimeter cells above a certain threshold are considered to suppress
electronic noise.
3.6. DATA QUALITY AND PRESELECTION OF EVENTS FOR EARLY DATA ANALYSES
33
3.6 Data quality and preselection of events for early data analyses
After data are taken, several data quality flags are assigned, defining if the data are good enough to be used for
physics analyses. Data quality flags are assigned for each sub-detector and for each reconstructed object in each
detector region (e.g. barrel or end-cap) and for each luminosity block corresponding to several minutes of data
taking. Information from the online and offline data quality monitoring is combined into a database containing
LHC beam conditions, detector status and data flow information which can be used to create lists of runs and
luminosity blocks usable for analyses (so called Good Runs List, GRL). Those lists are created for particular
studies. This is because some analyses do not use the full detector, so even if some of the data for a muon analysis
for instance are not collected correctly because of technical problems with the muon spectrometer, an analysis
based only on the ID information can still use the data. The bad quality data events are removed from the analysis
by applying the dedicated GRL list as the first selection on the data sample.
Following the basic data quality checks, further event cleaning is performed. Discharges in the hadronic
calorimeter or coherent noise in the EM calorimeter can occasionally occur simultaneously with the proton-proton
interaction. Cosmic rays or beam background can also lead to energy deposits, which are not part of the main
collision. Those can lead to the high energy calorimeter deposits or leave high quality tracks in the detector and
thus create incorrectly reconstructed jets, τ candidates and wrong ETmiss measurement [135]. To avoid such effects,
cleaning requirements are applied on τ candidates and jets which do not overlap with electrons and muons. This
cleaning is based on several jet properties, which are used to check quality of calorimeter energy deposits.
During data taking not functional Front End Boards and isolated not functional or high noise channels in the
EM Calorimeter were observed. The inefficiencies are of 6% per electron during data taking in 2010. Using
so called object Quality Maps, the two-dimensional histograms in η and φ, the information can be recovered of
whether an electron is built from a cluster affected by detector problems, in which case it can be rejected [120].
This avoids large differences between data and Monte Carlo predictions which do not simulate the non-functioning
areas.
Pile-up events can come from both the same bunch-crossing as well as from previous bunch-crossings. This
leads to in-time and out-of-time pile-up, respectively. They are characterised by having more than one primary vertex. In early data analyses Monte Carlo pile-up samples are re-weighted such that their default vertex distributions
match the data distribution.
34
CHAPTER 3. THE ATLAS DETECTOR AT THE LARGE HADRON COLLIDER
Life can be very difficult for a little sub-atomic particle in a
great big universe.
Terry Pratchett
4
Reconstruction and identification of τ leptons at ATLAS
As described in Chapter 2, the τ lepton has a short life time and thus cannot be detected directly. Instead it is
identified through its decay products such as electrons, muons, pions, kaons and neutrinos. The τ lepton decays
hadronically 65% of all cases, and the remaining fraction of decays are to lighter leptons. The leptonic decay
modes cannot be distinguished from primary electrons or primary muons. Thus reconstruction of τ leptons in the
ATLAS experiment is understood as a reconstruction of hadronic τ decay modes.
Reconstruction of τ leptons at hadron colliders remains a very difficult task in terms of distinguishing them
from background processes dominated by QCD multijet production. However, τhad decays possess certain properties that can be used to differentiate them from QCD jets, as shown in Figure 4.1. They decay in 72% of the cases
with one charged particle (1-prong) and in 23% with three charged particles (3-prong). This leads to a low track
multiplicity as compared to the QCD jets. The decay products are well collimated, forming a narrow hadronic
shower in the calorimeters. The shape difference of the hadronic τ lepton decay and the QCD jet is due to the
colour flow of these two objects. The τ lepton decays colour neutral via a W boson and thus its decay products
form a narrow cone. Compared to this, the QCD jet, consisting of quarks and gluons, is not a colour neutral object.
The colour field in such a jet can have enough energy to produce new quark-antiquark pairs, which fragment into
colour-neutral hadrons. There is no energy limit in the colour field of a jet, which is why the jet shape is much
broader compared to a hadronically decaying τ lepton.
(a)
(b)
Figure 4.1: Illustration of (a) a hadronic τ decay and (b) a gluon-initiated QCD jet.
35
36
CHAPTER 4. RECONSTRUCTION AND IDENTIFICATION OF τ LEPTONS
Also in τhad decay, due to the presence of π0 ’s, a significant electromagnetic component, different than for the
QCD jets, can be observed. Additionally, isolation from the rest of the event is visible both in the Inner Detector
and the calorimeter. The visible invariant mass is smaller than the τ lepton mass, due to not detectable neutrino.
The lifetime of the τ lepton in principle allows for the reconstruction of its decay vertex in the case of 3-prong
decays. The flight path in the detector increases with the Lorentz boost of the τ lepton, and at the same time the
angular separation of the decay products decreases. The resulting decay vertex can be resolved from the primary
interaction vertex in the silicon tracker. These features are exploited in reconstruction and identification algorithms
used in the ATLAS experiment in order to select efficiently τhad decays.
4.1 Reconstruction of τ decays
The τ leptons reconstruction algorithm is based on information already provided by different sub-detectors, such
as tracks reconstructed in the Inner Detector and energy deposits in the calorimeter. Reconstruction is done only
for the visible part of the decay products (without neutrino), however, for specific studies the complete invariant
mass of the ττ system may be reconstructed as described in Appendix A.
Historically, two different reconstruction algorithms, a track-based and a calorimeter-based, were developed in
the ATLAS offline reconstruction software [59]. In the first data analysis they were run in a merged configuration.
• Calorimeter-based algorithm builds τ candidates from calorimeter jets reconstructed with the anti-kT algorithm [127] (using a distance parameter R = 0.4) from topological clusters [128] with transverse energy
above 10 GeV. The pT of the τ candidate is further adjusted by applying multiplicative factors derived from
Monte Carlo studies. Tracks within a cone size of ∆R < 0.2 of the jet seed are associated to the τ candidate.
The tracks are required to pass track quality criteria described in the next Section. The direction of the τ
candidate is obtained from the η and φ of the seeding jet.
• Track-based algorithm builds τ candidates from a track with pT > 6 GeV which is assumed to come from
the charged pion and reproduces well the direction of the τ candidate (so called leading track). Then, other
tracks around the seed track within a cone size of ∆R < 0.2 are associated (so called associated tracks). It is
also required that there are no tracks in the isolation ring 0.2 < ∆R < 0.4. Both the leading and associated
tracks have to satisfy quality criteria as described in the next Section. The τ candidate energy is determined
using the energy flow algorithm [59]. This method uses the measured track momentum to improve the
overall measurement of the energy in the calorimeters, particularly for the low energy range. The direction
of the τ candidate is calculated from tracks as pT -weighted track barycentre.
τ candidates from the two algorithms are merged, providing they overlap within the cone of ∆R < 0.2. Merged
candidates are expected to be identified with higher purity, but in most first data analyses all calorimeter-based
candidates are used in order to increase the yield. They include nearly all track-based candidates, as there are very
few track-based candidates without a calorimeter-seed.
4.1.1 Track selection criteria for τ leptons reconstruction
Track selection should ensure high efficiency and quality of the reconstructed tracks over a broad dynamic momentum range, from 1 GeV to a few hundred GeV. Both the calorimeter-based and the track-based algorithms
determine the charge of the τ candidates by summing up the charge of particle tracks reconstructed in the core
region, ∆R < 0.2 around the reconstructed direction of visible decay products. Therefore, the selection criteria
for tracks of charged pions arising in τhad decays are important factors in an efficient τ leptons identification. The
incorrect charge assignment for τ candidates is dominated by combinatorial effects: 1-prong decays may migrate
to 3-prong category due to photon conversions or the presence of additional tracks from the underlying event. A
3-prong decay might be reconstructed as a 1-prong decay due to inefficiencies in track reconstruction and selection.
In the low-pT range, the inefficiency is due to hadronic interactions in the Inner Detector material. In the high-pT
4.1. RECONSTRUCTION OF τ DECAYS
37
Table 4.1: Track quality criteria for tracks of calorimeter-based and track-based τ candidates.
Track criteria
pT (GeV)
|η|
B layer hit
Hits in pixel detector
Hits in pixel and SCT detectors
|d0 | (mm)
|z0 sinθ| (mm)
>
<
≥
≥
≥
<
<
calorimeter-based
candidate
1
2.5
1
2
7
1
1.5
track-based candidate
leading track
6
2.5
no cut
no cut
7
2
10
track-based candidate
associated track
1
2.5
1
2
7
1
1.5
range, the performance is degraded due to strong collimation of the multiple tracks from 3-prong decays. Also the
contribution from the incorrect charge assignment of the individual tracks should not be neglected.
The quality criteria are applied on the number of hits in the pixel and SCT detectors, in the pixel detector and
in the B-layer of the pixel detector as well as on the transverse, d0 , and longitudinal, z0 , impact parameters1 . All
quality criteria are listed in Table 4.1.
The τ candidates are classified as one or multi-prong depending on the number of tracks counted in the core
region. For calorimeter-based candidates, tracks within the isolation annulus, 0.2 < ∆R < 0.4, where ∆R is a cone
around the seed jet, are also counted for variable calculations, and are required to satisfy the same track quality
criteria.
4.1.2 Energy calculation
Energy of τ candidates is calculated in two different ways, depending on their seed type. The basic energy of a τ
candidate, reconstructed from calorimeter seed, is obtained as a sum over the energies of cells, within ∆R < 0.4 of
the seed jet axis, that form the topoclusters of the jet seed. This energy reconstructed at the electromagnetic (EM)
energy scale is further calibrated by applying correction factors. For this purpose response functions, R(pEM
T ),
EM /pgen where pEM is the p of the τ candidate at the EM scale and pgen is the true
are defined as R(pEM
)
=
p
T
T
T
T
T
T
generated pT of the candidate. Response functions are constructed using MC samples for different categories of
τ candidates depending on the number of tracks and their |η|. 1-prong candidates are divided accordingly to EM
energy fraction ( fEM ), in an attempt to further classify these candidates based on the π0 content. In order to derive
gen
response functions, τ candidates are binned in pT and the correction factor is constructed for each bin. In each
bin the response is fitted to an asymmetric Gaussian and the mean of the fit gives the correction factor. Correction
gen
factors are associated for every pT bin to a value of pEM
T . Obtained response function is used for calibrating
reconstructed τ candidates to their final energy at the τ energy scale, pTES
T . An example of the response function is
shown in Figure 4.2 (a) for 1-prong τ candidates with fEM > 0.15 in the barrel region. Markers show the correction
factors and the solid line, the response function, being the result of a fit to these markers. The response function
EM
approaches unity for high values of pEM
T . For low values of pT , the functional form of the response function
diverges, so the minimum of the response function is used instead, indicated by the dashed line.
An example of the resolution obtained at the τ energy scale for 1-prong τ candidates in barrel region can be
gen
seen in Figure 4.2 (b). Resolution is defined as pTES
T /pT . The fitted function is an asymmetric Gaussian.
TES
Systematic uncertainty on the obtained pT is evaluated from six distinct sources: Monte Carlo event generator and underlying event model, hadronic shower model, amount of detector dead material, topological clustering
noise thresholds, EM energy scale and, finally, non-closure. The non-closure accounts for deviations of kinematics
of the calibrated τ candidate from the true kinematics. Individual contributions are added in quadrature. An ex1
Impact parameter is a distance between the point of closest approach of a track and the interaction vertex. Transverse impact parameter
is this distance in transverse plane (x,y) and longitudinal impact parameter is the z-coordinate of this point.
CHAPTER 4. RECONSTRUCTION AND IDENTIFICATION OF τ LEPTONS
38
1.1
Tau Candidates
Response
1.2
ATLAS Preliminary
1
0.9
40000
35000
30000
1 prong
|η| ≤ 1.3
25000
Fit mean = 0.99
20000
15000
0.8
ATLAS Preliminary
10000
1 Prong, f
0.7
EM
> 0.15
5000
|η| ≤ 1.3
0.6
0
1
2
3
4
5
6
7
8
9
ln(pEM
T
0
0
10
0.5
1
1.5
2
2.5
3
gen
pTES/p
[GeV])
T
(a)
T
(b)
Underlying event
Hadronic shower
Detector material
Noise threshold
EM Scale
Non-closure
Total sys. error
T
0.08
0.06
T
∆(pTES/p
gen
)
Figure 4.2: Response functions for 1-prong τ candidates with fEM > 0.15 in the barrel region (a). Resolution for
1-prong τ candidates in the barrel region (b) [136].
ATLAS Preliminary
1 prong: |η| ≤ 1.3
0.04
0.02
0
-0.02
-0.04
10
20
30
40
50
60
70
pgen
[GeV]
T
Figure 4.3: Final systematic uncertainty on the τ energy scale. Different markers represent various sources of
uncertainty as indicated in the legend. The yellow band shows the combined uncertainty from all
sources [136].
ample of the total systematic uncertainty on the τ energy calibration scale, along with contributions from different
sources of systematic uncertainties are shown in Figure 4.3 for 1-prong τ candidates in the barrel region.
An energy flow algorithm is used for track-seeded τ candidates. This method divides the energy deposited in
cells into following categories:
• The pure electromagnetic energy, Eemcl
T , seeded by an electromagnetic cluster isolated from the τ candidate
tracks and with no substantial hadronic leakage. The energy is collected in a narrow window around the
seed.
chrgEM
• The charged electromagnetic energy, ET
, seeded by the impact point of τ candidate tracks in each layer
of the EM calorimeter. The energy is collected in a narrow window around seeds.
chrgHAD
• The charged hadronic energy, ET
, seeded by the (η, φ) of τ candidate tracks in each layer of the
hadronic calorimeter. The energy is collected in a cone of ∆R = 0.2 around seeds.
4.1. RECONSTRUCTION OF τ DECAYS
39
• The neutral electromagnetic energy, EneuEM
seeded by the (η, φ) of τ candidate tracks in presampler and two
T
first layers of the EM calorimeter. The energy is collected from not yet used cells in a cone of ∆R = 0.2
around seeds.
chrgEM
chrgHAD
The energy deposits ET
and ET
are replaced by the track momenta (no hadronic neutrals) in order to
. To account for
and EneuEM
define the τ energy scale. The contribution from neutral pions is included in Eemcl
T
T
overlapping of energy deposits of neutral and charged pions and energy leakage outside a narrow cone around the
P
chrgEM
track, correction terms resET
and resEneuEM
are used. These terms are derived empirically from parametriT
sation of effects mentioned above, based on the Monte Carlo studies [137]. This leads to the following energy,
Eeflow
, definition:
T
X
X
Eeflow
= Eemcl
+ EneuEM
+
T
T
T
ptrack
+
T
chrgEM
resET
+ resEneuEM
.
T
(4.1)
An advantage of the above approach for defining the energy scale is that it performs well for true hadronic decays
of τ leptons but significantly underestimates the nominal energy of fake τ candidates from QCD jets. This effect
comes from the fact that a cone of ∆R = 0.2 is too narrow to efficiently collect the energy of a QCD jet (particularly
with low transverse momentum) and also since a large fraction of the neutral hadronic component is omitted in
the definition itself, as the energy deposit in the hadronic calorimeter does not contribute to the energy calculation.
This method leads, however, to more pronounced non-Gaussian tails in the fractional energy response than the
more conventional energy estimates from calorimetry only.
4.1.3 π0 reconstruction
High granularity of the EM calorimeter in ATLAS allows for the identification of isolated sub-clusters from π0
mesons inside the core region of the reconstructed τ candidates. It is done by the reconstruction of the topological
sub-clusters from cells in a cone size of ∆R < 0.4 around the direction of the leading track of the τ candidate.
Only sub-clusters with a centre within ∆R < 0.2 and with transverse energy above 1 GeV are considered. A cell
subtraction procedure is applied to reduce the impact from energy deposits of nearby charged pions. Namely,
before the clustering process, cells being closest to the impact point of the track (∆R < 0.0375) are removed.
In addition, sub-clusters are accepted if their reconstructed energy in the first and presampler layers of the EM
calorimeter exceeds 10% of their total energy. This methods finds 50% of the π0 clusters in τ decays with one
or two π0 mesons, while approximately 65% of τ → πν decays are reconstructed correctly without any π0 ’s [59].
Until now, the described method has been optimised with MC samples only for the track-based candidates.
4.1.4 τ lepton trigger
The L1 τ trigger is a hardware trigger based on EM and hadronic calorimeter information, using trigger towers of
approximate size ∆η × ∆φ = 0.1 × 0.1, with a coverage up to |η| < 2.5. At this level τ candidates are identified
using three key features: the EM and hadronic energy in two-by-two collection of trigger towers and energy in the
isolation region between two-by-two collection of trigger towers and the four-by-four collection surrounding it.
Different thresholds to these quantities define various L1 τ triggers.
The L2 τ trigger is software-based. After refining the L1 position using the second sample layer in the EM
calorimeter, its algorithm selects narrow jets by means of calorimeter lateral shape and transverse energy variables.
Tracks are also reconstructed in regions passing the L1 trigger using the full detector granularity. The characteristic
narrowness of tracks and calorimeter deposition and low track multiplicity of the τhad decay are used to discriminate
against background.
At the EF level, parts of the offline τ reconstruction algorithms are used on the seeds passing L2. Data from the
whole detector can be accessed if necessary. This provides a wide range of more accurate identification variables.
Rejection against dominant QCD multijet background by the High Level Triggers (L2 together with EF) is of the
order of 10 or more, depending on the pT range and tightness of the selection.
Different τ trigger signatures were used for collecting early data and for increasing instantaneous luminosities.
Typically, the pT threshold applied at EF was tightened with increasing luminosities. Additionally, different quality
40
CHAPTER 4. RECONSTRUCTION AND IDENTIFICATION OF τ LEPTONS
requirements (loose, medium, tight) are available for each chain. The τ trigger and its performance in 2010 ATLAS
data is fully documented in Ref. [138].
4.2 τ leptons identification
The reconstruction of τ candidates provides very little rejection against QCD multijets, electrons or muons. Their
rejection comes from a separate identification step using variables calculated by the reconstruction algorithms. The
identification is based on the combined information from the Inner Detector and the calorimeters. A traditional
cut-based selection method as well as multivariate discrimination techniques are used. For early data only robust
variables are used. These variables are expected to be well understood even with non-optimal detector calibration
and limited knowledge of the detector performance.
4.2.1 Rejection of QCD jets
The variables used to discriminate against the QCD multijet background are described below. They are calculated
for the calorimeter-based candidates.
Electromagnetic radius: Shower width weighted with the transverse energy in the EM calorimeter:
REM =
P∆Ri <0.4
i
EM ∆R
ET,i
i
P∆Ri <0.4
i
EM
ET,i
,
where i runs over cells in the first three layers of the EM calorimeter associated to the τ candidate, ∆Ri is
EM is the cell transverse energy. It is expected to be
defined relative to the τ candidate jet seed axis and ET,i
narrower for τhad decays compared to QCD multijets.
Track radius: Tracks width weighted with the track pT :
Rtrack =
P∆Ri <0.4
pT,i ∆Ri
i
,
P∆Ri <0.4
pT,i
i
where i runs over all core and isolation tracks of the τ candidate, ∆Ri is defined relative to the τ candidate
jet seed axis and pT,i is the track transverse momentum. Similar to the REM it tends to be smaller for τhad
decays than for QCD multijets.
Leading track momentum fraction:
ftrack =
ptrack
T,1
pT
,
where ptrack
T,1 is the transverse momentum of the leading core track of the τ candidate and pT is the transverse
momentum of the τ candidate. In case of τhad decays, the leading track carries significant fraction of τ
momentum.
Core energy fraction: Fraction of transverse energy in the core (∆R < 0.1) of the τ candidate:
P∆R<0.1
fcore = Pi∆R<0.4
i
ET,i
ET,i
,
where i runs over all cells associated to the τ candidate within ∆Ri of the τ candidate jet seed axis. This
variable measures the concentration of calorimeter energy deposits around the jet axis. For τhad decays,
energy tends to be more concentrated, resulting in a higher fcore compared to QCD multijets.
4.2. τ LEPTONS IDENTIFICATION
41
Electromagnetic fraction: Fraction of uncalibrated transverse energy of the τ candidate deposited in the EM
calorimeter:
P∆Ri <0.4
E EMscale
i; i∈EM Calo T,i
,
fEM = P∆R <0.4
EMscale
i
j; j∈Calo E T, j
where ET,i (ET, j ) is the uncalibrated transverse energy deposited in cell i ( j), and i runs over the cells in the
first three layers of the EM calorimeter, while j runs over the cells in all layers of the calorimeter. For τhad
decays larger energy deposits in the EM calorimeter are expected due to the presence of neutral pions.
Cluster mass: Invariant mass computed from constituent clusters of the seed jet, mclusters . This variable has larger
values for QCD jets due to their higher multiplicity.
Track mass: Invariant mass of tracks in a cone of size ∆R = 0.4, mtracks . This variable has larger values for QCD
jets due to their higher multiplicity.
Transverse flight path significance: The decay length significance of the secondary vertex for multi-track τ candidates in the transverse plane:
flight
LT
flight
ST =
,
flight
σ(LT )
flight
flight
where LT is the reconstructed signed decay length in the transverse plane and σ(LT ) is its uncertainty.
The tracks used for the secondary vertex fit are those associated to the τ candidate, but additional tracks
with pT > 6 GeV within ∆R < 0.2 of the jet seed, and satisfying |d0 | < 2.0 mm, and |z0 sin θ| < 10 mm, are
also added to the vertex fit, even if they fail the B-layer and pixel detector criteria, and the tighter impact
parameter criteria that are required for associated tracks.
Using those variables as an input, discriminants are designed to accept true τ candidates and reject fake τ candidates
reconstructed from QCD multijet events. There are three different discriminants used for the early data-taking
period: a cut based selection, projective likelihood identification, and identification with boosted decision trees.
The cut based τ identification uses cuts on only three uncorrelated variables: REM , Rtrack and ftrack , binned for
τ candidates that have one or multiple tracks. The cuts on REM and Rtrack are parametrised as a function of the pT
of the τ candidate, since the optimal cuts are strongly pT -dependent due to the Lorentz collimation of the decay
products in hadronic τ decays.
In the projective likelihood identification seven variables are used, three for 1-prong τ candidates (REM , Rtrack ,
mclusters ) and five for 3-prong τ candidates (REM , ftrack , fEM , mtracks , number of vertices reconstructed in the event).
The probability density functions (PDFs) used by this method are split into different categories, or bins, in order to
maximise the discriminatory power. This categorisation is based on properties both of the τ candidate (pT , seed,
number of prongs) and of the event (number of reconstructed primary vertices). The PDFs are also produced for
three separate pT bins.
The identification of τ leptons with boosted decision trees algorithm (BDT) [139] uses all discriminating
variables mentioned above. The BDT is trained separately on candidates with one track and with three tracks.
Additionally, the BDT is binned by the number of reconstructed primary vertices (less than 3, and more than
2). The selections on the BDT score are made that yield roughly flat signal or flat background efficiency. The
selections employ pT -dependent cuts which compensate for the pT -dependence of the BDT score.
4.2.2 Electron and muon vetos
In addition to the QCD multijets rejection, identification methods are also used to distinguish τhad decays from
electrons and muons. The cut-based electron veto provides a good separation between electrons and reconstructed
τ candidates. Requirements are made on four variables:
42
CHAPTER 4. RECONSTRUCTION AND IDENTIFICATION OF τ LEPTONS
strip
Emax : The maximum energy deposited in the strip layer of the EM calorimeter, not associated with that of the
leading track. This variable tends to be larger for τhad decays due to presence of neutral pions and hadronic
interactions in front and inside EM calorimeter.
EEM / pLtrk : The ratio between the energy deposited in the EM calorimeter, EEM , and the momentum of the leading
track, pLtrk . For electrons this variable is close to unity.
EHad / pLtrk : The ratio between the energy deposited in the first layer of the hadronic calorimeter, EHad , and the
leading track momentum. For electrons this ratio is smaller than for hadrons.
NHT/NLT : The number of high threshold hits over the number of low threshold hits in the TRT. This ratio is
higher for electrons than for pions as electrons are more likely to produce the transition radiation that leaves
high threshold hits in the TRT.
One of the main characteristics of muons is the small amount of energy deposited in the calorimeters. The
muon veto algorithm rejects events with total energy deposition in the electromagnetic and hadronic calorimeters
(at the electromagnetic scale) below 5 GeV. Since the energy threshold for the calorimeter-seeded reconstruction
of a τ candidate is 10 GeV (at the jet energy scale), this veto is fully efficient for these candidates.
4.3 τ reconstruction and identification performance in data
Prior to the start of data-taking, understanding of the expected performance of the τ reconstruction and identification relied on Monte Carlo simulations [59, 140]. More detailed understanding could only be achieved after the
detector was in place and physics signals could be used for performance studies and for validation or tuning of the
simulation.
In years 2008-2009 the ATLAS detector, already commissioned in its underground cavern, collected several
hundred million cosmic ray events. Because cosmic ray muons interact with the detector mainly as minimumionising particles, most traverse all of the sub-detectors along their flight path. So, in addition to each sub-detector
specific cosmic ray studies, these data samples provided the first opportunity to study the combined performance
of different detector components and thus were used also for the test of the τ reconstruction and identification [9].
Since no τ leptons were expected in the cosmic ray data sample, the focus of this study was to exercise the
algorithms designed to identify them, and to investigate how well the quantities used for the selection are modelled
in the simulation. Good agreement between data and cosmic ray Monte Carlo for the properties of track- and
calo-seeded τ candidates was found, in particular for quantities used in the identification algorithms.
The studies on the τ performance algorithms were continued with the first data coming from pp collisions.
In December of 2009, shortly after the single-beam commissioning of the LHC, the ATLAS experiment recorded
data from pp collisions at the centre-of-mass energy of 900 GeV. This data set was used to study τ identification
variables [10]. These events were preselected using a minimum-bias trigger and dominated by soft interactions.
While the number of actual τ leptons in this data sample was expected to be negligible, it still could be used to
prepare for the commissioning of the τ reconstruction and identification algorithms at higher energies. The analysis
was continued with the data from pp collisions at the centre-of-mass energy of 7 TeV [11, 12]. The following, more
evolved, studies of the background rates for the τ identification are described below.
4.3.1 Estimation of QCD multijets background efficiency as a function of signal efficiency
Results presented in this Section are obtained with the signal derived from Monte Carlo samples with true hadronic
τ decays (W → τν, Z → ττ) and the background evaluated on data sample obtained from a selection of di-jet events
collected by ATLAS in autumn 2010 [136]. As the signal, only reconstructed τ candidates coming from true τ
hadronic decays and with |η| < 2.5 and pT > 10 GeV, are used. The reconstructed number of tracks is required to
match the true number of prongs. Background di-jet events have to pass the L1 jet trigger and have at least two τ
candidates, a leading one with pT > 30 GeV and a sub-leading one with pT > 15 GeV. ∆φ between leading and
4.3. τ RECONSTRUCTION AND IDENTIFICATION PERFORMANCE IN DATA
43
0.16
0.14
Arbitrary Units
Arbitrary Units
sub-leading candidates should be ∆φ > 2.7 rad. The leading candidate should be the one used by the L1 trigger
and it is further ignored to avoid trigger bias. Only the sub-leading candidate is considered for identification and
efficiency calculations. Using the reconstructed variables described in Section 4.2.1 as an input, discriminants for
identification (Id) of τ candidates are designed to accept true hadronic decays of τ leptons and reject fake candidates
reconstructed from QCD multijet events. Distributions of those variables for both signal and background are shown
in Figures 4.4-4.6.
ATLAS Preliminary
W→τν+Z→ττ
1 prong 15 GeV<p <60 GeV
dijet Monte Carlo
T
2010 dijet data dt L = 23 pb-1
∫
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W→τν+Z→ττ
3 prongs 15 GeV<p <60 GeV
dijet Monte Carlo
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2010 dijet data dt L = 23 pb-1
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dijet Monte Carlo
T
2010 dijet data dt L = 23 pb-1
∫
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REM
Arbitrary Units
Arbitrary Units
REM
0.1
0.25
ATLAS Preliminary
W→τν+Z→ττ
3 prongs 15 GeV<p <60 GeV
dijet Monte Carlo
T
2010 dijet data dt L = 23 pb-1
∫
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T
2010 dijet data dt L = 23 pb-1
∫
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Arbitrary Units
Arbitrary Units
Rtrack
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ATLAS Preliminary
W→τν+Z→ττ
3 prongs 15 GeV<p <60 GeV
dijet Monte Carlo
T
2010 dijet data dt L = 23 pb-1
∫
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1
1.2
1.4
f track
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
f track
Figure 4.4: Distributions of REM , Rtrack , and ftrack , for 1-prong (left) and 3-prong (right) τ candidates. The dashed
lines indicate the cut boundaries for the cut-based identification. Since the cuts on REM and Rtrack are
parametrised in pT , the characteristic range of the cut values is shown for candidates with pT = 20 GeV
(60 GeV) by the right (left) dashed line [136].
Arbitrary Units
0.12
Arbitrary Units
CHAPTER 4. RECONSTRUCTION AND IDENTIFICATION OF τ LEPTONS
44
ATLAS Preliminary
W→τν+Z→ττ
1 prong 15 GeV<p <60 GeV
dijet Monte Carlo
T
2010 dijet data dt L = 23 pb-1
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∫
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0
ATLAS Preliminary
W→τν+Z→ττ
3 prongs 15 GeV<p <60 GeV
dijet Monte Carlo
T
2010 dijet data dt L = 23 pb-1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
ATLAS Preliminary
W→τν+Z→ττ
1 prong 15 GeV<p <60 GeV
dijet Monte Carlo
T
2010 dijet data dt L = 23 pb-1
0.14
∫
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1
f core
Arbitrary Units
Arbitrary Units
f core
0.08
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ATLAS Preliminary
W→τν+Z→ττ
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dijet Monte Carlo
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ATLAS Preliminary
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dijet Monte Carlo
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2010 dijet data dt L = 23 pb-1
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mclusters [GeV]
∫
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ATLAS Preliminary
W→τν+Z→ττ
3 prongs 15 GeV<p <60 GeV
dijet Monte Carlo
T
2010 dijet data dt L = 23 pb-1
0.1
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f EM
Arbitrary Units
Arbitrary Units
f EM
0
0
1
2
3
4
5
6
7
8
9
10
mclusters [GeV]
Figure 4.5: Distributions of fcore , fEM , and mclusters , for 1-prong (left) and 3-prong (right) τ candidates [136].
