Search for Drell Yan in sqrt(s)=41.6 GeV p-N Collisions at HERA-b

Search for Drell Yan in sqrt(s)=41.6 GeV p-N Collisions at HERA-b
Dissertation
submitted to the
Combined Faculties for the Natural Sciences and for
Mathematics
of the Ruperto-Carola University of Heidelberg, Germany
for the degree of
Doctor of Natural Sciences
presented by
Diplom-Physicist Jens Kessler
born in Dillingen/Saar
Oral examination: 31.10.2007
√ Search for Drell Yan
in s = 41.6 GeV p-N Collisions
at HERA-b
Referees:
Prof. Dr. Franz Eisele
Prof. Dr. Karl-Tasso Knöpfle
Abstract
In this thesis, the data taken with the HERA-b detector in the running period 2002/2003 is used to measure the cross section of the Drell Yan process
q q̄ → l+ l− , where quark and antiquark annihilate and produce a lepton pair.
HERA-b, a fixed target spectrometer, is one of the four experiments at the storage ring HERA at DESY. It uses the proton beam to produce collisions with wire
targets of different materials.
The main challenge of the thesis is to extract a Drell Yan signal from the dataset
without loosing too many events and to find a suitable background simulation
which can be subtracted from the kinematical distributions. For this purpose,
a Single Track Monte Carlo is generated to calculate event weights, which are
applied to the likesign dataset. This procedure is necessary since the detector
acceptance of HERA-b is dependant on the charges of the leptons.
After background subtraction and acceptance and luminosity corrections, differential cross sections of the Drell Yan process are plotted, for the first time in the
negative xF regime. These are compared to results from E772 and NA50. Also,
the dependance of the Drell Yan cross section on the mass number of the target
material is calculated.
Kurzfassung
Im Rahmen dieser Arbeit werden Daten, die am HERA-b Detektor gesammelt
wurden, benutzt um den Wirkungsquerschnitt des Drell Yan Prozesses q q̄ → l+ l−
zu messen. Bei diesem Prozess annihilieren Quark und Antiquark und bilden ein
Leptonenpaar. HERA-b ist ein Fixed-Target Experiment am Speicherring HERA
am DESY in Hamburg. Dort wird der Protonenstrahl von HERA mit Drähten
aus verschiedenen Materialien zur Kollision gebracht.
Die größte Herausforderung dieser Arbeit ist, aus den Daten das Drell Yan
Signal zu extrahieren, ohne zuviele Ereignisse zu verlieren. Ausserdem muss
eine geeignete Untergrundsimulation gefunden werden, um in den kinematischen Verteilungen den Untergrund abziehen zu können. Zu diesem Zweck werden Ereignisse mit Leptonenpaaren gleicher Ladung mit Gewichten versehen,
die aus einer speziellen Einzelspur-Monte Carlo Simulation gewonnen werden.
Diese Gewichte sind notwendig, da die Akzeptanz des HERA-b Detektors von
der Ladung der Leptonen abhängig ist.
Nach der Subtraktion des Untergrundes und der Korrektur auf Detektorakzeptanz und Luminosität werden differentielle Wirkungsquerschnitte gezeigt, die
zum ersten Mal im negativen xF Bereich gemessen wurden. Diese werden mit
Ergebnissen der Experimente E772 und NA50 verglichen. Ausserdem wird die
Abhängigkeit des Drell Yan Wirkungsquerschnitts von der Massenzahl des Materials, in dem die Wechselwirkung stattfindet, berechnet.
Contents
1 The HERA-b Experiment
1.1 Storage Ring . . . . . . . . . . . . . . .
1.2 HERA-b . . . . . . . . . . . . . . . . . .
1.2.1 Target . . . . . . . . . . . . . . .
1.2.2 Vertex Detector . . . . . . . . . .
1.2.3 Tracking . . . . . . . . . . . . . .
1.2.4 Ring Imaging Cherenkov Detector
1.2.5 Electromagnetic Calorimeter . . .
1.2.6 Muon System . . . . . . . . . . .
1.2.7 Trigger . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2 Drell Yan Theory
2.1 The Drell Yan Process . . . . . . . . . . . .
2.2 Quark Parton Model and Pertubative QCD
2.3 Angular Distributions . . . . . . . . . . . . .
2.4 Violation of the Lam Tung Relation . . . . .
2.4.1 Higher Twist Contributions . . . . .
2.4.2 Spin and pt Correlations of Quarks .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
7
7
8
10
11
11
13
13
14
17
.
.
.
.
.
.
19
19
20
24
25
29
30
3 Data Selection & Background Subtraction
3.1 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Event Mixing to Simulate Background . . . . . . . . . . . . . . .
3.3 Likesign Data as Background . . . . . . . . . . . . . . . . . . . .
3.3.1 Acceptance Differences between Likesign and Unlikesign Data
3.3.2 Corrections for the Acceptance Difference
of Opposite- and Likesign Data . . . . . . . . . . . . . . .
3.3.3 Single Track Monte Carlo to calculate Acceptance Correction Factors . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Reweighting of Likesign Data to the Acceptance of the Opposite sign Background . . . . . . . . . . . . . . . . . . . .
3.3.5 Crosscheck of Acceptance Reweighting Method . . . . . .
3.4 Simulation of the Drell Yan Process . . . . . . . . . . . . . . . . .
3.5 Optimization of Event Selection . . . . . . . . . . . . . . . . . . .
5
33
35
36
39
39
45
46
52
56
60
65
6
CONTENTS
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
65
70
73
75
76
4 Determination of Cross Sections
4.1 Luminosity Determination . . . . . . . . . . .
4.2 Υ(1S) Cross Section . . . . . . . . . . . . . .
4.3 Detector Acceptances . . . . . . . . . . . . . .
4.4 Acceptance corrected Kinematic Distributions
4.5 Systematic Checks of the Mass Distribution .
4.6 Angular Distributions . . . . . . . . . . . . . .
4.7 Comparisons with other Experiments . . . . .
4.7.1 E772 . . . . . . . . . . . . . . . . . . .
4.7.2 NA50 . . . . . . . . . . . . . . . . . .
4.8 Systematic effects . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
79
79
84
87
89
93
98
100
100
102
104
3.6
3.5.1 Consecutive Kinematic Cuts
3.5.2 Further Geometrical Cuts .
3.5.3 Cut on Event Likelihood . .
3.5.4 Final Data Sample . . . . .
Electron Data . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
5 Conclusions
107
List of figures
111
List of tables
113
Bibliography
115
Chapter 1
The HERA-b Experiment
1.1
Storage Ring
Figure 1.1: Overview of the HERA accelerator complex. The left
side shows HERA with the four experiments, the right side shows
an enlarged view of the PETRA preaccelerator and the injection
points into HERA ([Des00]).
The storage ring HERA (Hadron-Elektron Ringanlage – hadron electron ring
facility) is an electron proton collider at DESY (Deutsches Elektronen Synchrotron – german electron syncrotron) in Hamburg. A schematic view is shown
in Fig. 1.1. HERA consists of two separate rings sharing a tunnel measuring
6.3 km in circumference, one for protons and one for electrons or positrons. Protons are accelerated to 920 GeV, electrons in the opposite direction to 27.5 GeV.
7
8
CHAPTER 1. THE HERA-B EXPERIMENT
The two beams are brought to collision at two points along the accelerator. At
these points, the two largest experiments, H1 and ZEUS are situated. Both use
the e-p collisions to measure the proton structure functions via deep inelastic
scattering of the electrons. The HERA-b experiment is located in Hall West and
utilizes the proton beam only, while the fourth experiment at HERA, HERMES
only uses the electron beam which is polarized before reaching it.
The proton beam is divided into bunches of 30 cm length. The circumference
of the storage ring can accomodate 220 of such bunches. The time between two
bunches crossing the interaction region is 96 ns. Only 180 bunches are filled with
protons, as the preaccelerator PETRA (Positron-Elektron-Tandem-Ring-Anlage
– Positron Electron Tandem Ring Facility) can only contain 60 bunches at a time.
The other 40 bunches remain empty.
1.2
HERA-b
The HERA-b detector is one of the four experiments at HERA. Unlike the experiments H1 and ZEUS which examine electron proton collisions, HERA-b is
a fixed target experiment where the proton beam is brought into collision with
wire targets of different materials. The original physics goal was to measure CP
violation in neutral B mesons via the “golden decay” channel, where a neutral B
meson decays into J/ψ and K0S ([Abt94]).
A schematic view of the detector is given in Fig. 1.2. In the picture, the protons
enter the detector from the right. The first component interacting with the proton beam is the wire target. The silicon strip vertex detector (VDS) shares the
vacuum vessel with the wire target. Behind the VDS, the tracking system starts
which consists of an Inner Tracker (ITR) and an Outer Tracker (OTR). After the
first tracking station, a magnet with a field strength of 0.85 T and a horizontal
deflection plane is situated. At the far end of the tracking system, a Ring Imaging
Cherenkov detector (RICH) and an electromagnetic calorimeter (ECAL) provide
particle identification. Behind the last tracking station follows the muon system,
consisting of detector stations and layers of absorbing material.
The coordinate system of HERA-b has the z axis pointing in direction of the proton beam, the y axis up and the x axis to the left, to the center of the storage ring.
1.2. HERA-B
Figure 1.2: Schematic overview of the detector ([Spe04]). The top
picture shows a view from above the detector, the bottom picture
from the side. The detector components and tracking stations are
labelled.
9
10
1.2.1
CHAPTER 1. THE HERA-B EXPERIMENT
Target
The wire target system consists of two stations with four wires each. Wires made
of different materials can be used in these stations. Carbon, Tungsten, Titanium,
Palladium and Aluminum wires were installed during the data taking period.
Only Carbon and Tungsten wires were inserted into the beam in lepton triggered
runs which were used in this analysis for a significant amount of time. The wires
are moved perpendicular to the beam by a target steering system. Charge integrators on each wire are used to measure the current interaction rate, which is
kept constant by the steering system. If the beam position changes during a run,
the interaction rate changes and the steering system adjusts the wire position
until the nominal interaction rate is restored. The target wires are only moved
into the outer halo of the proton beam in order not to disturb the beam to keep
it usable for the collision experiments. More than one wire can be used at a
time, which is important for target mass dependance studies. Fig. 1.3(a) shows
a schematic drawing of the vacuum vessel containing the vertex detector and the
target stations. In Fig. 1.3(b), the reconstructed primary vertex positions mea-
(a)
(b)
Figure 1.3: (a): Schematic view of the vertex detector and the target system ([Brä01]). Protons enter the system from the right. (b):
Reconstructed primary vertex positions during a special multiwire
run which used all eight target wires ([Mas00]).
sured during a special run using all eight wires are plotted. The position of the
eight wires can easily be distinguished.
1.2. HERA-B
1.2.2
11
Vertex Detector
The silicon strip based vertex detector shares a vacuum vessel with the wire target. It consists of eight superlayers of detectors which contain four modules each.
Two double sided microstrip detectors mounted orthogonally make up one module. The first seven superlayers are mounted on roman pots which can retract
the detectors from the beam during machine studies and proton injection. The
eighth superlayer is in front of the exit window of the vacuum vessel. With all
superlayers in their nominal position, the angular acceptance of the VDS extends
from 10 to 250 mrad.
Monte Carlo simulations have shown that the vertex resolution achieved by the
VDS is roughly 50 µm perpendicular to and 500 µm along the beam axis. These
values were confirmed in data taken in 2000. [Bau03] gives a value of 530 ± 40 µm
for the resolution along the beam axis in data.
1.2.3
Tracking
The tracking system is responsible for connecting hits in muon chambers, RICH
and ECAL to vertices found in the VDS. Also, particle momenta can be measured
in conjunction with the dipole magnet. Two separate detector systems make up
the tracking system. The Inner Tracker covers the inner part of the detector up
to a distance of about 30 cm to the beampipe, the Outer Tracker the rest of
the acceptance of 250 mrad in the horizontal plane and 160 mrad in the vertical. The tracking system consists of seven stations. One station (MS1/MC1) is
placed in front of the magnet, four (MS10/PC1 to MS13/PC4) between magnet
and RICH, and two (MS14/TC1 and MS15/TC2) between RICH and ECAL.
The names given in parentheses are the names of the Inner and Outer Tracker
modules in each station.
Inner Tracker
The Inner Tracker consists of MicroStrip Gaseous Chambers (MSGC). MSGCs
are a type of drift chamber, where both anodes and cathodes are in the form of
alternating strips of conductive material on a glass plate. A schematic view of
such a chamber is shown in Fig. 1.4. The ionization produced by charged particles crossing the chamber drifts to the glass plate. The charge is multiplied in
the field between anodes and cathodes. Extensive ageing tests have shown that
MSGCs of the size used in HERA-b (25 × 25 cm2 ) suffer from severe damage in
hadronic environments. Large gains are needed to reach an acceptable ratio of
signal to noise, which increases the danger of damage to the strip anodes by large
discharges caused by heavily ionizing particles. Thus, a gas electron multiplier
(GEM) foil was introduced which provides a second signal amplification step and
12
CHAPTER 1. THE HERA-B EXPERIMENT
reduces the gain factor needed at the microstrip plates.