0.3
0.25
Arbitrary Units
Arbitrary Units
4.3. τ RECONSTRUCTION AND IDENTIFICATION PERFORMANCE IN DATA
ATLAS Preliminary
W→τν+Z→ττ
3 prongs 15 GeV<p <60 GeV
dijet Monte Carlo
T
2010 dijet data dt L = 23 pb-1
∫
0.2
0.18
45
ATLAS Preliminary
W→τν+Z→ττ
3 prongs 15 GeV<p <60 GeV
dijet Monte Carlo
T
2010 dijet data dt L = 23 pb-1
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∫
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flight
ST
mtrack [GeV]
ATLAS Preliminary
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15 GeV<p <60 GeV
dijet Monte Carlo
T
2010 dijet data dt L = 23 pb-1
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dijet Monte Carlo
T
2010 dijet data dt L = 23 pb-1
0.16
∫
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Arbitrary Units
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Figure 4.6: Top: Distributions of mtracks (left) and S T (right) for 3-prong τ candidates. Bottom: Distribution of
the number of associated tracks to the τ candidates [136].
0.12
0.1
ATLAS Preliminary
W→τν+Z→ττ
3 prongs 15 GeV<p <60 GeV
dijet Monte Carlo
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2010 dijet data dt L = 23 pb-1
∫
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Likelihood Score
(a)
1
BDT Score
(b)
Figure 4.7: The projective likelihood (a) and BDT (b) scores for 3-prong τ candidates [136].
Inverse Background Efficiency
Inverse Background Efficiency
CHAPTER 4. RECONSTRUCTION AND IDENTIFICATION OF τ LEPTONS
46
Cuts
BDT
Likelihood
103
102
10
ATLAS Preliminary
Cuts
102
10
1-Prong p >20GeV
0.2
0.3
ATLAS Preliminary
3-Prong p >20GeV
T
1
BDT
Likelihood
103
T
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1
0.2
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Signal Efficiency
(a)
0.7
0.8
0.9
Signal Efficiency
(b)
Figure 4.8: Inverse background efficiency versus signal efficiency for all discriminants on 1-prong and 3-prong τ
candidates with pT > 20 GeV [136].
As described in Section 4.2.1 three different discriminants are used: a cut-based selection, projective likelihood
identification, and identification with BDT. An example of the projective likelihood and BDT scores for 3-prong τ
candidates is shown in Figure 4.7.
The following definitions of the signal and background efficiencies are used.
Signal efficiency:
1/3-prong
εsig
# of τ candidates with 1/3 reconstructed track(s), passing Id, and
truth-matched to a simulated 1/3-prong decay
=
# of simulated τhad with 1/3 prong(s)
Background efficiency:
1/3-prong
εbkg
# of τ candidates with 1/3 reconstructed track(s), passing Id
=
(# of τ candidates with 1/3 reconstructed track(s))
The discriminants are optimised in pT , η and one or 3-prong bins. Candidates with no reconstructed tracks fail the
identification by definition. Multi-prong candidates use the same discriminant as for 3-prong candidates.
The τhad signal and QCD multijet background efficiencies for each identification method are presented in
Figure 4.8 for 1-prong and 3-prong candidates with pT > 20 GeV. The upper bound on the signal efficiency is
limited by the tracking reconstruction efficiency and hence worse for 3-prong candidates.
The background efficiency depends on the pT distribution of the τ candidates and the type of partons that
initiated the jets. It can differ by as much as a factor of five, depending on whether the jet is quark or gluon
initiated [141].
Physics analyses use the τ Id mainly in combination with an electron veto. Therefore, signal efficiencies and
their systematic uncertainties are also evaluated in combination with the electron veto. Several combinations,
called working points, of τ Id for 1-prong candidates, 3-prong candidates and electron veto are studied.
Expected signal efficiencies for the looser working point are in the range of 50 − 60% for the cut-based and
likelihood-based identification methods and 40 − 50% for the BDT. For the tighter working point, the expected
signal efficiencies are reduced to about 30% for the cut-based and about 40% for the likelihood-based identification
methods and about 30% for the BDT. Figure 4.9 shows signal efficiencies for one exemplary working point corresponding to tighter selection, for each of the three discriminating methods. The systematic uncertainties on the
τ Id efficiencies are evaluated using Monte Carlo samples with varied conditions in the event generation, detector
4.3. τ RECONSTRUCTION AND IDENTIFICATION PERFORMANCE IN DATA
47
material, shower modelling, and reconstruction. Signal efficiencies obtained with those samples are presented by
different labels in Figure 4.9. The yellow bands correspond to the final systematic uncertainty obtained by adding
in quadrature the contributions from each source of systematic uncertainty.
For the looser working points, the estimated systematic uncertainty is in the range of (4-7)%, while for the
tighter working points, the systematic uncertainty is near 10%. For candidates with pT < 20 GeV, the systematic
uncertainty is dominated by the shower modelling and the topological clustering noise threshold, while for higher
pT candidates, only the systematic contribution of the clustering threshold dominates.
First attempt to estimate the τ signal efficiency from data using the Standard Model process W → τν is
described in Section 5.3.
4.3.2 Measurement of the τ mis-identification probability from QCD jets
The mis-identification of QCD jets as τ candidates is determined using different processes [141]. Events, where
jets originate mainly (∼ 90%) from quarks are obtained in the γ+jet selection. Events with a fraction of ∼ 65% of
jets originating from quarks are selected in the Z(→ ℓℓ)+jets analysis. Finally, events with a fraction of ∼ 50% of
jets originating from quarks are selected in the di-jet/three-jet topology.
The di-jet/three-jet events
The data events considered have to pass one of jet triggers: L1 trigger with ET threshold between 5 and 75 GeV
for the early data-taking period and EF trigger with ET threshold between 20 and 95 GeV for the later data-taking
period. Events are required to have two jets with |η| < 2.5 and pT > 15 GeV, which are balanced in φ (∆φ ≥ π − 0.3
max is the p of the leading jet. From these pairs of jets, one is chosen
radians) and pT (|∆pT | ≤ pmax
T
T /2), where pT
randomly as the tag jet and the other as as probe jet. Only the latter is used for the mis-identification measurement.
In order to remove a very small fraction of events with real τhad pairs, it is required in addition that the tag jet has
at least four tracks associated with it. No further requirements are imposed on the probe jet. It is then required that
a reconstructed τ candidate with at least one track and with pT > 15 GeV is within ∆R = 0.2 of the probe jet.
The mis-identification probability, fId , is then calculated as a ratio between number of probe jets identified
as τ candidates and number of probe jets reconstructed as τ candidates. Obtained fId is presented in Figure 4.10
for tighter working point of the cut-based identification algorithm as a function of τ candidate pT for 1-prong and
3-prong τ candidates and for events with 1,2 or >2 reconstructed primary vertices.
The following sources of systematic uncertainties are included: the requirement on the exact level of pT and φ
balance of the tag and the probe jet and the requirement on the number of tracks in the tag jet. Thus each of these
criteria is varied separately and the observed difference in the mis-identification probability is taken as a systematic
uncertainty. In addition, the influence of the matching criterion of the probe jets to the reconstructed τ candidates,
and the contamination of real τ leptons in the sample of probe jets was investigated and found to be negligible.
For the three-jet topology study, triplets of jets are selected, each of them satisfying pT > 15 GeV and |η| < 2.5.
These triplets are selected such that one of the jets is balanced in pT and φ by the two other jets. From the latter,
one is chosen randomly as a probe jet. The mis-identification probabilities are calculated in the same way as for
the di-jet topology. Differences in the mis-identification probability compared to the di-jet topology of up to 40%
are observed, due to the softer probe jet pT spectrum and the denser environment in the three-jet events.
The γ+jet events
The mis-identification probability of τ candidates from hadronic jets can also be determined from topologies where
a jet is balanced in pT and φ by a photon. In order to select such events, EF photon triggers with ET thresholds
between 10 and 40 GeV including loose and tight photon identification are used. Exactly one isolated photon
candidate is required in the event, with pT > 15 GeV and within the pseudorapidity range of |η| < 2.47, excluding
the transition region in the calorimeters. The jet in the event is selected requiring the same criteria for pT , η and
φ balance as for the di-jet topology. The results for the mis-identification probability obtained with these events
0.8
0.7
Tighter Cuts working point
1 prong
ATLAS Preliminary
Nominal
Detector Material
Hadronic Shower
Underlying Event
Noise threshold
Total sys. error
0.6
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40
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0.8
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Tighter Likelihood working point
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ATLAS Preliminary
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Ratio
0.1
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40
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100
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Tighter Likelihood working point
Nominal
3 prongs
Detector Material
ATLAS Preliminary
Hadronic Shower
Underlying Event
Noise threshold
Total sys. error
0.6
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40
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Tau efficiency
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Detector Material
Hadronic Shower
Underlying Event
Noise threshold
Total sys. error
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T
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Hadronic Shower
Underlying Event
Noise threshold
Total sys. error
20
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3 prongs
ATLAS Preliminary
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100
T
Ratio
Tau efficiency
Ratio
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ATLAS Preliminary
80
Visible p of truth tau [GeV]
T
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60
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Hadronic Shower
Underlying Event
Noise threshold
Total sys. error
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T
Tau efficiency
Tau efficiency
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Visible p of truth tau [GeV]
T
1
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Detector Material
Hadronic Shower
Underlying Event
Noise threshold
Total sys. error
1.1
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3 prongs
ATLAS Preliminary
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Tau efficiency
Ratio
1
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Tau efficiency
CHAPTER 4. RECONSTRUCTION AND IDENTIFICATION OF τ LEPTONS
48
0.8
60
Visible p of truth tau [GeV]
T
Figure 4.9: Signal efficiencies for the tighter working point as a function of pT for 1-prong (left) and 3-prong
candidates (right). Different labels correspond to signal efficiencies obtained for the different sources
of systematic uncertainties. The ratio of the signal efficiency obtained from the modified event samples
to that in the sample used in the analysis (nominal sample) is also presented. The first row shows the
efficiency for the cuts; the second shows the likelihood; the third shows the BDT. The yellow band
shows the total systematic uncertainty [136].
4.3. τ RECONSTRUCTION AND IDENTIFICATION PERFORMANCE IN DATA
1
f Id
f Id
1
Tighter cuts working point
ATLAS Preliminary
-1
Tighter cuts working point
-1
10
10
10-2
10-2
10-3
10-3
-4
10
1 prong
Data 2010
3 prong
s = 7 TeV
-4
10
1, 2 primary vertices
10-50
49
ATLAS Preliminary
1 prong
Data 2010
3 prong
s = 7 TeV
>2 primary vertices
20 40 60 80 100 120 140 160 180 200 220 240
10-50
20 40 60 80 100 120 140 160 180 200 220 240
pT [GeV]
(a)
pT [GeV]
(b)
Figure 4.10: The mis-identification probability of QCD multijets from di-jet topologies as τ candidates shown
as a function of τ candidate pT for 1-prong and 3-prong τ candidates in events with one or two
primary vertices (a) and more than two primary vertices (b) for the tighter working point of the cutbased identification algorithm. The statistical errors are represented by vertical bars; the shaded areas
correspond to the total uncertainty. Large errors in some bins are due to the statistical fluctuations in
samples used for estimation of systematic uncertainties [141].
are shown in Figure 4.11 for the tighter working point of the cut-based identification algorithm as a function of τ
candidate pT for 1-prong and 3-prong τ candidates and for events with 1,2 or >2 reconstructed primary vertices.
The same sources of systematic uncertainty as for the di-jet topology are considered with one exception:
instead of considering requirement on the number of tracks in the tag jet, the effect of loosening the photon
identification criteria by dropping the isolation requirement is considered. This increases the contamination of the
selected event sample with di-jet events, thereby increasing the fraction of gluon-initiated probe jets and reducing
the mis-identification probability by about 10%. This difference is included in the total systematic uncertainty.
The Z(→ ℓℓ)+jets events
Finally, the mis-identification probability of τ candidates from QCD jets can be derived from the additional jets in
Z(→ ℓℓ)+jets events. Events are selected with one electron (muon) with an ET (pT ) threshold of 15 GeV at EF
trigger level. Electrons are required to have ET > 20 GeV and be inside |η| < 2.47, excluding the transition region
in the calorimeters. Both electrons are required to pass medium electron identification. Muons are required to
have pT > 20 GeV and be within |η| < 2.5. Additional quality criteria for each muon track reconstructed in the ID
have to be satisfied [125]. Only events where the invariant mass of the tag leptons fall inside the Z mass window
71 < mℓℓ < 111 GeV are selected.
The probability of QCD jets to be mis-identified as τ candidates is calculated from the additional τ candidates
reconstructed in the event, satisfying pT > 15 GeV, |η| < 2.5 cuts and having one or three associated track. It
is required in addition, that no electron or muon candidates are reconstructed within ∆R < 0.4 around the τ
candidate. The mis-identification probability is displayed in Figure 4.12 for the tighter working point of the cutbased identification algorithm as a function of τ candidate pT for 1-prong and 3-prong τ candidates.
The sources of systematic uncertainties are the choice of the invariant mass window for the tag leptons which
is varied, 80 < mℓℓ < 100 GeV, reducing the expected background by roughly a factor of two, and the uncertainty
on the energy scale of the electrons or muons, which is assumed to be 2%.
CHAPTER 4. RECONSTRUCTION AND IDENTIFICATION OF τ LEPTONS
50
1
f Id
f Id
1
Tighter cuts working point
Tighter cuts working point
10-1
10-1
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3 prong
>2 vertices
ATLAS Preliminary
20
40
60
80
100
120
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pT [GeV]
(a)
(b)
Figure 4.11: The mis-identification probability of hadronic jets from γ+jet topologies as τ candidates. These are
shown as a function of τ candidate pT for 1-prong and 3-prong τ candidates in events with one or
two primary vertices (a) and more than two primary vertices (b) for tighter working point of the cutbased identification algorithm. The statistical errors are represented by vertical bars; the shaded areas
correspond to the total uncertainty. Large errors in some bins are due to the statistical fluctuations in
samples used for estimation of systematic uncertainties [141].
1
f Id
f Id
1
ATLAS
10-1
Preliminary
ATLAS
10-1
10-2
10-2
2010 Data
10-3
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-1
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-1
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-4
20
40
60
80
100
120
140
160
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tighter cuts
200
10-5 0
20
40
60
80
pT [GeV]
(a)
s = 7 TeV
stat.+sys. uncertainties
-4
1-prong tau candidates
tighter cuts
10-5 0
Preliminary
100
120
140
160
180
200
pT [GeV]
(b)
Figure 4.12: The probability of hadronic jets from Z(→ ℓℓ)+jets to be mis-identified as τ candidates as a function
of τ candidate pT for 1-prong (a) and 3-prong (b) τ candidates, for the tighter working point of
the cut-based identification algorithm. The statistical errors are represented by vertical bars; the
shaded areas correspond to the total uncertainty. Large errors in some bins are due to the statistical
fluctuations in samples used for estimation of systematic uncertainties [141].
4.4. SUMMARY
51
Summary of the measurements of the mis-identification from QCD jets
The mis-identification probabilities range from 10% to 0.1%, depending on the τ identification algorithm chosen,
the number of prongs of the τ candidate, its pT , the origin of the QCD jet being reconstructed as a τ candidate
and the number of primary vertices found in the event. The differences in mis-identification probabilities found in
the various topologies are attributed to the different fraction of quark-initiated jets (as opposed to gluon-initiated
jets) in the topologies studied. When separating quark-initiated and gluon-initiated jets on truth-level, Monte Carlo
studies indicate that good agreement of the mis-identification probabilities is observed across the three different
samples studied.
4.3.3 Measurement of the mis-identification from electrons
The probability of an electron to be mis-identified as τ candidate is measured in a sample of Z → ee events. Events
passing the electron EF trigger with a threshold of ET = 15 GeV and medium identification criteria are selected.
The electron candidate used by the trigger is required to have pT > 30 GeV and |η| < 2.47 (excluding the transition
region in the calorimeters). In addition, the tag electron has to pass tight identification and has to be isolated from
0.4 < 0.06. As the probe, a reconstructed τ candidate with p > 15 GeV and |η| < 2.5 is
the rest of the event, IPT
T
selected. It has to have exactly one track associated. The 3-prong τ candidates are not used due to the too high
background level.
The invariant mass of the tag-and-probe pair is required to fall inside the Z mass window 80 < mee < 100 GeV.
In order to suppress remaining backgrounds, mainly from W → eν processes, ETmiss < 20 GeV is required, where
the simple definition of the missing transverse energy is used as described in Section 3.5.
The probe candidates, satisfying the criteria above, are then subjected to the τ identification algorithms and
to the electron veto. The mis-identification probability, fId , is defined as a ratio of number of probe candidates
passing electron veto and τ Id and number of probe candidates. The mis-identification probabilities for the tighter
working point of the cut-based identification algorithm are shown in Figure 4.13 as a function of pT and |η| of the
probe candidate. The mis-identification probability is of the order of 1% for probe candidates with pT > 20 GeV
independent of the τ identification algorithm applied. The influence of pile-up on the mis-identification probability
of electrons as τ candidates is negligible.
Sources of systematic uncertainties considered are the background estimation, the energy scale of the probe
electron and the choice of the signal mass window. However, the result is dominated by the current statistical
uncertainties that are as large as ±50%.
4.4 Summary
The ATLAS package for reconstruction and identification of hadronically decaying τ leptons has gone a long way
from a simple calorimeter-based algorithm [142] to the sophisticated, robust and effective one, described in this
Chapter. The algorithm, tuned primarily only on Monte Carlo samples, was successfully validated on cosmic ray
data and then on the first proton-proton collisions and finally optimised using full data sample collected in 2010. It
appeared as ready to be used in the first studies with τ leptons in final states. Obtained performance is comparable
to the one reported by the CMS collaboration [143].
In this Chapter, the reconstruction, energy scale calibration and identification of hadronically decaying τ leptons are presented. Three alternative identification methods are optimised to discriminate τ leptons from QCD
jets: a cut-based discriminant, discrimination with a projective likelihood, and discrimination with boosted decision trees. A cut-based discriminant is optimised to reject electrons mis-identified as τ leptons. The versions of the
algorithms described are those defined for data analysis of 2010 data and first half of 2011. The τ signal efficiency
and the τ energy scale calibration and their systematic uncertainties are estimated from Monte Carlo samples. The
mis-identification rate of QCD jets as τ candidates is determined using data samples with di-jet/three-jet events,
γ+jet and Z(→ ℓℓ)+jets events. The probability of an electron to be mis-identified as τ candidate is measured in a
sample of Z → ee events.
f Id
0.08
0.07
∫ L dt = 37 pb
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Z(→ ee)+jets
-1
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0.06
f Id
CHAPTER 4. RECONSTRUCTION AND IDENTIFICATION OF τ LEPTONS
52
0.08
0.07
0.06
0.05
0.05
0.04
0.04
0.03
0.03
0.02
0.02
0.01
0.01
0
10
20
30
40
50
60
70
80
90
100
p [GeV]
0
0
∫ L dt = 37 pb
Data 2010 at s = 7 TeV
Z(→ ee)+jets
-1
ATLAS Preliminary
0.5
1
T
(a)
1.5
2
2.5
|η|
(b)
Figure 4.13: The mis-identification probabilities as a function of τ candidate pT (a) and |η| (b) for the tighter working point of the cut-based identification algorithm. The dots are the data and the error bars represent
the statistical uncertainty of the measurement with the shaded areas representing the total uncertainty. The squares represent the predictions from Monte Carlo, with the shaded areas representing
the statistical uncertainty of the simulation [141].
Presented results are based on the first data collected by the ATLAS experiment and thus on small statistics.
However it should be mentioned that since then, upon completion of this monograph, a lot of progress has been
done. It concerns mainly performance of the τ reconstruction and identification [144] and determination of the τ
energy scale and the associated systematic uncertainty [145]. In the latter case the first attempts to use Z → ττ
events for the in-situ measurement of the τ energy scale are presented.
As will be shown in the next Chapters, analyses with τhad in final states suffer from background coming from
mis-identification of electrons as τ candidates. In this Chapter only cut-based electron veto was described as used
on the first data but presently also the BDT based electron veto exists giving a much better performance.
Polarisation in τ lepton decays can be measured through the kinematics of their decay products, especially
in τhad decays. The key element in those studies is reconstruction of neutral pions from τhad decays. Their
reconstruction can also improve τ identification by considering different decay modes separately. Even simple
counting of neutral pions can help as decays without them will have an excellent energy resolution from the ID
tracks. Good mass resolution is the only handle against dominant Z → ττ background in H → ττ searches.
There is ongoing work on identification of π0 ’s within τ candidates using topoclusters from τ candidates jet seeds.
Another developed method is similar to the one described in this Chapter but using parametrised hadronic shower
profiles for subtracting the contribution from charged pions.
The remaining issue is also optimisation of τ reconstruction and identification for high pT , when τ candidates
form very narrow jets and reconstruction of 3-prong candidates starts to be challenging for the tracker. Such studies
are crucial for searches for high mass resonances described in Section 2.5. Also, better fake τ candidates rejection
is the key for improving the sensitivity for the H → ττ searches. Finally, the τ reconstruction algorithm should be
re-optimised to be less sensitive to pile-up which increased significantly in 2011 and 2012 data runs.
All above possible improvements are mentioned here only for completeness. Their detailed description and
first results are out of the scope of this monograph.
Nothing is a waste of time if you use the experience wisely.
Auguste Rodin
5
Standard Model processes with τ leptons
In Chapter 2 the role of τ leptons in the search for New Physics phenomena at the LHC was discussed. Decays
of Standard Model gauge bosons to τ leptons, W → τν and Z → ττ are important background processes in
such searches and their production cross sections need to be measured precisely. This is described in detail in
Sections 5.1 and 5.2. Given a large cross section for these processes, they offer the first opportunity to study τ
hadronic decays in the ATLAS experiment. The W → τν and the Z → ττ decays are crucial to estimate τ lepton
detection performance. An example application of the measured W → τν cross section to τ identification studies
is presented in Section 5.3.
The data sample used in described analyses corresponds to a total integrated luminosity of (34 − 36) pb−1 ,
recorded with stable beam conditions and a fully operational ATLAS detector in 2010.
5.1 Z → ττ cross section measurement
The Z → ττ cross section measurement is performed using four different final states [16]. Two of them are the
semileptonic modes, τµ τhad : Z → τlep τhad → µ + hadrons + 3ν and τe τhad : Z → τlep τhad → e + hadrons + 3ν
with branching fractions (22.50 ± 0.09)% and (23.13 ± 0.09)%, respectively [46]. The remaining two final states
are the leptonic modes, τe τµ : Z → τlep τlep → eµ + 4ν and τµ τµ : Z → τlep τlep → µµ + 4ν with branching fractions
(6.20 ± 0.02)% and (3.01 ± 0.01)%, respectively [46]. The semileptonic final state consists of an isolated lepton
ℓ1 and a τ candidate of opposite charge, as well as missing energy from the two τ decays. Those final states are
advantageous as they provide an isolated lepton which can be triggered on. This feature makes them attractive for
studies of the τ trigger and offline τ identification, as they can provide an unbiased sample of hadronic τ decays.
Due to the large expected QCD multijet background contamination, the Z → τhad τhad and Z → τlep τlep → 2e + 4ν
final states are not considered.
The Z → ττ cross section has been measured previously in p p̄ collisions at the Tevatron using the semileptonic
τ decay modes [146, 147]. More recently the cross section was measured in pp collisions at the LHC by the CMS
Collaboration, using both the semileptonic and leptonic modes [148].
As mentioned in Section 4.2, identification of τhad decays is difficult and suffers from high fake rates, much
higher than the fake rates from the identification of electrons or muons. Because of this, most of the backgrounds
relevant for these final states involve a true lepton along with a QCD jet mis-identified as a τ candidate. The two
leptonic modes are characterised by two isolated leptons of typically lower transverse momentum than those in
Z → ee/µµ decays. The τe τµ mode gives much cleaner signature as it does not suffer from τ mis-identification but
1
The ℓ refers to either an electron or a muon in this monograph.
53
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
54
its yield is much lower. The τµ τµ leptonic mode is overwhelmed by the γ∗ /Z → µµ production. A brief summary
of the considered backgrounds is given below:
• QCD multijet - dominant background due to its large cross section. The lepton could be true (e.g. muons
produced from heavy flavour decays) or fake, while the τ candidate is typically a mis-identified quark or
gluon-initiated jet.
• W + jets - with a cross section about an order of magnitude higher than the signal, where the W decays
leptonically while an associated mis-identified quark or gluon jet provides the fake τ candidate or second
lepton, real or fake. The lepton and the jet in this process are biased towards having an opposite sign,
similarly to the signal.
• γ∗ /Z → ee, µµ - produces two oppositely charged leptons of the same flavour and is a dominant background
in the τµ τµ channel. The τe τµ channel is affected by this background if one of the leptons escapes detection
and additional jets in the event contain hadrons that either decay leptonically or fake leptons. In the semileptonic final states this process can form a background if one of the leptons is mis-identified as a τ candidate,
or if the γ∗ /Z is produced in association with a jet mis-identified as a τ candidate and at the same time one
of the leptons is not reconstructed.
• t t̄ - can contain a true τ lepton, or either jets or leptons that fake a τhad as well as at least one real electron
or muon. However, compared to other backgrounds the cross section for this process is small, making it less
important.
Di-boson production has a much smaller cross section than the signal, and contributes to the background only in
a very minor way. Possible contributions to the background from single-top and γ+jet production are found to be
negligible.
5.1.1 Data and Monte Carlo samples
Events are selected using either single-muon or single-electron triggers. For the τµ τhad and τµ τµ final states, singlemuon triggers requiring pT > (10 − 13) GeV, depending on the run period, are used. For the τe τhad and τe τµ final
states, a single-electron trigger requiring ET > 15 GeV is used. The efficiency for triggers is determined from data
using a tag-and-probe method. The muon trigger efficiency is measured using Z → µµ events and found to be close
to 95% in the end-cap region, and around 80% in the barrel region. The electron trigger efficiency is measured
using W → eν and Z → ee events and found to be ∼ 99% for offline electron candidates with ET > 20 GeV and
∼ 96% for electron candidates with ET between 16 and 20 GeV [105].
The inclusive W and γ∗ /Z signal and background MC samples are generated with PYTHIA 6.421 [112] and
are normalised to next-to-next-to-leading order (NNLO) cross sections [149, 150, 151]. For the tt¯ sample the
MC@NLO generator is used [152], while the di-boson samples are generated with HERWIG [113]. In all samples
τ decays are modelled with TAUOLA [114]. All generators are interfaced to PHOTOS [116] to simulate the effect
of final state QED radiation.
5.1.2 Selection of Z → ττ candidates
Objects selection
Only events containing at least one primary vertex with three or more associated tracks, as well as fulfilling preselection requirements described in Section 3.6 are used in the analysis. As the next step following reconstructed
objects are selected.
Combined muon candidates with pT > 15 GeV for the τµ τhad final states and pT > 10 GeV for the τe τµ and
τµ τµ final states are used. Muon candidates are required to have |η| < 2.4 and a longitudinal impact parameter of
less than 10 mm with respect to the primary vertex. In the final muon selection, combined muon tracks are also
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T
0.2
0.25
0.3
0.3
I E / ET(e)
T
(b)
0.4 /p and (b) I 0.3 /E for muon and electron candidates, after selecting one τ candidate
Figure 5.1: Isolation (a) IET
T
T
ET
and one lepton with opposite signs in τµ τhad and τe τhad final states. The QCD multijet background is
estimated from data (see Section 5.1.3), other processes are estimated using MC [16].
required to pass several Inner Detector track quality criteria [125], resulting in an efficiency of ∼ 92%, as measured
in data using Z → µµ events.
Electron candidates are selected if they have ET > 16 GeV and |η| < 2.47, excluding the transition region
in the calorimeters. For the τe τµ final state, candidates are required to pass the medium identification, with an
efficiency of ∼ 89%. For the τe τhad final state, electron candidates are required to pass the tight identification, with
an efficiency of ∼ 73%. Efficiencies are measured in data using W → eν and Z → ee events.
Jets used in this analysis are required to have a transverse momentum pT > 20 GeV and |η| < 4.5.
τ candidates are selected if they have pT > 20 GeV and |η| < 2.47, excluding the calorimeter transition
region, and if they pass cut-based identification. Additionally, a dedicated selection to reject fake τ candidates
from electrons is applied. This leads to an efficiency of ∼ 40% (∼ 30%) for 1-prong (3-prong) τ candidates as
determined from the signal Monte Carlo sample. For fakes from QCD multijets the efficiency is ∼ 6% (∼ 2%) for
1-prong (3-prong) τ candidates, as measured in data using a di-jet selection. Details of these measurements are
described in the previous Chapter.
For missing transverse energy the simple definition described in Section 3.5 is used. There is no direct requirement on ETmiss applied in this analysis but the quantity and its direction is used in several selection criteria
described later.
Leptons from Z → ττ decays are typically isolated from other particles, in contrast to electrons and muons
from QCD multijet events coming mainly from heavy-flavours decays. Hence, isolation requirements (as defined
in Section 3.5) are applied to both electron and muon candidates used in the four final states considered. A selection
0.4 /p < 0.06 for the muon candidate and I 0.4 /E < 0.06 for the electron candidate is used for all final
requiring IPT
T
T
PT
states but the τµ τµ . Due to the presence of two muon candidates, the QCD multijet background is smaller in the
0.4 /p < 0.15, increases the signal yield. In addition, for muon
latter one, and a looser isolation requirement, IPT
T
0.4 /p < 0.06 is applied to all final states except the τ τ final state where a looser
candidates, the requirement IET
T
µ µ
0.4 /p < 0.2, is applied. For electron candidates, a selection requiring I 0.3 /E < 0.1 is applied in both
selection, IET
T
T
ET
τe τhad and τe τµ final states. The efficiencies for these isolation requirements are measured in data using Z → µµ
and Z → ee events and found to be (75−98)% for muons and (60−95)% for electrons, depending on the transverse
0.4 /p variable for muon and I 0.3 /E
momentum or energy respectively. Figure 5.1 shows the distribution of the IET
T
T
ET
variable for electron candidates.
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
56
(a) Z → ττ → µτhad
(b) W → µν
(c) W → τν → µννν
Figure 5.2: Drawings of the transverse plane orientations of W and Z decay products and the ETmiss . The shaded
angles indicate the angle (less than π) between the lepton and the (fake) τ candidate. In (a), the Z is
depicted to have nonzero pT , which must be balanced on the left by some other activity omitted for
clarity [14].
Event selection
Semileptonic final states For the τµ τhad (τe τhad ) final state, at least one isolated muon (tight electron) candidate
with pT > 15 GeV (ET > 16 GeV) and one τ candidate with pT > 20 GeV are required in the event. The QCD
multijet background is largely suppressed by the τ identification and lepton isolation requirements. Any event with
more than one muon or electron candidate is vetoed, which strongly suppresses background from γ∗ /Z → ℓℓ + jets
events. To increase background rejection, the selection criteria for the second lepton are relaxed: the ID track
quality requirements are dropped for the muons, and the electrons need only to pass the medium selection and
have ET > 15 GeV.
After the selection described above, the largest background is W+jets production. It is suppressed by two
additional selection criteria based on variables that exploit kinematic correlations between the lepton and the
ETmiss . Because the mass of the Z boson is much larger than the mass of the τ lepton, the τ leptons in Z → ττ
are boosted such that their decay products are collimated along the trajectory of the parent τ lepton. Ignoring
underlying interactions in the event and mis-measurements of ETmiss , the ETmiss is the vector sum of the pT of the
neutrinos, as shown in Figure 5.2(a). The majority of the produced Z bosons have low pT , and therefore the τ
leptons are produced back-to-back, but in the case when the Z has a significant nonzero boost in the transverse
plane, the ETmiss vector falls in the angle between the decay products of the Z.
In contrast, in events from the W → ℓν + jets background, the neutrino, jet, and lepton all point in different
directions, balancing pT in the transverse plane, as shown in Figure 5.2(b). Ignoring underlying interactions in the
event and mis-measurements of ETmiss , the ETmiss vector should therefore point along the neutrino which is not in
the angle between the fake τ candidate and the lepton. In W → τlep ν events, shown in Figure 5.2(c), there are two
additional neutrinos, but the ETmiss still tends to point outside of the angle between the fake τ candidate and the
lepton. In this analysis this is explored by placing a requirement on:
X
(5.1)
cos ∆φ = cos φ(ℓ) − φ(ETmiss ) + cos φ(τhad ) − φ(ETmiss ) .
P
The variable cos ∆φ is positive when the ETmiss vector points towards the direction bisecting the decay products
P
and is negative when it points away. The distributions of cos ∆φ are shown in Figure 5.3(a) and 5.3(b) for the
τµ τhad and τe τhad final states, respectively. The peak at zero for Z → ττ corresponds to events where the decay
P
products were back-to-back in the transverse plane. The W + jets backgrounds accumulate at negative cos ∆φ
P
whereas the γ∗ /Z → ττ distribution has an asymmetric tail extending into positive cos ∆φ values, corresponding
P
to events where the Z boson has higher pT . Events are therefore selected by requiring cos ∆φ > −0.15. The
P
cos ∆φ variable, in addition to being a good discriminating variable against the W + jets background, is robust
against mis-measurements of ETmiss . It is also only a function of the direction of the ETmiss , which is generally more
accurately measured than its magnitude. The ETmiss direction is most susceptible to mis-measurement when the
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120 140
mT [GeV]
0
0
20
40
60
80
100
120 140
mT [GeV]
(d) τe τhad final state
P
Figure 5.3: Distributions of cos ∆φ for the (a) τµ τhad and (b) τe τhad final states. Distributions of mT for the τµ τhad
(c) and τe τhad (d) final states. Distributions are shown after the object selection and requirements of
one electron or muon candidate and the charge of the τ candidate to be of opposite sign to that of
the lepton. The QCD multijet background is estimated from data and other processes from Monte
Carlo [14].
magnitude is small. Events with small ETmiss tend to have the decay products back-to-back, which is accepted by
P
the cos ∆φ cut regardless of the direction of the ETmiss .
The second quantity used to suppress the W + jets background is the transverse mass:
mT =
q
2 pT (ℓ) · ETmiss · 1 − cos ∆φ(ℓ, ETmiss ) .
(5.2)
Figures 5.3(c) and 5.3(d) show its distribution for the τµ τhad and τe τhad final states. The Z → ττ distribution piles
up towards zero because when the ETmiss and the lepton align, cos ∆φ tends towards one and mT tends towards zero.
In Z → τlep τhad events, the ETmiss usually aligns with the lepton because there are two neutrinos on the side of the
leptonic decay. For W → ℓν events, mT is maximal when the momentum vectors of the neutrino and lepton have
zero z-components in the W rest frame, in which case mT is a measure of the W mass. Only a loose cut on the
P
transverse mass, mT < 50 GeV, is required as many W + jets events are already rejected by the cut on cos ∆φ
variable.
Three additional selection criteria are required to select a clean sample of Z → ττ events. The τ candidate
and the isolated lepton are combined to reconstruct the invariant mass of the visible decay products of the two τ
leptons, the visible mass, mvis . Only events with 35 < mvis < 75 GeV are selected in order to include majority
Events / 5 GeV
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CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
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30
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mvis(µ, τ ) [GeV]
h
Data
45 ATLAS Preliminary
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5
0
0
20
40
60
80 100 120 140
mvis(e, τh) [GeV]
∫
(a) τµ τhad final state
(b) τe τhad final state
ATLAS Preliminary
250
Data
γ */Z→ττ
Multijet
W→lν
W→τ ν
γ */Z→ll
tt
s = 7 TeV
∫ Ldt = 36 pb
-1
200
150
Events
Events
Figure 5.4: Distributions of the visible mass, mvis , for the (a) τµ τhad and (b) τe τhad final states. Distributions are
shown after the full event selections, except for the visible mass window [14].
180
ATLAS Preliminary
160
Data
γ */Z→ττ
Multijet
W→lν
W→τ ν
γ */Z→ll
tt
s = 7 TeV
∫ Ldt = 36 pb
-1
140
120
100
80
100
60
40
50
0
20
0
2
4
6
(a) τµ τhad final state
8
10
Ntracks(τh)
0
0
2
4
6
8
10
Ntracks(τh)
(b) τe τhad final state
Figure 5.5: The final τ candidate track distribution after all cuts in opposite signed bin, except the requirement on
the number of tracks and on the magnitude of the τ candidate charge [14].
of the signal, while excluding Z → ℓℓ events. For Z → µµ events, the peak of mvis is at slightly lower values
than for Z → ee events as muons mis-identified as τ candidates leave less energy in the calorimeter compared
to mis-identified electrons, and the proportion of events where the τ candidate arises from a mis-identified jet, as
opposed to a mis-identified lepton, is higher in Z → µµ events.
The chosen τ candidate is required to have 1 or 3 associated tracks and unit charge. Additionally, the chosen τ
candidate and the chosen lepton are required to have opposite charges as expected from Z → ττ decays.
The distribution of the visible mass after the full selection except the visible mass window requirement is
shown in Figure 5.4. The τ candidate track distribution after the full selection except the requirements on the
number of associated tracks and on the magnitude of the τ candidate charge is shown in Figure 5.5.
Final state with electron and muon For τe τµ final state exactly one isolated medium electron candidate with
ET > 16 GeV and one isolated muon candidate with pT > 10 GeV of opposite electric charge are required. Because
signal events contain two leptons of different flavors, the contributions from γ∗ /Z → ee and γ∗ /Z → µµ processes
P
are small. The requirement
cos ∆φ > −0.15 is applied as in the semileptonic final states, discriminating against
P
¯
W → ℓν, and tt backgrounds. Figure 5.6 (a) shows the distribution of cos ∆φ after the described selection
50
40
59
Events / 10 GeV
Events / 0.1
5.1. Z → ττ CROSS SECTION MEASUREMENT
Data
' */Z&%%
tt
W & l(
' */Z & ll
Multijet
ATLAS Preliminary
s = 7 TeV
$ L dt=35.5 pb
-1
30
25
ATLAS Preliminary
20
-1
15
20
10
10
5
0
-2
-1.5
-1
-0.5
0
0.5
1
s = 7 TeV
" L dt=35.5 pb
0
0
1.5
2
# cos("!)
Data
% */Z$##
tt
W $ l&
% */Z $ ll
Multijet
50 100 150 200 250 300 350 400 450 500
! ET + ETmiss [GeV]
(a)
(b)
! Ldt=35.5 pb
-1
30
s = 7 GeV
Data 2010
QCD Est
# */Z " ee
# */Z " µµ
W " e$
W " µ$
W " %$
tt
WW/ZZ/WZ
# */Z"%%
25
20
15
10
5
0
0
20 40 60 80 100 120 140 160 180 200
Meµ (GeV)
Events / 5 GeV
Events
P
P
Figure 5.6: Distributions of the (a) cos∆φ and (b) ET + ETmiss after the isolation cuts for the τe τµ final state.
The multijet background is estimated from data, other processes are estimated from Monte Carlo [14].
25
20
Data
γ */Z→ττ
γ */Z→ll
W→ lν
Multijet
tt
ATLAS Preliminary
s = 7 TeV
∫ Ldt = 36 pb
-1
15
10
5
0
0
10
(a) τe τµ final state
20
30
40
50
60
70
80 90 100
m(µ, µ) [GeV]
(b) τµ τµ final state
Figure 5.7: Distributions of the visible mass for the (a) τe τµ and (b) τµ τµ final states after the full event selection.
For the τe τµ final state the visible mass window selection is not applied [14].
criteria. Further reduction of the tt¯ background is based on the topology of tt¯ events characterised by the presence
P
of high-pT jets and leptons, as well as large ETmiss . The selection is made by requiring that events satisfy ET +
P
ETmiss < 150 GeV cut, where ET + ETmiss variable is defined as:
X
X
(5.3)
pT + ETmiss .
ET + ETmiss = ET (e) + pT (µ) +
jets
P
P
The distribution of ET + ETmiss variable for data and Monte Carlo after the cos ∆φ requirement is shown in
Figure 5.6 (b).
Finally, the invariant mass of the two leptons is calculated. It is required to be within a wider range than
in the semileptonic case, 25 < meµ < 80 GeV, as γ∗ /Z → ℓℓ events are a small background in this final state.
Figure 5.7(a) shows the distribution of the visible mass.
Two muons final state For τµ τµ final state exactly two isolated muon candidates, one with pT > 10 GeV and
one with pT > 15 GeV, are required. The muon candidates should have opposite charge. The signal region for this
final state is defined by the invariant mass of the two muon candidates, 25 < mµµ < 65 GeV.
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
600
500
ATLAS Preliminary
s = 7 TeV
∫ Ldt = 36 pb
-1
400
Events / 0.2
Events / 0.1
60
Data
γ */Z→ττ
γ */Z→ll
Multijet
400
350
300
250
300
Data
γ */Z→ττ
γ */Z→ll
Multijet
ATLAS Preliminary
s = 7 TeV
∫ Ldt = 36 pb
-1
200
150
200
100
100
0
0
50
0.5
1
1.5
2
2.5
0
0
3
3.5
∆(φ(µ , µ ))
1
300
s = 7 TeV
2
2.5
3
∆(φ(µ, EMiss))
(b)
Data
γ */Z→ττ
γ */Z→ll
Multijet
∫ Ldt = 36 pb
-1
250
1.5
T
Events / 0.005 mm
Events / 1 GeV
ATLAS Preliminary
1
2
(a)
350
0.5
200
150
500
400
ATLAS Preliminary
s = 7 TeV
∫ Ldt = 36 pb
-1
300
Data
γ */Z→ττ
γ */Z→ll
Multijet
200
100
100
50
0
0
5
10
15
20
25
30
35
40 45 50
p (µ ) - p (µ )
T
(c)
1
T
2
0
0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Σ d0 (µ ,µ ) [mm]
1 2
(d)
Figure 5.8: Distributions for the τµ τµ final state for the signal and γ∗ /Z → ℓℓ MC samples and data after the
di-lepton, isolation and visible mass selections. The multijet QCD background is estimated from data.
Other backgrounds are negligible on those plots. The observed differences are consistent with the
assumed systematic uncertainties [14].
A boosted decision trees algorithm, BDT, is used to distinguish efficiently between signal and the main background. It is trained using MC samples, Z → ττ as signal and γ∗ /Z → µµ as background after the selection
described above. To maximise the available MC statistics for training and testing, no isolation requirements are
applied to the muon candidates. The five variables are used for the BDT training: the differences in azimuthal
angles between the two muon candidates (∆φ(µ1 , µ2 )) and between the leading muon candidate and the ETmiss vector (∆φ(µ1 , ETmiss )), the difference in the pT of the two muon candidates (pT (µ1 )− pT (µ2 )), the transverse momentum
of the leading muon candidate (pT (µ1 )), and the sum of the absolute transverse impact parameters of the two muon
P
candidates ( d0 (µ1 , µ2 ) = |d0 (µ1 )| + |d0 (µ2 )|), which has the highest discriminating power. Distributions of these
variables, except pT (µ1 ), for the events that are used for the BDT selection are shown in Figure 5.8. Differences
between data and Monte Carlo are consistent with the estimated systematic uncertainties, and the agreement is the
best in the regions most relevant for the signal and background separation.
In the analysis it is required that the BDT output is greater than 0.07, resulting in an efficiency of 0.38 ± 0.02.
This cut is chosen as giving the best signal significance. The visible mass distribution after the full selection except
the mass window requirement is shown in Figure 5.7(b).
3500
ATLAS Preliminary
Data
γ */Z→ττ
W→lν
W→τ ν
γ */Z→ll
tt
s = 7 TeV
∫ Ldt = 36 pb
-1
3000
2500
2000
120
ATLAS Preliminary
Data
γ */Z→ττ
W→lν
W→τ ν
γ */Z→ll
tt
s = 7 TeV
∫ Ldt = 36 pb
-1
100
80
60
1500
40
1000
20
500
0
0
61
Muons / 5 GeV
Muons / 5 GeV
5.1. Z → ττ CROSS SECTION MEASUREMENT
20
40
60
80
100
120 140
p (µ) [GeV]
0
0
20
40
60
80
100
T
(a) no τ identification
120 140
p (µ) [GeV]
T
(b) tight τ candidate
Figure 5.9: Muon pT distributions in the W control region, with no (a) and tight (b) τ identification. Plots are for
the τµ τhad final state. A similar effect is seen in the τe τhad final state [14].
5.1.3 Background estimation
In order to estimate the final purity and significance of the selected signal events, the number of background events
passing the selection has to be estimated. The estimated number of background events from electroweak processes
(W → ℓν, W → τν, Z → ℓℓ, di-boson production) and tt¯ are taken from MC, providing that these backgrounds are
small and the MC prediction agrees well with the observed data. To obtain such agreement, W boson MC samples
are renormalised with a scale factor described below.
Rates of real and fake leptons produced in QCD multijet events, on the other hand, are not expected to be
modelled well with MC. Thus estimated number of background events from QCD is data driven.
W+jets background
In the two di-leptonic final states, the W → ℓν and W → τν backgrounds are found to be small, and their contribution is obtained from simulations. In the two semileptonic final states, where these backgrounds are important,
they are instead estimated from data by obtaining their normalisation from a W boson-enriched control region. A
P
high-purity W sample is provided by requiring events to pass all selection criteria except those on mT and cos ∆φ,
rejecting the W background. The QCD multijet background contamination in this region is negligible. The MC
estimate of the small γ∗ /Z → ℓℓ and tt¯ contribution is subtracted before calculating the normalisation factor.
As shown in Figure 5.9(a), the MC agrees with the data reasonably well before requiring the τ identification
and overestimates the data after applying tight τ identification as shown in Figure 5.9(b). This is in agreement with
results described in Section 4.3 where the τ fake rate from jets is overestimated by the MC. The W MC is therefore
corrected by normalising it to the number of events observed in the data in the W control region. The obtained
normalisation factor is 0.73 ± 0.06 (stat) for the τµ τhad final state and 0.63 ± 0.07 (stat) for the τe τhad final state.
Since the differences between data and W MC are due to different τ fake rates in data and MC, a second method
was also used, as a cross check, to normalise the W MC in the signal region. A scale factor for the τ fake rate
measured in data with a dedicated fake rate study as described in Section 4.3 is estimated on Z → ℓℓ+jet events,
and applied as an event weight. The resulting estimated W background is in agreement with the W background
estimate obtained using normalisation in the W control region.
γ∗ /Z → µµ background
The γ∗ /Z → µµ process is the most important electroweak background to the τµ τµ final state. The normalisation of
the Monte Carlo sample is checked after the di-muon selection, for events with invariant masses between 25 GeV
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
62
1#+2
%$#/,&'0(
$"
%"
.$#/,&'0(
!"
#"
!""#$%&'(
)%*+(
),-'(
)%*+(
Figure 5.10: Schematic diagram of the control regions for the QCD multijet background estimation method.
and 65 GeV. In this region, the γ∗ /Z → µµ process is dominant and is expected to contribute to over 94% of
the selected events. The expected backgrounds arising from other electroweak processes are subtracted and the
QCD multijet contribution is estimated using a data-driven method described in the next Section. The number of
γ∗ /Z → µµ events in the selected mass window is consistent between MC and data within the uncertainties of
∼ 8% (to be compared with a 7% difference in rate). Therefore no correction factor is applied to the γ∗ /Z → µµ
MC prediction.
QCD multijets background
The QCD multijet background estimation is made using data-driven methods in all final states. In the τe τµ and
semileptonic final states, the method takes advantage of the fact that the QCD multijet background is expected to
be approximately the same regardless of whether the lepton and the τ candidate or second lepton have the same or
the opposite sign. The following relation is used:
A
NQCD
B
NQCD
=
C
NQCD
D
NQCD
,
(5.4)
i
where NQCD
is the number of QCD multijet events in four statistically independent regions, denoted by i =
{A, B, C, D} and defined as follows:
• A: signal region with the isolated lepton and the opposite sign requirement;
• B: control region with the isolated lepton and the same sign requirement;
• C: control region with the reversed lepton isolation requirement and the opposite sign requirement;
• D: control region with the opposite sign requirement and the isolation requirements reversed.
The four regions are illustrated schematically in Figure 5.10. This method uses the fact that the signal is composed
of almost exclusively isolated leptons whose charges are opposite to the τ candidates or the second lepton charges,
and therefore signal contributions can effectively be excluded in all control regions B, C and D.
The QCD multijet estimate is scaled from region B to region A, using Eq. 5.4:
A
NQCD
=
C
NQCD
D
NQCD
The following values of ROS /S S are obtained:
B
B
NQCD
= ROS /S S NQCD
.
(5.5)
5.1. Z → ττ CROSS SECTION MEASUREMENT
63
Table 5.1: Estimated background events, expected number of signal events and number of events observed in data,
Nobs , after the full selection, for each final state. The quoted uncertainties are statistical only [14].
γ∗ /Z → ℓℓ
W → ℓν
W → τν
tt¯
Di-boson
QCD multijet
Total background events
Expected signal events
Total expected events
Nobs
τµ τhad
11.1 ± 0.5
9.3 ± 0.7
3.6 ± 0.8
1.3 ± 0.1
0.28 ± 0.02
24 ± 6
50 ± 6
186 ± 2
235 ± 6
213
τe τhad
6.9 ± 0.4
4.8 ± 0.4
1.5 ± 0.4
1.02 ± 0.08
0.18 ± 0.01
23 ± 6
37 ± 6
98 ± 1
135 ± 6
151
τe τµ
1.9 ± 0.1
0.7 ± 0.2
< 0.2
0.15 ± 0.03
0.48 ± 0.03
6±4
9±4
73 ± 1
82 ± 4
85
τµ τµ
36 ± 1
0.2 ± 0.1
< 0.2
0.8 ± 0.1
0.13 ± 0.01
10 ± 2
47 ± 2
44 ± 1
91 ± 3
90
1.07 ± 0.04 (stat) ± 0.04 (syst) τµ τhad final state
1.07 ± 0.07 (stat) ± 0.07 (syst) τe τhad final state
1.55 ± 0.04 (stat) ± 0.20 (syst) τe τµ final state.
Electroweak backgrounds in all three control regions are subtracted using MC simulations. For the samesign control regions of the semileptonic final states, the W normalisation factor, calculated as described earlier, is
applied. The QCD multijet background is estimated after the full selection in the two semileptonic final states,
and after the di-lepton selection in the τe τµ final state, due to limited statistics. In this case the efficiency of the
remaining selection criteria is obtained from the same-sign non-isolated control region.
This method assumes that the ROS /S S ratio is the same for non-isolated and isolated leptons. The measured
variation of this ratio as a function of the isolation requirements is taken as a systematic uncertainty.
The QCD multijet background to the τµ τµ final state is estimated in a control region defined after applying
the full selection, but requiring the sub-leading muon candidate to fail the isolation selection criteria. A scaling
factor is then calculated in a separate pair of control regions, obtained by requiring that the leading muon candidate
fails the isolation selection and that the sub-leading muon candidate either fails or passes it. This scaling factor is
further corrected for the correlation between the isolation variables for the two muon candidates. The QCD multijet
background in the signal region is finally obtained from the number of events in the primary control region scaled
by the corrected scaling factor.
Final background estimation
Table 5.1 shows the estimated number of background events per process for all final states. Also shown are the
expected number of signal events, as well as the total number of events observed in data in each channel after the
full selection.
5.1.4 Methodology for cross section calculation
The measurement of the cross section is done in each final state separately, and then the obtained values are
combined. The calculation is performed using the formula:
σ(Z → ττ) × B =
where
Nobs − Nbkg
,
AZ · C Z · L
• B is the branching fraction for the considered final state;
(5.6)
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
64
• Nobs is the number of observed events in data;
• Nbkg is the number of estimated background events;
• L is the integrated luminosity for the final state of interest;
• CZ is the correction factor that accounts for the efficiency of triggering, reconstructing and identifying the
Z → ττ events within the fiducial regions, defined as:
– τµ τhad final state: muon with pT > 15 GeV and |η| < 2.4; τ candidate with pT > 20 GeV and |η| < 2.47
(excluding transition region in the calorimeters); events with Σ cos ∆φ > −0.15, mT < 50 GeV and
35 < mvis < 75 GeV
– τe τhad final state: electron with ET > 16 GeV and |η| < 2.47 (excluding transition region in the
calorimeters); τ candidate with pT > 20 GeV and |η| < 2.47 (excluding transition region in the
calorimeters); events with Σ cos ∆φ > −0.15, mT < 50 GeV and 35 < mvis < 75 GeV
– τe τµ final state: electron with ET > 16 GeV and |η| < 2.47 (excluding transition region in the calorimeters); muon with pT > 10 GeV and |η| < 2.4; event with Σ cos ∆φ > −0.15 and 25 < mvis < 80 GeV
– τµ τµ final state: leading muon with pT > 15 GeV and |η| < 2.4; sub-leading muon with pT > 10 GeV
and |η| < 2.4; events with 25 < mvis < 65 GeV.
The CZ factor is determined as the ratio between the number of events passing the full selection after a
complete detector simulation and the number of events in the fiducial region at the generator level. The fourmomenta of electrons and muons are calculated including photons radiated within a cone of size ∆R < 0.1.
The four-momenta of τ candidates are defined by including photons radiated by both the τ leptons and their
decay products within a cone of size ∆R < 0.4. By construction CZ accounts for migrations from outside of
the acceptance. The correction by the CZ factor provides the cross section within the fiducial region of each
measurement
Nobs − Nbkg
,
(5.7)
σfid (Z → ττ) × B =
CZ · L
which is independent of the extrapolation procedure to the full phase space, and therefore is less affected by
theoretical uncertainties in the modelling of the Z production;
• AZ is the acceptance factor allowing the extrapolation of σfid to the total cross section, defined by Eq. 5.6.
The AZ factor is determined from Monte Carlo as the ratio of events at generator level whose ττ invariant
mass, before final state radiation, lies within the mass window [66, 116] GeV, and the number of events
at generator level that fall within the fiducial regions defined above. In this case the bare τ lepton decay
products were dressed with photons radiated as described above for the CZ factor. Dressing the τ lepton
decay products allows to perform a partial QED final state radiation correction back to the Born level, that
however excludes the radiation at wide angles. Using a dedicated sample, where the QED final state radiation
was switched off, it was checked that the impact of the radiation at wide angles on the acceptance was -1.2%
for the muon channel and -1.4% for the electron channel.
The AZ factor accounts for events that migrate from outside the invariant mass window into the fiducial
region after applying selection criteria. The central values for AZ and CZ are determined using a PYTHIA
Monte Carlo sample generated with the modified LO parton distribution functions MRSTLO* [153].
5.1.5 Systematic uncertainties
Several possible sources of systematic uncertainties on the AZ and CZ factors as well as on the background estimation are evaluated.
5.1. Z → ττ CROSS SECTION MEASUREMENT
65
Systematic uncertainty on signal and background predictions
The efficiency of the lepton trigger, reconstruction, identification and isolation requirements are each measured
separately in data, and the corresponding Monte Carlo efficiency for each step is corrected to agree with the measured values. These corrections are applied to all relevant Monte Carlo samples used for this study. Uncertainties
on the corrections arise both from statistical and systematic uncertainties on the efficiency measurements. The
largest contribution to the electron efficiency uncertainty comes from the identification efficiency for low-ET electrons, where the statistical uncertainty on the measurement is very large. The total electron uncertainty is estimated
to be between 5-9% relative to the efficiency, depending on the selection. For muons, the uncertainty is estimated
to be 2-4% relative to the efficiency.
The uncertainties on the τ reconstruction and identification efficiencies are evaluated as described in Section 4.3. They are estimated to be around 10% relative to the efficiency for most cases, varying between 9% and
12% with the τ candidate pT , number of tracks, and number of vertices in the event [154].
The probability for an electron or a QCD jet to be mis-identified as a hadronic τ is measured in data as
described in Section 4.3. Correction factors are derived for the MC mis-identification probability for electrons,
binned in η and applied to τ candidates matched in simulation to a generator-level electron. The uncertainty on the
correction factor is taken as the systematic uncertainty. The QCD jet mis-identification probability is measured in
Z → ℓℓ+jet events. The difference with respect to the MC prediction for the same selection, added in quadrature
with the statistical and systematic uncertainties of the measurement, is taken as the systematic uncertainty. These
corrections are applied to τ candidates not matched to a generator-level electron.
The τ energy scale uncertainty is estimated as described in Section 4.1.2. The electron energy scale is determined from data by constraining the reconstructed di-electron invariant mass to the well-known Z → ee line
shape. For the barrel region, the linearity and resolution are in addition controlled using J/ψ → ee events. The
jet energy scale uncertainty is evaluated from simulations by comparing the nominal results to MC simulations
using alternative detector configurations, alternative hadronic shower and physics models, and by comparing the
relative response of jets across pseudo-rapidity between data and simulation [128]. Additionally, the calorimeter
component of the ETmiss is sensitive to the energy scale, and this uncertainty is evaluated by propagating first the
electron energy scale uncertainty into the ETmiss calculation and then shifting all topological clusters not associated
to electrons according to their uncertainties [128].
The electron, τ and jet energy scale uncertainties, as well as the calorimeter component of the ETmiss , are
all correlated. Their effect is therefore evaluated by simultaneously shifting each up and down by one standard
deviation; the jets are not considered in the semileptonic final states, while the τ candidates are not considered for
the di-lepton final states. The muon energy scale, and the correlated effect on the ETmiss , is also evaluated but found
to be negligible in comparison with other uncertainties.
The uncertainty on the QCD multijet background estimation comes from three different sources. Electroweak
and tt¯ backgrounds are subtracted in the control regions and all sources of systematics on these backgrounds are
taken into account. Each source of the systematic error is varied up and down by one standard deviation and the
effect on the final QCD multijet background estimation is evaluated. The second set of systematic uncertainties is
related to the assumption of the method used for the τe τhad , τµ τhad and τe τµ final state QCD multijet background
estimations, namely that the ratio of opposite-sign to same-sign events in the signal region is independent of
the lepton isolation. These systematic uncertainties are evaluated by studying the dependence of ROS /S S on the
isolation criterion and, for the τe τµ channel, comparing the efficiencies of the subsequent selection criteria in the
opposite- and same-sign regions. For the estimation of the QCD multijet background in the τµ τµ final state, the
uncertainties due to the correlation between the isolation of the two muon candidates are evaluated by propagating
the systematic uncertainties from the subtracted backgrounds into the calculation of the correlation factor. The
third uncertainty on the QCD multijet background estimation arises from the statistical uncertainty on the number
of data events in the various control regions.
The uncertainty on the W+jets background estimation method is dominated by the statistical uncertainty on
the calculation of the normalisation factor in the control region, as described in Section 5.1.3, and the energy scale
uncertainty.