During the shutdown 2000/2001, the ITR chambers were removed from the de-
Figure 1.4: Schematical representation of a GEM MSGC
([Bag02]). The main gas gain occurs on the MSGC plate at the
anode. By applying a second high voltage to the two sides of the
GEM foil, an additional source of gain is introduced which allows
the gain on the MSGC plate to be lowered. The drift cover is used
as a cathode and to seal the gas volume.
tector to upgrade the readout electronics of the chambers included in the trigger
chain. Unfortunately, during the reattachment of the electronics to the chambers a problem occured with the conducting glue used for the bonding. Not all
readout strips were connected to the electronics. In stations MS10, MS13 and
MS15, between 50 − 60% of the readout channels were not usable, in stations
MS11, MS12 and MS14, 18% of channels were dead. Station MS01 was relatively
uneffected, only 8% of the strips were not read out ([Gor03]).
Outer Tracker
The Outer Tracker is made up of small drift chambers with a hexagonal profile (“honeycomb”) of two diameters. The honeycomb profile, the construction
method and the cross section of a single and a double layer secton are illustrated
in Fig. 1.5. The inner chambers consist of drift volumes of 5 mm diameter, the
outer ones are 10 mm in diameter. Each drift volume contains a wire along the
main axis as the anode, while the hexagonal walls made out of conducting foil
function as cathode. Stereo layers1 provide position information in the direction
of the y axis, along the wires.
1
Stereo layers are detector layers rotated along the beam axis by ±5% with respect to the
vertical orientation of the standard chambers.
1.2. HERA-B
13
Figure 1.5: Illustration of the honeycomb structure used for the
Outer Tracker ([Otr02]). The top picture shows the construction
out of two layers of preshaped material, the lower sketch shows the
geometry of a single and a double layer.
1.2.4
Ring Imaging Cherenkov Detector
The RICH detector uses the Cherenkov effect to separate light particles (e.g.
pions and muons) from heavier ones (kaons, protons). Charged particles emit
photons at the Cherenkov angle θC = arccos(1/βn) when travelling through a
medium of refractive index n if their speed is larger than the speed of light in
the medium, or if β > 1/n. The RICH focuses these photons using a series
of spherical and planar mirrors onto a focal plane outside the acceptance of the
detector, where they are detected via photomultipliers. Photons coming from a
single particle form a ring in the focal plane.
Fig. 1.6(a) shows a cross section of the RICH detector. The mirrors and the path
of the Cherenkov photons are shown. Fig. 1.6(b) is a plot of the relation between
particle momentum and Cherenkov angle for several particle types. Pions, kaons
and protons are clearly separated up to a momentum of 40 GeV.
1.2.5
Electromagnetic Calorimeter
The electromagnetic calorimeter used at HERA-b is built using cells stacked in
Shashlik style. Layers of plastic scintillators and absorber plates are assembled in
sandwich fashion. The area covered by the ECAL is divided into three concentric
areas: outer, middle and inner. These areas are shown in Fig. 1.7(a). Cells in the
outer area are the largest at 11.18 × 11.18 cm2 . middle ECAL cells are smaller,
5.59 × 5.59 cm2 , while cells in the inner part, where the track density is highest,
14
CHAPTER 1. THE HERA-B EXPERIMENT
Photon
Detectors
Cere
hoto
ns
vP
nko
Particle
from target
Beampipe
Planar
Mirrors
Radiator C4 F10
Spherical
Mirrors
Photon
Detectors
1m
(a)
(b)
Figure 1.6: (a): Schematic view of the Ring Imaging Cherenkov
Detector. Protons enter the system from the right. (b): Cherenkov
angle of pions, kaons and protons depending on momentum. A clear
separation between the three particles is seen (both figures [Ari04]).
are 2.24 × 2.24 cm2 . Due to the difference in flux between outer and inner detector, different materials were used. Both outer and middle cells are built out of
lead absorber and standard plastic scintillators, while the cells in the inner part
consist of a radiation hard polystyrene based material and absorbers made out
of an tungsten iron nickel alloy. The scintillation photons created by the impact
of a charged particle are guided by wavelength shifter rods to photomultiplier
tubes behind the sandwich cells. Each cell has its own photomultiplier tube. A
schematic drawing of a cell is given in Fig. 1.7(b).
1.2.6
Muon System
The muon system consists of four stations. In front of the first three stations,
hadron absorbers made of iron are placed. There is only a small absorber between station three and four to increase the precision of the track measurement
and remove uncertainities induced by multiple scattering. Similarly to the tracking system, the muon system also consists of an inner and an outer part. The
inner detector in all stations consists of gas pixel chambers of size 9 × 9 × 30 mm3 .
Each station contains five wires oriented along the beam axis, a central anode
wire and four thicker potential wires.
1.2. HERA-B
15
(a)
(b)
Figure 1.7: (a): Schematic overview of the three detector regions
of the ECAL ([Bru02]. (b): Overview of a single detector cell of
the ECAL ([Har95]).
The outer muon detector part uses two different technologies. Each of the first
two stations (MU1 and MU2) consists of three layers of tube chambers. These
are built from closed cell proportional wire chambers. The last two stations use
pad chambers. These are similar to the tube chambers but are built from an aluminum profile open on one side, which is closed by a panel containing additional
cathode pads. These pads are used in the muon pretrigger. Since there is no
large absorber between the two stations, a coincidence between two pads can be
required to cause a pretrigger signal. A cutout schematic drawing of the detector
is shown in Fig. 1.8.
16
CHAPTER 1. THE HERA-B EXPERIMENT
Figure 1.8: Cutout illustration of the muon stations ([Hus05]).
The four stations consisting of inner pixel and outer tube/pad chambers and the three large iron/concrete absorbers in front of stations
MU1, MU2 and MU3 are shown.
1.2. HERA-B
1.2.7
17
Trigger
The trigger system at HERA-b has two methods of operation. The first one
is the Minimum Bias trigger mode which is an interaction trigger that discards
empty events without enriching any special physics states. The second one was
designed to trigger the decay products of the “golden decay” of the B meson.
These are lepton pairs produced by the decay of a J/ψ. Both triggers were used
at different times in the data taking period of 2002-2003, but only data taken
with the dilepton trigger is used in this analysis.
The dilepton trigger consists of several stages which reduce the event rate from
the maximum of 10.4 MHz down to the rate of 1 kHz at which events can be
written to the data storage system. For further information, see [Dam04].
Pretrigger
The pretrigger system is designed to find two tracks with large transverse momentum. The muon pretrigger uses data from the last two muon stations and
searches for coincidental pad hits in both stations which show a large pt . The
electron pretrigger looks for two ECAL clusters, again with sufficiently large pt .
If either pretrigger finds two candidates in an event, the information is passed on
to the First Level Trigger stage. The muon pretrigger suffers from a low overall efficiency of roughly 10%. The main contribution to this is the efficiency of
the muon pads, which is on average 40% when requiring two coincident hits in
stations MU3 and MU4. The efficiency of the muon pretrigger was studied in
[Hus05].
First Level Trigger (FLT)
The First Level Trigger is implemented by custom made electronic boards dedicated to a fast reconstruction of tracks starting with the pretrigger candidates.
Hits in the muon stations MU4, MU2 and MU1 and in the tracking stations TC2,
TC1, PC4 and PC1 are used, in that order. Starting out from the pretrigger message in either the muon system or the ECAL, the algorithm (similar to a Kalman
filter algorithm) follows the tracks iteratively from station to station by defining
regions of interest (RoI) in the next chamber based on the hit in the current
and all previous chambers. Hits in all stereo layers of the tracking stations are
required to improve track quality and reduce the event rate.
The FLT can be used in two modes, as a count trigger where the trigger decision
is based on the number of events surviving the FLT track criteria, or as a pair
trigger, where a minimum reconstructed mass of a track pair can be required.
During the data taking period of 2002/2003, the FLT was set to count trigger
mode with a single track as the requirement.
The data is transferred between the components of the FLT via optical links.
18
CHAPTER 1. THE HERA-B EXPERIMENT
These links suffered from irreparable problems, leading to spontaneous loss of
data (see [Sch01]). This inefficiency is implemented in the Monte Carlo simulations used at HERA-b by a detector map giving an FLT efficiency relative to the
Second Level Trigger.
Second Level Trigger (SLT)
The Second Level Trigger is a software trigger running on a PC farm of 240 CPUs.
It fully reconstructs two tracks based on the pretrigger seeds independantly of
the FLT. The reconstruction includes a track following through the magnet and
a vertexing step using information from the VDS. Track pairs with a vertex fit
with χ2 > 20 are discarded.
Third Level Trigger (TLT)
It was originally foreseen to implement a Third Level Trigger step which uses a
full reconstruction of the event to be able to trigger on additional tracks in an
event, e.g. single leptons from semileptonic decays of mesons. During the data
taking period of 2002/2003, this trigger was not used.
Fourth Level Trigger (4LT)
The Fourth Level Trigger consists of an online full reconstruction of events. Track
segments are built in VDS and the tracker and matched to full tracks. Information
from the muon system, ECAL and RICH are used for particle identification.
Finally, tracks are assigned to primary and secondary vertices.
Chapter 2
Drell Yan Theory
2.1
The Drell Yan Process
The invariant mass spectrum of dileptons above 2 GeV observed at hadronic
collisions consists of two parts: a series of sharp peaks and a continuum that drops
with increasing mass. The peaks are produced by the charmonium and bottonium
resonances (J/ψ, ψ 0 , Υ etc), while the continuum production of lepton pairs is
known as the Drell Yan process ([Dre70]). In hadronic collisions, it has been the
object of study for quite some time. Its basic reaction, the annihilation of quark
and antiquark into a virtual photon and the subsequent decay into lepton and
antilepton, q q̄ → γ ∗ → l+ l− is an ideal testing ground for pertubative QCD
and a tool for probing the parton distributions of hadrons, especially mesons.
µ
q
γ
*
µ
q
+
Figure 2.1: Feynman graph of the Drell Yan process at parton
level.
19
20
CHAPTER 2. DRELL YAN THEORY
2.2
Quark Parton Model and Pertubative QCD
The Drell Yan process is an example of a hard process at parton level. The
parton model was ([Fey69]) used first in explaining the deep inelastic electron
nucleon scattering. It describes a nucleon as consisting of constituents, the so
called partons, which were later identified as quarks. The basic assumption of
the model is that the typical time scale of an interaction between electron and
parton is much less than that of the binding effects inside the nucleon.
Drell and Yan were the first to use the parton model to explain lepton pair
production and to derive the Drell Yan cross section. Fig. 2.1 shows the Feynman
graph of the reaction. The cross section of this process in leading order is
4πα2 Q2q
·
,
(2.1)
3ŝ
N
where ŝ corresponds to the center-of-mass energy available in the process (ŝ =
(p1 + p2 )2 ), Qq to the charge of the quark flavor and N to a color factor giving the
probability that quark and antiquark have the same color charge (N = 3). ŝ is
related to the total center-of-mass energy s by ŝ = x1 x2 s, where x1 and x2 are the
momentum fraction of quark and antiquark inside the hadrons. This cross section
corresponds to that of the creation of quarks in electron positron annihilation.
The differential cross section as a function of the dilepton mass is
σ̂qq̄ =
4πα2 Q2q
dσ̂qq̄
=
·
· δ(ŝ − Mll2 ),
(2.2)
dMll
6Mll N
where Mll is the invariant mass of the lepton pair.
To find the cross section of the proton colliding with a nucleon of the target
wires, it is necessary to include the parton density functions fi/h (x), which give
the probability to find a parton i with momentum fraction x inside of a hadron
h. This separation between density functions and cross section of the subprocess
is the factorisation model ([Col89]), which is illustrated in Fig. 2.2. Convoluting
the parton cross section with the density functions then yields after summing,
over all possible flavors i and integrating over the momentum fractions x1 and x2
of the two quarks then yields:
XZ
σh1 h2 → l+ l− =
dx1 dx2 fq/h1 (x1 )fq̄/h2 (x2 )σ̂qq̄ → l+ l−
(2.3)
q
The corresponding differential cross section again as a function of the dilepton
mass Mll is given by:
Mll3 ·
dσ
1 4πα2
=
·
· τ · F(τ ),
dMll
2N
3
(2.4)
where
Z
F(τ ) =
!
1
dx1 dx2 δ(x1 x2 − τ )
0
X
q
Q2q (fq/h1 (x1 )fq̄/h2 (x2 ) + (q ↔ q̄) .
(2.5)
2.2. QUARK PARTON MODEL AND PERTUBATIVE QCD
21
fq (x 1)
µ
γ*
+
µ
fq (x 2)
Figure 2.2: Factorisation model of the Drell Yan Process. Quark
and antiquark out of two incident hadrons interact and annihilate,
the hadron remnants disappear along the beam axis.
In leading order the Drell Yan differential cross section Eq. (2.4) only depends on
the dimensionless variable τ = Mll2 /s, not on Mll or s individually. This scaling
behavior makes it possible to compare results measured at different center-ofmass energies.
However, contributions from higher order processes are not negligible. The Feynman graphs of the most important processes of order O(αs ) and O(αs2 ) are given
in Fig. 2.3. These include initial state radiation of gluons, a process alike to
Compton scattering in QED and gluon exchange between the incident quarks.
At energies attainable by current fixed target and collider experiments, these next
to leading order corrections are large, up to 50% of the total cross section in the
mass range covered by this thesis, 4 to 9 GeV. Fig. 2.4 shows a calculation of the
differential Drell Yan cross section in the mass range of 8 to 70 GeV in O(αs0 ),
O(αs1 ) and O(αs2 ). The difference is clearly visible.
22
CHAPTER 2. DRELL YAN THEORY
(a) Gluon Bremsstrahlung
(b) Compton like QCD processes
(c) Vertex correction
Figure 2.3: QCD corrections in leading (a, b) and next to leading
order (c) to the Drell Yan Process. Figures from [Gra01].
2.2. QUARK PARTON MODEL AND PERTUBATIVE QCD
Figure 2.4: Theoretical calculation of the differential Drell Yan
cross section including corrections of O(αs ) and O(αs2 ). Calculations by [Nee92].
23
24
2.3
CHAPTER 2. DRELL YAN THEORY
Angular Distributions
The large correction factors from higher order contributions discussed in Sec. 2.2
diminish the use of the integrated Drell Yan cross sections as tests of the parton
model. The angular distribution of the lepton pair is more useful for this.
In the parton model with massless quarks, the lepton pair is produced by the
decay of a transversely polarized virtual photon. The differential cross section is
then expected to be:
dσ
∝ 1 + cos2 θ,
(2.6)
dΩ
where θ is the polar angle of the positive lepton in the rest frame of the virtual
photon. There are several possible choices for a coordinate system in which the
virtual photon is at rest. In this thesis, the so called Collins Soper frame ([Col77])
will be used.
In the Collins Soper frame the virtual photon is at rest. It’s x−z plane is spanned
y
µ+
x
φCS
θ
CS
β
β
proton
z
Nucleon
µ−
Figure 2.5: Illustration of the Collins Soper reference frame and
of the angles θCS and φCS .
by the momentum vectors of proton and nucleon, which are not collinear if the
virtual photon has a nonzero transverse momentum. The z axis is defined to be
the bisector of the angle between incoming nucleon and inverse incoming proton.
The definition of the CS reference frame is illustrated in Fig. 2.5. The angle φCS is
defined as the angle between the xz plane and the plane spanned by the positive
muon and the z axis, the angle θCS as the angle between positive muon and z
axis.
The inclusion of the higher order processes given in the last section leads to a
2.4. VIOLATION OF THE LAM TUNG RELATION
25
cross section that not only depends on the polar, but also the azimuthal angle:
1 dσ
3 1
ν
2
2
=
(2.7)
1 + λ cos θ + µ sin 2θ cos φ + sin θ cos 2φ
σ dΩ
4π λ + 3
2
Here, φ is the azimuthal angle of the positive lepton. The three coefficients λ,
µ and ν are structure functions. While they are independant of the angles, they
may depend on other kinematic variables, such as the transverse momentum or
the mass of the virtual photon. The parameter µ is only relevant at energies where
contributions by the exchange of a Z boson instead of a photon are significant.
The other two coefficients are correlated via the Lam Tung relation ([Lam80]):
1 − λ − 2ν = 0
(2.8)
This relation is the analogon to the Callan Gross relation ([Cal69]), which relates
the structure functions F1 (x) and F2 (x) in deep inelastic scattering. Unlike the
Callan Gross relation though, the Lam Tung relation is unchanged by QCD corrections of first order. Even after the inclusion of higher order corrections it is
still approximately valid, but 1 − λ − 2ν is predicted to be slightly positive.
2.4
Violation of the Lam Tung Relation
Two experiments have performed measurements of the angular dependance of the
Drell Yan cross section in collisions of pion beams with fixed targets. These were
NA10 ([And84]), a fixed target experiment located at CERN and E615 ([Bii86]),
a Fermilab experiment. Both experiments reported a violation of the Lam Tung
relation in π−N collisions at large transverse momenta of the virtual photon. The
results of NA10 are given in Fig. 2.6, those of E615 in 2.7. Both measurements
clearly show an increasing value of ν at large transverse momenta, while λ stays
constant. This leads to a dependancy of 1 − λ − 2ν on pt which is a violation of
the Lam Tung relation. Interestingly both experiments give a negative value for
1−λ−2ν, the opposite of the prediction of higher order QCD. The measurements
of µ do not agree. While NA10 measured no dependance of µ on the transverse
momentum, E615 does see a correlation; at higher pt µ is measured to be positive
and large, up to 0.5.
More recently, the Fermilab experiment E866 ([Web02]) measured the angular
distributions of Drell Yan using an 800 GeV proton beam at a fixed target. The
results published in [Zhu06] show no violation of the Lam Tung relation and no
dependance of ν on the transverse momentum in p − N collisions. Fig. 2.8 shows
the three coefficients and the value 2ν − (1 − λ) as a function of the transverse
momentum of the virtual photon for the three experiments listed above. None of
the coefficients show a dependance on the transverse momentum in p − N data.
26
CHAPTER 2. DRELL YAN THEORY
Figure 2.6: Measurement of λ, µ and ν as a function of pt
of the muon pair and for three different beam energies at NA10
([Gua88]). The dashed lines show the QCD predictions including
terms of O(αs ). The discrepancy for ν between measurement and
prediction at large pt is distinctive.
2.4. VIOLATION OF THE LAM TUNG RELATION
Figure 2.7: Left plots: Measurement of λ, µ and ν as a function
of pt of the muon pair at E615 ([Con89]). Right plots: from the
measured values of λ and ν, the Lam Tung relation is plotted as
a function of the momentum fraction of the parton in the incident
pion xπ , mass and pt of the muon pair in three reference frames
(Gottfried Jackson, Collins Soper and u channel).
27
28
CHAPTER 2. DRELL YAN THEORY
Figure 2.8: Measurement of λ, µ and ν as a function of pt of the
virtual photon at E866, compared to the measurements of NA10 and
E615. While the latter show a deviation of the value 2ν − (1 − λ)
from zero, the measurement from E866 ([Zhu06]) is compatible with
zero.
2.4. VIOLATION OF THE LAM TUNG RELATION
29
Several theoretical models beyond conventional perturbative QCD have been
suggested to explain the violation seen in pion–nucleon collisions.
2.4.1
Higher Twist Contributions
Higher Twist Contributions to the Drell Yan cross section are caused by interactions of the annihilating quarks with spectator quarks prior to the collision by
gluon exchange. In [Bra94] this model is applied to the Drell Yan process. It is
found that the angular coefficients λ, µ and ν are still defined
(2.7) but
√ as2 in Eq.
2
are explicit functions of the kinematic variables xL = 2pt / s, pt /M and M 2 /s.
The prediction of the model strongly depends on the parton density function of
the incident pion, as can be seen in Fig. 2.9, where the predictions for different
parton density functions are compared with the data measured by E615.
Especially at high transverse momenta of the virtual photon, the model cannot
Figure 2.9: Comparison of the predictions of the Higher Twist
model to data measured by E615 ([Bra94]) as a function of pt of the
virtual photon. The four lines represent calculations using different
parton density functions of the incident pion. The model fails to
reproduce the violation of the Lam Tung relation measured by E615,
especially at high pt .
30
CHAPTER 2. DRELL YAN THEORY
reproduce the violation of the Lam Tung relation seen at π − N collisions. While
the dependance of λ and µ on pt is simulated, the values of ν disagree.
2.4.2
Spin and pt Correlations of Quarks
The underlying assumption of the Lam Tung relation is that the incident quarks
are not polarized if the corresponding hadrons are unpolarized. Two separate approaches suggest that this is not necessarily the case. The first approach published
in [Bra93] suggests that non perturbative vacuum fluctuations induce correlations
between the partons of the colliding hadrons via initial state interactions. It assumes a general two particle spin density matrix for the quark antiquark pair
before annihilation which contains a correlation term that connects the spins of
the two interacting quarks. It was shown that for a non zero correlation coefficient κ, the experimental observation of the violation of the Lam Tung relation
can be explained. Fig. 2.10 shows a calculation of the model prediction for the
dependance of the structure functions λ, µ and ν on the transverse momentum of
the virtual photon, once for a correlation coefficient κ = 0 and once with a non
zero value of κ fitted to the data.
The second approach ([Boe99]) suggests time reversal (T) odd distribution functions, which introduce non trivial spin and pt correlations between the quarks
even in unpolarized hadrons. This again leads to a non zero value of the correlation coefficient κ. A calculation of the pt dependance of the value of ν is shown in
Fig. 2.11. In [Boe05] it is suggested that a measurement using a different type of
beam than the pions used at E615 and NA10 would help to distinguish between
the two approaches, as while the vacuum fluctuations are independant of the flavor of the quarks, the distribution functions used in [Boe99] may well depend on
the flavor. For this, HERA-b and the proton beam of HERA was thought to be
an ideal testing ground.
The sensitivity of HERA-b to the Drell Yan process was investigated in [Gra01],
which estimated that 25,000 events would be needed to measure the angular distributions. This would correspond to a year of data taking with a good detector
performance. First extrapolations of the yield of Drell Yan events from the number of detected J/ψ show that the dataset of 2002/2003 only contains roughly
1,500 Drell Yan produced dimuons and the same number of events with dielectrons. Nevertheless an analysis searching for Drell Yan events was performed,
as the HERA-b detector is uniquely sensitive in the negative xF range and can
extend existing measurements into this region.
2.4. VIOLATION OF THE LAM TUNG RELATION
(a)
31
(b)
(c)
Figure 2.10: The dependance of the three structure functions λ, µ
and ν on the transverse momentum of the virtual photon ([Bra93]).
The dashed lines correspond to the prediction of the parton model
for κ = 0 and no quark polarization, the full lines to the prediction
with a non zero value of κ. The data points are from E615.
32
CHAPTER 2. DRELL YAN THEORY
Figure 2.11: Dependance of ν on the transverse momentum of the
virtual photon. Data from E615 and a calculation using a non zero
value of κ ([Boe99]) are shown.
Chapter 3
Data Selection and Background
Subtraction
The data used in this analysis has been taken at the HERA-b detector using the
dilepton trigger during the period from November 2002 to February 2003. After
this time, the accelerator was shut down for upgrades and repairs.
To extract the Drell Yan signal from the data, selection criteria have to be applied.
Choosing these cuts requires a good knowledge of signal and background distributions. While the Drell Yan signal is described by a Monte Carlo simulation, no
such simulation exists for the background. Monte Carlo studies ([Egb02]) have
shown that while it is possible to simulate the processes involved, the computer
time needed to generate a sufficient number of events is prohibitively large due
to the small phase space involved. To simulate one second of datataking with
full event reconstruction, a Pentium III processor would need about ten years of
CPU time at an interaction rate of 10 MHz. A dedicated Monte Carlo simulation
concentrating on pions and kaons decaying in flight can reduce the time needed
by a factor of four to five, which is still not enough. For this reason, other methods of background description have to be found.
The data runs used for this analysis have been selected by the charmonium analysis group for acceptable data quality ([Cha03]). In total, they consist of roughly
150 million events.
This analysis is based on the preselection of the dimuon group, which uses a
different analysis software. As a first step, the data available in the ARTE1 dst
format was converted into root files for use in the BEE2 analysis framework. The
BEE software has the advantage of smaller data files and useful routines, e.g. to
find vertices.
During this conversion the data was reduced by asking for a minimum of two
1
The Event Reconstruction and Analysis Tool ARTE is the main framework used to analyse
data and Monte Carlo events ([Alb95]).
2
The analysis framework BEE discards detector hit information contained in the ARTE files
and only keeps reconstructed tracks for faster processing ([Gle01])
33
34
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
PC1
y
(19.9/20.25)
1111111111111111111
0000000000000000000
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
(−19.9/−20.25)
MU3
x
y
(52.4/45.8)
1111111111
0000000000
0000000000
1111111111
0000000000
1111111111
0000000000
1111111111
(65.5/5.1)
000
111
0000000000
1111111111
000
111
0000000000
1111111111
000
111
0000000000
1111111111
000
111
0000000000
1111111111
000
111
0000000000
1111111111
000
111
0000000000
1111111111
(−52.4/−45.9)
000
111
000
111
000
111
000
111
000
111
000
111
000
111
x
(39.3/−117)
(a) Station PC1
(b) Station MU3
Figure 3.1: Fiducial cuts in the stations PC1 (a) and MU3 (b).
Tracks crossing the hatched regions are removed. The coordinates
of the corners of the removed areas are given in cm.
tracks triggered by the Second Level Trigger (SLT) with at least five hits in the
muon chambers and a muon likelihood of greater than 0.01 per event. Events
without at least two muons are not relevant for the analysis, neither are muon
track candidates with extremely low muon likelihood or too few hits in a muon
chamber.
Three fiducial cuts proposed in [Hus05] are applied to real and Monte Carlo data
to remove detector areas which are not described correctly by the simulation. One
cut is applied at the z position of station PC1 around the Inner Tracker area, the
other two at the z position of station MU3. They are shown in Fig. 3.1. The two
cuts around the beampipe area remove tracks in the transition region between
inner and outer tracker, which poses problems for the Monte Carlo simulation.