66
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
In the τµ τµ final state, a smearing is applied to the transverse impact parameter of muons (d0 ) with respect to
the primary vertex to match the Monte Carlo resolution with the value observed in data. The muon d0 distribution
is compared between data and Monte Carlo using a sample of Z → µµ events and is found to be well-described
by a double Gaussian distribution. The 20% difference in width between data and simulation is used to define
the smearing function which is applied to the d0 of each simulated muon. The systematic uncertainty due to
the smearing procedure is estimated by varying the widths and relative weights of the MC impact parameter
distributions of the two muon candidates, within the estimated uncertainties on their measurement.
The uncertainty on the luminosity is taken to be 3.4%, as determined in [106, 107]. A number of other sources,
such as the uncertainty due to the object quality requirements for τ candidates and jets, are also evaluated, but have
a small contribution to the total uncertainty.
The MC is reweighted so that the distribution of the number of vertices matches that observed in data; the
systematic uncertainty from the reweighting procedure amounts to a permille effect.
The lepton resolution and charge mis-identification are found to have only a sub-percent effect on CZ and the
background predictions.
Systematic uncertainties due to a few problematic calorimeter regions, affecting electron reconstruction, are
also evaluated and found to have a very small effect.
The uncertainties on the theoretical cross sections by which the background Monte Carlo samples are scaled
are also found to have only a very small impact on the corresponding background prediction, except for the τµ τµ
final state, which has a large electroweak background contamination.
Systematic uncertainty on the acceptance
The theoretical uncertainty on the geometric and kinematic acceptance factor AZ is dominated by the limited
knowledge of the proton Parton Distribution Functions (PDF) and the modelling of the Z boson production at the
LHC. The uncertainty due to the choice of PDF set is evaluated by considering the maximal deviation between the
acceptance obtained using the default sample and the values obtained by reweighting this sample to the CTEQ6.6
and HERAPDF1.0 [155] PDF sets. The uncertainties within the PDF set are determined by using the 44 PDF
error eigenvectors available for the CTEQ6.6 NLO PDF set [156]. The variations are obtained by reweighting the
default sample to the relevant CTEQ6.6 error eigenvector.
The uncertainties due to the modelling of W and Z production are estimated using MC@NLO interfaced with
the HERWIG for parton showering, with the CTEQ6.6 PDF set and ATLAS MC10 tune and a lower bound on the
invariant mass of 60 GeV. Since HERWIG, in association with external generators, does not handle τ polarisation
correctly [157], the acceptance obtained from the MC@NLO sample is corrected, and the correction is of the order
of 2% for the τe τhad and τµ τhad channels, 8% for the τe τµ channel, and 3% for the τµ τµ channel. The deviation
with respect to the AZ factor obtained using the default sample reweighted to the CTEQ6.6 PDF set central value
and with an applied lower bound on the invariant mass of 60 GeV is taken as uncertainty.
In the default sample the QED radiation is modelled by PHOTOS which has an accuracy of better than 0.2%,
and therefore has a negligible uncertainty compared to uncertainties due to PDFs. Summing in quadrature the
various contributions, total theoretical uncertainties of 3% are assigned to AZ for both the semileptonic and the
τe τµ final states and of 4% for the τµ τµ final state.
Summary of systematic uncertainties
The uncertainty on the experimental acceptance CZ is due to the effect of the uncertainties described above on the
signal MC, after correction factors are applied. For the total background estimation uncertainties, the correlations
between the electroweak and tt¯ background uncertainties and the QCD multijet background uncertainty, arising
from the subtraction of the former in the control regions used for the latter, are taken into account. The largest
uncertainty results from the τ identification and energy scale uncertainties for the τµ τhad and τe τhad final states.
Additionally, in the τe τhad final state, the uncertainty on the electron efficiency has a large contribution. This
is also the dominant uncertainty in the τe τµ final state. In the τµ τµ final state, the uncertainty due to the muon
5.1. Z → ττ CROSS SECTION MEASUREMENT
67
Table 5.2: Relative statistical and systematic uncertainties in % on the total cross section measurement. The electron and muon efficiency terms include the lepton trigger, reconstruction, identification and isolation
uncertainties, as described in the text. The last column indicates whether a given systematic uncertainty
is treated as correlated (X) or uncorrelated (X) among the relevant channels when combining the results. For the QCD multijet background estimation method, the uncertainties in the τµ τhad , τe τhad and
τe τµ channels are treated as correlated while the τµ τµ uncertainty is treated as uncorrelated, since a
different estimation method is used, as described in Section 5.1.3 [14].
Systematic uncertainty
Muon efficiency
Muon d0 (shape and scale)
Muon resolution and energy scale
Electron efficiency, resolution and
charge mis-identification
τ identification efficiency
τ mis-identification
Energy scale (e/τ/jets/ETmiss )
QCD multijet background estimate
W normalisation factor
Object quality selection criteria
Pile-up description in simulation
Theoretical cross section
AZ systematics
Total Systematic uncertainty
Statistical uncertainty
Luminosity
τµ τhad
3.8%
–
0.2%
τe τhad
–
–
–
τe τµ
2.2%
–
0.1%
τµ τµ
8.6%
6.2%
1.0%
Correlation
X
X
X
–
8.6%
1.1%
10%
0.8%
0.1%
1.9%
0.4%
0.2%
3%
15%
9.8%
3.4%
9.6%
8.6%
0.7%
11%
2%
0.2%
1.9%
0.4%
0.1%
3%
17%
12%
3.4%
5.9%
–
–
1.7%
1.0%
–
0.4%
0.5%
0.3%
3%
7.3%
13%
3.4%
–
–
–
0.1%
1.7%
–
0.4%
0.1%
4.3%
4%
14%
23%
3.4%
X
X
X
X
(X)
X
X
X
X
X
X
X
efficiency is the dominant source, with the muon d0 contribution being important in the background estimate for
that channel. The correlation between the uncertainty on CZ and on (Nobs − Nbkg ) is accounted for in obtaining the
final uncertainties on the cross section measurements, which are summarised in Table 5.2.
5.1.6 Cross section measurement
To improve the accuracy of the cross section measurement the results for the various final states can be combined. The uncertainty of a combined cross section measurement is reduced by taking into account correlations of
uncertainties between different final states.
A summary of the numbers of observed events in data and estimated signal events in data after subtraction of
background contributions is given in Table 5.3. It shows also the acceptance factor AZ , the correction factor CZ ,
the branching fraction for each final state and the integrated luminosity.
From those numbers the individual cross sections are derived. They are calculated following Equation 5.6.
The results are used as input numbers for the combined cross section and presented in Table 5.4. Both the fiducial
cross sections and the total cross sections for an invariant mass window of [66, 116] GeV are shown.
The combination of the cross section measurements from the four final states is obtained by using the Best
Linear Unbiased Estimate (BLUE) method [158, 159]. This technique is used for a combined estimate of individual estimates which may be correlated. The systematic uncertainties on the individual cross sections due to
different sources are assumed to be either fully correlated or fully uncorrelated. This is summarised in Table 5.2
where the last column indicates whether a given source of systematic uncertainty has been treated as correlated
or uncorrelated amongst the relevant channels when calculating the combined result. The total combined cross
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
68
Table 5.3: The components of the Z → ττ cross section calculations for each final state. For Nobs − Nbkg the first
uncertainty is statistical and the second systematic. For all other values the total error is given [14].
Nobs
Nobs − Nbkg
AZ
CZ
B
L
τµ τhad
213
164 ± 16 ± 4
0.117 ± 0.004
0.20 ± 0.03
0.2250 ± 0.0009
35.5 ± 1.2 pb−1
τe τhad
151
114 ± 14 ± 3
0.101 ± 0.003
0.12 ± 0.02
0.2313 ± 0.0009
35.7 ± 1.2 pb−1
τe τµ
85
76 ± 10 ± 1
0.114 ± 0.003
0.29 ± 0.02
0.0620 ± 0.0002
35.5 ± 1.2 pb−1
τµ τµ
90
43 ± 10 ± 3
0.156 ± 0.006
0.27 ± 0.02
0.0301 ± 0.0001
35.5 ± 1.2 pb−1
Table 5.4: The production cross section times branching fraction for the Z → ττ process in each final state. The
fiducial cross sections measurements include also the branching fraction of the τ to its decay products.
The first error is statistical, the second systematic and the third comes from the luminosity [14].
Final State
τµ τhad
τe τhad
τe τµ
τµ τµ
Fiducial cross section (pb)
23 ± 2 ± 3 ± 1
27 ± 3 ± 5 ± 1
7.5 ± 1.0 ± 0.5 ± 0.3
4.5 ± 1.1 ± 0.6 ± 0.2
Total cross section ([66, 116] GeV) (nb)
0.86 ± 0.08 ± 0.12 ± 0.03
1.14 ± 0.14 ± 0.20 ± 0.04
1.06 ± 0.14 ± 0.08 ± 0.04
0.96 ± 0.22 ± 0.12 ± 0.03
section of
σ(Z → ττ, 66 < minv < 116 GeV) = 0.97 ± 0.07 (stat) ± 0.06 (syst) ± 0.03 (lumi) nb
(5.8)
is obtained from the four final states, τµ τhad , τe τhad , τe τµ , and τµ τµ .
A comparison of the individual cross sections with the combined result is shown in Figure 5.11, along with the
combined Z → ℓℓ cross section measured in the Z → µµ and Z → ee final states by ATLAS [49]. The theoretical
expectation of 0.96 ± 0.05 nb for an invariant mass window of [66, 116] GeV is also shown.
The obtained total production cross section for Z → ττ can be also compared to results from other experiments.
It agrees with the Z → ττ cross section in four final states measured by the CMS collaboration [148], 1.00 ±
0.05 (stat)±0.08 (syst)±0.04 (lumi) nb, in a mass window of [60, 120] GeV. A comparison is shown in Figure 5.12.
This figure includes also the combined measurements of the Z → µµ and Z → ee production cross sections by
the ATLAS [160] and CMS [161] collaborations. The measured Z → ττ cross section agrees well with other
measurements and the theory prediction.
5.1. Z → ττ CROSS SECTION MEASUREMENT
69
Z → ττ combined
ATLAS
36pb-1
Z → ee/µµ
33-36pb-1
τµ τhad
τe τhad
Stat
τe τµ
Syst ⊕ Stat
τµ τµ
Theory (NNLO)
Syst ⊕ Stat ⊕ Lumi
0.6
0.8
1
1.2
1.4
1.6
σ(Z → ll, 66<minv<116 GeV) [nb]
Figure 5.11: The individual cross section measurements by final state, and the combined result. The Z → ℓℓ
combined cross section measured by ATLAS in the Z → µµ and Z → ee final states is also shown
for comparison. The grey band indicates the uncertainty on the NNLO cross section prediction [14].
ATLAS Z → τ τ , 36pb-1
(66<m <116 GeV)
inv
Stat
Syst ⊕ Stat
ATLAS Z → ee/ µµ, 33-36pb-1
(66<m <116 GeV)
Syst ⊕ Stat ⊕ Lumi
inv
Theory (NNLO)
CMS Z → τ τ , 36pb-1
(60<m <120 GeV)
inv
ATLAS Preliminary
CMS Z → ee/ µµ, 36pb-1
(60<m <120 GeV)
inv
0.1
0.4
0.7
1
1.3
1.6
σ(Z → ll) [nb]
Figure 5.12: Comparison of the combined Z → ττ cross section to the combined cross section measured by
ATLAS and CMS in the Z → µµ and Z → ee final states and to the combined measurement of the
Z → ττ cross section from the CMS collaboration. CMS measured the Z cross section in the mass
range 60 < minv < 120 GeV [14].
70
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
5.2 W → τν cross section measurement
Since purely leptonic τ decays cannot be easily distinguished from electrons and muons from W → eν and W → µν
decays, the analysis presented in this section uses only hadronically decaying τ leptons [162]. The signature of
this process is the presence of a τ candidate and missing transverse energy. W → τν decays are dominated by
events with relatively low-pT W bosons decaying into τ leptons with typical τ transverse momenta between 10 and
40 GeV. In addition, the distribution of the missing transverse energy, associated with the neutrinos from the W
and τhad decays, has a maximum around 20 GeV and a significant tail up to about 80 GeV.
Previous measurements at hadron colliders of W boson production with the subsequent decay W → τν based
√
on p p̄ collisions were reported by the UA1 collaboration [163] at the centre-of-mass energies of s = 546 GeV and
√
√
s= 630 GeV and by the CDF and D0 collaborations [164, 165] at the centre-of-mass energy of s = 1.8 TeV.
A brief summary of backgrounds important for this analysis is given below:
• QCD multijet - the dominant background source due to its large production cross section with events where
one jet is incorrectly identified as τ candidate and a significant amount of mis-reconstructed ETmiss .
• W → eν/µν - processes contributing to the background if the lepton from the W boson decay is misidentified as a single-prong τ candidate or if a fake τ candidate is reconstructed from a jet in the event. The
ETmiss signature arises from a W decay neutrino or the mis-reconstruction of jets or of other objects in the
event.
• W → τlep ν → eν/µν - processes that are difficult to distinguish from primary electrons and muons therefore
they contribute to the background similarly to W → eν and W → µν.
• Z → ττ - the rate for this process is about ten times smaller than for the signal process. It contributes to the
background if one of the τ leptons is identified as a τ candidate and second is lost.
• Z → ee/µµ - processes contributing if one of the decay electrons/muons is incorrectly reconstructed as τ
candidate and the other one is lost, giving fake ETmiss . These backgrounds are found to be negligible.
• t t̄ - process that has a much smaller cross section than the signal and contributes to the background if one of
the W bosons produces a τ lepton in its decay and the other one decays into a pair of quarks, an electron, or
a muon which are not reconstructed. Fully hadronic decays can also contribute to the fake τ identification.
This background is found to be negligible.
5.2.1 Data and Monte Carlo samples
The data used are collected using combined τ and ETmiss triggers. In the earlier part of the 2010 data taking,
corresponding to an integrated luminosity of 11 pb−1 , a loosely identified τ candidate with pT > 12 GeV (as reconstructed at the trigger level) in combination with ETmiss > 20 GeV is required. In the second part of the period
(24 pb−1 ), a tighter τ identification and higher thresholds of 16 GeV and 22 GeV have to be used for pT of τ candidate and ETmiss , respectively, due to the increased luminosity. The signal efficiencies of these two triggers with
respect to the offline selection as estimated from the simulation are (81.3±0.8)% and (62.7±0.7)%, respectively.
The MC samples used are the same as described in Section 5.1.1. The simulated events are re-weighted so that
the distribution of the number of reconstructed primary vertices per bunch crossing matches that in the data.
5.2.2 Selection of W → τhad ν candidates
Events satisfying the trigger selection are required to have at least one reconstructed primary vertex formed by
three or more tracks with pT > 150 MeV. Further preselection follows requirements described in Section 3.6.
Events are rejected if a jet or a τ candidate is reconstructed in the calorimeter transition regions to ensure a
uniform ETmiss measurement.
5.2. W → τν CROSS SECTION MEASUREMENT
71
In events where the ETmiss is found to be collinear with one of the jets (mainly QCD multijet events), the
reconstructed ETmiss is likely to originate from an incomplete reconstruction of this jet. Therefore, a minimum
separation |∆φ(jet, ETmiss )| > 0.5 rad is required for jets with pT > 20 GeV.
Objects selection
The following reconstructed objects are selected. τ candidates are selected if they have a transverse momentum
20 GeV < pT < 60 GeV and |η| < 2.47 (excluding the calorimeter transition region). They are also required to pass
tight identification criteria based on the BDT method. For τ candidates with transverse momenta above 20 GeV,
the efficiency of the τ identification at the tight working point of the BDT identification is about 30% with a jet
rejection factor of 100 for 1-prong τ candidates, while for 3-prong τ candidates it is about 35% with a rejection
factor of 300 [154]. Additionally, a dedicated selection to reject fake τ candidates from electrons and muons is
applied.
The missing transverse energy is obtained from the simple definition as described in Section 3.5. It is required
to be above 30 GeV.
Event selection
In order to suppress electroweak backgrounds, electron and muon vetoes, additional to those provided by the τ
identification algorithm, are applied. Events containing identified medium electrons or combined muons with
pT > 15 GeV are rejected.
Only the highest-pT identified τ candidate in the event is considered for further analysis. In order to reject
more QCD multijet events, an additional cut to the ETmiss > 30 GeV requirement
√P is introduced. With a good
ET , where the scaling factor a
approximation, the resolution of ETmiss components is proportional to a ×
P
depends on both the detector and reconstruction
performance and ET is calculated from all calorimeter energy
√
clusters. The factor a is about 0.5 GeV for minimum bias events [133]. Thus the significance of ETmiss , S Emiss , is
T
defined as:
ETmiss [GeV]
.
(5.9)
S Emiss =
√
√P
T
0.5 GeV ( ET [GeV])
In order to remove events with large reconstructed ETmiss due to fluctuations in the energy measurement, events are
rejected if S Emiss < 6.
T
5.2.3 Background estimation
A good agreement between data and MC simulation in the W boson cross section measurement at ATLAS, where
the W boson decays into an electron or muon is observed [160]. Therefore, the number of expected events from
signal and electroweak background processes is obtained from simulation. An embedding technique is used as a
cross-check of the results derived from MC. The muon in a high-purity sample of W → µν events is replaced by a
simulated τ lepton. A good agreement between that sample and the corresponding MC sample is observed.
The data-driven method, similar to the one described in Section 5.1.3 is used to estimate the QCD multijet
background contribution. It has been already used in the analysis which led to the first observation of W → τhad ν
decays in ATLAS [166]. The method selects four independent data samples, three QCD multijet backgrounddominated regions (control regions) and one signal-dominated region (signal region). The samples are selected
with criteria on S Emiss and on τ Id, which are assumed to be uncorrelated. An indirect correlation may arise
T
anyhow due to the dependence of the τ Id rejection on the pT of the τ candidate. This effect is taken into account
when computing the systematic uncertainty. The following four regions are used in this analysis as shown in
Figure 5.13:
• A: signal region with S Emiss > 6.0 and τ candidates satisfying the τ Id described in Section 5.2.2;
T
• B: control region with S Emiss < 4.5 and τ candidates satisfying the τ Id described in Section 5.2.2;
T
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
72
Figure 5.13: Schematic diagram of the four regions used for the QCD multijet background estimation, signal
region A and the three control regions B,C and D.
Table 5.5: Estimated sample compositions in the signal region A and control regions B, C, and D [162].
Ni
(Data)
i
Nsig
i
NEW
i
NQCD
A
2335
1811 ± 25
284 ± 7
127 ± 8
B
4796
683 ± 16
118 ± 4
3953 ± 75
C
1577
269 ± 8
388 ± 9
885±45
D
27636
93 ± 5
90 ± 4
27444± 166
• C: control region with S Emiss > 6.0 and τ candidates satisfying a looser τ Id but failing the signal region τ Id
T
requirements;
• D: control region with S Emiss < 4.5 and τ candidates satisfying a looser τ Id but failing the signal region τ Id
T
requirements.
The looser τ Id region is defined with BDT score < 0.5 for 1-prong τ candidates and BDT score < 0.45 for
multi-prong τ candidates.
Under the assumption that the shape of the S Emiss distribution for QCD multijet background is independent
T
of the τ Id and the signal and electroweak background contribution in the three control regions is negligible,
an estimate for the number of QCD multijet background events in the signal region A is provided by N A
QCD =
B
C
D
i
N N /N , where N , i = B, C, D, is the number of observed events in region i. The expected number of signal
i , and of the electroweak background events is denoted as N i . The
events in a given region is denoted as Nsig
EW
statistical error on N A
includes
both
the
uncertainty
on
the
estimation
of
this
contamination,
due
to
the MC
QCD
statistics, and the statistical uncertainty of the data in the four regions. The resulting estimates of the sample
compositions are summarised in Table 5.5.
A good quality of the description of the selected data by the background models can be seen in Figure 5.14,
where data and the background estimates are shown. This Figure presents the distribution of S Emiss in regions A
T
and B and the distribution of ETmiss , the pT spectrum of τ candidates, the number of tracks associated to the τ
q
miss
candidate, the distribution of ∆φ(τ, ET ) and the transverse mass, mT = 2 · pτT · ETmiss · 1 − cos ∆φ τ, ETmiss ,
in the selected signal region A. In all the distributions a reasonable agreement is observed between the data and
Monte Carlo prediction.
5.2. W → τν CROSS SECTION MEASUREMENT
73
5.2.4 Method for cross section calculation
The calculation of the fiducial and the total cross sections follows equations 5.6 and 5.7 from Section 5.1.4. The
fiducial region is defined by the following cuts: τ with 20 GeV < pT < 60 GeV and |η| < 2.5 (excluding transition
P
P
P
region in the calorimeters); events with ( pν )T > 30 GeV and |∆φ(τ, pν )| > 0.5 where ( pν )T is the transverse
component of the sum of the simulated neutrino four-vectors. τ momentum is calculated from the sum of the
four-vectors of the decay products from the simulated hadronic τ decay, except for the neutrinos. This momentum
also includes photons radiated both from the τ lepton and from the decay products themselves, considering only
photons within ∆R < 0.4 with respect to the τ direction.
5.2.5 Systematic uncertainties
Summary of the systematic uncertainties is presented in Table 5.6.
The differences between the measured trigger responses of the two trigger components in data and Monte Carlo
are used to determine the systematic uncertainty. A pure and unbiased sample enriched with W → τhad ν events is
obtained in data by applying an independent τ (ETmiss ) trigger and some requirements on the event selection like
the BDT τ Id. The corresponding τ (ETmiss ) trigger part is applied to this sample and the response of this trigger is
compared to the response in MC. The observed differences are integrated over the offline pT of τ candidates and
ETmiss range used for the cross section measurement. The total systematic uncertainty after the combination of the
different trigger parts is 6.1%.
The uncertainties on the τ reconstruction and identification efficiencies are evaluated as described in Section 4.3. The corresponding changes in the signal and EW background efficiencies due to those uncertainties are
found to be 9.6% and 4.1%, respectively.
The rate of jets that are mis-identified as τ candidates is obtained from W→ ℓν+jets events by measuring the
fraction of reconstructed τ candidates passing the τ identification. The difference of this mis-identification rate in
MC compared to that in data is 30% and this is applied as a systematic uncertainty to the fraction of background
events, where the lepton is not reconstructed and the τ candidate is mistaken by a jet. The overall uncertainty on
the EW background is 7.2%.
The mis-identification probability of electrons as τ candidates is measured in data as described in Section 4.3.
The systematic uncertainty is the difference between the fake rate in data and MC as a function of η, and it results
in 4.5% relative uncertaintes for the EW background.
The signal and background acceptance depends on the energy scale of the clusters used in the computation of
ETmiss and S Emiss and the energy scale of the calibrated τ candidates. The uncertainty due to cluster energy within
T
the detector region |η| < 3.2 is at most 10% for pT of 500 MeV and about 3% at high pT [134]. In the forward
region |η| > 3.2 it is estimated to be 10%. All clusters in the event are scaled corresponding to these uncertainties
P
and ETmiss and ET are recalculated to determine the uncertainty. Simultaneously, the energy scale of τ candidates
is varied according to its uncertainty [136]. As described in Section 4.1.2 this uncertainty depends on the number
of tracks associated to the τ candidate, its pT and the η region in which it was reconstructed, and ranges from
2.5% to 10%. Additionally, the sensitivity of the signal and background efficiency to the ETmiss resolution has
been investigated [133]. Consequently, the yield of signal and EW background varies within 6.7% and 8.7%,
respectively.
The uncertainty of the QCD multijet background estimation accounts for two different sources, the stability of
the method of estimating the QCD multijet background events from data and the contamination of signal and EW
background events in the control regions. The stability of the method and the small correlation of the two variables
(τ Id and S Emiss ) used to define the control regions have been tested by varying the S Emiss threshold.
T
T
The systematic uncertainty due to the correction for signal and EW background contamination in the control
regions was obtained by varying the fraction of these events in the regions within the combined systematic and
statistical uncertainties on the MC predictions discussed above. The total uncertainty on the QCD background
estimation is 3.4%.
Number of events / 0.5
ATLAS
Data 2010 ( s = 7 TeV)
W → τhadντ
EW background
QCD background (CD)
3
10
∫
102
-1
L dt = 34 pb
10
Number of events / 5 GeV
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
74
1
103 ATLAS
Data 2010 ( s = 7 TeV)
W → τhadντ
EW background
QCD background (C)
102
∫ L dt = 34 pb
-1
10
1
0
2
4
6
8
10
12
14
16
18
20
40
60
80
100
120
SEmiss
T
(b)
800 ATLAS
Data 2010 ( s = 7 TeV)
W → τhadντ
EW background
QCD background (B)
700
600
∫ L dt = 34 pb
500
-1
400
Number of events
(a)
Number of events / 5 GeV
140
Emiss
[GeV]
T
2500
ATLAS
Data 2010 ( s = 7 TeV)
W → τhadντ
EW background
QCD background (B)
2000
∫ L dt = 34 pb
-1
1500
1000
300
200
500
100
0
20
25
30
35
40
45
50
55
0
0
60 65 70
τhadp [GeV]
1
2
3
4
5
6
(c)
Number of events / 5 GeV
Number of events / (π/31)
600
Data 2010 ( s = 7 TeV) ATLAS
W → τhadντ
EW background
QCD background (C)
∫ L dt = 34 pb
-1
400
200
0
0
8
9
10
(d)
1000
800
7
Number of tracks
T
600 ATLAS
Data 2010 ( s = 7 TeV)
W → τhadντ
EW background
QCD background (C)
500
∫ L dt = 34 pb
400
-1
300
200
100
0.5
1
1.5
2
2.5
∆φ
(e)
(τhad,Emiss
)
T
3
0
0
20
40
60
80
100
120
140
mT [GeV]
[rad]
(f)
Figure 5.14: (a) Distribution of S Emiss in the combined region AB, extended over the full S Emiss range. The QCD
T
T
background shape has been extracted from regions CD. (b) ETmiss in signal region A. The QCD multijet background shape has been extracted from control region C. (c) Transverse momentum and (d)
number of tracks of τ candidates in signal region A. The QCD multijet background shape has been
extracted from control region B. (e) Distribution of ∆φ(τ, ETmiss ) and (f) transverse mass mT in signal region A. The QCD multijet background shape has been extracted from control region C. The
expectation from Monte Carlo signal and EW background in region A are also shown [162].
5.2. W → τν CROSS SECTION MEASUREMENT
75
Table 5.6: Summary of systematic uncertainties for the W → τν cross section measurement. For the systematic
uncertainty on the fiducial cross section measurement, correlations between the systematic uncertainties
affecting CW and N EW are taken into account [162].
Systematic uncertainty on
Trigger efficiency
Energy scale
τ Id efficiency
Jet τ mis-identification
Electron τ mis-identification
Pile-up reweighting
Electron reconstruction/identification
Muon reconstruction
Underlying event modelling
Cross section
QCD estimation: Stability/correlation
QCD estimation: Sig./EW contamination
Monte Carlo statistics
Total systematic uncertainty
CW
NEW
NQCD
σfid
W→τhad ν
6.1%
6.7%
9.6%
1.4%
1.3%
1.4%
13.4%
6.1%
8.7%
4.1%
7.2%
4.5%
1.2%
1.2%
0.3%
1.1%
4.5%
2.4%
15.2%
2.7%
2.1%
6.0%
6.9%
7.0%
8.0%
10.3%
1.1%
0.7%
1.6%
0.2%
0.04%
1.5%
0.7%
0.2%
0.1%
1.5%
15.1%
The procedure to include pile-up effects, the uncertainty on the lepton selection efficiency entering via the veto
of electrons and muons and the influence of the underlying event modelling on ETmiss quantities is also evaluated
and is found to have only small effects on the resulting cross section measurement.
The uncertainties on the cross sections used for the EW background are taken from ATLAS measurements,
when available, or theoretical NNLO calculations, and lie between 3 and 9.7% [49, 167, 47, 168]. The uncertainty
on the integrated luminosity is 3.4% [106, 107].
Systematic uncertainty on acceptance is estimated as in Section 5.1.5. The uncertainty resulting from the
choice of the PDFs set is 1.9%. The difference in acceptance due to the modelling of W production is found to be
smaller than 0.5%.
5.2.6 Cross section measurement
A summary of the numbers of observed events in data and estimated background contributions as well as the
acceptance AZ and the correction CZ factors is given in Table 5.7. From those numbers the cross sections are
derived. The measured fiducial cross section of the W → τhad ν is
σfid
W→τhad ν = 0.70 ± 0.02 (stat) ± 0.11 (syst) ± 0.02 (lumi) nb,
(5.10)
and the total cross section is found to be
σtot
W→τhad ν = 7.2 ± 0.2 (stat) ± 1.1 (syst) ± 0.2 (lumi) nb.
(5.11)
Alternative analyses are performed to confirm these results. For example, the BDT τ Id is replaced by the cutbased identification. Also, in order to study the influence of pile-up on the result, the signal selection is restricted
to events with only one reconstructed primary vertex. In both cases consistent results are found.
Correcting the cross section for the hadronic τ decay branching ratio BR(τ →hadrons ν) = 0.6479 ± 0.0007 [46]
gives the following inclusive cross section σtot
W→τν :
σtot
W→τν = 11.1 ± 0.3 (stat) ± 1.7 (syst) ± 0.4 (lumi) nb.
(5.12)
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
76
Table 5.7: Final numbers used in the cross section calculation. The errors include statistical and systematic uncertainties added in quadrature [162].
Nobs
NQCD
NEW
AW
CW
2335
127 ± 9
284 ± 43
0.0975 ± 0.0019
0.0799 ± 0.0107
ATLAS
ATLAS W → τ ντ
Data 2010 ( s = 7 TeV)
Stat uncertainty
Sys ⊕ Stat
Sys ⊕ Stat ⊕ Lumi
Prediction (NNLO)
Theory uncertainty
ATLAS W → e νe
ATLAS W → µ νµ
6
7
8
9
10
11
12
13
14
15
16
σ(W → l νl) [nb]
Figure 5.15: Cross sections for the different W → ℓνℓ channels measured in ATLAS with 2010 data (points).
Systematic, luminosity and statistical uncertainties are added in quadrature. The theoretical NNLO
expectation is also shown (dashed line), together with its uncertainty (shaded area) [162].
The measured cross section is in good agreement with the theoretical NNLO cross section of 10.46±0.52 nb [49,
47, 168] and the ATLAS measurements of the W → eν and W → µν cross sections [160, 169]. The comparison
of the cross section measurements for the different lepton final states and the theoretical expectation is shown in
Figure 5.15.
5.3 Measurement of the τ identification efficiency using W → τν process
In both cross section measurements presented in previous sections the information about the τ identification efficiency was estimated in Z → ττ MC samples as described in Section 4.3. In the following sections two complementary methods to measure the data-based τ identification efficiency using W → τhad ν events are presented [170].
The first method uses a tag-and-probe technique, where events are tagged by selection imposed on the missing
transverse energy of the event and the probe is the reconstructed τ candidate with no identification requirements
applied. The track multiplicity spectrum of τ candidates is then fitted to templates in order to determine the τ
signal contribution in data. The fitting is performed before and after applying a particular set of τ identification
criteria, hence determining the identification efficiency.
The second method assumes that the W → τhad ν production cross section is known. This and the fits using
the background templates allow to extract the fraction of τ signal in selected W → τhad ν events in data for given τ
identification requirements. Obtained yield of τ candidates is compared to the Monte Carlo prediction in order to
5.3. MEASUREMENT OF THE τ IDENTIFICATION EFFICIENCY USING W → τν PROCESS
77
derive the MC scale factor for the used τ identification method and working point.
Events used in this measurement have to pass the ETmiss trigger in order to apply a minimal bias on τ candidates.
The ETmiss trigger threshold varied during data taking together with increasing luminosity and is required to be above
20 − 40 GeV at the EF level. The tag-and-probe method does not depend on the luminosity thus the used data set
contains many trigger items with or without prescales. In contrary, in the cross section normalisation method only
un-prescaled triggers are used to accurately evaluate the acceptance.
The signal and background Monte Carlo samples are the same as for the W → τhad ν cross section measurement
described in the previous Section. The only exception are samples used in the cross section normalisation method
since the analysis requires the presence of jets depending on the trigger conditions. In this case the ALPGEN [171]
W+ multi-jets samples interfaced with HERWIG and multi-parton interactions modelled by JIMMY [172] are
used.
The existing backgrounds and the standard preselection of events are the same as for the W → τhad ν cross
section measurement. In order to suppress W → ℓν and Z → ℓℓ backgrounds, events with electrons passing
medium identification criteria and with pT > 20 GeV or combined muons with pT > 15 GeV are rejected.
5.3.1 Tag-and-probe method
The tag-and-probe method selects W → τhad ν events by requiring significant ETmiss on the tag side, and a reconstructed τ candidate on the probe side. For such τ candidates, the efficiency is determined if the events pass the
τ identification criteria. This method suffers from the purity of the τ signal before identification and from the
imperfect estimation of the QCD multijet background.
Similar event selection as this described for the W → τhad ν cross section measurement in Section 5.2.2 is
applied. The ETmiss is required to be above 30 GeV and S Emiss ≥ 6. In addition the azimuthal separation between
T
ETmiss and any jet with pT > 20 GeV is required to be ∆φ(ETmiss , jet) ≥ 0.7 rad. This is to reject di-jet events where
the energy of one of the jets is mis-measured and leads to large fake ETmiss . The reconstructed probe τ candidates
should have pT > 20 GeV and the leading track of the τ candidate is required
to have pT > 2.4 GeV. If several
q
candidates are present, the one leading to the transverse mass mT = 2pT · ETmiss 1 − cos ∆φ(τ, ETmiss ) closest
to 65 GeV (the most probable value from a true τ in a W → τhad ν event) is kept, while mT itself must not be
> 80 GeV. Also lepton vetoes provided by the τ identification algorithm are applied.
As already mentioned, the particle structure in QCD jets is more spread out than that in a τ candidate and a
jet has higher track multiplicity. However, the association of tracks in the reconstructed τ candidate is restricted
within ∆R < 0.2 of the τ direction, as described in Section 4.1. Thus, the jets faking τ candidates can not get higher
track multiplicity due to the limited cone size. To obtain better separation against QCD multijet events before τ
identification, an anti-kT style track counting method is introduced [127]. It takes into account the momentum
correlation between tracks in the core of the reconstructed object (∆R < 0.2) and tracks around it (0.2 < ∆R < 0.4).
For real τhad decays, tracks belonging to the τhad decay are within the core and there is no correlation between these
tracks and tracks in the outer region coming from pileup or the underlying event. For QCD jets, on the contrary,
tracks from the jet are correlated over the full extent of the jet up to ∆R < 0.4, but still uncorrelated to pile-up and
underlying event tracks. This increases the average number of tracks associated to jet candidates while leaving the
number of tracks associated to τ candidates almost unchanged.
The track multiplicity distribution is fitted in order to extract the signal contribution from data. The fit is
done twice, before and after τ identification. In each fitting, the signal contribution in data is extracted. The ratio
between values of the fits is the τ identification efficiency. The selection reduces background from Z → ll to a
negligible level, and the small remaining W → µν background is absorbed, for simplicity, in the QCD multijet
background modelling when an extra jet fakes a τ candidate and in the W → eν template when a real muon fakes
a τ candidate. Thus, three contributions are considered: signal τ, electron and QCD multijet events. It results in
six track multiplicity templates constructed. The QCD multijet background templates used in the fit come from
the data (as described below), while the τ signal and electron contributions come from MC W → τν and W → eν
samples. Since the electron fake rate is already measured in data as described in Section 4.3.3, the fraction of high
Events
1200
Data 2010 (34 pb-1)
τ (W→ τν )
e (W→ eν )
Jet background
1000
800
ATLAS Preliminary
600
Before tau Id
Events
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
78
800
Data 2010 (34 pb-1)
τ (W→ τν )
e (W→ eν )
Jet background
700
600
500
ATLAS Preliminary
400
After tau Id
300
400
(cut−based looser working point)
200
200
0
0
100
2
4
6
8
10 12 14 16
Number of tracks
(a)
0
0
2
4
6
8
10 12 14 16
Number of tracks
(b)
Figure 5.16: Track multiplicity before (a) and after (b) cut-based τ Id looser working point. The hatching represents the systematic uncertainty. The normalisation of the different processes is determined through
a fit to the track multiplicity spectrum [170].
pT electrons is constrained in the fit using this result.
A QCD multijet enriched control region is defined by requiring 2 < S Emiss ≤ 4.5. As obtained sample has a
T
different pT spectrum of the τ candidates as compared to the signal region, it is therefore reweighted by comparing
pT spectra in the control and signal regions for τ candidates with at least four tracks to avoid bias by the true signal.
It has been checked that the track multiplicity spectrum is not strongly dependent on the chosen S Emiss range or on
T
the pT reweighting function. The slight differences observed are treated as systematic uncertainties.
Systematic uncertainties are estimated by comparing the τ identification efficiency obtained with nominal
templates to the τ identification efficiency obtained with templates generated based on various systematic effects.
The sources of systematic uncertainty considered are: ETmiss trigger, the modelling of the jet template (pT -weighting
and ETmiss significance cut), electron mis-identification probability, pile-up, shower model used in the simulation,
the MC detector description and underlying event modelling. The total systematic uncertainty found is 3.7% for
the cut-based τ Id looser working point.
Track multiplicity distributions are shown in Figure 5.16 before and after the cut-based τ identification looser
working point. In all figures the different contributions are normalised to their respective number of events as
measured from the track multiplicity fit. Data are well modelled and the (1,3)-track structure from real τhad decays
is visible.
The τ identification efficiency is evaluated for the different working points, as summarised in Table 5.8. Purities
of 45–65% are obtained after identification when including all track multiplicities. They increase to 60–80% for
candidates with pT > 30 GeV and one or three tracks. Although the signal purity is high enough after identification,
the obtained statistical uncertainty on the efficiency determination is dominated by the background fluctuation
/εId is also reported. It can be
before identification. A data/MC scale factor for the identification efficiency εId
data MC
seen that the measured efficiency in data is very close to the expected efficiency measured in MC (scale factors
close to 1), and compatible within uncertainties.
5.3.2 Cross section normalisation method
In this method events passing the full selection in data are compared to the prediction in order to derive a scale factor for τ identification, assuming the W → τν production cross section is known and equal, via lepton universality,
to the W → eν, µν cross sections measured by ATLAS [160].
5.3. MEASUREMENT OF THE τ IDENTIFICATION EFFICIENCY USING W → τν PROCESS
79
Table 5.8: Total relative systematic uncertainty (Syst.), measured efficiency, and data/MC scale factor for different
τ identification methods and working points. The first uncertainty is statistical, the second is systematic [170].
Method
Cut-based looser
Cut-based tighter
Likelihood looser
Likelihood tighter
BDT looser
BDT tighter
Syst.
3.7%
9.9%
5.0%
5.7%
4.4%
5.1%
Efficiency
0.77 ± 0.05 ± 0.03
0.56 ± 0.06 ± 0.06
0.82 ± 0.07 ± 0.04
0.60 ± 0.06 ± 0.03
0.78 ± 0.05 ± 0.03
0.55 ± 0.04 ± 0.03
Scale factor
1.04 ± 0.06 ± 0.04
0.98 ± 0.11 ± 0.10
1.02 ± 0.09 ± 0.05
0.95 ± 0.09 ± 0.05
1.05 ± 0.06 ± 0.05
0.92 ± 0.07 ± 0.05
The track multiplicity of τ candidates is fitted after the selection described below, using templates from MC
samples for W → τν (only using truth-matched events) and electroweak backgrounds, and the QCD multijet
background from data in order to extract the fraction of τ signal in data. While performing the fit to data, the
normalisation of electroweak components is fixed to their measured cross sections [160] and the fraction of τ is
the only free parameter. The statistical uncertainty on templates is taken into account by the fit and propagated to
the fit uncertainty.
Each event is assigned to one of the three categories based on the ETmiss trigger and jet multiplicity (no extra
jet with pT > 20 GeV, or 1 or 2 extra jets). Only unprescaled ETmiss triggers are used. Because of limited statistics
in the high ETmiss trigger sample, all jet multiplicities are kept in one sample. ETmiss is required to be above 30 GeV
or 40 GeV depending on the trigger used. ∆φ(ETmiss , jet) ≥ 0.5 rad is required for events with extra jets to reject
large fake ETmiss events. Additional rejection of fake ETmiss events is achieved with a requirement on the ETmiss
p
√
significance partly based on tracks, defined as S vtxmiss = ETmiss /(1.0 GeV ΣpT ), where ΣpT is the scalar sum of
ET
pT of tracks associated to the primary vertex. ΣpT is quite well modelled by MC and relatively robust against pileup because of the primary vertex constraint. S vtxmiss is therefore quite stable with varying instantaneous luminosity.
ET
S vtxmiss > 6(7) is required for low ETmiss trigger sample with no (1 or 2) extra jets and S vtxmiss > 8 for the high ETmiss
ET
ET
trigger sample. Selection of τ candidates is the same as for the tag-and-probe method. Depending on the trigger
and jet multiplicity, different transverse mass windows are required: 60 < mT < 100 GeV for low ETmiss trigger
sample with no extra jet; 30 < mT < 90 GeV when 1 or 2 extra jets are present; 30 < mT < 80 GeV for the high
ETmiss trigger sample.
The ETmiss trigger efficiency estimate, crucial for this analysis, is measured in data using a pure W → eν sample.
It is further corrected by the ratio of the efficiencies of the ETmiss trigger in W → τν and W → eν MC samples.
An obtained efficiency is applied as a weight to the W → τν MC sample instead of using the trigger simulation
information directly.
The modelling of the jet multiplicity template is one of the crucial tasks in this study. The track multiplicity
distributions are expected to be significantly different between high and low S vtxmiss samples due to the S vtxmiss variable
ET
ET
definition. Thus, the ETmiss significance sidebands cannot be used here to obtain the track multiplicity template
from jets, as it is done in the tag-and-probe method. Instead, the jet template is extracted from W → eν+jets
events, selected by requiring a single electron trigger, a single electron passing medium identification requirements,
ETmiss > 30 GeV, S vtxmiss > 6 as for the signal region, exactly one τ candidate not overlapping with the electron within
ET
∆R < 0.2 and 30 < mT < 90 GeV. The track multiplicity thus obtained is well described by MC simulation, and
used in the fit to represent jets.
Systematic uncertainties are estimated by comparing the fit result with nominal templates to the fit result with
templates generated with varied conditions to account for various systematic effects. The considered sources of
systematic uncertainty are: jet background modelling, uncertainty on the W production cross section measured by
Events
600
Cut−based looser working point
500
Data 2010 (L=34 pb-1 )
W→ τ ν
Electroweak
Jet background
400
Events
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
80
350
300
250
200
300
200
100
100
50
0
2
4
6
8
10
12
ATLAS Preliminary
150
ATLAS Preliminary
0
Cut−based looser working point
Data 2010(L=34 pb-1)
W→ τ ν
Electroweak
Jet background
14
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
f core
Number of tracks
(a)
(b)
Figure 5.17: Track multiplicity (a) and core energy fraction, fcore (b) distributions in the signal region after cutbased τ identification looser working point, summed over the three event categories. The hatching
represents the systematic uncertainty [170].
ATLAS, trigger efficiency, lepton identification, electron mis-identification, τ, electron and jet energy scale, pileup and underlying event. The total systematic uncertainty found for the cut-based τ identification looser working
point is 12.9%. The dominant systematic effect is the τ energy scale.
The track multiplicity distribution (summed over the three event categories) is shown in Figure 5.17(a) after
the looser-cuts τ identification is applied. The jet and τ contributions are normalised to the fractions as predicted
by the fit. The model reproduces the data quite accurately and the (1,3)-track structure of real τhad decays is clearly
visible. Identification variables are also reasonably well described, as shown in Figure 5.17(b).
The data over MC τ identification efficiency scale factor is evaluated for different working points, as summarised in Table 5.9. They are all compatible with unity within uncertainties. Systematic uncertainties are significantly larger with the cross section method because it suffers from a large uncertainty on the τ energy scale.
Table 5.9: Data over MC τ identification efficiency scale factors measured with the cross section method for
different τ identification methods and working points. The first uncertainty is statistical, the second is
systematic [170].
Method
Scale factor
Cut-based looser
1.00 ± 0.05 ± 0.13
Cut-based tighter 0.96 ± 0.05 ± 0.14
Likelihood looser 1.02 ± 0.04 ± 0.16
Likelihood tighter 1.00 ± 0.07 ± 0.13
BDT looser
0.94 ± 0.07 ± 0.13
BDT tighter
0.89 ± 0.05 ± 0.10
5.4 Summary
This Chapter presents the first measurements of Z → ττ and W → τν cross sections in the ATLAS experiment, the
milestones for the physics with τ leptons in final states.
5.4. SUMMARY
81
The Z → ττ cross section is measured in four different final states defined by the decay modes of the τ leptons:
muon-hadron, electron-hadron, electron-muon, and muon-muon. Cross sections are measured separately for each
final state in fiducial regions of a high detector acceptance, as well as in the full phase space, over the mass region
66 - 116 GeV. The individual cross sections are combined and the product of the total Z production cross section
and Z → ττ branching fraction is measured to be 0.97 ± 0.07 (stat) ± 0.06 (syst) ± 0.03 (lumi) nb in agreement with
NNLO calculations and other experimental results.
The cross section for the production of W bosons with subsequent decay W → τν is also measured in a region
of high detector acceptance and then extrapolated to the full phase space. The product of the total W production
cross section and the W → τν branching ratio is measured to be 11.1 ± 0.3 (stat) ± 1.7 (syst) ± 0.4 (lumi) nb. The
measured cross section is also in good agreement with the theoretical NNLO cross section.
The first study to determine the hadronic τ decay identification efficiency with W → τν events is reported.
Two approaches are used. In the tag-and-probe method, events are tagged by having significant missing transverse
energy, while the probe is the hadronic τ decay candidate. The track multiplicity spectrum is fitted simultaneously
before and after applying τ identification, hence determining the efficiency. The second technique assumes that the
W → τν production cross section is known and compares expected yields to those measured in data. The results
are consistent with Monte Carlo predictions and with each other.
All presented measurements were performed using data collected in 2010 only, but during completing the
presented monograph more studies have been done with higher statistics data sets.
The Z → ττ cross section was re-measured using the integrated luminosity of 1.34 − 1.55 fb−1 [173] for 2011
data sample. The statistical error on the cross section was decreased by a factor of three in respect to the result
presented in this Chapter.
Also the τ identification efficiency measurement with W → τν events was repeated with 2011 data and the first
measurement of this efficiency with Z → ττ process was performed [144].
The W → τν decay was also used for the first measurement of τ polarisation at hadron colliders [174]. Similar
analysis with Z → ττ process is under preparation.
As mentioned in Section 2.2, a measurement of the cross section of top quark pair production with τ leptons
in final state is of interest because it can open a window to physics beyond the Standard Model. The ATLAS
collaboration published recently such studies [175] based on an integrated luminosity of 2.05 fb−1 . Events with an
isolated electron or muon and a τ lepton decaying hadronically are used. No New Physics signs are found. The
measured cross section is in good agreement with the Standard Model prediction.
82
CHAPTER 5. STANDARD MODEL PROCESSES WITH τ LEPTONS
Be careful what you wish for; you may get it.
Old proverb
6
Standard Model Higgs boson searches with τ final states
As mentioned in Section 2.3, the decay of the neutral Higgs bosons into a pair of τ leptons is a valuable channel
for the SM Higgs boson searches at the LHC. This search is complementary to searches with other decays in the
same mass range. Two analyses have been performed. The first one, fully leptonic, with both τ leptons decaying
into leptons, and requiring the Higgs boson to be produced in association with jets. The second one, semi-leptonic,
with one τ lepton decaying into lepton and second decaying hadronically. The first one is an independent search
for the Standard Model Higgs boson [176] and the second is part of the search for the Minimal Supersymmetric
Standard Model Higgs boson, done in conjunction with other search channels [177]. Both analyses are based on a
data sample corresponding to an integrated luminosity of 1.06 fb−1 collected at the LHC in the first half of 2011.
6.1
H → τlep τlep + jets final state
The H → τlep τlep → ℓℓ + 4ν final state is characterised by a back-to-back configuration of the two τ leptons
in the Higgs boson rest frame. The sensitivity of the search is enhanced by requiring that the Higgs boson is
produced in association with jets. In this case, the Higgs boson is more boosted in the transverse plane. This
enhances the transverse momenta of the Higgs decay products and, as a consequence, the ETmiss of the event due to
the undetected neutrinos from the two τ decays. The presence of large ETmiss and a high pT jet allows this topology
of Higgs boson decays to be differentiated from background processes as shown by previous studies [58]. The
signal contributions considered here include the dominant gluon fusion production process, vector boson fusion
(VBF) and W/Z associated production. Three final states are considered, two same flavour (SF) ee, µµ final states
and one different flavour (DF) eµ final state.
The following are the dominant background processes:
• γ∗ /Z(→ ll)+jets: γ∗ /Z → ττ decays form a largely irreducible background as they have similar event
kinematics as the signal. This background is particularly important for low Higgs boson masses where the
signal falls on the tail of the Z mass peak in the ττ mass distribution. γ∗ /Z production with electron or muon
pairs in the final state also contribute.
• W(→ lν)+jets: this process contributes to the background due to the presence of a charged lepton and ETmiss
in the final state and its large cross section. Hadronic jets accompanying the W boson can be mis-identified
as an electron, or a semi-leptonic decay in the cascade can give a signature similar to the one of an isolated
lepton.
83
84
CHAPTER 6. STANDARD MODEL HIGGS BOSON SEARCHES WITH τ FINAL STATES
• Di-boson production: can lead to final states with two or more charged leptons from the leptonic decays of
the W and Z bosons.
• t t̄ : can lead to final states with two leptons and ETmiss in the final state.
• Single-t production: contributes if W decays leptonically and one of the leptons is either due to a misidentified hadronic jet or, for Wt production, comes from the decay of the second W boson.
• QCD multijets: contributes with true (e.g. produced from heavy flavour decays) or fake leptons and has a
large cross section.
Requiring, after all the other selection criteria, at least one high pT jet, reduces the γ∗ /Z → ℓℓ acceptance by a
factor of 7 and the Z → ττ acceptance by a factor of 2.5, while the signal acceptance is reduced only by 30%.
6.1.1 Data and Monte Carlo samples
Events in eµ and µµ final states are selected using a combined muon trigger of pT > 18 GeV. Events passing
a stand-alone muon trigger in the barrel region with pT > 40 GeV are also accepted. For eµ final state also an
electron trigger with ET > 20 GeV passing medium identification criteria is used. For di-electron final state, a dilepton trigger requiring two electron trigger objects with ET > 12 GeV and passing medium electron identification
criteria is applied. The trigger efficiencies are measured in data as a function of the offline lepton pT with the
tag-and-probe method in a data sample enriched in Z → ℓℓ events. The single electron trigger efficiencies are
about 98% while for the single muon trigger the efficiencies are between 73% and 87% for the barrel and endcap regions, respectively. The di-electron trigger efficiency is calculated to be 98%. Monte Carlo simulation is
corrected to agree with data by applying the trigger scale factors parametrised as a function of η, φ and pT .
The cross sections for Higgs boson production were calculated following the prescriptions of the LHC Higgs
cross section working group [55]. In gluon fusion they were calculated using HIGLU [178] and ggh@nnlo [179] at
the NNLO. For the vector-boson fusion, the NNLO calculation was performed with VBF@NNLO [180, 55]. The
SM gg → H production via gluon fusion was simulated with MC@NLO and the vector-boson production with
HERWIG . The production of W and γ∗ /Z bosons in association with jets is simulated with the ALPGEN generator,
apart from the γ∗ /Z → ττ and W → τν processes, that are simulated with PYTHIA. The tt¯ and single-t (s-channel)
processes are generated with MC@NLO, the single-t (t-channel, Wt) process is generated with AcerMC [181],
and di-boson production processes are generated with HERWIG. For all MC@NLO samples parton showers and
hadronisation are simulated with HERWIG and the activity of the underlying event with JIMMY. The programs
TAUOLA and PHOTOS are used to model respectively the decay of τ leptons and additional photon radiation in
decays produced in PYTHIA, MC@NLO and HERWIG.
Residual differences in the pile-up between data and Monte Carlo samples are corrected by re-weighting the
Monte Carlo events to reproduce the pile-up distributions in data.
6.1.2 Objects and event selection
Only events containing at least one primary vertex with three or more associated tracks, as well as fulfilling preselection requirements described in Section 3.6 are used in the analysis. As the next step, the following reconstructed
objects are chosen.
Electron candidates are selected if they have ET > 15 GeV and |η| < 2.47 (excluding the transition region in the
calorimeters) and pass the tight identification requirements. In addition, they should have ET > 22 GeV if the event
0.2 /E < 0.08
is triggered by the single electron trigger. Identified electron candidates are required to be isolated, IET
T
0.4
and IPT /pT < 0.06. Electron transverse energy scale and resolution in Monte Carlo are made to agree with data by
applying rescaling and smearing of the simulated electron transverse energy.
Combined muon candidates are required to have pT > 10 GeV and |η| < 2.5. If the event is triggered by the
single muon trigger, the muon candidate is required to have pT > 20 GeV. Additionally, the difference between the
z-position of the point of closest approach of the muon Inner Detector track to the beam-line and the z-coordinate
Events/ 20 GeV
6.1. H → τLEP τLEP + JETS FINAL STATE
45
85
ATLAS Preliminary
∫ L = 1.06 fb
40
-1
Data
diboson
single top
35
tt→lν lν +jets
30
Z→ττ+jets
Z→ee,µ µ +jets
30x H(120) →ττ→ll GG
25
30x H(120) →ττ→ll VBF
fake leptons
20
MC stat+fake uncert.
15
10
5
0
0
50 100 150 200 250 300 350 400
mττ [GeV]
Figure 6.1: mττ invariant mass after all analysis cuts except the final cut on mττ . The backgrounds with fake
leptons and the Z → ττ contribution are estimated from data. All other contributions are estimated
using simulated event samples [176].
of the primary vertex is required to be less than 1 cm. This requirement reduces the contamination due to cosmic
events and beam-induced backgrounds. Finally, Inner Detector hit requirements and muon quality criteria are
applied in order to achieve a high-quality measurement of the muon momentum and reduce the mis-identification
0.2 /E < 0.04 and I 0.4 /p < 0.06. Muon transverse momentum
rate. Muon candidates are required to be isolated, IET
T
T
PT
resolution in Monte Carlo is made to agree with data by applying smearing of the simulated muon transverse
momentum.
Jets are required to have pT > 20 GeV and |η| < 4.5. Missing transverse energy used in this analysis follows
the simple definition as described in Section 3.5.
Objects reconstructed from the same localised response in the detector are removed, namely any selected
electron within a distance ∆R < 0.2 of a selected muon is removed from further consideration in the analysis.
Similarly, any selected jet within ∆R < 0.2 of a selected muon or electron is also removed.
Events are selected if they contain exactly two isolated leptons of opposite charge and of invariant mass
mℓℓ > 20 GeV. Further, this requirement is tightened depending on the final state: 30 < mℓℓ < 75 GeV for the
SF final states and 30 < mℓℓ < 100 GeV for the DF final state. The requirement is tighter in the SF final state
in order to reject γ∗ /Z → ee, µµ backgrounds. As a next step, at least one jet with transverse momentum above
40 GeV and ETmiss > 30 GeV for SF events and ETmiss > 20 GeV for DF events is required.
The final invariant mass is reconstructed using the collinear approximation described in Appendix A. Events
have to fulfil the following selection: 0.2 < x1 < 0.8 and 0.1 < x2 < 0.6, where x1,2 are momentum fractions
carried away by visible τ decay products with momenta pvis1,2 and pmis1,2 are momenta carried by neutrinos:
x1,2 =
pvis1,2
.
(pvis1,2 + pmis1,2 )
(6.1)
The requirement of an extra jet in the event improves the efficiency of these cuts. The next selection is 0.3 <
∆φℓℓ < 2.5 rad for SF events and 0.3 < ∆φℓℓ < 2.8 rad for DF events in order to reject γ∗ /Z → ℓℓ and tt¯ processes.
A selected jet has to have |η| > 0.5 as jets produced in the tt¯ decays tend to be more central than the ones produced
in SM Higgs boson decays.
86
CHAPTER 6. STANDARD MODEL HIGGS BOSON SEARCHES WITH τ FINAL STATES
Table 6.1: Number of events after all selection criteria in data, expected background events and expected SM
Higgs boson signal for a data sample corresponding to 1.063 fb−1 . The contribution of backgrounds
with fake leptons and the Z → ττ are estimated in a data-driven way. Errors are statistical only [176].
ee + µµ + eµ
Observed data
46
∗
γ /Z → ττ
25.4 ± 2.7
γ∗ /Z → ℓℓ
3.7 ± 1.2
¯
tt
13.2 ± 2.2
Single-t
1.2 ± 0.5
Di-boson
1.6 ± 0.6
Backgrounds with fake leptons
2.2 ± 0.9
Total Background expectation
47.4 ± 3.9
Expected signal events
gg → H
VBF
mH = 110 GeV
0.39 ± 0.06 0.35 ± 0.02
mH = 115 GeV
0.39 ± 0.06 0.35 ± 0.02
mH = 120 GeV
0.44 ± 0.05 0.38 ± 0.02
mH = 130 GeV
0.40 ± 0.04 0.33 ± 0.01
mH = 140 GeV
0.21 ± 0.02 0.19 ± 0.01
The invariant mass of the system formed by the two τ leptons and the leading jet, mττ j , has to be above
225 GeV. The four-momentum of the two τ system is calculated in the collinear approximation (see Appendix A).
This requirement reduces the background from γ∗ /Z → ll processes [58]. Finally, only events with invariant mass
of the two τ leptons system, mττ , between 100 GeV and 150 GeV are considered. The acceptance of this selection
is above (70-80)% for the SM Higgs signal in the Higgs mass range 110 GeV ≤ mH ≤ 140 GeV.
Figure 6.1 shows the mττ distribution of events passing the full selection described above except the final cut
on mττ . Table 6.1 shows the corresponding yields of events and MC expected number of events for 1.063 fb−1 . The
expected numbers of signal and background events from simulations are normalised according to the theoretical
cross section predictions described in the previous Section. Details on the estimated background events are given
in the following Section.
6.1.3 Background estimation
The description of the dominant, largely irreducible Z → ττ process in the simulation is confirmed by using the
τ-embedding method: in a sample of selected γ∗ /Z → µµ data events, the muon tracks and associated calorimeter
cells are removed and replaced by τ leptons from a simulated Z → ττ decay.
The contribution of the tt¯, single t, Z → ℓℓ and electroweak di-boson production backgrounds are estimated
from simulation. Their MC description is confirmed by data by selecting control regions enriched in these background processes.
Backgrounds arising from the presence of fake leptons are derived from data in signal free control samples.
The main sources of fake leptons are the QCD multijets, W+jets and semi-leptonic tt¯ processes. Non-isolated
leptons produced in heavy flavour meson decays, are included in this background.
The normalisation and the shape of the backgrounds with fake leptons are obtained from data with a template
method [182] using a control region in which the lepton isolation criterion is reversed. The chosen template shape
is the pT distribution of the sub-leading lepton. After subtraction of the simulated backgrounds, the template shape
of this background is obtained from a control sample, while the normalisation is obtained from a fit of the analysis
data sample with the template shape. The uncertainty related to the estimation of backgrounds with fake leptons is
6.1. H → τLEP τLEP + JETS FINAL STATE
87
Table 6.2: Individual systematic uncertainties for SM Higgs signal and backgrounds. All numbers are relative
errors expressed as percentages [176].