The second cut in station MU3 removes tracks in muon chamber 99, which also
shows inefficiencies which are not present in the simulation.
After clone removal3 and a cut on the minimum number of tracker hits per muon
trigger track of four hits, the dimuon sample consists of 3.1 million events. As
the muon trigger has no requirements concerning the muon charge, this sample
contains muon pairs with opposite and with equal charge, namely 1.8 million
unlikesign, 775,000 positive likesign and 605,000 negative likesign muon pairs.
Since the magnetic field inside the detector is oriented upwards, positive particles are deflected to the right (seen from the interaction point) while negative
particles are deflected to the left. Due to their track configuration, unlikesign
muon pairs travelling through the detector with the negative muon on the left
and the positive on the right are called “outbending”, as the magnet deflects both
muons away from each other. Likewise, µ+ µ− pairs with the opposite charge dis3
If a particle passing the silicon detector undergoes a hard scattering, it is possible that the
reconstruction algorithm assigns two tracks to this particle. The second track is called clone
and is flagged during reconstruction ([Kis99])
10
10
35
outbending: 7144 evts
inbending: 3589 evts
3
2
counts per 333 MeV
counts per 333 MeV
3.1. EVENT SELECTION
10
10
10
10
1
1
4
5
6
7
8
9
10 11 12
M µµ [GeV]
(a) unlikesign data
positive: 5133 evts
negative: 3799 evts
3
2
4
5
6
7
8
9
10 11 12
M µµ [GeV]
(b) likesign data
Figure 3.2: Invariant mass of muon pair data after preselection:
(a) unlikesign muon pairs, divided into inbending and outbending,
(b) likesign muon pairs, divided into positive and negative pairs.
tribution are called “inbending”.
The distribution of the dimuon mass is shown in Fig. 3.2, separated into the
four categories unlikesign out-/inbending and positive and negative likesign muon
pairs in the mass range above Mµµ = 4GeV. As one can see the number of events
in this mass range is much lower than the total number of muon pairs, as most
of them have a lower reconstructed invariant mass.
3.1
Event Selection
The background in the dimuon channel has two contributions:
• Combinatorical background consisting of pairings of unrelated particles.
These are muons from pions and kaons decaying in flight, prompt muons
from the vertex and other particles misidentified as muons (punch through,
high energy protons reaching the muon system), and
• muon pairs from decays of charmonium and upsilon.
While the latter can be eliminated by cuts on the invariant mass of the muon
pair, the first are spread over the whole mass spectrum, making their rejection
36
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
more difficult. Several cuts on kinematic variables have to be applied to reduce
this background.
The main difference between muon pairs produced by the Drell Yan process and
those from combinatorics is that the Drell Yan muons both come from the primary vertex4 , while muon tracks from decays in flight do not necessarily point
back to the primary vertex. This leads to different dependances of signal and
background on the distance of closest approach between the two muons, the distance of muon to primary vertex and the reduced χ2 of the track fit to hits in
the detector. These variables are therefore used to improve the ratio of signal to
background.
The limited number of events provided by HERA-b makes it impractical to choose
very hard cut values which would result in high purity but low efficiency. Softer
cuts result in a larger data sample with a lower signal to background ratio. The
background still remaining after the selection process distorts the angular and
kinematic distributions of the Drell Yan process. To remove this distortion, a
method of background subtraction in each of the plotted variables is necessary.
Both the cut optimization and the background subtraction require a simulation
of the combinatorical background. Previous analyses have used the method of
event mixing to generate a combinatorical background sample ([Abt06]).
3.2
Event Mixing to Simulate Background
Event mixing describes a method frequently used to simulate combinatorical
background. Combinatorical background consists of random combinations of unrelated tracks. As tracks from different events are by definition unrelated, an
obvious solution is to mix tracks (in this case muons) from different events into
a single one. The result is then a purely combinatorical sample of muon pairs.
As shown in Fig. 3.3, the muons generated by a a Drell Yan process carry a
significant part of the total momentum of 920 GeV in an event. Unfortunately,
event mixing does not conserve momentum, due to the random combination of
unrelated tracks from different events. This introduces a bias into kinematic
distributions generated by this sample. Fig. 3.4 show comparisons between distributions of likesign and event mixed data in different kinematic variables. Since
likesign muon pairs also consist of combinatorical background only (see also Sec.
3.3), the distributions from event mixing must reproduce those of likesign data to
be usable as a background simulation. As one can see, every distribution shows
differences between likesign distributions and those of mixed events data.
Several methods have been applied to remove these discrepancies. [Hul02] suggests to apply weights after the event mixing procedure to match the generated
4
The primary vertex is the location of the main interaction between incident proton and the
target wire, reconstructed from all tracks of an event.
counts per 10 GeV
3.2. EVENT MIXING TO SIMULATE BACKGROUND
10
10
10
37
4
3
2
10
1
0
20 40 60 80 100 120 140 160 180 200
p [GeV]
Figure 3.3: Reconstructed momentum distribution of muons generated by the Drell Yan process in simulated events. The muons
carry up to 20% of the total momentum of 920 GeV of an event.
distributions to the expected ones. While this technique works in matching the
event mixed sample to likesign data in one variable, it is not possible to match
all distributions simultaneously.
A second possibility is to select mixed muon tracks according to their momentum to restore momentum conservation approximately and only match those with
compatible momenta. However, this method also failes to reproduce the likesign
data distributions. If one chooses loose bounds on the muons, the resulting distributions still do not match those of likesign data. If the bounds are too strict,
no real mixing between events occurs as only the muon pair from the original
event fulfills the preselection criteria.
Ultimately, the bias introduced by the nonconservation of momentum intrinsic to
event mixing leaves this method unusable in this analysis, where a background
subtraction in several kinematic distributions at the same time is needed.
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
event mixing data
likesign data
10
10
3
2
counts per 300 MeV
counts per 333 MeV
38
10
10
10
event mixing data
likesign data
3
2
1
4
5
6
7
8
9
10 11 12
M µµ [GeV]
0
10
3
event mixing data
likesign data
10
10
10
2
3
4
5
6
p t [GeV]
(b) Transverse momentum of muon pair
counts
counts
(a) Invariant mass of muon pair
1
event mixing data
likesign data
3
2
2
10
10
1
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1
(c) xf of muon pair
-0
0.1
xf
-8
-6
-4
-2
0
2
(d) pseudorapidity of muon pair
Figure 3.4: Comparison of distributions depending on several
kinematic variables between likesign muon pair data and muon pairs
generated by an event mixing procedure.
η
4
3.3. LIKESIGN DATA AS BACKGROUND
3.3
39
Likesign Data as Background
Monte Carlo studies ([Ric03]) have shown that likesign combinations of muons
can be used as a simulation of the combinatorical background. The background
muons contributing to the combinatorical background are mainly generated by
decays in flight of pions and kaons with both charges in equal probability with
a uniform distribution in φ. Thus, the four possible charge combinations µ+ µ− ,
µ− µ+ , µ+ µ+ and µ− µ− are expected to have the same probability to occur at
production.
Since there is no decay producing two muons of the same charge, both data sets
of likesign muon pairs consist entirely of combinatorical background:
++
++
−−
−−
Ntotal
= Nbg
and Ntotal
= Nbg
On the other hand, the unlikesign muon pair sets contain background and signal
events even after the optimization of the selection criteria presented in Sec. 3.5,
which are inseparable by further cuts:
+−
+−
+−
−+
−+
−+
Ntotal
= NDY
+ Nbg
and Ntotal
= NDY
+ Nbg
Subtracting the likesign datasets from the unlikesign after correction for acceptance differences results in a pure signal sample.
3.3.1
Acceptance Differences between Likesign and Unlikesign Data
The probability to detect a muon pair strongly depends on the charges, the positions of the muons in the magnet and their momentum in the detector. These
quantities determine whether a track crosses the active detector volume, disappears in the beampipe or inner tracker region or leaves the detector at the outside. Fig. 3.5 schematically shows the effect of the insensitive region around the
beampipe for the four different charge combinations in the detector. Inbending
muon pairs travelling close to the beampipe before the magnet are unlikely to be
triggered, as the magnet forces the tracks to cross the insensitive inner detector
region behind it. On the other hand, outbending muon pair tracks are unlikely
to be found close to the inner tracker at the far end of the detector because these
tracks pass through the dead inner detector region between the magnet and the
last stations and are not detected. Since the track density drops off with increasing distance from the beampipe before the magnet, the total sample of inbending
muon track pairs is lower than that of outbending ones.
Likewise, muons from positive likesign pairs can be detected closer to the beampipe
if they are on the right side of the detector as seen from the interaction point,
while muons from negative likesign pairs tend to be closer on the left side of the
0000000000000000000
1111111111111111111
111111111111111
000000000000000
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
00
11
00 11
11
00
00
00 11
11
00
11
MU3
The bending of tracks by the magnet can be simulated by two straight tracks connected by
a kink at a vertical plane in the magnet. This plane is called the focal plane.
5
TC2
PC1
(a) Unlikesign data
outbend
inbend
Magnet plane
Vertex
Insensitive
tracker region
Sensitive
tracker region
MU3
Magnet plane
0000000000000000000
1111111111111111111
111111111111111
000000000000000
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
0000000000000000000
1111111111111111111
0000000000000000000
1111111111111111111
000000000000000
111111111111111
00000000000000
11111111111111
00
11
00
11
00
11
00
11
00
11
00
11
40
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
TC2
+−
−+
++
−−
NDY = Ntotal
+ Ntotal
− C1 Nbg
− C2 Nbg
with C1,2 =
PC1
++ likesign
−− likesign
Vertex
Insensitive
tracker region
Sensitive
tracker region
(b) Likesign data
Figure 3.5: Schematical representation of the difference in acceptances between unlike- and likesign muon pairs. The tracks closest
to the beam axis that will still pass through the active detector region
and thus be accepted by the trigger are shown. Positive particles
are deflected to the right as seen from above by the magnet, negative particles to the left. Fig. (a) shows inbending and outbending
unlikesign track pairs, Fig. (b) positive and negative likesign track
pairs. The different angles of the track pairs at the vertex illustrate
the differences in acceptance between the four charge combinations.
detector. This asymmetrical distribution of tracks can also be seen in Fig. 3.6,
where the x position of tracks in the magnet focal plane5 is plotted.
This only applies to tracks passing through the detector to the left or right of
the insensitive region, not above or below, since the magnet only deflects tracks
in the horizontal plane. As one can see in Fig. 3.7, which shows the positions of
all tracks in station PC1, the majority of tracks are passing to the left or right
of the insensitive central detector region. These differences in acceptance have
to be accounted for before likesign data can be used to optimize the cuts or to
subtract the background from the data distributions.
The final number of Drell Yan events can then be calculated by
unlikesign acceptance
likesign acceptance
20 x10
2
outbending
inbending
18
counts
counts
3.3. LIKESIGN DATA AS BACKGROUND
20 x10
16
14
14
12
12
10
10
8
8
6
6
4
4
2
2
0
20
2
positive
negative
18
16
0
-80 -60 -40 -20
41
0
-80 -60 -40 -20
40 60 80
x magnet [cm]
(a) Unlikesign data
0
20
40 60 80
x magnet [cm]
(b) Likesign data
40
200
30
180
20
160
20
10
140
10
120
0
100
-10
80
-20
60
50
100
80
60
40
20
20
-40
-50
0
-50
(a) Unlikesign data
120
-20
-40
40 60
x PC1 [cm]
140
-10
40
20
160
0
-30
0
180
30
-30
-60 -40 -20
200
40
-60 -40 -20
0
20
40 60
x PC1 [cm]
(b) Likesign data
Figure 3.7: x vs. y position of muon tracks in station PC1 after
fiducial cuts. (a) shows all unlikesign, (b) all likesign data. The
majority of tracks pass the station to the left and right of the insensitive inner detector region within −20 cm < y < 20 cm.
0
counts
220
counts
50
y PC1 [cm]
y PC1 [cm]
Figure 3.6: x position of muon tracks in the focal plane of the
magnet after fiducial cuts. (a) shows outbending and positive likesign data, (b) inbending and negative likesign data. The difference
between in- and outbending unlikesign and between positive and negative likesign distributions is caused by the dependance of the acceptance on the muon charge combinations.
42
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
ITR
TC2
111111111111111111111111111111111
000000000000000000000000000000000
000000000000000000000000000000000
111111111111111111111111111111111
000000000000000000000000000000000
111111111111111111111111111111111
ITR
11111111111111111111
00000000000000000000
00000000000000000000
11111111111111111111
00000000000000000000
11111111111111111111
µ+
I
µ
II
−
µ+
III
IV
PC1
µ
−
V
magnet
vertex
Figure 3.8: The figure shows tracks which touch the insensitive
inner tracking regions on their path through the detector. These
boundery tracks define five regions (I-V) at the central magnet position which separate accepted from not accepted tracks for the different charge combinations. Muons from inbending (µ+ µ− ) muon
pairs passing through regions II, III or IV are not detected, outbending (µ− µ+ ) muon pairs are only lost if one or both muons pass
region III. Likewise positive likesign muon pairs in regions II and
III and negative likesign muon pairs in regions III and IV are not
seen.