Relative Uncertainty (%)
Signal (mH =120 GeV) Background
Object selection
Lepton scale factors (%)
-2.7/+2.1
-4.2/+1.8
Lepton energy scale (%)
-0.3/+0.3
-0.8/+0.8
Lepton energy resolution (%)
-0.5/+0.2
-2.6/+0.3
Jet energy scale (%)
-7.8/+4.1
-9.8/+7.0
Jet energy resolution (%)
-2.0/+2.0
-2.5/+2.5
Jet reconstruction efficiency (%)
0.0
0.0
ETmiss reconstruction (%)
-5.3/+4.4
-2.7/+0.4
Pile-up (%)
-1.5/+1.5
-0.8/+0.8
Detector modelling (%)
-1.6/+1.6
-1.6/+1.6
Process rate
Fakes normalisation (%)
-1.9/+1.9
Z → ττ embedding (%)
-0.5/+0.5
Cross section Z+jets (%)
-2.9/+2.9
Cross section tt¯(%)
-4.8/+4.8
Cross section singleTop (%)
-0.2/+0.2
Cross section di-bosons (%)
-0.4/+0.4
Cross section H(mH =120GeV) (%)
-10.8/+10.8
Monte Carlo modelling
Signal MC Generator (%)
-4.4/+4.4
PDF (%)
-4.8/+4.8
-3.0/+3.0
Luminosity (%)
-3.7/+3.7
-3.5/+3.5
MC statistics (%)
-6.5/+6.5
-8.0/+8.0
Uncertainty Source
calculated from the uncertainty on the subtraction of other processes from MC simulation and from the difference
in the pT distribution shape between the control and the signal regions. The statistical contribution is the main
component after all the selection cuts and it is around 50%, while the systematic uncertainty is up to 30% in the
eµ channel.
6.1.4 Systematic uncertainties
The systematic uncertainties considered for the Higgs boson signal (mH =120 GeV) and backgrounds are presented
in Table 6.2. Uncertainty connected to the lepton scale factors takes into account correcting the MC samples for
differences between MC and data. The muon momentum scale and resolution as well as electron energy resolution are smeared to match that is observed in data. The electron energy is corrected in data according to in-situ
calibrations. The uncertainties associated to the re-scaling and smearing are taken into account. The uncertainty
on the jet energy is determined from “up” and “down” variations corresponding to 1σ uncertainties obtained from
data studies. The systematic uncertainty of the jet reconstruction efficiency accounts for the difference between
data and MC in the reconstruction efficiency of calorimeter jets with respect to track jets, measured with a tagand-probe method in QCD di-jet events. The efficiency depends on the jet pT and the difference between data and
MC has a negligible effect for jets with pT >40 GeV. For estimating the ETmiss reconstruction uncertainty, the lepton
and jet energy scale and resolution systematics are propagated to ETmiss . Other uncertainties specific to the ETmiss
reconstruction are also taken into account. Uncertainty connected to pile-up is introduced by reweighting of the
MC events to match pile-up in data. Also a systematic uncertainty is assigned to the MC modelling of the detector
CHAPTER 6. STANDARD MODEL HIGGS BOSON SEARCHES WITH τ FINAL STATES
95% CL. limit on σ / σSM
H
88
140
H→ττ→ ll
Observed CLs
Expected CLs
±2σ
± 1σ
120
100
80
s = 7 TeV,
∫ Ldt = 1.06 fb
-1
ATLAS Preliminary
60
40
20
0
110 115 120 125 130 135 140
mH [GeV]
Figure 6.2: Expected and observed exclusion limits for neutral Higgs boson production in the SM as a function
of mH . The region above the solid limit curve is excluded at the 95% confidence level. The expected
limit in confidence levels (CLs) are shown as the black dashed line. The green and yellow bands
correspond to the 1σ and 2σ error bands on the expected limit, respectively. The red line represents
the SM production rate [176].
acceptance. In particular, systematic effects on the treatment of the data with missing front-end boards for the LAr
calorimeter are considered.
The uncertainties on the estimation of fake lepton background, described in previous Section, are considered.
The τ-embedding sample is normalised to PYTHIA MC and the uncertainties on the MC prediction of Z → ττ are
taken into account. Additionally, the systematic uncertainty of the embedding method is obtained by comparing
the central prediction, obtained from Z → µµ events selected without any isolation requirement imposed on the
muons, and an alternative sample, where a track-based isolation is required in the Z → µµ selection.
An uncertainty of 4% is assumed in the inclusive cross section of the vector bosons production. In addition,
relative uncertainty of 24% is applied to W/Z+1-jet uncertainty on the inclusive cross section. For the top quark
pair production and single production of a top quark, the uncertainties are about 10% [183]. An uncertainty of 5%
is assumed for all di-boson production processes. The uncertainties on the signal cross-sections depend on mH and
are in the range of (15 − 20)% for gg → H and (2.5 − 3)% for VBF production. The estimated uncertainty of 3.7%
on the luminosity measurement [184] is applied to the normalisation of all MC samples.
In order to quantify the systematic uncertainty due to the choice of the signal MC generator, the default
MC@NLO and HERWIG samples are compared with samples generated with POWHEG [185]. For the comparison, both generators are interfaced to HERWIG/JIMMY for hadronisation. A PDF uncertainty of 3% as an
additional normalisation uncertainty on all the MC background samples, 7.8% on the Higgs boson gg fusion process and 2.3% on the Higgs boson VBF process are considered.
As can be seen from Table 6.2, the largest uncertainty is due to the jet energy scale.
6.1.5 Results
As shown in Table 6.1, no significant excess is observed in the data compared to the SM expectation.
The procedure to compute exclusion limits is based on the confidence levels method (CLs ) [186, 187]. The
data is compared with two models: the null-signal hypothesis (background only) and the signal plus background
6.2. H → τLEP τHAD FINAL STATE
89
Table 6.3: Main correlated systematic uncertainties used in the analysis of H → τlep τhad final state. These relative
uncertainties (%) correspond to the overall effect on the per-event signal efficiency under the ±1σ
variation of the sources of systematic uncertainty [177].
H → ττ
Luminosity
Electron efficiency
Electron energy scale
Muon efficiency
Jet/τ/ETmiss energy scale
τlep τhad
±3.7
±3.5
+1.3
−0.1
±1.0
+19
−16
hypothesis applied to the profile-likelihood test statistics [188]. The asymptotic approximation is used rather than
performing pseudo-experiments, because it is much less computational intensive.
Exclusion limits at the production of a SM Higgs boson are determined as a function of the Higgs boson
mass. Only events in the mass region of 100 GeV < mττ < 150 GeV are considered in the limit setting procedure,
that is based on counting events in the mass window. The Higgs boson exclusion is performed for the range
110 GeV ≤ mH ≤ 140 GeV.
A particular mH is excluded if the signal hypothesis is rejected at the 95% confidence level (CL). The systematic uncertainties described in Section 6.1.4 are included as nuisance parameters. Correlation of the systematic
uncertainties among processes are taken into account. The uncertainties on the luminosity, energy scale and acceptance are assumed to be correlated. Others, like the uncertainty on background process normalisation, are process
specific and are considered to be uncorrelated.
Figure 6.2 shows the resulting exclusion limit for a SM Higgs boson production as a function of the Higgs boson mass. The limit is expressed relative to the cross section predicted by the SM. The expected and observed 95%
confidence level limits are shown as dashed and solid lines, respectively. The green and yellow bands correspond
to 1σ and 2σ error bands on the expected limit. Exclusion limits at the 95% confidence level of the order of 30
times the Standard Model rate are obtained.
6.2
H → τlep τhad final state
Signal events in this final state are characterised by exactly one isolated lepton from leptonic τ decay and one τ
candidate. The backgrounds considered, MC samples used and preselection of events are similar to the ones used
for the H → τlep τlep → ℓℓ + 4ν final state.
The lepton transverse momentum has to be pT > 20 GeV for muons and pT > 25 GeV for electrons. The
τ candidate has to have pT > 20 GeV, one or three tracks and charge opposite to the one of the lepton. Missing
transverse energy in the event should be larger than 20 GeV. Events with an additional lepton are removed to
suppress the γ∗ /Z → ℓℓ and tt¯ background processes. Finally, to suppress
the W → ℓν background process,
q
the transverse mass of the lepton and missing energy system, mT = 2 pT (ℓ) · ETmiss · 1 − cos ∆φ(ℓ, ETmiss ) , is
required to be smaller than 30 GeV. The Missing Mass Calculator technique, described in Appendix A, is used to
estimate the invariant mass of the pair of τ leptons.
The main background in this analysis is the same as for fully leptonic final state, the γ∗ /Z → ττ process. The
invariant mass shape for this background is also estimated using the embedding technique. The QCD multijet
and W+jets backgrounds are estimated from data using events with the same charges of τ candidate and lepton in
the background-enhanced QCD and W+jets control regions. The difference between number of events with the
same and opposite charges of τ candidate and lepton is added from simulation. The remaining backgrounds are
estimated from simulation.
CHAPTER 6. STANDARD MODEL HIGGS BOSON SEARCHES WITH τ FINAL STATES
Events / 10 GeV
90
350
Data 2011, s = 7 TeV,
300
∫ Ldt = 1.06 fb
-1
ATLAS Preliminary
250
Data
200
mH=120 GeV, 12xSM
150
Total background
100
H→τlτh
50
0
0
50
100
150
200
250
300
350
400
mττ [GeV]
Figure 6.3: The invariant mass distributions for the candidate events selected, the total background and the signal
expected in the H → τlep τhad final state. Higgs boson mass hypothesis used to illustrate the signal and
the multiplicative factor applied to its normalisation are indicated in the legend [177].
With such a selection, 1072 events is observed in data. The expected number of signal (mH =120 GeV) is 8 with
1218 background events.These numbers are estimated in an interval containing about 90% of the signal around the
most probable value of the invariant or transverse mass distributions of the pair of τ leptons. The distribution of the
reconstructed invariant mass can be seen in Figure 6.3. The dominant contributions to the systematic uncertainty
of the signal yield are summarised in Table 6.3.
The 95% CL limit on the cross section for individual final states and their combination are illustrated in
Fig. 6.4(a), normalised to the Standard Model Higgs boson cross section, as a function of the Higgs boson mass.
Exclusion limits obtained for the H → τlep τhad final state at the 95% confidence level are of the order of 10
times the Standard Model rate. The combination of individual final states with the ±1σ and ±2σ variations of
the background only expectation is illustrated in Fig. 6.4(b). As the H → τlep τhad final state is significantly more
sensitive than the H → τlep τlep final state, the combination differs only slightly from the H → τlep τhad final state
alone.
6.3 Summary
In this Chapter, the first search for a neutral Higgs boson produced according to the mechanism predicted by
the SM and decaying into ττ channel in proton-proton collisions at the centre-of-mass energy of 7 TeV with the
ATLAS experiment is presented. Both, the fully leptonic and the semi-leptonic final states are considered. No
significant excess over the expected background is observed in the considered Higgs boson mass range of 100 <
mH < 140 GeV. The observed (expected) upper limits on the cross section times the branching ratio of H → ττ
are between 6 (10) and 14 (30) times the Standard Model prediction. This search is complementary to searches
with other decays in the same mass range.
A small statistics sample of the first data, corresponding to 1.06 fb−1 is used in the presented studies. The most
recent results corresponding to the luminosity of 4.7 fb−1 [189] improve those limits to the observed (expected)
limit between 2.9 (3.4) and 11.7 (8.2) in the mass range 100 < mH < 150 GeV. In this latter analysis, additionally,
the H → τhad τhad final state is used in order to increase the signal yield. The studies of dataset collected in 2012
with the centre-of-mass energy of 8 TeV are ongoing.
For completeness of this Chapter, even though is out of the scope of this monograph, the recent Higgs search
results should be mentioned [53]. The ATLAS experiment reports studies of the H → ZZ ∗ → 4ℓ, H → γγ and
H → WW ∗ → eµ 2ν channels with 5.8 − 5.9 fb−1 of pp collision data recorded during April to June 2012 at the
6.3. SUMMARY
91
90
100
H→ττ
Observed CLs
Expected CLs
Observed ll only
Expected ll only
Observed lh only
Expected lh only
80
70
60
50
ATLAS Preliminary
s = 7 TeV,
40
∫ Ldt = 1.06 fb
-1
95% CL. limit on σ / σSM
H
95% CL. limit on σ / σSM
H
100
90
70
60
50
20
20
10
10
110
120
130
140
150
s = 7 TeV,
40
30
100
ATLAS Preliminary
Observed CLs
Expected CLs
±2σ
± 1σ
80
30
0
H→ττ
0
100
110
∫ Ldt = 1.06 fb
120
mH [GeV]
(a)
-1
130
140
150
mH [GeV]
(b)
Figure 6.4: The observed and expected 95% CL upper limit on the SM Higgs boson production cross section
divided by the Standard Model expectation as a function of mH for the individual H → τlep τhad
(lh) and H → τlep τlep (ll) final states and their combination (a). The H → ττ combined observed
and expected 95% CL upper limits (b). The green and yellow bands reflect ±1σ and ±2σ variation
respectively in the expected limit [177].
centre-of-mass energy of 8 TeV. These results are combined with results based on 2011 data (4.6 − 4.8 fb−1 ). The
Standard Model Higgs boson is excluded at 95% CL in the mass range 111−559 GeV, except for the narrow region
122 − 131 GeV. In this region, an excess of events with a significance of 5.9 σ is observed. Taking into account
the entire mass range of the search, 110 − 600 GeV, the global significance of the excess is 5.1 σ. These results
provide conclusive evidence for the discovery of a new particle with mass 126.0 ± 0.4(stat)±0.4 (syst) GeV. The
CMS experiment reports similar results [54]. In this case also searches in ττ and bb channels are included, but no
significant excess of events is found in those final states.
The decays to pairs of vector bosons identify the new particle as a neutral boson. The observation in the
di-photon channel disfavours the spin-1 hypothesis. Although these results are compatible with the hypothesis
that the new particle is the Standard Model Higgs boson, more data are needed to assess its nature in detail. The
H → ττ final state starts to be critical in this task as with it we can check if a new boson couples to fermions. τ
leptons can probe the leptonic Higgs-Yukawa coupling which is not accessible from decays to a pair of photons or
heavy bosons, WW/ZZ. The τ final state has also sensitivity both to SM and SUSY Higgs bosons. Its observation
or exclusion can tell a lot about its nature and possible New Physics. Finally the H → ττ final state can be used to
study Higgs CP properties and in particular to study CP violation in the Higgs sector [190, 191].
92
CHAPTER 6. STANDARD MODEL HIGGS BOSON SEARCHES WITH τ FINAL STATES
There are two possible outcomes: if the result confirms the hypothesis, then
you’ve made a measurement. If the result is contrary to the hypothesis, then
you’ve made a discovery.
Enrico Fermi
Somewhere, something incredible is waiting to be known.
Carl Sagan
7
MSSM Higgs bosons searches with τ lepton final states
The coupling of the Higgs boson to the third generation down-type fermions is strongly enhanced for large regions
of the MSSM parameter space. Hence, the final states with τ leptons are the most promising channels for MSSM
Higgs boson searches at the LHC. In this Chapter the first studies in the ATLAS experiment on searches for neutral
and charged Higgs bosons with τ lepton final states are presented. The data used in those searches were recorded
with the ATLAS detector during the first half of 2011, corresponding to an integrated luminosity of (1.03-1.06)
fb−1 .
7.1 Neutral MSSM Higgs bosons decaying to ττ pairs
A search for neutral MSSM Higgs bosons in the decay mode H → ττ includes eµ4ν (eµ), eτhad 3ν (eτhad ), µτhad 3ν
(µτhad ),and τhad τhad 2ν (τhad τhad ) final states [177]. These decays have branching ratios of 6%(eµ), 23%(eτhad ),
23%(µτhad ), and 42%(τhad τhad ). The combination of eτhad and µτhad is referred to as ℓτhad . Similar searches for
neutral Higgs bosons have been performed at the Tevatron [67, 68] and the LHC [192, 193].
The production of W or Z bosons that subsequently decay into leptons constitutes the most important background for the eµ and ℓτhad final states. These processes include W+jets, γ∗ /Z, tt¯, single-top and electroweak
di-boson production. γ∗ /Z → ττ events constitute an irreducible background for Higgs boson masses close to the
Z boson mass. γ∗ /Z → ℓℓ events contribute if one of the charged leptons or an accompanying jet is mis-identified.
QCD multijet production provides a significant background contribution if there are real leptons from decays of
heavy quarks or if jets are mis-identified as electrons, muons, or τhad decays. It is the dominant background in the
τhad τhad final state as it is more probable for a jet to be mis-identified as a hadronic τ decay than as a light lepton.
7.1.1 Data sample and Monte Carlo simulations
Events in eµ and eτhad final states are selected using a single-electron trigger with a pT threshold of 20 GeV. Events
in µτhad final state are selected with a single-muon trigger with a pT threshold of 18 GeV. The same trigger can
select eµ final state if the event is not triggered by an electron. The τhad τhad events are selected by a hadronic
τ decay trigger, which requests at least two τ candidates. The transverse energy thresholds used are 29 GeV on
the leading τ candidate and 20 GeV on the sub-leading one. The total trigger efficiencies, with respect to the
event selection described in the next Section, are 99%, 82% and ∼ 60% for electron, muon and the di-τ triggers
respectively.
The cross section for Higgs boson production in the gluon fusion process are calculated using HIGLU [178]
and ggh@nnlo [179]. For the b-quark associated production, a matching scheme [194] is used to combine the NLO
93
94
CHAPTER 7. MSSM HIGGS BOSONS SEARCHES WITH τ LEPTON FINAL STATES
calculation for gg → bb̄A/H/h in the four-flavor scheme [195, 196] and the NNLO calculation for bb̄ → A/H/h
in the five-flavor scheme [197]. In both cases, the MSTW2008 set of parton distribution functions [48] has been
used. The masses, couplings, and branching ratios of the Higgs bosons are computed with FeynHiggs [198].
The direct gg → A/H/h production is simulated with POWHEG [185], and the associated bb̄A/H/h production
with SHERPA [199]. Both gg → A and bb̄A samples are generated at values of mA in the range from 90 to
600 GeV. To obtain simulated samples for the decays of the H and h bosons, events with A boson decays with
mass mA closest to mH and mh respectively are scaled to the H/h production cross section. For any given mA and
MSSM benchmark scenario and
tan β, the masses mH and mh of the H and h bosons are calculated in the mmax
h
A boson events with mA closest to mH and mh , respectively, are combined with these samples with appropriately
scaled cross sections to obtain a signal sample for A/H/h production. The increase of the Higgs boson natural
width with tan β is neglected as it is small compared with the experimental resolution of the mass definition used.
For processes of W, Z bosons, tt¯ and single-top production the same Monte Carlo samples as described in
Section 6.1.1 are used. The loop-induced process gg → WW is generated with gg2WW [200]. The generation
of parton shower, hadronisation, the underlying event, the decays of τ leptons and the QED radiation follow
description in Section 6.1.1.
The cross section for single gauge boson production is calculated at NNLO in QCD perturbation theory [150],
for tt¯ production at NLO+NLL [201, 202], and for single-top and di-boson production at NLO [152]. For the
background processes the PDFs MSTW2008 (W → ℓ, Z/γ∗ → ℓ+ ℓ− , single-top and di-boson) and CTEQ6.6 [156]
(tt¯) are used.
To match the pile-up observed in the data, events are reweighted so that the average number of interactions per
bunch crossing agrees with the data.
7.1.2 Object and event selection
Events passing the trigger requirements are selected as collision events if they have a reconstructed vertex that is
formed by three or more tracks and lies within 15 cm of the nominal interaction point along the beam axis.
Selection of electron and combined muon candidates follows the description in Section 6.1.2. τ candidates are
required to have a transverse momentum pT > 20 GeV, |η| < 2.5, 1 or 3 associated tracks and a charge of ±1. The
identification with BDT is required for the ℓτhad final state and with a projective likelihood for the τhad τhad final
state. The efficiency of the likelihood (BDT) τ identification for τ candidates with pT > 20 GeV is about 55%
(60%) and the probability to mis-identify a jet as a τ lepton, as determined from a di-jet control sample, is about
5% (5%). The missing transverse energy is derived from the simple definition described in Section 3.5.
When candidates fulfilling the above criteria overlap with each other geometrically (within ∆R < 0.2), only
one of them is selected. The overlap is resolved by selecting muons, electrons and τ candidates in this order of
priority.
The signature in the leptonic final state is one isolated electron, one isolated muon and ETmiss due to the undetected neutrinos from the two τ decays. The tt¯, single-top and di-boson backgrounds are suppressed by the
following requirements. The scalar sum of the transverse momentum of the electron, the transverse momentum of
the muon and ETmiss must be smaller than 120 GeV, and the azimuthal opening angle between the electron and the
muon must be larger than 2.0 rad.
The signatures of the semileptonic final state are an isolated electron or muon, a τ candidate, and ETmiss
due to the undetected neutrinos from the two τ decays. Exactly one electron with pT > 25 GeV or muon with
pT > 20 GeV and one oppositely-charged τ candidate with pT > 20 GeV are required in the event. In order to
suppress events from γ∗ /Z → ℓℓ decays and from tt¯ or single-top production only one reconstructed electron or
muon candidate is allowed in the event. For the second lepton selection the less strict requirements are applied: the
threshold for the transverse momentum of electron candidates is lowered to pT > 15 GeV and a loose identification
is used, for muon candidates the threshold for the transverse momentum is lowered to pT > 10 GeV. Further rejection of γ∗ /Z → ℓℓ events and QCD multijets is achieved by requiring ETmiss > 20 GeV. Events with leptons from
q
W → ℓν decays are suppressed by requiring the transverse mass, mT = 2 pT (ℓ) · ETmiss · 1 − cos ∆φ(ℓ, ETmiss ) ,
7.1. NEUTRAL MSSM HIGGS BOSONS DECAYING TO ττ PAIRS
95
to be below 30 GeV.
The signature of the fully hadronic final state is characterised by two identified hadronic τ decays and ETmiss
from the undetected neutrinos. Events with exactly two oppositely charged τ candidates that match the τ trigger
objects inside a cone of radius ∆R = 0.2 around the direction of the τ candidates are required. The τ candidates
are also required to have pT > 45 GeV for the highest-pT candidate and pT > 30 GeV for the second-highestpT candidate. These thresholds ensure that τ candidates are on the plateau of the trigger turn-on curve and help
suppressing electroweak backgrounds. To further reject QCD jet processes and Z boson production a missing
transverse energy of ETmiss > 25 GeV is required. Finally, events are rejected if they contain an electron candidate
with pT > 15 GeV or a muon candidate with pT > 10 GeV.
Corrections are applied to simulation to account for differences in the τ trigger efficiency between data and
simulation. These are derived using control regions rich in Z → ττ → µ + hadrons + 3ν events. Trigger and
mis-identification scale factors for QCD multijets mis-identified as τhad decays are measured from data using
W → µν+jets events [160] and are applied to Monte Carlo.
After the selection of signal candidates, different ττ mass reconstruction methods are used as described in
Appendix A. The reconstructed mass is the best discriminating variable to distinguish between Z and neutral
Higgs bosons. The effective mass, meffective , is used for the eµ final state, the Missing Mass Calculator (MMC)
, for the ℓτhad final state and the visible mass, mvis , for the τhad τhad final state.
mass, mMMC
ττ
7.1.3 Background estimation
Data control samples are used to estimate or validate the most relevant background sources, QCD multijet production for all final states, and W+jets in the ℓτhad final state. The remaining backgrounds are estimated from Monte
Carlo simulation.
The shapes of the mass distributions for the irreducible Z → ττ background are determined from data with the
embedding technique described in Section 6.1.3. For the τhad τhad final state, the W+jets background is validated
with an embedding technique as well. A sample of W → µν decays is selected based on Ref. [160] and the muon
is replaced by a simulated hadronic τ decay.
Background estimation in the eµ final state The QCD multijet background estimation uses four independent
samples selected with criteria on the isolation of the electron and muon and product of their charges as described
in Section 5.1.3. The shape of the meffective distribution in the signal region A is taken from control region C
and the normalisation is derived by nA = rC/D × nB . Here, nA and nB denote the event yields in regions A
and B and rC/D the ratio of the event yields in regions C and D after subtracting the contribution from non-QCD
backgrounds estimated from simulation. This method relies on the assumption that the two variables used to define
the four regions are uncorrelated and that the shape of the meffective distribution does not depend on the isolation
or product of the charges requirement. Obtained QCD multijet event yield in the signal region is estimated to be
nQCD
= 120 ± 20 (stat). The resulting meffective distribution is shown in Fig. 7.1 (a).
A
Background estimation in the ℓτhad final state For the background estimation in the signal region, apart from
the Z → ττ background, it is assumed that the shape of the MMC mass distribution is the same regardless of
whether the lepton and the τ candidate have the same (SS) or the opposite (OS) charges. The OS backgrounds
are therefore estimated from data as SS events and the difference between OS and SS is added from simulation
separately. It is done for each bin in the MMC mass distribution, thus not only an estimation of the background
normalisation but also of the MMC mass shape is obtained.
The ratio of OS and SS events for the QCD multijet background should be close to unity. It is checked with a
QCD
data control sample that is dominated by low-ET jets from QCD processes. The observed deviation of rOS
/S S from
unity is taken into account in the systematic uncertainties. For the W+jets background, a significant deviation of the
W
from unity is expected and is estimated from a W+jets dominated control region selected by replacing
ratio rOS/SS
the mT < 30 GeV requirement in the nominal selection by mT > 50 GeV. The contributions from Z → ττ are
Events / 10 GeV
700
eµ channel
Events / 10 GeV
CHAPTER 7. MSSM HIGGS BOSONS SEARCHES WITH τ LEPTON FINAL STATES
96
Data 2011
A(120)/h/H → ττ, tanβ=20
Z/ γ *(→ττ) embedded
Others
Diboson
QCD multi-jet
600
500
t t & single-t
syst.
400
s = 7 TeV,
300
∫ Ldt = 1.06 fb
Data 2011
A(120)/H/h→ττ, tanβ=20
Z/γ *(→ττ) emb.(OS-SS)
Others(OS-SS)
W+jets (OS-SS)
Same Sign
stat.
350
300
250
200
-1
s = 7TeV,
150
ATLAS Preliminary
∫ L = 1.06 fb
-1
ATLAS Preliminary
200
100
100
0
0
400 eτhad + µτhad channels
50
50
100
150
200
0
0
250
50 100 150 200 250 300 350 400
MMC mττ [GeV]
mττ effective [GeV]
(b)
Events / 15 GeV
(a)
70
τhadτhad channel
Data 2011
A(200)/H/h → τ τ, tanβ=20
60
Multi-Jet
Z/ γ *(→τ τ )
50
W(→τ ν ) + jets
Others
40
stat.
30
∫
-1
s = 7 TeV, Ldt = 1.06 fb
20
ATLAS Preliminary
10
0
0
100
200
300
400
500
600
mττ visible [GeV]
(c)
Figure 7.1: Effective mass distribution for the eµ (a), MMC mass distribution for the ℓτhad (b) and visible mass
distribution for the τhad τhad (c) final states. The data are compared with the background expectation
and an added hypothetical MSSM signal (mA = 120 GeV, tanβ = 20 for (a) and (b), mA = 200 GeV,
tanβ = 20 for (c)). “OS-SS” denotes the difference between event yields with the opposite or the same
charges of the lepton and the τ candidate [177].
taken from the embedded samples and remaining backgrounds from simulation. The total estimated background
is (2.10 ± 0.05 (stat)) × 103 . The resulting MMC mass distribution is shown in Fig. 7.1 (b).
Background estimation in the τhad τhad final state The QCD multijet background is estimated by using a similar
method as described for the eµ final state where the four control samples are defined by selection criteria on the
product of the two τ candidates charges and the tightness of the τ identification criteria. For the latter, the nominal
τ identification used in this analysis has been relaxed to the loose τ identification, corresponding to an 80% τ
identification efficiency. The shape of the mvis distribution is taken from sample C with τ candidates with the
opposite charges and passing loose τ identification. It is scaled by the ratio of event yields in samples B and D with
τ candidates with the same charges and passing nominal/loose τ identification. In all control samples the non-QCD
background contributions are subtracted. The resulting estimate for the QCD multijet background in the signal
sample is 157 ± 18 (stat) events. The electroweak backgrounds are the other sizable background components in
this final state. They are estimated from simulation and validated with data using embedded samples. The resulting
visible mass distribution is shown in Fig. 7.1 (c).
7.1. NEUTRAL MSSM HIGGS BOSONS DECAYING TO ττ PAIRS
97
Table 7.1: Uncertainties on the number of selected events for those background contributions that are at least
partially estimated from simulation and for a hypothetical signal (mA = 120 GeV and tan β = 20 for the
eµ and ℓτhad final states and mA = 200 GeV and tan β = 20 for the τhad τhad final state). All numbers
are given in %. When three numbers are given the first refers to the eµ final state, the second to the
ℓτhad final states and the third to the τhad τhad final state. If an uncertainty is not relevant for a certain
background, this is indicated by a “-”. For the eµ final state, the uncertainty on the W+jets background
is dominated by the statistical component and the systematic uncertainty is neglected; for the ℓτhad final
state the W+jets background is estimated from data [177].
W+jets
Di-boson
-/-/5
7
tt¯+
single-top
σinclusive
10
γ∗ /Z →
γ∗ /Z →
Signal
5/5/-
5
14/14/16
ℓℓ
ττ
Acceptance
-/-/20
4/2/7
3/2/9
2/14/-
5/14/14
5/7/9
e efficiency
-/-/0.8
4/3.1/0.5
4/3.6/0.3
4/3.1/-
4/3.0/0.5
4/3.6/0.1
µ efficiency
-/-/0.3
2/1.2/0.4
2/1.1/0.0
2/1.3/-
2/1.8/0.4
2/1.0/0.1
τ efficiency and fake rate
-/-/21
-/9.1/15
-/9.1/13
-/48/-
-/9.1/15
-/9.1/15
Energy scales and resolution
Luminosity
-/-/+34
−21
-/-/3.7
+26
2/+19
−9 /−12
6/+5
−4 /12
3.7
1/+39
−25 /-
3.7/3.7/-
1/11/+63
−23
+9
1/+30
−23 /−8
Total uncertainty
-/-/+45
−36
+32
10/+23
−16 /−22
13/15/23
8/+64
−56 /-
9/21/+67
−31
+26
16/+35
−30 /−25
3.7
3.7
3.7
7.1.4 Systematic uncertainties
Systematic effects on the signal efficiency and the estimated number of background events can be grouped in the
following categories: theoretical inclusive cross sections, acceptance, knowledge of detector performance (lepton
identification and mis-identification efficiencies, trigger efficiencies, energy scales and resolution) and systematic
uncertainties of the data-driven background estimation methods.