3.3. LIKESIGN DATA AS BACKGROUND
43
It is necessary to calculate the total number of Drell Yan events using both
inbending and outbending, positive and negative likesign datasets at the same
time. As Fig. 3.8 and Tab. 3.1 show, each dataset consists of muons found
in different regions of the detector. Every charge combination dataset contains
tracks passing through regions I and V. Tracks in region II are only detected if
the muon pair is either outbending or negative likesign, tracks in region IV only
in the outbending or positive likesign datasets. Muon pairs with tracks passing
through region III are not detected regardless of muon charges. While it is possible to correct acceptances downwards using weights, there is no way to restore
the data lost in an insensitive region. A negative likesign dataset reweighted to
outbending acceptance will thus not correctly describe the outbending combinatorical background. The reason for this is that muon pairs travelling through
region IV are present in the outbending unlikesign dataset but not the negative
likesign. If both unlikesign and likesign datasets are added though, the numbers
of regions containing data match. Regions I and V are seen in both unlikesign
datasets, regions II and IV once each, the same as for both likesign datasets.
Unfortunately, the missing central detector region is not the only detector inefficiency present. The First Level Trigger (FLT) shows a very strong dependance
on muon track position and has regions with very low efficiency. Fig. 3.9 shows
the average FLT efficiency in the x − y plane, plotted at the position of trigger
station TC2. Each of the areas with low efficiency contributes further to the
difference in statistics seen by the four charge combinations. While it would be
possible to reweight both positive and negative likesign datasets to the acceptance
of inbending unlikesign data if the acceptance difference was caused only by the
missing Inner Tracker, the overlapping areas with little or no data available in
one or more datasets caused by the FLT inefficiencies only allow the reweighting
to succeed if all datasets are used.
44
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
Dataset
Outbending µ− µ+
Inbending µ+ µ−
Positive like µ+ µ+
Negative like µ− µ−
Unlikesign total
Likesign total
Detector Regions
I
II
III IV
V
X
X
X
X
X
X
X
X
X
X
X
X
2·X 1·X - 1·X 2·X
2·X 1·X - 1·X 2·X
Table 3.1: Detector regions at the magnet as defined in Fig. 3.8
which contain data, separate for the four muon charge combinations. Also, the data in the combined unlikesign and likesign dataset
is shown.
Figure 3.9: FLT efficiency averaged over the datataking period in
the x − y plane at the z position of tracker station TC2 (generated
with [Bal03]).
3.3. LIKESIGN DATA AS BACKGROUND
3.3.2
45
Corrections for the Acceptance Difference
of Opposite- and Likesign Data
The dilepton trigger implemented at HERA-b has two stages that have to be
considered for the acceptance correction: the First Level Trigger (FLT) and the
Second Level Trigger (SLT). The FLT starts from pretrigger messages sent by the
muon system and then tries to follow the tracks through the muon stations MU4,
MU3 and MU1 and the tracking stations TC2, TC1, PC4 and PC1. The SLT uses
a full detector simulation to reconstruct tracks starting with the same pretrigger
message. After the track reconstruction, the vertex is determined using the VDS
system. Since the vertex system is located between wire target and magnet, the
path of tracks through the VDS is independant of their charge and determined
by their momentum vectors only.
The process from which the muon tracks originate does have an influence on
the vertexing efficiency. Muons from Drell Yan or a J/ψ decay are more likely
to pass the vertex criterium of the trigger, since they come from a common
vertex. Muons from the decay of a kaon or a pion are less likely to combine to
a vertex with low χ2 . Provided the muons are created by the same process –
combinatorical background or Drell Yan – the vertexing efficiency only depends
on the momentum vector of the tracks, not their charge.
During the data taking period of 2002-2003, the HERA-b trigger ran in the so
called “1FLT/2SLT*” (star) mode. In this mode, the FLT is used as a count
trigger which simply counts the number of tracks found. The SLT reconstructs
the leptons independently of the FLT, starting at the pretrigger seeds passed on
from the FLT. The final trigger decision requires two pretrigger messages and one
track from the FLT and at least two tracks with a common vertex from the SLT.
The only connection between the two tracks of each muon pair in the SLT comes
from the vertexing, which is not sensitive to the muon charges. Apart from this,
both tracks are reconstructed independently in both triggers. The probability
to detect a pair of muons with momenta p~L and p~R and charges qL and qR can
then be written as the product of the probabilities to detect the single muons
(PµL (~pL , qL ), PµR (~pR , qR )) and the vertexing efficiency (εvertex ):
PµL µR (~pL , qL , p~R , qR ) = PµL (~pL , qL )PµR (~pR , qR )εvertex (~pL , p~R )
The indices L and R denote the left and right muon of each muon pair, as seen
from the interaction point. Since the FLT and SLT efficiencies are independant
of each other and it is not known which muon fulfilled the FLT requirement to
find at least one muon track, the single track muon probabilities PµL and PµR
have to be further separated. The three possible trigger combinations are:
• The two pretrigger messages lead to tracks found by both triggers,
• the left muon was found by both the FLT and the SLT, the right one only
by the SLT, or
46
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
• the left muon was only found in the SLT, while the right muon was triggered
by both the FLT and the SLT.
This leads to the event detection probability:
pL , qL )PµSLT
pR , qR ) + PµSLT
pL , qL )PµFLT
pR , qR )
PµL µR (~pL , qL , p~R , qR ) = PµFLT
L (~
R (~
L (~
R (~
FLT
FLT
−PµL (~pL , qL )PµR (~pR , qR ) εvertex (~pL , p~R )
(3.1)
The pretrigger efficiencies are included in the trigger probabilities.
In a Monte Carlo simulation, all tracks accepted by the FLT are also accepted
by the SLT, the sample of FLT triggered tracks is a subset of the sample of
SLT triggered tracks. Therefore, both probabilities PµFLT
pL , qL )PµSLT
pR , qR ) and
L (~
R (~
SLT
FLT
PµL (~pL , qL )PµR (~pR , qR ) include the probability to find both tracks in the FLT
PµFLT
pL , qL )PµFLT
pR , qR ). This probability is thus counted twice and has to be
L (~
R (~
subtracted once.
If the single track muon probabilities P are known, it is possible to calculate event
weights that reflect the difference in acceptance between two charge combinations
(qL , qR ) and (qL0 , qR0 ) for a given muon pair with momenta (~pL , p~R ):
w(~pL , p~R , qL , qL0 , qR , qR0 )
P (~pL , qL0 , p~R , qR0 )
=
P (~pL , qL , p~R , qR )
(3.2)
This event weight gives the probability that a muon pair accepted by the trigger with momenta (~pL , p~R ) and charges (qL , qR ) would also have been accepted
if their momenta had been the same but the charges had been (qL0 , qR0 ). As discussed above, the vertexing efficiency only depends on the momentum vectors
of the muons and the process the muons come from, not the charges. The only
difference between the two probabilities in (3.2) is the charge of the muons, creation process and momentum vectors are the same. Thus, the vertexing efficiency
is also the same in both cases and cancels out in the ratio of the two probabilities.
3.3.3
Single Track Monte Carlo to calculate Acceptance
Correction Factors
While it is not possible to generate a full Monte Carlo simulation of the combinatorical background, a simpler model can be used to find the single track detection
probabilities described in the previous section. For this purpose, a special Single
Track Monte Carlo (STMC) sample was generated in which each event consists
of only a single muon of varying momentum and charge. These muons were generated in equal amounts for both charges with a flat distribution in px and py ,
3.3. LIKESIGN DATA AS BACKGROUND
47
distributed throughout the whole detector (see Fig. 3.10). The pz of the tracks
was sampled during the Monte Carlo generation from a histogram showing the
pz distribution of likesign data tracks. This constraint on the longitudinal momentum leads to a limit on the usable total momentum of muons. Outside a
momentum range of 10 GeV < p < 106 GeV, the likesign data sample is too
small to be used during the pz sampling described above. To ensure that this
limit on the Single Track Monte Carlo muons introduces no bias in the correction weights for the acceptance differences, muons outside the momentum range
given above are also removed from unlikesign data and Drell Yan Monte Carlo.
This leads to an loss of efficiency of 4.2%. The sample was reconstructed using
a modified trigger simulation which skipped the vertexing stage of the SLT and
applied flags to each track whether it was accepted by both triggers or by the
SLT only. The result of this are four Monte Carlo selections:
• µ+ accepted by both FLT and SLT,
• µ+ accepted by SLT only,
• µ− accepted by both FLT and SLT, and
• µ− accepted by SLT only.
3
x10
counts
counts
x10
7
7
6
6
5
5
4
4
µ+
µ-
3
2
1
1
-3
-2
-1
(a)
0
µ+
µ-
3
2
0
-4
3
1
2
3
4
p x [GeV]
0
-4
-3
-2
-1
0
1
2
3
4
p y [GeV]
(b)
Figure 3.10: Distributions of px and py of generated Single Track
Monte Carlo muons. The data points of the µ+ distribution hide
those of the µ− distribution as both are identical.
The px and py distributions of accepted events for the four selections are shown
in Fig. 3.11 and 3.12. The px distributions show large differences between µ+ and
48
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
µ− because of the different bending direction in the magnet. Also the difference
in trigger efficiency is evident in the different numbers of accepted events. Also
evident is the difference in efficiency of the First and the Second Level Trigger.
Comparing Fig. 3.11(a) and 3.11(c) leads to roughly a factor of eight between
the two efficiencies (see also Tab. 3.2). Fig. 3.13 illustrate the cause of this
difference in FLT and SLT acceptance. They show the position of the tracks
accepted by each trigger in the magnet focal plane. While the tracks accepted
by the SLT are distributed throughout the detector with the exception of the
central inner tracker region and the “shadow” in the lower right quadrant caused
by the electron beampipe, the FLT triggered track distribution shows many low
efficiency regions which roughly match the areas of low efficiency seen in Fig. 3.9.
Trigger
FLT
SLT
generated muons
574523
574523
accepted muons trigger efficiency
38214
6.6%
312757
54.4%
Table 3.2: Generated and accepted muon tracks for both triggers
and corresponding trigger efficiencies in the Single Track Monte
Carlo.
3.3. LIKESIGN DATA AS BACKGROUND
2
x10
µ+
µ-
8
counts
counts
x10
49
7
2
µ+
µ-
9
8
7
6
6
5
5
4
4
3
3
2
2
1
1
0
-4
-3
-2
-1
0
1
2
0
-4
3
4
p x [GeV]
(a) Muons accepted by both triggers
3
x10
µ
µ-
+
5
4
3
3
2
2
1
1
-3
-2
-1
0
1
2
3
4
p x [GeV]
(c) Muons accepted by the SLT
-1
0
1
2
3
4
p y [GeV]
3
µ+
µ-
5
4
0
-4
-2
(b) Muons accepted by both triggers
counts
counts
x10
-3
0
-4
-3
-2
-1
0
1
2
3
4
p y [GeV]
(d) Muons accepted by the SLT
Figure 3.11: Distributions of px and py of reconstructed Single
Track Monte Carlo muons that were accepted by both the FLT and
the SLT (a and b). Muons with a negative py are less likely to be detected, as expected from Fig. 3.9 since the FLT efficiency generally
is higher in the upper half of the detector. The same distributions
requiring only an SLT trigger flag (c and d) show a much less pronounced asymmetry in py since most of this asymmetry is caused
by FLT inefficiencies. The remaining asymmetry is caused by the
electron beampipe.
3
2
200
150
0
-1
200
2
150
0
100
-1
100
-2
-2
50
50
-2
-1
0
1
2 3 4
p x [GeV]
-4
-4
0
(a) Positive muons accepted by both triggers
3
10
2
-2
-1
0
1
2 3 4
p x [GeV]
0
(b) Negative muons accepted by both triggers
2
counts
x10
12
4
-3
x10
12
4
3
10
2
1
8
1
8
0
6
0
6
-1
-1
4
-2
-3
-4
-4
4
-2
-3
-2
-1
0
1
2 3 4
p x [GeV]
2
-3
0
-4
-4
(c) Positive muons accepted by the SLT
2
-3
-2
-1
0
1
2 3 4
p x [GeV]
0
(d) Negative muons accepted by the SLT
Figure 3.12: Distributions of px vs. py of (a) positive and (b)
negative reconstructed Single Track Monte Carlo muons accepted
by both triggers and (c) positive and (d) negative muons requiring
only a SLT trigger flag.
2
counts
-3
-3
p y [GeV]
-3
p y [GeV]
250
3
1
1
-4
-4
4
counts
250
p y [GeV]
4
counts
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
p y [GeV]
50
10
60
40
20
51
80
2
10
60
40
20
10
0
0
-20
-20
-40
10
-40
1
1
-60
0
20
-80
-80 -60 -40 -20
40
60 80
x magnet [cm]
(a) Positive muons accepted by both triggers
counts
80
60
2
40
10
2
40
0
0
-40
40 60 80
x magnet [cm]
60
20
10
20
80
20
-20
0
(b) Negative muons accepted by both triggers
y magnet [cm]
-80
-80 -60 -40 -20
counts
-60
y magnet [cm]
counts
2
y magnet [cm]
80
counts
y magnet [cm]
3.3. LIKESIGN DATA AS BACKGROUND
10
10
-20
-40
-60
-60
1
-80
-80 -60 -40 -20
0
20
40
60 80
x magnet [cm]
(c) Positive muons accepted by the SLT
1
-80
-80 -60 -40 -20
0
20
40
60 80
x magnet [cm]
(d) Negative muons accepted by the SLT
Figure 3.13: Track position in the magnet focal plane of (a) positive and (b) negative reconstructed Single Track Monte Carlo muons
detected by both triggers. The inefficiency regions closely match
those seen in 3.9. Requiring only an SLT trigger flag (c and d)
shows a much smoother distribution, only disturbed by the electron
beampipe passing through the detector in the lower right quadrant.
52
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
3.3.4
Reweighting of Likesign Data to the Acceptance of
the Opposite sign Background
Using these Single Track Monte Carlo selections, it is possible to calculate the single track detection probabilities PµL (~pL , qL ) and PµR (~pR , qR ) used in (3.1). Since
the detection efficiency depends on geometrical detector effects such as inefficient chambers, these probabilities are calculated as a function of the geometrical
variables (p, xmagnet , ymagnet , q) instead of the momentum vector (~p, q). Mathematically, both sets of variables are equivalent, the latter is used in the formulas
for clarity.
+
−
−
The two generated (µ+ and µ− ) and four accepted (µ+
FLT , µSLT µFLT and µSLT ) Single Track Monte Carlo samples are divided into ten momentum subsets. Two dimensional histograms are filled with the x − y position of the muon in the
magnet focal plane from these subsets. A four dimensional efficiency matrix
P (p, xmagnet , ymagnet , q) is then obtained by dividing the histograms filled with accepted by the corresponding ones with generated MC data, once for each trigger.
Finally, a local averaging is applied to the x − y distributions in the form of a
bilinear interpolation.
To keep the equations readable, the following substitutions are applied in the
calculation of the relative acceptance of likesign to the unlikesign events:
PµL µR (~pL , +, p~R , −) −→ P +− (~pL , p~R ),
PµL µR (~pL , +, p~R , +) −→ P ++ (~pL , p~R ),
PµL µR (~pL , −, p~R , +) −→ P −+ (~pL , p~R )
PµL µR (~pL , −, p~R , −) −→ P −− (~pL , p~R )
PµFLT
pL , +) −→ PF+L ,
L (~
PµSLT
pL , +) −→ PS+L
L (~
PµFLT
pR , +) −→ PF+R ,
R (~
PµSLT
pR , +) −→ PS+R
R (~
PµFLT
pL , −) −→ PF−L ,
L (~
PµSLT
pL , −) −→ PS−L
L (~
PµFLT
pR , −) −→ PF−R ,
R (~
PµSLT
pR , −) −→ PS−R
R (~
The event detection probabilites (3.1) of the four charge combinations then are:
P +− (~pL , p~R ) =
P
−+
(~pL , p~R ) =
P
++
(~pL , p~R ) =
P −− (~pL , p~R ) =
(PF+L PS−R + PS+L PF−R − PF+L PF−R )εvertex (~pL , p~R )
(3.3a)
(PF−L PS+R
(PF+L PS+R
(PF−L PS−R
PF−L PF+R )εvertex (~pL , p~R )
PF+L PF+R )εvertex (~pL , p~R )
(3.3b)
− PF−L PF−R )εvertex (~pL , p~R )
(3.3d)
+
+
+
PS−L PF+R
PS+L PF+R
PS−L PF−R
−
−
(3.3c)
Using these four formulas, it is possible to calculate the probability that a muon
pair with given momenta and likesign charge would also have been accepted if
one muon had the opposite charge by dividing the probability of the changed
unlikesign charge combination ((3.3a) or (3.3b)) by the probability of the original
3.3. LIKESIGN DATA AS BACKGROUND
53
likesign one ((3.3c) or (3.3d)). This leads to four weights (3.2), two for reweighting positive likesign data to simulate outbending and inbending opposite sign
background, and two for reweighting negative likesign data to outbending and
inbending background:
+−
w++
(~pL , p~R )
P +− (~pL , p~R )
PF+L PS−R + PS+L PF−R − PF+L PF−R
= +L +R
P ++ (~pL , p~R )
PF PS + PS+L PF+R − PF+L PF+R
PF−L PS+R + PS−L PF+R − PF−L PF+R
P −+ (~pL , p~R )
=
P ++ (~pL , p~R )
PF+L PS+R + PS+L PF+R − PF+L PF+R
P +− (~pL , p~R )
PF+L PS−R + PS+L PF−R − PF+L PF−R
=
P −− (~pL , p~R )
PF−L PS−R + PS−L PF−R − PF−L PF−R
P −+ (~pL , p~R )
PF−L PS+R + PS−L PF+R − PF−L PF+R
=
P −− (~pL , p~R )
PF−L PS−R + PS−L PF−R − PF−L PF−R
=
−+
w++
(~pL , p~R ) =
+−
w−−
(~pL , p~R ) =
−+
w−−
(~pL , p~R ) =
(3.4a)
(3.4b)
(3.4c)
(3.4d)
These ratios w (3.4a) to (3.4d) can be applied as event weights to correct the likesign background to the acceptance of the opposite sign background. Fig. 3.2(a)
shows that the data sample containing outbending opposite sign muon pairs is
larger than that containing inbending ones. Consequently is is expected that
weights correcting the acceptance difference between likesign and outbending opposite sign (−+) data are on average larger than those correcting to inbending opposite sign (+−) data. Both distributions in Fig. 3.14 show this clearly:
+−
−+
+−
−+
i = 0.7. Also, it
i = 0.9 > hw−−
i = 0.6 and hw−−
i = 0.9 > hw++
hw++
can be seen in Fig. 3.2(b) that the sample of positive likesign is larger than that
of negative likesign muon pairs. Thus the weights applied to positive likesign
data should be smaller on average than those to negative likesign. In the case of
reweighting to inbending acceptance, this is the case in Fig. 3.14. For reweighting
to outbending acceptance, a prediction of the average weight is not possible, as
neither likesign sample can be reweighted to simulate the outbending background
alone. According to Fig. 3.14, both weights have the same average.
This strong dependance of the weights on the charge combinations shows that the
reweighting of the likesign data to the acceptance of the opposite sign background
is an essential part of the background subtraction.
Assuming that the number of background events per charge combination fulfill
the relation Nµ+ µ+ = Nµ− µ− = Nµ+ µ− = Nµ− µ+ at generation, the number of
Drell Yan signal events can then be calculated as:
NDY =
+−
Ntotal
+
−+
Ntotal
N++
N++
1 X −+
1 X +−
−
w (~pL , p~R ) −
w (~pL , p~R )−
2 i=1 ++
2 i=1 ++
N−−
N−−
1 X −+
1 X +−
w (~pL , p~R ) −
w (~pL , p~R )
2 i=1 −−
2 i=1 −−
The factors
1
2
(3.5)
are necessary since each likesign event is counted twice, once
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
counts
x10
3
x10
1.2
counts
54
to outbend
to inbend
1
2
5
to outbend
to inbend
4
0.8
3
0.6
2
0.4
1
0.2
0
0
0.5
1
1.5
2
2.5
3
0
0
0.5
1
1.5
2
2.5
3
w
w
(a) Weights applied to positive likesign data
(b) Weights applied to negative likesign data
Figure 3.14: Distribution of the weights that are applied to likesign data and calculated according to (3.4). The weights applied
to positive likesign data are plotted in (a), those used to reweight
negative likesign data in (b). The large entries at zero come from
likesign muon pairs that would not have been seen by the detector
if their charges had been unlike.
reweighted to simulate outbending background, once to simulate inbending. The
mass distribution of all data sets after the likesign acceptance correction is shown
in Fig. 3.15. These simulated opposite sign background distributions can now be
used in a study to optimise the signal to background ratio by using kinematic
selections.. They can also be subtracted from the unlikesign data to extract the
Drell Yan signal.
A crosscheck of the method applied above is given in the next section.
10
10
unlike data
++ likesign data
-- likesign data
3
counts per 333 MeV
counts per 333 MeV
3.3. LIKESIGN DATA AS BACKGROUND
10
10
2
10
10
1
1
4
5
6
7
8
9
10 11 12
M µµ [GeV]
55
unlike data
++ likesign data
-- likesign data
3
2
4
5
6
7
8
9
10 11 12
M µµ [GeV]
(a) Outbending unlikesign and reweighted like- (b) Inbending unlikesign and reweighted likesign data
sign data
Figure 3.15: Mass distribution of the data after fiducial cuts and
likesign reweighting. (a) Outbending and (b) inbending muon pairs,
each with corresponding simulated opposite sign background from
reweighted likesign distributions. While the positive and negative
likesign distributions agree within errors after reweighting to the
acceptance of inbending data, the two likesign distributions after
reweighting to outbending acceptence differ significantly, as expected
(see Sec. 3.3).
56
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
3.3.5
Crosscheck of Acceptance Reweighting Method
The acceptance reweighting method described in the last section can be checked
by applying the event detection probability shown in Eq. (3.1) as a weight to
each generated Drell Yan Monte Carlo event and comparing the result to the
reconstructed Drell Yan Monte Carlo. Since the vertexing efficiency εvertex (~pL , p~R )
contained in Eq. (3.1) is not known, only the track efficiencies will be used:
∗
pL , qL )PµSLT
pR , qR ) + PµSLT
pL , qL )PµFLT
pR , qR )
PµL µR (~pL , qL , p~R , qR ) = PµFLT
L (~
R (~
L (~
R (~
FLT
FLT
−PµL (~pL , qL )PµR (~pR , qR )
(3.6)
The result will not be an exact match beween the two samples due to the missing vertexing efficiency, which can of course depend on the kinematic variables.
The comparison is still useful, as though the exact dependance of the vertexing
efficiency is not known, one expects the shape of the functions to be smooth.
Fig. 3.16 shows the x positions of tracks at three different z positions in the
detector both from the reconstructed and the generated Drell Yan Monte Carlo
simulation. To the latter the probabilities given in Eq. (3.6) are applied as event
weights. These geometrical distributions are chosen because they directly show
the influence of the acceptance differences. Both distributions are normalized to
an area of one. While the general shape of the distributions is reproduced, efficiency differences on small scales are naturally not reproduced in the reweighted
generated Monte Carlo distributions, due to the averaging effect of the rather
coarse grained Single Track Monte Carlo efficiency matrix. An exact reproduction
of geometrical distributions is not necessary, as the ones in which the background
subtraction is finally applied are kinematic distributions, which themselves average over the geometry. If the Single Track efficiencies correctly reflect the reconstruction efficiencies in the Drell Yan Monte Carlo simulation, the kinematic
distributions should be identical except for the vertexing efficiency, which itself
can be a function of the plotted variable.
Two kinematic distributions are plotted in Fig. 3.17. The left plots show the
distributions of generated Drell Yan Monte Carlo data, to which Single Track
Monte Carlo weights have been applied, and those of accepted Drell Yan Monte
Carlo data as a function of the reconstructed mass and the transverse momentum
of the muon pair. As expected the integrals of the reweighted generated Monte
Carlo distributions are larger than those of the accepted Monte Carlo distributions by roughly a factor of three due to the vertexing efficiency not present in
the reweighted generated Monte Carlo sample. The right plots show a ratio of
the two distributions on the left side, which corresponds to the missing vertexing
efficiency. As one can see in both kinematic distributions this is a smooth function.
3.3. LIKESIGN DATA AS BACKGROUND
57
The crosscheck shows no evidence of problems with the calculation of event
weights from the Single Track Monte Carlo, the differences between the reweighted
generated and reconstructed distributions are compatible with the explanation of
the missing vertexing efficiency.
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
1 x10
-1
gen MC with stmc weights
0.9
reconstructed MC
counts
counts
58
1 x10
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
-40
-20
0
20
60
x magnet [cm]
-2
gen MC with stmc weights
6
reconstructed MC
7
5
4
4
3
3
2
2
1
1
-60
-40
-20
0
20
0
40
60
x PC1 [cm]
(c) Outbending muon pairs
gen MC with stmc weights
0.6
reconstructed MC
0.4
0.3
0.3
0.2
0.2
0.1
0.1
100 150 200
x MU3 [cm]
(e) Outbending muon pairs
40
60
x magnet [cm]
-2
gen MC with stmc weights
reconstructed MC
-60
-40
-20
0
20
40
60
x PC1 [cm]
-1
gen MC with stmc weights
0.6
0.4
50
x10
0.7 x10
0.5
0
20
(d) Inbending muon pairs
0.5
0
-200 -150 -100 -50
0
counts
-1
counts
0.7 x10
-20
6
5
0
-40
(b) Inbending muon pairs
counts
counts
x10
reconstructed MC
0
-60
40
(a) Outbending muon pairs
7
gen MC with stmc weights
0.9
0.8
0
-60
-1
reconstructed MC
0
-200 -150 -100 -50
0
50
100 150 200
x MU3 [cm]
(f) Inbending muon pairs
Figure 3.16: Comparison between the x position of tracks in the
magnet focal plane (a and b), in station PC1 (c and d) and in
station MU3 (e and f ). The left distributions show outbending, the
right inbending muon pairs. Both reconstructed and generated Drell
Yan Monte Carlo are shown. Single Track Monte Carlo weights
have been applied to generated Drell Yan Monte Carlo events according to Eq. (3.3a) and (3.3b), without the vertexing efficiency
εvertex .