The uncertainties from different sources of various background processes which are partially or completely
estimated from simulated events are summarised in Table 7.1.
Systematic uncertainties for simulated samples account for the following effects. The uncertainty on the theoretical inclusive cross section (σinclusive ) for each individual signal and background process is obtained from
variations of the renormalisation and factorisation scales and a variation of the strong coupling constant and the
PDF sets within their uncertainties. The uncertainty on the acceptance is estimated by varying the renormalisation
and factorisation scales, the matching parameters in ALPGEN and the choice of the PDF to MRST2001J [203] in
the generation of simulated event samples.
The uncertainty on the trigger efficiencies (included in lepton efficiencies in Table 7.1) for electrons and muons
is 1%. For the τ triggers this efficiency is determined from data in pT bins for τ candidates and QCD multijets
mis-identified as hadronic τ decays. The uncertainty for QCD multijets that are mis-identified as τ candidates is
combined with the uncertainty of the offline mis-identification probability, resulting in a combined uncertainty of
≈ 10%. The uncertainties due to the limited knowledge of the detector performance are evaluated by varying the
trigger, reconstruction and identification efficiencies for electrons, muons and τ candidates, and by varying the
energy resolution and energy scale of electrons, muons, τ candidates, and energy deposits outside of these objects.
These are propagated in a fully correlated way into the ETmiss scale and resolution. The difference in the impact
of the energy scale and resolution uncertainty on the expected event yields in different final states is caused by
requiring a hadronic τ decay(s). The luminosity uncertainty is 3.7% [106]. The uncertainties, apart from the ones
related to the data-driven techniques, are treated as fully correlated between the three final states.
The systematic uncertainties from the data-driven estimate of the QCD background differ between final states.
In the eµ final state it includes the systematic uncertainty on the subtracted non-QCD background and on the
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CHAPTER 7. MSSM HIGGS BOSONS SEARCHES WITH τ LEPTON FINAL STATES
Table 7.2: Observed numbers of events in data and total expected background contributions for the final states
considered in this analysis, with their combined statistical and systematic uncertainties [177].
Final state
Data
Expected Background
eµ
2472
ℓτhad
1913
(2.6 ± 0.2) × 103
τhad τhad
245
Sum
4630
(2.1 ± 0.4) × 103
233 +44
−28
(4.9 ± 0.6) × 103
assumption of identical meffective shapes in the different control regions.
For the ℓτhad final states, the most important uncertainties for the data-driven estimation of the QCD multijet
and W+jets backgrounds are the statistical uncertainty on the number of SS events in the signal region and the
uncertainty on the ratios between the OS and SS regions for QCD multijets and W+jets. An additional uncertainty
of 10% is derived from the mT dependence of this ratio for W+jets events.
For the τhad τhad final state, the statistical uncertainty on the number of SS events in the signal region is the
dominant uncertainty of the data-driven estimate of the QCD multijet contribution. The systematic uncertainties
on the non-QCD background contributions in the control regions are propagated to the QCD multijet estimate. The
systematic uncertainty is dominated by the energy scale and τ mis-identification efficiency uncertainty.
For the energy scale uncertainty, variations of the electron, muon, τ candidate, and ETmiss not only changes
in normalisation but also in the shapes of the discriminating mass variables and therefore it was included as an
additional uncertainty in the derivation of the Higgs boson exclusion limits in Section 7.1.5. In the channels where
embedded data are used, systematic uncertainties are derived for the final decay products that are taken from
simulation.
Systematic effects of the embedding method are estimated from variations of the embedding procedure. While
in the analysis no isolation is required for the selected muons in order to avoid a bias on the embedded objects,
the procedure is repeated on Z → µµ data fulfilling standard isolation criteria for the eµ and the ℓτhad channel. A
second variation accounts for the energy deposition from the selected muons in the calorimeter, which is by default
completely removed in a cone of radius ∆R < 0.1 around the muon direction. The systematic uncertainties from
these variations enter the limit calculation in the form of shape systematics. All other systematic uncertainties have
no significant effect on the mass shape.
7.1.5 Results for the neutral MSSM Higgs bosons searches
Combining the estimated contribution from the various background processes and their uncertainties results in the
final background estimate shown in Table 7.2. No significant excess of events over the Standard Model background
expectation is observed in the data in any of the studied final states.
Exclusion limits at the 95% confidence level are set for MSSM Higgs boson A/H/h production as a function
of the parameters mA and tan β. The exclusion limits are derived with the profile likelihood method [188] based
on the CLs parameter from the analysis of the meffective distribution for the eµ final state, the mMMC
distribution for
ττ
the ℓτhad final state and the mvis distribution for the τhad τhad final state.
For the limit derivation, systematic uncertainties are separated into common, fully correlated (energy scale,
acceptance, luminosity) and final state specific ones and are included as nuisance parameters. The meffective , mMMC
ττ
and mvis shape uncertainties due to the uncertainties in the energy scales of leptons, hadronic τ candidates and
ETmiss for the backgrounds, obtained from simulation, are taken into account. Asymptotic formulae are used to find
the median expected limit along with the ±1σ and ±2σ error bands. The combined limit and the contributions of
the individual channels to the combination limits on the production of neutral MSSM Higgs bosons A/H/h in the
60
50
40
tanβ
tanβ
7.2. SEARCH FOR CHARGED HIGGS BOSONS IN tt¯ DECAYS
All channels
Observed CLs
Expected CLs
± 1σ
± 2σ
LEP
ATLAS 36 pb -1 observed
ATLAS 36 pb -1 expected
All channels
mmax
h , µ>0
50
40
30
30
20
10
60
99
mmax
h ,
s = 7 TeV,
ATLAS
µ>0
∫ Ldt = 1.06 fb
20
-1
10 s = 7 TeV,
Preliminary
∫ Ldt = 1.06 fb
-1
ATLAS Preliminary
0
100 150 200 250 300 350 400 450
Observed (hh only)
Observed (lh only)
Observed (emu only)
Observed CLs
Expected (hh only)
Expected (lh only)
Expected (emu only)
Expected CLs
LEP
0
100 150 200 250 300 350 400 450
mA [GeV]
(a)
mA [GeV]
(b)
Figure 7.2: Expected and observed exclusion limits in the mA − tan β plane of the MSSM as derived from the
combination of the analyses for the eµ, ℓτhad and τhad τhad final states. The exclusion limits from
analysing of 36 pb−1 of data and from LEP are also shown (a). The region above the drawn limit
curve is excluded at the 95% confidence level. The dark grey (green) and light grey (yellow) bands
correspond to the ±1σ and ±2σ error bands, respectively. The contribution of the individual channels
to the combined limit (b) [177].
scenario and Higgsino mass parameter µ > 0 [65] are shown in Figure 7.2. These
tan β − mA plane, for the mmax
h
results exclude regions of parameters space beyond the existing limits from previous experiments at LEP [66] and
the Tevatron [67, 68] and are similar to those recently obtained by the CMS Collaboration [192].
7.2 Search for charged Higgs bosons in tt¯ decays
This section describes a search for charged Higgs bosons with masses in the range 90 − 160 GeV, using tt¯ events
with a leptonically or hadronically decaying τ lepton in the final state. Two final states, which are expected to give
the highest sensitivity, are analysed:
• τhad +jets [204]: tt¯ → bb̄W H + → bb̄W(qq̄′)H + (τhad ν), i.e. both W and τ decay hadronically;
• τlep +lepton/jets [205]: tt¯ → bb̄W H + → bb̄W(qq̄′ /ℓν)H + (τlep ν), i.e. τ decays leptonically and W decays
leptonically or hadronically, so called one or two leptons final state.
7.2.1 Data sample and Monte Carlo simulations
For the τhad +jets final state, the combined τ and ETmiss trigger [206, 138], with a threshold of 29 GeV on the τ
object and of 35 GeV on ETmiss is used for data selection. The one or two leptons final state analysis relies on events
passing a single-lepton (electron or muon) trigger, with a pT threshold at 20 GeV for the electron trigger and at
18 GeV for the muon trigger.
The Monte Carlo simulation of tt¯, single-top, single vector boson and di-boson events is the same as described
in Section 6.1.1. Overlap between tt¯ and single-top final states is taken into account. A tt¯ production cross section
of 165 pb [207] obtained from the approximate NNLO calculations [202] is used (both for SM tt¯ decays and decays
via a charged Higgs boson). A top quark mass of 172.5 GeV is assumed and the PDFs is CTEQ66 [156]. The H +
100
CHAPTER 7. MSSM HIGGS BOSONS SEARCHES WITH τ LEPTON FINAL STATES
signal events are generated with PYTHIA using TAUOLA for τ lepton decays and PHOTOS for charged leptons
radiating photons.
The Monte Carlo pile-up samples are reweighted in order to match vertex distribution in data. Only events
with a reconstructed primary vertex with at least five associated tracks are considered.
7.2.2 The τhad +jets final state
This study relies on the detection of τ+jets in tt¯ events, where the hadronically decaying τ lepton comes from
H + → τhad ν, while jets originate from hadronically decaying W boson. This topology has several advantages:
the W boson can be fully reconstructed, the H + candidate can be reconstructed in the transverse plane, and the
branching ratio of the W boson decay to quarks is larger than that to leptons. However, it needs to be distinguished
from a large QCD multijet background. The background processes include the production of tt¯, single-top, W+jets,
γ∗ /Z+jets, and QCD multijet events where there is either a true τ lepton, or another object mis-identified as a
hadronically decaying τ.
Objects and events selection
Electron candidates are required to have ET > 20 GeV and |η| < 2.47 (excluding the transition region in the
0.2 < 3.5 GeV. Combined muon candidates are required to have p > 10 GeV and
calorimeters) and to be isolated IET
T
0.3 and I 0.3 < 4 GeV.
|η| < 2.5 and isolation IET
PT
Jets are reconstructed with the anti-kt algorithm with a size parameter of R = 0.4. They are required to have
pT > 20 GeV and |η| < 2.5. To identify jets initiated by b quarks, a combination of a discriminant based on
an impact parameter in three dimensions and a secondary-vertex-tagger [208] with an identification efficiency of
about 60% for b jets with pT > 20 GeV in tt¯ events is applied.
τ candidates are required to have pT > 20 GeV, |η| < 2.3 and 1 or 3 associated tracks. They are identified
using a likelihood identification method with an efficiency of about 30% for τ candidates with pT > 20 GeV in
Z → ττ events. In some control regions, a loose τ identification is used corresponding to an efficiency of 60%. A
dedicated algorithm is used to reject electrons.
The missing transverse energy is calculated using a refined calibration method described in Section 3.5.
When candidates, selected using the above criteria, overlap geometrically within ∆R < 0.2, only one candidate
in the following order of priority: muon, electron, τ, or jet, is kept.
An event is required to have a τ candidate and at least 4 jets with pT > 20 GeV and |η| < 2.5. A τ candidate
is asked to have pT > 35 GeV and to be matched to the τ trigger object within ∆R < 0.1. Events with a second
identified τ candidate with pT > 20 GeV or any identified electron (ET > 20 GeV) or muon (pT > 10 GeV) are
vetoed. ETmiss is required to be larger than 40 GeV. Events with large reconstructed ETmiss due to the limited resolution of the energy measurement are rejected with a cut on the significance of ETmiss (as defined in Section 5.2.2),
S Emiss > 8. At least one b-tagged jet is required. The qqb candidate, built from three jets with one of them b-tagged,
T
with the highest sum of the constituents transverse momenta, must satisfy m(qqb) ∈ [120, 240] GeV in order to
be consistent with the q
top decay. For events passing the above selection cuts, the transverse mass of the τ candi-
date and ETmiss , mT = 2pT ETmiss (1 − cos ∆φ(τ, ETmiss )), is defined. This variable discriminates between W → τν
background and the H + signal.
At the end of the selection cut flow, after applying data-driven methods as detailed in the next Section, 37 ±
7 background events are expected for mT > 40 GeV. A potential signal yield depends on the charged Higgs
boson mass and the branching ratio t → bH + . For example, 70 events are expected for mH + = 130 GeV and
BR(t → bH + )=0.1.
Background estimation
For backgrounds with intrinsic ETmiss from W decays the contribution from events in which electrons or jets are misidentified as τ candidates is predicted using appropriate control samples while events with correctly identified τ
7.2. SEARCH FOR CHARGED HIGGS BOSONS IN tt¯ DECAYS
101
candidates are studied with the embedding method. Backgrounds due to QCD multijet events with ETmiss generated
by detector effects are estimated using the shape of the ETmiss distribution in a suitable control region.
The background from events where electron is mis-identified as a τ candidate is measured with a tag-and-probe
method on γ∗ /Z → ee events (see Section 4.3.3). The result is compared to simulation and used to correct MC
samples.
To study the probability for jets to be mis-identified as hadronically decaying τ leptons, a γ-jet control sample
is used. The method is the same as described in Section 4.3.2 though based on a larger data set corresponding
to 1.03 fb−1 . Jets in the control sample, similarly to the dominant tt¯ background, originate predominantly from
quarks. The main difference between tt¯ and γ-jet events is the different fraction of b jets which is smaller in γ-jet
events. However, the probability for a b jet to be mis-identified as a τ candidate is smaller than the corresponding
probability for a light-quark jet. The average track multiplicity of b jets is higher, and variables which measure the
mass of the τ candidate allow for a good discrimination. Hence, using the γ-jet mis-identification probability leads
to a higher background estimate and is thus conservative. The denominator of the calculated mis-identification
probability is the number of events with the reconstructed τ candidate with pT greater than 20 GeV and |η| < 2.3,
which passes an electron veto. The mis-identification probability is evaluated separately for the τ candidate with
1 or 3 associated tracks and measured as a function of its pT and η. Further, it is applied to simulated tt¯, singletop, and W+jets events. These events are required to pass the full event selection except for the τ identification.
For these events, τ candidates, fulfilling the same requirements as in the denominator of the mis-identification
probability measurement which do not overlap with a true τ lepton, are identified. Out of the remaining τ candidates, each one is considered to be potentially mis-identified as a τ candidate separately. The identified jet that
corresponds to the τ candidate is removed from the event, affecting the number of reconstructed jets, the ETmiss
significance of the event, and the number of b-tagged jets. If, after taking this into consideration, the event still
passes the selection, then the event is counted as background event with a weight given by the mis-identification
probability corresponding to the pT and η of the τ candidate. The predicted number of events from the tt¯ sample
is 2.8 ± 1.0 (stat) ± 0.5 (syst). It is in agreement, within errors, with the MC prediction using truth information,
3.8 ± 0.6 (stat). All other backgrounds with jets mis-identified as τ candidates and with intrinsic ETmiss are at least
two orders of magnitude smaller than tt¯.
The QCD multijet background is estimated by fitting the ETmiss shape (and the ETmiss shape of other backgrounds)
to data. For this purpose a control region is defined where the τ identification and b-tagging requirements are
inverted. The τ candidates must pass a loose τ identification but fail the tight τ identification used in the baseline
selection. In addition, the event is required not to contain any b-tagged jets and therefore also the requirement on
the qqb mass is removed. Assuming that the shapes of ETmiss and mT distributions are the same in the control sample
and signal regions, the shape of the ETmiss distribution is used to model the ETmiss distribution for the QCD multijet
background (after subtracting the background from other processes). The ETmiss distribution measured in data (for
the baseline selection) is then fitted using two shapes: this QCD multijet model, and the sum of other processes
(dominated by tt¯, W+jets) for which the shape and the relative normalisation are taken from MC simulation. The
free parameters in the fit are the overall normalisation (to the one in data) and the QCD multijet fraction. The QCD
multijet fraction estimated with this method is (23 ± 10)%.
An embedding method is used for estimating the background from true τ candidates. The method consists of
collecting a control sample of tt¯, single-top, and W+jets events with a muon in data, and replacing the detector
signature of this muon with that of a simulated τ lepton. The method has been validated in τ+jets events using
early ATLAS data [182]. The contribution of backgrounds with the true τ to the final mT distribution is estimated
from this distribution for embedded events. The normalisation is taken from data in the region 0 − 40 GeV of this
distribution, where both the QCD background and the signal contamination for the expected range of sensitivity
(BR(t → bH + ≈ 5%)) are low. Such a contamination is dealt with by subtracting the expected signal from the
observed data before normalising the shape to the region mT < 40 GeV. In the range 40 < mT < 300 GeV, there
are 21 ± 5 background events with true τ candidates expected where the uncertainty is due to the limited number of
events in the control sample and in the data in the region to which the shape is normalised to. In data, 26 events are
observed after subtracting the background predicted by the mis-identification probability methods and the QCD
102
CHAPTER 7. MSSM HIGGS BOSONS SEARCHES WITH τ LEPTON FINAL STATES
multijet estimate. Within statistical uncertainties, the background prediction and data agree well.
Systematic uncertainties
The main detector-related systematic uncertainties are mostly related to identification efficiencies and the energy/momentum resolution and scale of the physics objects described above. Uncertainties on trigger efficiency,
luminosity, cross sections and acceptance are also taken into account.
The main systematic uncertainties on electron-τ candidates mis-identification include the systematic uncertainty due to the subtraction of QCD multijet and electroweak backgrounds and dependence on the tag selection.
The total uncertainties on the scale factors (combining the statistical and systematic uncertainties of the measurement) are 24% in the barrel, 29% in the end-caps, and 100% in the transition region. Except for the end-cap
region, they are dominated by statistical uncertainties. In total, the expected contribution of events with electrons
mis-identified as τ candidates in the signal region is about 2 events which is about 5% of the expected background. Thus, reducing the current relatively large uncertainties would only lead to a minor improvement in the
H + sensitivity.
The dominant systematic uncertainties on mis-identification of jets as τ candidates include contamination of
the control sample with true τhad from Z → ττ and W → τν events, contamination of the control sample with
QCD multijet events with a larger fraction of gluon-initiated jets than γ-jet events and contamination of the control
sample by three-jet events. Also uncertainties connected to the assumption that the measurement of the misidentification probability on the probe object is uncorrelated from the selection of the tag object is evaluated.
Additionally, the statistical uncertainty of the measurement of the mis-identification probability enters as uncertainty on any application of the mis-identification probability. The total systematic uncertainty is about (15 − 24)%,
depending on pT and η. The systematic uncertainties on the mis-identification probability are propagated into the
background prediction for the baseline selection and enter the statistical evaluation as shape uncertainties.
The dominant systematic uncertainties on the QCD multijet background estimate are the uncertainties on the
assumption that the ETmiss shape is identical in the signal and control regions and on the tt¯ and W+jets shapes and
relative normalisation from Monte Carlo (dominated by uncertainties on the tt¯ cross section). The uncertainty on
the QCD multijet fraction is dominated by the statistical uncertainty of the data set on which the fit is performed.
The systematic uncertainties on embedding method include the effect of additional QCD multijet background
in the embedding and control sample selection, difference in the mT shape as a consequence of loosening the
selection with respect to the baseline selection, the impact of the incomplete treatment of the τ polarisation in
embedded events and the impact on the mT distribution due to the uncertainty on the τ energy scale. The statistical
uncertainty of the estimate is 8% due to the limited size of the control sample, and additionally 20% due to the
normalisation to data.
Results for the τhad +jets final state
In Table 7.3 the final results on the backgrounds estimation are summarised. The obtained mT distribution is shown
in Fig. 7.3. The total systematic uncertainty on the background prediction is about 30% but can reach up to 70% for
mT > 100 GeV. For the signal, the total systematic uncertainty on the yield is about 40% with a small dependence
on mH + .
The number of events with true τ candidates is estimated with the embedding method. The number of events
with jets mis-identified as τ candidates and with intrinsic ETmiss is taken from γ+jets control samples and with
electrons mis-identified as τ candidates from γ∗ /Z → ee control samples. The QCD multijet contribution is
estimated by taking its shape from a sideband region and fitting it to the data. The number of events with mT > 40
GeV is given which allows for a better comparison of data and the expectation as the estimate from the embedding
method is normalised to data in the range mT < 40 GeV. A good agreement between the estimated background
and the observed number of events is seen. Therefore, using data-driven background estimates, no statistically
significant excess of events is observed in data.
7.2. SEARCH FOR CHARGED HIGGS BOSONS IN tt¯ DECAYS
103
Table 7.3: Expected number of background events from data-driven estimates after all selection cuts, and with
an additional requirement of mT > 40 GeV and number of events observed in data. Only statistical
uncertainties are given [204].
mT > 40 GeV
true τ jets
21 ± 5
Events with/from
jet → τ mis-id e → τ mis-id
2.4 ± 0.7
1.9 ± 0.2
QCD multijet
12 ± 5
expected (sum)
37 ± 7
data
43
Events / 20 GeV
Exclusion limits are set on the branching ratio for t → bH + , and in the mH + − tan β plane, by rejecting the
signal hypothesis at the 95% confidence level applying the CLs procedure. A profile likelihood ratio [188] is used
with the mT distribution as the discriminating variable. The statistical analysis is based on a binned likelihood
function for the mT distribution. Systematic uncertainties in shape and normalisation are incorporated via nuisance
parameters. The final limits are based on the asymptotic distribution of the test statistic [188].
25
ATLAS Preliminary
20
Data 2011
e→τ misid
Jet→τ misid
True τ
Multi−jets
15
+
H (130), B=0.1
+
H +background
10
∫ L dt=1.03 fb
-1
5
0
0
50
100
150
200
250
300
mT [GeV]
Figure 7.3: The mT distribution after event selection. The observation in data, and the estimates from datadriven methods are compared. The distribution of the H + signal is given for a reference point in
parameter space corresponding to BR(t → bH + ) = 10%, thus the SM-like tt¯ background is reduced
correspondingly [204].
The resulting exclusion limit is shown in Figure 7.4 in terms of BR(t → H + b) × BR(H + → τ+ ν). Values of
the product of branching ratios, BR(t → bH + ) × BR(H + → τ+ ν), larger than (0.03 − 0.10) have been excluded in
scenario of the
the H + mass range (90 − 160) GeV. Figure 7.5 shows the upper limit in the context of the mmax
h
MSSM in the mH + -tan β plane. No exclusion limit is shown for charged Higgs boson masses close to 160 GeV as
no reliable calculations for BR(t → H + b) exist for tan β values in the range of interest. Interpreted in the context
scenario of the MSSM, values of tan β above (22 − 30) (depending on mH + ) can be excluded in the
of the mmax
h
mass range 90 GeV < mH ± < 140 GeV as shown in Figure 7.4. This result constitutes a significant improvement
compared to existing limits provided by the Tevatron experiments [71] over the whole investigated mass range, but
104
CHAPTER 7. MSSM HIGGS BOSONS SEARCHES WITH τ LEPTON FINAL STATES
in particular for charged Higgs boson masses close to the top quark mass.
+
+
95% CL on B( t → H b) × B(H → τν )
0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
ATLAS Preliminary
Data 2011
∫ L dt= 1.03 fb
-1
Expected Limit
Expected ± 1σ
Expected ± 2σ
Observed Limit
D0 Observed
90
100
110
120
130
140
150
160
mH+ [GeV]
tan β
Figure 7.4: Expected and observed 95% CL exclusion limits for the charged Higgs boson production from top
quark decays as a function of mH + in terms of BR(t → H + b) × BR(H + → τ+ ν) [204]. For comparison,
the best limit provided by the Tevatron experiments is shown [71].
mmax
h
60
ATLAS Preliminary
Expected Limit
Expected ± 1σ
Expected ± 2σ
Observed Limit
Observed, ± 1 σ
theor. uncertainties
50
40
30
20
10
0
Data 2011
90
100
110
120
130
∫ L dt= 1.03 fb
140
150
-1
160
mH+ [GeV]
Figure 7.5: Limit for the charged Higgs boson production from top quark decays in the mH + -tan β plane. Results
[204].
are shown for the MSSM scenario mmax
h
7.2.3 The one or two light leptons final state
This analysis is focused on the search for charged Higgs bosons in tt¯ events with one or two electrons or muons
in the final state. For the charged Higgs boson from t → bH + process decaying only into τν, a small increase in
the branching fraction for single-lepton and di-lepton decays of tt¯ pairs occurs, as the τ decays leptonically more
often than the W boson: B(H + → τlep + ν) ≃ 35% while B(W → ℓ + Nν) ≃ 25%. In addition, the search strategies
for charged Higgs bosons use variables discriminating between light leptons produced in τlep decays (from W
or charged Higgs bosons) and light leptons arising directly from W boson decays. The background processes
that enter the search for a charged Higgs boson in tt¯ events with one or two leptons include the production of
tt¯ → bb̄WW, single top, γ∗ /Z+jets, W+jets and di-boson events, as well as QCD multijet events.
7.2. SEARCH FOR CHARGED HIGGS BOSONS IN tt¯ DECAYS
105
Object and event selection
Selection for electrons, muons, jets and ETmiss is the same as described in Section 7.2.2. The only difference is ET
selection for electrons (ET > 15 GeV) and pT selection for muons (pT > 15 GeV).
In order to distinguish between leptons produced in τlep decays and leptons from direct decays of W bosons,
the following discriminating variables are constructed. The first one is cos θℓ∗ , a variable connected to the invariant
mass of a b-quark and a light lepton coming from the same top quark, mbℓ , defined as:
cos θℓ∗ =
2m2bℓ
m2top − m2W
−1≃
4 pb · pℓ
− 1 with pb · pℓ = 2Eb Eℓ (1 − cos θbℓ ) = 4Eb Eℓ sin2 (θbℓ /2),
m2top − m2W
(7.1)
where pb and pℓ are the four-momenta of the b-quark and of the lepton ℓ (in any reference frame, since cos θℓ∗
contains an invariant product) and θbℓ is the angle between them. Note that both m2b and m2ℓ are neglected, hence
m2bℓ ≃ 2 pb · pℓ . If a top quark decay is mediated through H + and if the H + is heavier than the W boson, the b-quark
usually has a smaller momentum than in the case of a W-mediated top quark decay. Also, a light lepton ℓ arising
from a τ decay is likely to have a smaller momentum than a lepton coming directly from a real W boson. As a
result, the presence of a charged Higgs boson in a leptonic top quark decay strongly reduces the invariant product
pb · pℓ , leading to cos θℓ∗ values mostly close to −1.
A second discriminating variable is the charged Higgs boson transverse mass [205], mTH , obtained by fulfilling
the constraint (pmiss + pℓ + pb )2 = m2top on lepton+jets tt¯ events, with more than one neutrino accounting for missing
momentum and its transverse component ETmiss :
(mTH )2 =
q
b
2
m2top + (plT + pbT + pmiss
T ) − pT
2
2
− plT + ETmiss .
(7.2)
By construction, mTH gives an event-by-event lower bound on the mass of the charged (W or Higgs) boson produced
in the leptonic top quark decay.
In di-lepton tt¯ events, the final state includes two leptons and missing energy, making its full reconstruction
H , is computed by the
more complicated. In that case the generalised charged Higgs boson transverse mass, mT2
numerical maximisation of
H
mT2
= max [mTH (pTH )],
(7.3)
{constraints}
where
2 2
2 q
mTH (pTH ) =
m2top + (pTH + pbT )2 − pbT − pTH
(7.4)
and constraints stands for a set of constraints on masses of two top quarks, mass of W boson, ETmiss and momenta
of neutrinos. It leaves two free parameters over which the charged boson Higgs mass is maximised.
H are larger than the true charged Higgs boson mass m + and smaller than
The transverse masses mTH and mT2
H
the top quark mass used in the constraints, mtop . Therefore, they can serve as discriminants between top quark
decays mediated by a W or charged Higgs boson, based on their different masses.
Event selection for single-lepton events In order to select single-lepton tt¯ events the following cuts are applied.
Exactly one trigger-matched electron with ET > 25 GeV or muon with pT > 20 GeV is required. Only events
with at least four jets with pT > 20 GeV and |η| < 2.5, including exactly two b-tagged jets are accepted. To select
events with a large ETmiss while rejecting those in which the latter arises mostly from wrongly reconstructed leptons
(i.e. where the azimuthal angle φℓ,Emiss between the lepton and ETmiss is small), it is required that:
T
ETmiss > 40 GeV
if |φℓ,Emiss | ≥ π/6 rad,
T
ETmiss × | sin(φℓ,Emiss )| > 20 GeV if |φℓ,Emiss | < π/6 rad.
T
T
CHAPTER 7. MSSM HIGGS BOSONS SEARCHES WITH τ LEPTON FINAL STATES
106
Table 7.4: Number of selected events for the simulated SM processes in the single-lepton channel (here, the fitted
value of 165.1 pb is used for σbbWW ) compared to that observed in data. The expected number of events
for H + of mass 130 GeV is also given [205].
tt¯
(bbWW)
3081
Single
top quark
88
W+jets
Z+jets
Di-boson
QCD
85
5.2
2.0
56
P
SM
Data
3317
3421
130 GeV H +
B(t → bH + ) = 10%
190
The iteration over all selected jets is performed and the combination of one b-jet and two light-quark jets ( j)
minimising:
(m j jb − mtop )2 (m j j − mW )2
,
(7.5)
+
χ2 =
σ2top
σ2W
is chosen in order to assign correctly jets and b-jets to the W and top decays. σtop and σW are the assumed
mass widths of the reconstructed top quark and W boson, as estimated from correctly-identified combinations in
simulated tt¯ events. The corresponding assignment efficiency is 74%. At this stage, events are removed if χ2 > 5.
Events having a second electron with ET > 15 GeV or muon with pT > 15 GeV are also removed.
Table 7.4 shows the number of selected events of the SM processes and tt¯ events with at least one decay
t → bH + , assuming mH + = 130 GeV and a cross section of 38.7 pb. As expected, events surviving the selection
cuts are mainly single-lepton tt¯ events. The value of 165.1 pb is used for σbbWW , as obtained when setting the
exclusion limit for that mass point, and B(t → bH + ) = 10%. It is obtained from the control region enriched in
tt¯ → bb̄WW events, defined by requiring −0.2 < cos θℓ∗ < 1.
Figure 7.6 (a) shows the cos θℓ∗ distribution obtained by using the charged lepton and the associated b-jet. A
signal enriched region with tt¯ → bb̄H + W and tt¯ → bb̄H + H − events is selected by requiring cos θℓ∗ < −0.6, as
indicated by the arrow. Also, in order to enhance decays of charged (W or Higgs) bosons via τlep , the cut mW
T <
60 GeV is applied. In a such defined signal region, the transverse mass mTH is used as a discriminating variable to
search for charged Higgs bosons, as shown in Figure 7.6 (b). The data agree well with the SM expectations and
neither an excess of events nor a significant deformation of the mTH distribution is observed.
Event selection for di-lepton events In order to select di-lepton tt¯ events the following cuts are applied. Exactly two oppositely charged leptons, including at least one matched to the single-lepton trigger, electron with
ET > 25 GeV or muon with pT > 20 GeV, are required. An event is selected if at least two jets with pT > 20 GeV
and |η| < 2.5, including exactly two b-tagged jets are present. For ee and µµ events, the di-lepton invariant mass
mℓℓ must be larger than 15 GeV and must satisfy |mℓℓ − mZ | > 10 GeV (i.e. Z veto), together with ETmiss > 40 GeV.
For eµ events, the scalar sum of the transverse energies of the two leptons and all selected jets must satisfy
P
ET > 130 GeV.
There is a four-fold ambiguity in assigning the two leptons and the two b-jets to their parents. In the first stage,
the events which have a clearly incorrect pairing: cos θℓ∗ > 1 for either of the two ℓ-b pairs are rejected. For events
with cos θℓ∗ < 1 for all pairings, the two ℓ-b pairs that minimise the sum of the distances ∆R(ℓ, b)pair 1 +∆R(ℓ, b)pair 2
in the η-φ plane are chosen. In simulated tt¯ events, the assignment efficiency is 66%. The particles of the ℓ-b pair
with the smallest cos θℓ∗ value are then assigned to the “H + side” and its partner pair to the “W side”. In simulated
events with a 130 GeV charged Higgs boson, this second assignment has an efficiency of 62%. The events for
H does not converge are discarded.
which the numerical computation of mT2
Table 7.5 shows number of events surviving the selection cuts. As expected, surviving background events are
mainly tt¯ events. The expected number of events for the Monte Carlo tt¯ sample with at least one t → bH + decay is
also shown in the last column, assuming mH + = 130 GeV and a cross section of 35.3 pb. It corresponds to the fitted
7.2. SEARCH FOR CHARGED HIGGS BOSONS IN tt¯ DECAYS
∫Ldt = 1.03 fb
-1
ATLAS Preliminary
1200
mH+ = 130 GeV
+
Br(t
→ bH ) = 10%
1000
800
600
400
Events / 10 GeV
Events / 0.2
1400
+
tt (with H )
+ tt (W W )
Single top
Z + jets
W + jets
Diboson
QCD
Data 2011
120
∫
-1
ATLAS Preliminary Ldt = 1.03 fb
100
+
tt (with H ) mH+ = 130 GeV
+
+ tt (W W ) Br(t → bH ) = 10%
Single top
Z + jets
W + jets
Diboson
QCD
Data 2011
80
60
40
20
200
0
-1
107
-0.5
0
0.5
0
20 40 60 80 100 120 140 160 180
mHT [GeV]
1
cosθ*
(a)
(b)
Figure 7.6: Reconstruction of cos θl∗ (a) in the single-lepton events and of the transverse mass mTH (b) when
cos θl∗ < −0.6 and mW
T < 60 GeV. The fitted value of 165.1 pb is used for σbbWW and the hatched
area shows the systematic uncertainties for the SM backgrounds. The grey histogram shows the predicted contribution of events with a 130 GeV charged Higgs boson, assuming B(t → bH + ) = 10% and
B(H + → τν) = 1 [205].
Table 7.5: Number of selected MC events in the di-lepton analysis (here, a fitted value of 150.4 pb is used
for σbbWW ) compared to that observed in data and expected number of events for H + of mass
130 GeV [205].
tt¯
(bbWW)
864
Single
top quark
18
Z+jets
Di-boson
1.5
0.3
QCD and
W+jets
40
P
SM
924
Data
992
130 GeV H +
B(t → bH + ) = 10%
115
value of 150.4 pb for σbbWW (as obtained when setting the exclusion limit for that mass point) and B(t → bH + ) =
10%. Here, the control region enriched with tt¯ → bb̄WW events is defined by requiring −0.4 < cos θl∗ < 1. In this
final state, a downward fluctuation of data in the control region yields fitted values of σbbWW slightly smaller than
the SM prediction.
In Figure 7.7 (a) the cos θl∗ distribution on the “H + side” is shown. A signal region enriched with tt¯ → bb̄H + W
and tt¯ → bb̄H + H − events is selected by requiring cos θl∗ < −0.6 on the “H + side”, as indicated by the arrow. For
H is used as a discriminating variable
the events found in this signal region, the generalised transverse mass mT2
to search for charged Higgs bosons, as shown in Figure 7.7 (b). Neither an excess of events nor a significant
H distribution is observed.
deformation of the mT2
Estimation of background with mis-identified leptons
The backgrounds with mis-identified leptons come from non-isolated leptons, arising from the semileptonic decay
of heavy quarks, from the decay-in-flight of a π± or K-meson and, in the case of fake electron objects, from the
Events / 0.2
600
∫
-1
ATLAS Preliminary Ldt = 1.03 fb
500
mH+ = 130 GeV
+
Br(t → bH ) = 10%
400
300
200
+
tt (with H )
+ tt (W W )
Single top
Z + jets
Diboson
QCD & W
Data 2011
250
∫
-1
ATLAS Preliminary Ldt = 1.03 fb
200
150
100
+
tt (with H ) mH+ = 130 GeV
+
+ tt (W W ) Br(t → bH ) = 10%
Single top
Z + jets
Diboson
QCD & W
Data 2011
50
100
0
-1
Events / 10 GeV
CHAPTER 7. MSSM HIGGS BOSONS SEARCHES WITH τ LEPTON FINAL STATES
108
-0.5
0
(a)
0.5
1
+
cosθ*, H side
0
40 60 80 100 120 140 160 180 200
mHT2 [GeV]
(b)
Figure 7.7: Reconstruction of cos θl∗ on the “H + side” of the di-lepton events (a) and of the generalised transverse
H when cos θ∗ < −0.6 (b). A fitted value of 150.4 pb is used for σ
mass mT2
bbWW and the striped area
l
shows the systematic uncertainties for the SM backgrounds. The grey histogram shows the predicted
contribution of events with a 130 GeV charged Higgs boson, assuming B(t → bH + ) = 10% and
B(H + → τν) = 1 [205].
reconstruction of a π0 , photon conversion and shower fluctuations. All leptons coming from such mechanisms are
referred to as fake leptons, as opposed to true isolated leptons (e.g. from the decay of W and Z bosons) which are
referred to as real leptons. In the case of the single-lepton final state, fake leptons originate from QCD multijet
events, in which a jet is mis-identified as a lepton. In the di-lepton final state, fake leptons can originate from QCD
multijet events and W(→ ℓν) + jets. The background due to fake leptons is estimated from data. For this purpose,
the two data samples are defined, differing only in the lepton identification criteria. The first sample contains
mostly events with real leptons and is referred to as the tight sample. The second one, obtained by loosening the
lepton isolation requirements, contains mostly events with fake leptons and is referred to as the loose sample. In
case of di-lepton channel, due to the presence of two leptons in the event, one of the leptons is required to pass the
tight selection criteria, while the other lepton is required to pass the loose selection criteria in the loose sample, or
the tight selection criteria in the tight sample.
The number of events containing fake lepton can be estimated from those tight and loose samples using the
rates for a real or fake lepton to be identified as a tight lepton [205]. The measurement of these rates is derived
using a tag-and-probe method in data Z → ℓℓ events with a di-lepton invariant mass in the range 86–96 GeV, where
one lepton is required to fulfil the tight selection criteria. The rate at which the other lepton passes the same tight
selection criteria defines a rate for a real lepton to pass the tight identification criteria. On the other hand, a control
sample with fake leptons is selected by considering data events with exactly one lepton passing the loose criteria.
To select events dominated by QCD processes, ETmiss is required to be between 5 and 20 GeV. After subtraction of
other SM processes with true leptons, the rate at which a loose lepton passes tight selection criteria defines the fake
rate for a fake lepton to pass the tight identification criteria. In the final parametrisation of the rates, any significant
dependence on kinematical or topological observables such as the transverse momentum and pseudorapidity of the
lepton, the jet multiplicity, the number of b-tagged jets, etc, are taken into account.
7.2. SEARCH FOR CHARGED HIGGS BOSONS IN tt¯ DECAYS
109
Systematic uncertainties
As for τhad +jets final state, the main detector-related systematic uncertainties are due to identification efficiencies
and the energy/momentum resolution and scale of the physics objects used in the analysis. Uncertainties on trigger
efficiency, luminosity, cross sections and acceptance are also taken into account.
In the single-lepton channel, the W+jets background is not precisely predicted, especially after the b-tagging
requirement. Hence, a factor 2 up and down normalisation uncertainty is assigned to the Monte Carlo W+jets
background sample.
In the data-driven methods used to identify events with fake leptons, the main systematic uncertainties arise
from the control region selection (the fake rates are calculated in a control region dominated by gluon-initiated
events, but are later used in a data sample with a higher fraction of quark-initiated events) and from the Monte
Carlo samples used for the subtraction of real leptons in the determination of the fake efficiencies, which are
sensitive to the dominant detector-related systematic uncertainties.
Limits on the Branching Ratio of t → bH +
Assuming B(H + → τν) = 1, upper limits are extracted on the branching ratio B(t → bH + ) as a function of the
charged Higgs boson mass. As already mentioned, in the presence of a charged Higgs boson one can not rely on
the predicted cross section for tt¯ decaying into the bbWW final state and it has to be estimated from data. Since
the signal and the tt¯ background are correlated, the event rate of the tt¯ → bb̄WW background is derived from the
measurement in the control region with −0.2 < cos θℓ∗ < 1 in the single-lepton analysis or −0.4 < cos θℓ∗ < 1 in
the di-lepton analysis, while the signal region corresponds to cos θℓ∗ < −0.6 (with the additional cut mW
T < 60 GeV
in the single-lepton case). Because tt¯ → bb̄H + W can be found in the control region1 , σbbWW is treated as a free
parameter when the upper limits on the branching fraction B(t → bH + ) are derived.
H distribution for di-lepton
A profile likelihood ratio is used with the mTH distribution for single lepton and mT2
final state as the discriminating variables. The statistical analysis is based on a binned likelihood functions of those
distributions. The limit itself is derived using the CLs method.
Figure 7.8 shows the 95% confidence level upper limits on the branching fraction B(t → bH + ), obtained
with the assumption that B(H + → τν) = 1. In the single-lepton channel, the fitted values of tt¯ cross section lie
between 0.99 and 1.03 times the SM prediction, with uncertainties in the range (2–3)%. In the di-lepton channel,
a downward fluctuation of data in the control region yields fitted values of tt¯ cross section between 0.78 and 1.06
times the SM prediction, with uncertainties in the range (5–25)%. When a charged Higgs boson mass of 160 GeV
is assumed, the b-jets coming from t → bH + are usually so soft that they are not likely to survive the pT cut at
20 GeV, leading to a significant loss of sensitivity for that mass point.
In the combined exclusion limit for both final states, the systematic uncertainties are assumed to be 100%
correlated. Although the expected limit improves after the combination, the observed combined limit on B(t →
bH + ) is actually found to be slightly worse when combining the two analyses than for the single-lepton channel
only, see Figure 7.9 and Table 7.6. The compatibility with background is measured by p0 -values, which range
between 26% and 50%. Hence, no indication of an H + -like excess is found. Assuming B(H + → τν) = 1, leads to
the upper limits on the branching fraction B(t → bH + ) between 5.2% and 14.1% for charged Higgs boson masses
in the range 90 GeV < mH + < 160 GeV. This result constitutes an improvement compared to the limits provided
by the Tevatron experiments. Except for the mass point at 160 GeV, obtained exclusion limits are also comparable
to (or somewhat higher than) those presented by CMS [209] and by τhad +jets analysis.
scenario of the
Finally, Figure 7.10 shows the upper limit in the mH + -tan β plane, in the context of the mmax
h
MSSM. No exclusion limit is shown for charged Higgs boson masses above 140 GeV since no reliable calculations
of B(t → bH + ) exist for tan β values in the range of interest. Also, since the assumption B(H + → τν) = 1 is not
1
Also tt¯ → bb̄H + H − events can contribute, but they are not considered in the following. Other searches for charged Higgs bosons,
such as the one reported in Ref. [204], indeed suggest that top quarks decay into bH + in less than 10% of the cases, hence the contribution
from tt¯ → bb̄H + H − remains very small. By not considering these events, the estimation of the upper limit on B(t → bH + ) is somewhat
conservative.
CHAPTER 7. MSSM HIGGS BOSONS SEARCHES WITH τ LEPTON FINAL STATES
0.4
0.35
ATLAS Preliminary
Data 2011 s = 7 TeV
Observed CLs
Expected
± 1σ
± 2σ
0.3
0.25
95% CL. upper bound on Br t → bH+
95% CL. upper bound on Br t → bH+
110
∫Ldt = 1.03 fb
-1
0.2
0.15
0.1
0.05
0
90
100
110
120
130
140
150
1
ATLAS Preliminary
0.8
Observed CLs
Expected
± 1σ
± 2σ
Data 2011 s = 7 TeV
∫Ldt = 1.03 fb
-1
0.6
0.4
0.2
0
160
90
100
110
120
mH+ [GeV]
130
140
150
160
mH+ [GeV]
(a)
(b)
95% CL. upper bound on Br t → bH+
Figure 7.8: Upper limits on B(t → bH + ) in the single-lepton (a) and di-lepton (b) channels, as a function of the
charged Higgs boson mass, obtained with the assumption that B(H + → τν) = 1. All systematic
uncertainties are included, as described in the text. Solid lines denote the observed 95% CL upper
limits, while dashed lines represent the expected limits. The outer edges of the green and yellow
shaded regions show the 1σ and 2σ error bands on the expected limits [205].
0.4
0.35
ATLAS Preliminary
Data 2011 s = 7 TeV
Observed CLs
Expected
± 1σ
± 2σ
0.3
0.25
∫Ldt = 1.03 fb
-1
0.2
0.15
0.1
0.05
0
90
100
110
120
130
140
150
160
mH+ [GeV]
Figure 7.9: Upper limits on B(t → bH + ) for the combined single-lepton and di-lepton channels, as a function of
the charged Higgs boson mass, obtained with the assumption that B(H + → τν) = 1 [205].
scenario of the MSSM, values
fulfilled at low tan β, no limits are derived in this region. In the context of the mmax
h
of tan β larger than (30–56) are excluded in the mass range 90 < mH + < 140 GeV.
7.3 Summary
This Chapter presents the first searches for the MSSM Higgs bosons by the ATLAS experiment, based on the
√
1.03-1.06 fb−1 of proton-proton collision data at s = 7 TeV. In all presented studies, observed number of events
is consistent with the total number of background events.
A search for neutral Higgs bosons decaying to pairs of τ leptons is described. Four different di-τ decay final
states are considered. Exclusion limits at the 95% confidence level are derived for A/H/h production in MSSM as
a function of tan β and mA , for the mmax
scenario. These results exclude regions of parameters space beyond the
h
existing limits from previous experiments and are similar to those recently obtained by the CMS Collaboration.
7.3. SUMMARY
111
Table 7.6: Observed (expected) 95% CL upper limits on B(t → bH + ) in the single-lepton and di-lepton channels, and after their combination, as a function of the charged Higgs boson mass, obtained with the
assumption that B(H + → τν) = 1 [205].
90
100
110
120
130
140
150
160
11.1%
(11.6%)
9.9%
(9.5%)
9.3%
(9.7%)
6.3%
(7.0%)
5.8%
(7.2%)
5.2%
(7.7%)
4.2%
(5.3%)
11.6%
(14.6%)
20.0%
(24.7%)
19.2%
(22.6%)
20.7%
(22.4%)
32.0%
(26.9%)
18.8%
(19.8%)
24.2%
(22.6%)
22.7%
(19.0%)
47.3%
(43.7%)
10.4%
(10.2%)
9.8%
(8.5%)
9.5%
(8.9%)
7.7%
(6.9%)
6.6%
(6.7%)
7.1%
(7.5%)
5.2%
(5.2%)
14.1%
(12.9%)
tan β
mH + (GeV)
95% CL observed
(expected) limit on
B(t → bH + ) for the
single-lepton channel
95% CL observed
(expected) limit on
B(t → bH + ) for the
di-lepton channel
95% CL observed
(expected) limit on
B(t → bH + ) for the
combined channels
60
ATLAS Preliminary
50
40
30
mmax
h
20
Data 2011
10
0
90
100
∫Ldt = 1.03 fb
-1
110
120
Expected Limit
Expected ± 1σ
Expected ± 2σ
Observed Limit
Observed, ± 1σ
theor. uncertainties
130
140
mH+ [GeV]
Figure 7.10: Limits for charged Higgs boson production from top quark decays in the mH + -tan β plane, in the
scenario of the MSSM, obtained with the assumption that B(H + → τν) = 1.
context of the mmax
h
The 1σ band around the observed limit (blue dashed lines) is obtained by adjusting the theoretical
uncertainties listed in the text and adding them linearly [205].
A search for charged Higgs bosons with masses in the range 90 − 160 GeV using tt¯ events with a leptonically
or hadronically decaying τ lepton in the final state is also described. Assuming B(H + → τν) = 1, the upper limits
on the branching fraction B(t → bH + ) between 5.2% and 14.1% for charged Higgs boson masses in the range
scenario of the MSSM, values of tan β larger than (30–56)
90 < mH + < 160 GeV are set. In the context of the mmax
h
are excluded in the mass range 90 < mH + < 140 GeV Those results constitute an improvement compared to the
limits provided by the Tevatron experiments.
The most recent results for the neutral MSSM Higgs searches in the ATLAS experiment corresponding to the
luminosity of 4.7−4.8 fb−1 [210] tightened allowed phase space even more. The most recent results for the charged
√
Higgs searches [211] are based on 4.6 fb−1 of proton-proton collision data at s = 7 TeV. With respect to the early
112
CHAPTER 7. MSSM HIGGS BOSONS SEARCHES WITH τ LEPTON FINAL STATES
results presented in this Chapter, the upper limits on the branching fraction B(t → bH + ), assuming B(H + → τν) =
1, are narrowed to 1% and 7.5% for charged Higgs boson masses in the range 90 < mH + < 160 GeV. Interpreted
scenario of the MSSM, values of tan β larger than (14–28) can be excluded in the mass
in the context of the mmax
h
range 90 < mH + < 150 GeV.
In light of the recent observation of a Higgs-like boson at the LHC, there is still a considerable part of the
MSSM parameter space that is not excluded and is still compatible with the scenario that the recently discovered
boson corresponds to the lightest CP-even MSSM Higgs boson.
The studies of the dataset collected in 2012 with the centre-of-mass energy of 8 TeV are ongoing.
This is also the place to summarize my thoughts about the changes that have
occurred in elementary-particle physics in the past forty years. Most of the
changes have been very good: we know a tremendous amount more about
elementary particles; we have much more powerful and sensitive particle
detectors; we have much higher energy accelerators and colliders; and our
students are better trained. But some changes, I believe, are not so pleasant:
we have lost the freedom to move quickly into new experiments; almost
all experiments are large and complicated; usually experimenters have to
work in very large collaborations; and it is no longer possible for a particle
physicist to be a productive experimenter and at the same time be able to
make calculations from first principles in much of modern particle theory.
I do not see a way to reverse these unpleasant changes.
Martin L. Perl; Phys. perspect. 6 (2004) 401
8
Summary
This monograph summarises the first analyses of processes with τ leptons in the final state, performed with the data
√
collected by the ATLAS detector at LHC with proton-proton collisions at the centre-of-mass energy of s = 7 TeV
in 2010 and first few months of 2011. However, there is a long history behind those results.
The LHC accelerator was originally conceived in 1980’s and approved for construction by the CERN Council
in late 1994. In 1992 the ATLAS collaboration wrote a Letter of Intent in which the building of a general purpose
proton-proton detector for the LHC was proposed. Turning this ambitious scientific plans into reality proved to
be an extremely complex and long task. Physicists of the ATLAS collaboration, working only with Monte Carlo
simulations, were patiently waiting almost 20 years for real data to come. The last years before first collisions were
particularly difficult because of multiple delays in the date of the LHC start, the race for the Higgs boson with the
Tevatron and the infamous LHC accident in Autumn 2008.
Finally, in Autumn 2009, the LHC began operation and started probing completely new energy regimes. The
ATLAS experiment started to successfully collect real data. The last three years were quite successful for the field
of particle physics. Many known processes of the Standard Model were reproduced at the new, high centre-ofmass energies. The first results concerning New Physics processes were published in order to set new limits on
discovery potential. In addition, there is already a hint for the Higgs boson discovery, as a new boson with mass
of about (125-126) GeV was observed this Summer by both ATLAS and CMS collaborations.
With the first collision data, physics of τ leptons at hadron colliders entered a new era. After years of waiting,
we finally could see the first τ leptons decaying in the ATLAS detector. This monograph documents these first
observations.
As the first step, the ATLAS package for the reconstruction and identification of hadronically decaying τ
leptons was tested and optimised with data. The mis-identification probabilities for QCD multijets and electrons
to be reconstructed as τ candidates were measured with data using tag-and-probe methods. Also the first attempt
to estimate the τ signal efficiency from W → τν process was performed. The package for τ reconstruction and
identification was found to be robust and ready to be used in the first physics studies with τ leptons in final states.
With increasing statistics of data, the measurement of W → τν and Z → ττ cross sections was possible.
Although it was a rediscovery of well known processes, those measurements were done for the first time at the
centre-of-mass energy of 7 TeV. Furthermore, as W → τν and Z → ττ are important background processes
to Higgs boson(s) and New Physics searches, their production cross sections needed to be measured precisely.
Finally, they offered the first opportunity to study τ hadronic decays in detail. The measured cross sections agree
well with theory predictions and measurements by other experiments.
The first analyses of Higgs boson(s) searches with τ leptons in final states presented in this monograph cover
searches for both the SM and MSSM neutral Higgs boson(s) decaying into the ττ final state as well as MSSM
113
114
CHAPTER 8. SUMMARY
charged Higgs boson decays, H + → τν. No significant excess over the expected background is observed in any of
those studies. Nevertheless, even if performed on limited data statistics, they improved exclusion limits obtained
previously by the Tevatron experiment and paved the path to future, full statistics studies.
It has to be stressed that the H → ττ final state is particularly important for assessing properties of the new
recently found boson, and for checking if this new particle is the Standard Model Higgs boson. With this final state
we can check if the new boson couples to fermions and study its CP properties.
Presented studies represent only the very beginning of the ATLAS adventure with τ leptons. They open a
way for high statistics and more sophisticated analyses as, for example, the measurement of τ polarisation in
various production processes. Also, possible improvements in τ reconstruction and identification methods can
give better background rejection in almost all described final states with τhad decays. Those improvements can
include for example development of the reconstruction of sub-structure of τhad decays and also optimisation of the
τ reconstruction and identification for high pT .
All the great results obtained by the ATLAS collaboration and described in the presented monograph, as well as
all the following, high statistics studies, show that not all changes in the high particle physics are so unpleasant as
in pessimistic view of Marin Perl used as an opening quote above. The ATLAS collaboration, consisting of about
3000 physicists, is one of the largest collaborative efforts ever attempted in physics sciences. This community
proved that people from different countries and culture can work in harmony, share knowledge, perform very
complex analyses and in parallel enjoy their work a lot.
A
Appendix: τ+τ− mass reconstruction techniques
An accurate mass reconstruction of a τ+ τ− system is challenging due to the presence of multiple neutrinos in the
final state resulting in an ETmiss signature. Therefore, either partial reconstruction methods or approximations are
used to obtain information about the invariant mass of the τ+ τ− resonance. Four of them are commonly used in
the ATLAS experiment.
The simplest method is the so-called visible mass, mvis , defined as the invariant mass of visible τ decay products. The visible mass provides no direct link to the invariant mass of the resonance as the contributions of the
neutrino momenta are ignored.
The visible mass can be extended to the effective mass, meffective , by calculating the invariant mass of the visible
τ decay products and the ETmiss according to
q
(A.1)
meffective = (pτ+ + pτ− + pmiss )2 ,
where pτ+ and pτ− denote the four-vectors of the electron, the muon from τ decay or τ candidates, and the missing
momentum four-vector is defined as pmiss = (ETmiss , Exmiss , Eymiss , 0). This definition extends the visible mass with
information on the neutrino momenta. However, it provides an approximation, since the ETmiss measurement is
sensitive only to the sum of all neutrino transverse momenta which contains large cancellations. Additionally, it is
based on the assumption that ETmiss only accounts for neutrinos from the two τhad decays. This hypothesis ignores
possible contributions from detector effects and simultaneous proton-proton interactions.
The third technique, the collinear approximation method [212] makes use of the large boost of the τ leptons
and assumes that the neutrinos are produced along the direction of the visible τ lepton decay products (i.e. φν ∼ φvis
and θν ∼ θvis ). The second assumption is that ETmiss in the event is due only to undetected neutrinos of the τ decay.
In this case, the total invisible momentum carried away by neutrinos of each τ decay can be estimated by solving
two equations:
E miss
= pmiss1 sin θvis1 cos φvis1 + pmiss2 sin θvis2 cos φvis2 ,
x
(A.2)
Eymiss
(A.3)
= pmiss1 sin θvis1 sin φvis1 + pmiss2 sin θvis2 sin φvis2 ,
where E miss
and Eymiss are the x− and y−components of the ETmiss vector, pmiss1 and pmiss2 are the combined invisible
x
momenta (there can be two neutrinos in a τ decay) of each τ decay, and θvis1,2 and φvis1,2 are the polar and azimuthal
angles of the visible products of each τ decay. The invariant mass of the ττ system, mττ , is derived as:
mvis
,
mττ = √
x1 x2
115
(A.4)
APPENDIX A. APPENDIX: τ+ τ− MASS RECONSTRUCTION TECHNIQUES
116
where mvis is the visible mass, and x1,2 are momentum fractions carried away by visible τ decay products with
momenta pvis1,2
pvis1,2
x1,2 =
.
(A.5)
(pvis1,2 + pmis1,2 )
Despite offering a fully reconstructed invariant mass of the ττ pairs, the collinear approximation still have significant limitations. It can give a reasonable mass solution only for events where the ττ system is boosted and the
visible τ decay products are not back-to-back in the plane transverse to the beam line. This method is also sensitive
to the ETmiss resolution.
The last technique was introduced in Ref. [213] and is referred to as the Missing Mass Calculator (MMC).
Conceptually, the MMC is a more sophisticated version of the collinear approximation method, not assuming a
strict collinearity of the visible and invisible τ decay products. The only assumption is that there are no other
neutrinos in the even except for those from the τ lepton decays. For each di-τ event, the MMC solves a system of
four equations:
E miss
= pmiss1 sin θmiss1 cos φmiss1 + pmiss2 sin θmiss2 cos φmiss2 ,
x
(A.6)
Eymiss
(A.7)
Mτ2
= pmiss1 sin θmiss1 sin φmiss1 + pmiss2 sin θmiss2 sin φmiss2 ,
q
q
= m2miss1 + m2vis1 + 2 p2vis1 + m2vis1 p2miss1 + m2miss1 ,
(A.8)
Mτ2
−2pvis1 pmiss1 cos ∆θvm1 ,
q
q
= m2miss2 + m2vis2 + 2 p2vis2 + m2vis2 p2miss2 + m2miss2 ,
−2pvis2 pmiss2 cos ∆θvm2 ,
(A.9)
and Eymiss are the x- and y-components of the ETmiss vector, pvis1,2 , mvis1,2 , θvis1,2 , φvis1,2 are the momenwhere E miss
x
tum, the invariant mass, the polar and the azimuthal angle of the visible τ decay products, and Mτ =1.777 GeV is
the τ lepton mass. The other quantities are unknown, namely the combined momenta pmiss1,2 of the neutrino (or
neutrinos) for each of the two decaying τ leptons and the invariant mass of the neutrino(s) in the τ decay, mmiss1,2 .
Finally, ∆θvm1,2 is the angle between the vectors pmiss1,2 and pvis1,2 for each of the two τ leptons, and it can be
expressed in terms of other variables. The number of unknowns exceeds the number of constraints and thus the
system is solved for a grid of points in the (∆φ1 , ∆φ2 ) parameter space, where ∆φi is the difference between the
azimuthal angles of the visible and invisible τ decay products. To determine the best estimate for the di-τ invariant
mass in a given event, the mττ distribution from all scanned points in the grid are produced. At each scanned
point, ∆R between the momentum vector of the visible τ decay products and the neutrino momentum vector is
calculated and the obtained di-τ mass is weighted by a corresponding probability density function. The position
for a given event. The MMC
of the maximum of the obtained mττ distribution is used as the final estimator mMMC
ττ
is becoming more and more popular in di-τ searches at ATLAS because of its superior performance.
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