10
59
5
gen. DYMC with STMC weights
ratio
counts per 333 MeV
3.3. LIKESIGN DATA AS BACKGROUND
0.3
rec. DYMC
0.25
10
4
0.2
0.15
10
3
0.1
0.05
4
5
6
7
8
9
0
4
10 11 12
M µµ [GeV]
10
10
5
gen. DYMC with STMC weights
rec. DYMC
4
6
7
8
9
10 11 12
M µµ [GeV]
(b) Ratio of mass distributions
ratio
counts per 300 MeV
(a) Mass of muon pair
5
1
0.8
0.6
10
10
3
0.4
0.2
2
0
10
-0.2
-0.4
1
0
1
2
3
4
5
6
p t µµ [GeV]
(c) Transverse momentum of muon
pair
0
1
2
3
4
5
6
p t µµ [GeV]
(d) Ratio of pt distributions
Figure 3.17: Comparisons of kinematic distributions between reconstructed and reweighted generated Drell Yan Monte Carlo. The
weights applied to the generated distributions are calculated from
Single Track Monte Carlo. The left distributions show the original
distributions, the right ones the ratio of the two, which corresponds
to the vertexing efficiency.
60
3.4
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
Simulation of the Drell Yan Process
The Monte Carlo simulations used at HERA-b use the physics generator packages PYTHIA 5.7 and JETSET 7.4 ([Sjö94]). They are limited to proton nucleon
interactions and generate the particles belonging to the Drell Yan reaction itself.
All other particles present in an inelastic proton nucleon interaction are generated by the FRITIOF 7.02 package ([Pi92]) with the constraint that the sum of
the energies of particles from the inelastic collision and the Drell Yan process are
equal to the beam energy.
This event is then fed into a GEANT 3.21 ([Cer94]) detector simulation, which
tracks the Monte Carlo particles through the detector. This leads to simulated
hits after a digitalization and hit generation. Finally, a simulation of the HERA-b
trigger chain is applied. In this simulation, the order in which the triggers are
applied is reversed with respect to real data. A simulation of the Second Level
Trigger (SLT) is fed with the hit informations from the Monte Carlo tracks passing through the pretrigger detectors. Since the hit information is in the same
format as the real data, the same trigger algorithms can be used. The trigger
track parameters determined by the SLT are then passed on to the First Level
Trigger (FLT) simulation. The FLT efficiency is then determined from a FLT
efficiency map, which is a parametrization of the FLT efficiency in relation to the
SLT efficiency. A projection of this FLT efficiency map into the plane of station
TC2 is shown in Fig. 3.9.
The Monte Carlo runs used in the analysis are listed in table 3.3. After a first
loose set of preselection criteria (similar to those discussed later in Sec. 3.5) was
applied to Drell Yan Monte Carlo and data, several kinematic distributions of
Monte Carlo and data were compared. While most differential kinematic distributions show good agreement between data and MC, the Drell Yan Monte Carlo
simulation does not reproduce the distribution of the transverse momentum of
the muon pair, as seen in Fig. 3.18. This is a known effect, also seen in the J/ψ
analyses ([Hus05]). The Monte Carlo simulation only includes first order processes, while initial and final state radiation increase the transverse momentum.
A second effect is that partons with a pt of less than 1 GeV are dropped during
generation, further distorting the pt spectrum. These effects can be compensated
for by reweighting the MC events. A simple reweight in pt is not sufficient to
correct for this distortion, as mass and pt of the muon pair are correlated. For
this reason, a two dimensional reweighting procedure is applied. Instead of mass
and pt , mass and p2t are chosen, since the distribution of the latter has no peak
and is easier to fit. The mass vs. p2t distributions of both MC and data are separately fitted. Then for each Drell Yan Monte Carlo event, a weight is calculated
from the ratio of the two fitting functions. Fig. 3.19 shows both distribution and
fitting function of the reconstructed MC, Fig. 3.20 those of the data.
While the data distribution can be fitted with a simple two dimensional exponential function (Eq. 3.7), the phenomenological function used to fit the MC
3.4. SIMULATION OF THE DRELL YAN PROCESS
unlike-like data (signal)
Drell Yan rec. MC, not reweighted
10
2
2
3
10
counts per 500 MeV
counts per 300 MeV
10
61
unlike-like data (signal)
Drell Yan rec. MC, not reweighted
10
10
3
2
10
1
1
0
1
2
3
(a)
4
5
6
p t [GeV]
0
1
2
3
4
5
6
7
8 9 10
2
p 2t [GeV ]
(b)
Figure 3.18: Distribution of the transverse momentum of the
muon pair in data and Monte Carlo with no reweighting applied
to the Drell Yan Monte Carlo. The Drell Yan Monte Carlo distribution clearly peaks at a lower transverse momentum than the
data distribution. p2t was chosen as a reweighting variable since it
is easier to fit as it contains no peak.
distribution is more complicated (Eq. 3.8) and consists of 25 free parameters:
fdata (m, p2t ) = exp c0 + c1 m + c2 p2t
(3.7)
fMC (m, p2t ) = g(m, p2t ) × h(p2t ) + i(m, p2t )
(3.8)
The p2t dependance of the MC distribution can be described by a sum of two
exponential functions. A suitable function for the mass dependance was found in
BaBar literature, the so called Novosibirsk function g(m, p2t ) ([Ada05]):
√





sinh(ĉ
ln
4)
m
−
ĉ
3
1
2
√
·
)



 1  ln (1 +
ĉ2




ln
4
2 
2
+ ĉ3  − ĉ4  (3.9)
g(m, pt ) = c0 exp − 
2
ĉ3

 2


Especially the peak position ĉ1 , but also the other parameters of the Novosibirsk
function show a dependance on the transverse momentum. This can be seen in
Fig. 3.19(a). For p2t = 0.5 GeV2 , the peak of the mass distribution is outside the
graph, below 4 GeV. For p2t = 3.5 GeV2 , the peak is at Mµµ = 4.75 GeV. To find
the subfunctions (3.10) to (3.13), the Drell Yan Monte Carlo data was plotted as
a function of the mass Mµµ in ten bins of p2t . Each of these ten distributions was
fitted separately with a Novosibirsk function whose parameters were then plotted
62
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
105
104
104
103
103
2
10
10
4
1
0
102
10
1
0
5
2
6
4
7
6
8
8 s
as
9
10
m
pt 2
4
5
2
6
7
4
6
(a)
8
8 s
as
9
10
m
pt 2
(b)
Figure 3.19: (a) mass vs. p2t distribution of reconstructed Drell
Yan Monte Carlo events, (b) corresponding fit.
as a function of p2t . Phenomenological fits to these distributions of parameters
are:
1
(3.10)
ĉ1 = c1 1 −
c11 + c12 p2t
ĉ2 = c2 (1 + c13 p2t + c14 p4t )
(3.11)
2
4
ĉ3 = c3 (1 + c15 pt + c16 pt )
(3.12)
2
4
ĉ4 = c4 (1 + c17 pt + c18 pt )
(3.13)
2
2
h(p2t ) = c5 ec6 +c7 pt + c8 ec9 +c10 pt
(3.14)
Still, the Novosibirsk function alone multiplied with the sum of two exponential
functions of p2t was insufficient to fully describe the Monte Carlo distribution. A
third exponential term depending on both Mµµ and p2t was needed:
i(m, p2t ) = c26 exp (c21 + c19 p2t + c20 p4t ) ln m + c22 m2 + c23 m3
+ c24 ln p2t + c25 p4t (3.15)
The result of this reweighting can be seen in Fig. 3.21. Here, data and Monte
Carlo simulated distributions agree well. This reweighted Drell Yan Monte Carlo
sample is then used again in an iterative process to optimize the cuts applied to
data, which is again compared to the MC distributions and used to adjust the
reweighting.
3.4. SIMULATION OF THE DRELL YAN PROCESS
102
63
102
10
10
1
1
-1
4
5
-1
10
0
6
2
4
7
6
8
10
4
10-2
0
5
6
2
4
8 s
as
9
10
m
pt 2
7
6
(a)
8
8 s
as
9
10
m
pt 2
(b)
10
2
unlike-like data (signal)
counts per 500 MeV
counts per 300 MeV
unlike-like data (signal)
Drell Yan reconstructed MC
2
Figure 3.20: (a) mass vs. p2t distribution of data events after cuts
and likesign background subtraction, (b) corresponding fit.
Drell Yan rec. MC, reweighted
10
10
2
10
1
1
0
1
2
3
(a)
4
5
6
p t [GeV]
0
1
2
3
4
5
6
7
8 9 10
2
p 2t [GeV ]
(b)
Figure 3.21: pt and p2t distribution in data and Monte Carlo simulation after reweighting. Data and Monte Carlo agree well.
64
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
wire
b1
b1
b1(b1o2)
b1(b1o2)
b1(b1i2)
b1(i1b1)
b1(b1b2)
b1(b1b2)
b2
b2(b1b2)
b2(b1b2)
i1(i1i2)
i1(i1i2)
i1(i1b1)
i2
i2(i1i2)
i2(i1i2)
i2(b1i2)
o2
o2(b1o2)
o2(b1o2)
MC process id
15200
15200
15200
15200
15200
15200
15200
15200
15202
15202
15203
15203
15203
15203
15200
15200
15200
15200
15203
15203
15203
#events (k) calibration period run number
379
Jan
09 1566
654
Jan
09 1567
333
Jan
09 1569
688
Jan
09 1570
524
Jan
09 1573
523
Nov
09 1580
524
Feb
09 1564
524
Oct
09 1581
315
Nov
09 1562
315
Oct
09 1563
585
Feb
09 1565
502
Nov
09 1575
401
Dec
09 1577
502
Nov
09 1579
1033
Nov
09 1558
654
Nov
09 1576
401
Dec
09 1578
523
Jan
09 1574
709
Feb
09 1568
465
Jan
09 1571
928
Jan
09 1572
Table 3.3: List of Drell Yan Monte Carlo runs used.
3.5. OPTIMIZATION OF EVENT SELECTION
3.5
65
Optimization of Event Selection
In addition to the general event based and fiducial cuts introduced in Sec. 3, cuts
on the properties of the muon tracks are applied.
The data sample suffers from a rather large background as can be seen in Fig. 3.15,
which makes it difficult to measure Drell Yan cross sections and leads to large
errors.
However, the ratio of signal to background can be improved by choosing appropriate cuts to reduce background while keeping a large portion of the signal.
As a first step in extracting the Drell Yan signal from the data, the invariant
mass range of the reconstructed muon pair is restricted. Below 4 GeV, muon
pairs coming from J/ψ decays contaminate the signal, while Υ(1S) decaying into
µ+ µ− dominate the mass spectrum between 9.3 and 9.6 GeV. Also, above 9 GeV
there is not sufficient signal leading to a final mass range of 4 to 9 GeV.
3.5.1
Consecutive Kinematic Cuts
Using the reweighted likesign dataset as background and the Monte Carlo simulation as signal, it is now possible to identify cut variables to improve the signal
to background ratio.
The following variables show significant differences between signal and background and are used to improve the signal to background ratio:
• First, tracks with a high reduced χ2 or
χ2
n.d.f.
in the track fit are removed.
High values point to badly reconstructed tracks or kinks due to decays in
flight. Eliminating these tracks mainly removes muons coming from decays
in flight and bad matches between track segments (Fig. 3.22(a)).
• Both muons from a Drell Yan process are generated at the interaction
point in contrast to background muons. Muon pairs with a large significance of the distance between muon vertex and primary vertex Svv =
vertex distance
√ muon vertex − primary
, the impact parameter, are therefore
2
2
(muon vertex error) +(primary vertex error)
rejected, reducing random combinations between decay muons (Fig. 3.22(b)).
• As a criterion of vertex quality, a cut on the distance of closest approach ddoc
of both muons is applied, again removing random combinations of unrelated
muons or muons coming from kaon or pion decays (Fig. 3.22(c)).
• Background muons from decays in flight have a lower value of the muon
likelihood6 Lµ . A minimum cut on the product of the muon likelihood of
both muons is applied (Fig. 3.22(d)).
6
The tracking software used at HERA-b calculates for each track the likelihood of a muon
hypothesis from input from the muon detector.
66
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
• The average transverse momentum of the muons in Drell Yan decays is
higher than that of background muons as seen in Fig. 3.22(e).
• Finally, background muons from decays in flight have a higher kaon likelihood7 value LK (Fig. 3.22(f)), hence a cut on the maximum kaon likelihood
is applied.
Fig. 3.22 shows the dependance of signal and background on the six variables. The
signal and background samples in these plots are normalized to an area of one.
An optimization of the ratio of signal to background is not the best strategy. Due
to the low statistics available and the background subtraction procedure applied
to data, a high cut efficiency is preferable over a high purity of the remaining
data. For this reasons the significance
S=√
signal
signal + background
(3.16)
was chosen as an optimization criterium.
The final choice of cut values is decided on the basis of the distributions shown in
Fig. 3.23. In these histograms, the x axis represents the current cut value and the
left y axis the number of Drell Yan Monte Carlo signal and simulated opposite
sign background events remaining after the cut, normalized to the corresponding
number of events with only event based, fiducial and mass range cuts applied.
The right y axis represents the value of the significance S depending on the cut.
The tightness of the cuts increases in the direction of the arrows.
The six cuts are applied successively in the order of the histograms. Fig 3.23(b)
includes the cut chosen from Fig 3.23(a), Fig 3.23(c) includes those chosen from
Fig 3.23(a) and 3.23(b), and so on. The chosen cut values are indicated by the
dashed lines and are also listed in table 3.4. Events with cut values in the direction of the arrows are accepted by the cut. The values were chosen to maximize
the significance S in all six variables.
7
Similar to the muon likelihood, the likelihood of a kaon hypothesis is also provided using
data from the RICH.
3.5. OPTIMIZATION OF EVENT SELECTION
cut criterium
clone removal
fiducial cuts
mass range
hits per track
in muon system
track fit χ2 / ndf
Svv
ddoc
Lµ (µ1 ) · Lµ (µ2 )
max(pt (µ1,2 ))
max(LK (µ1,2 ))
67
cut value
n.a.
n.a.
4GeV < Mµµ < 9 GeV
efficiency
S/B
S
>4
100%
0.22 17.1
< 1.45
< 2.5
< 0.012 cm
> 0.3
> 1.75 GeV
< 0.8
90.8%
88.2%
86.1%
79.5%
71.0%
69.8%
0.52
0.61
0.64
0.78
1.62
1.92
22.2
23.0
23.1
23.5
25.9
27.0
Table 3.4: Cuts used in muon analysis. Listed are the cut, the
chosen value, the amount of signal remaining (efficiency), the signal
to background ratio ( S/B) and the significance (S) after the cut and
all above are applied. Tracks that fail the clone removal, the cut on
the number of hits per track in the muon system or the mass cut do
not enter the analysis, thus the efficiency is defined to be 100% after
these are applied. All cuts were chosen to maximize the significance
S.
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
MC signal
likesign bg
10
10
-1
probability per bin
probability per bin
68
MC signal
likesign bg
10
-2
10
10
-1
-2
-3
10
-3
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
χ 2 /n.d.f.
MC signal
likesign bg
10
10
10
-1
1
1.5
2
2.5
3 3.5 4
significance
1
10
MC signal
likesign bg
-1
-2
10
-3
0
0.01
0.02
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2
likelihood
10
-2
(d) Product of muon likelihoods
probability per bin
10
MC signal
likesign bg
-1
1
10
10
10
-2
0.03
doc [cm]
(c) Distance of closest approach of
muons
probability per bin
0.5
(b) Impact parameter significance
probability per bin
probability per bin
(a) Reduced χ2
0
MC signal
likesign bg
-1
-2
-3
10
0
1
2
3
4
5
6
p t [GeV]
(e) Transverse momentum of muon
vertex
-3
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
likelihood
(f) Kaon likelihood
Figure 3.22: Dependance of signal MC and likesign background
on (a) the reduced χ2 of the muon track fit to the detector hits,
(b) the impact parameter significance, (c) the distance of closest
approach of the muons, (d) the product of the muon likelihood of
the two tracks, (e) the transverse momentum of the reconstructed
vertex and (f ) the kaon likelihood of the tracks.
22
20
18
0.8
16
14
0.6
12
69
24
1
22
20
0.8
18
16
14
0.6
MC signal
likesign bg
10
0.4
6
likesign bg
4
6
0.2
4
2
2
0
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
χ 2/n.d.f.
0
0
0.5
1
1.5
20
0.8
18
16
MC signal
likesign bg
significance
14
20
0.8
15
0.6
12
MC signal
10
likesign bg
0.4
0.2
x10
0
0.25
0.3
doc [cm]
-1
0
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
2
(muon likelihood)
1
25
0.8
20
0.6
15
(d) Product of muon likelihoods
remaining after cut
S
remaining after cut
(c) Distance of closest approach of
muons
S
2
0.15
5
0.2
4
0.1
10
significance
6
0.05
0
3 3.5 4
significance
1
8
0
0
2.5
25
22
remaining after cut
24
1
0.2
2
(b) Impact parameter significance
S
remaining after cut
(a) Reduced χ2
0.4
10
8
significance
0.6
12
1
25
0.8
20
0.6
15
MC signal
likesign bg
0.4
10
significance
0.4
MC signal
10
likesign bg
0.2
0
0
5
0.5
1
1.5
2
S
0.2
MC signal
significance
0.4
8
S
1
remaining after cut
S
remaining after cut
3.5. OPTIMIZATION OF EVENT SELECTION
0
2.5
3
p t [GeV]
(e) Transverse momentum of muon
vertex
0.2
significance
5
0
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
kaon likelihood
(f) Kaon likelihood
Figure 3.23: Effect of the consecutive cuts on signal and background rates and on the value S, the significance as defined in
Eq. (3.16). (a) shows the cut on the reduced χ2 of the track fit, (b)
on the impact parameter significance, (c) on the distance of closest
approach of the muons, (d) on the product of the muon likelihoods
of the tracks, (e) on the transverse momentum of the reconstructed
vertex and (f ) on the kaon likelihood of the tracks. The left axis
shows the percentage of signal and background events remaining
after this and all previous cuts, the right axis corresponds to the
optimization value S.
70
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
3.5.2
Further Geometrical Cuts
After the definition of the selection criteria they are applied to all data sets and the
final Drell Yan Monte Carlo weights can be determined as described in Sec. 3.4.
After subtraction of the background, the signal distribution is now compared for
the first time to the distributions of accepted Drell Yan Monte Carlo events.
In a first step, geometrical distributions of tracks which are relatively independent
of the details of the kinematics are compared in order to verify if data and Monte
Carlo are in agreement. Fig. 3.24 shows the x position in the magnet focal plane
and in the muon station MU3 of all tracks passing through tracking station PC1
with a y coordinate of −20.0 cm < y < 20.0 cm.
It can be noted that the agreement between data and Monte Carlo is rather poor
(a)
(b)
Figure 3.24: x position of tracks passing station PC1 left and right
of the insensitive inner region (−20.0 cm < y < 20.0 cm). (a)
shows the x coordinate in the magnet focal plane, (b) in the muon
station MU3.
in the transition region between Inner and Outer tracker. This is not unexpected.
The fiducial cuts introduced at the beginning of the chapter were applied because
of discrepancies between simulation and reality in the detector description in
this area. Additionally, the Single Track Monte Carlo simulation uses the same
detector simulation as the Drell Yan Monte Carlo which introduces an additional
bias in the transition region. For these reasons, the fiducial cuts were expanded
to include tracks with the coordinates −14.0 cm < xmag < 14.0 cm in the
magnet focal plane and −65.0 cm < xMU3 < 65.0 cm at the z position of the
muon station MU3. Tracks passing within either one of these regions are also
removed. The distributions after the additional geometrical cut can be seen in
3.5. OPTIMIZATION OF EVENT SELECTION
71
70
data signal
reconstructed MC
60
counts
counts
Fig. 3.25. The remaining differences can be explained by statistics. A comparison
of the distributions gives a χ2 /ndf = 39.4/26 and a probability of 4.5%.
The data sample remaining after applying all fiducial, kinematic and geometrical
50
data signal
reconstructed MC
40
50
30
40
30
20
20
10
10
0
-40 -30 -20 -10
(a)
0
10
20 30 40
x magnet [cm]
0
-100
-50
0
50
100
x MU3 [cm]
(b)
Figure 3.25: x position of tracks passing station PC1 left and right
of the insensitive inner region (−20.0 cm < y < 20.0 cm). (a)
shows the x coordinate in the magnet focal plane, (b) in the muon
station MU3. A geometrical cut is applied, all tracks passing the
magnet focal plane wiothin −14.0 cm < xmag < 14.0 cm and the
station MU3 within −65.0 cm < xMU3 < 65.0 cm are removed.
cuts consists of 930 ± 30 outbending and 566 ± 24 inbending unlikesign muon
pairs. The mass distribution of the unlikesign data after cuts is shown in 3.26.
Also included are the likesign distributions with the acceptance reweights from
the Single Track Monte Carlo applied. Here a problem is already visible: the bin
at a reconstructed invariant mass of 6.1 GeV contains too few unlikesign and too
many likesign events compared to the bins to the left and the right. This will be
discussed in more detail in Sec. 4.5.
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
counts per 333 MeV
unlike data: 930 evts
++ likesign data: 389 evts
10
-- likesign data: 290 evts
2
unlike data: 566 evts
counts per 333 MeV
72
++ likesign data: 248 evts
10
2
-- likesign data: 224 evts
10
10
1
1
4
5
6
7
8
9
10 11 12
M µµ [GeV]
(a) Outbending muon pairs
4
5
6
7
8
9
10 11 12
M µµ [GeV]
(b) Inbending muon pairs
Figure 3.26: Mass distribution of data after cuts and reweighting
of likesign background. (a) Outbending and (b) inbending muon
pairs, each with correspondingly reweighted likesign pairs. The data
has not yet been corrected for detector acceptance and no background
subtraction has been applied.
3.5. OPTIMIZATION OF EVENT SELECTION
3.5.3
73
Cut on Event Likelihood
Whereas the first data selection is cutbased, a likelihood based method was also
implemented to check if the significance S can be improved. Fig. 3.22 show the
dependance of signal and background events as a function of the cut variables i,
normalized to unity. The y axis is then proportional to the probability to find
a signal or background event with a given value vi of the plotted variables. For
bg
each data event, these probabilities for signal psig
i (vi ) and background pi (vi ) are
extracted from the distributions, once for each of the six cut variables. The twelve
values are then used to calculate a total event signal likelihood Psignal by
psig
i (vi )
i
= Q sig
Q
pi (vi ) + pbg
i (vi )
Q
Psignal
i
(3.17)
i
MC signal
likesign bg
-1
10
remaining after cut
probability per bin
Instead of applying a hard cut on the six variables this method allows to apply
only one cut on the combined variable Psignal (3.17).
The distribution of Psignal is shown both for Monte Carlo simulated events and
1
25
0.8
20
0.6
MC signal
15
likesign bg
10-2
significance
0.4
10
0.2
10-3
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Psignal
(a)
5
0
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
P signal
(b)
Figure 3.27: Event likelihood. (a) shows the distribution of likelihood values Psignal for Monte Carlo simulated events and simulated
opposite sign background. (b) illustrates the effect of a cut on the
event likelihood on both Monte Carlo signal and likesign background.
simulated opposite sign background in Fig. 3.27(a). The signal events have a clear
peak at a value of 1, while the background events are distributed evenly across the
distribution with a smaller peak around 0. The effect of a cut on Psignal on signal
and background depending on the chosen value is shown in Fig. 3.27(b). From
this distribution, a value of 0.87 was picked, maximizing again the significance S.
74
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
76.2% of signal and 9.0% of background survive this cut, leading to a significance
of 26.5 and a signal over background ratio of 1.89. Both of these values are slightly
lower than those after the cutbased analysis.
The result of this cut is shown in Fig. 3.28(b), compared to the result of the six
consecutive cuts. Both results are compatible within errors.
3.5. OPTIMIZATION OF EVENT SELECTION
3.5.4
75
Final Data Sample
After background subtraction according to equation (3.5), a Drell Yan signal of
921 ± 43 events remains using the consecutive cuts method, while the likelihood
method results in 911 ± 50 events. The result of both methods is identical within
errors. Since the likelihood method does not give a better significance, the cut
based method was chosen to derive cross sections. It has the advantage that the
effects of the different variables can be seen more easily. The mass distribution
after the six kinematic cuts is shown in 3.28(a), the one after a cut on the the
signal likelihood in 3.28(b). The dip in the mass distribution at 6.1 GeV, which
was already visible in the distributions of opposite sign data shown in Fig. 3.15
before and in Fig 3.26 after cuts, is still present after background subtraction.
(a) Cut based
(b) Likelihood based
Figure 3.28: Mass distribution of signal extracted after cuts and
background subtraction, not yet corrected for luminosity and acceptance. Histogram (a) shows the data after applying the six consecutive kinematic cuts, histogram (b) after the single cut on Psignal
(3.17). The results of both analysis methods are consistent.
76
3.6
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
Electron Data
At HERA-b not only muon pairs were observed, a similar sized data sample of
electron pairs was also taken. The distribution of the dielectron mass is shown in
Fig. 3.29. The data is plotted in the J/ψ and Drell Yan mass region separately
for three different selection criteria. Distributions 3.29(a) and 3.29(b) contain the
full dataset while 3.29(c) and 3.29(d) show the data that pass a set of preliminary
selection criteria. These criteria were chosen to maximize signal over background
of the J/ψ peak, since the decay of a J/ψ has a similar experimental signature as
the Drell Yan process. They consist of cuts on the value of E/p and the reduced
χ2 of the track fit of both electrons, the significance of the distance between
electron vertex and primary vertex Svv , the distance of closest approach of the
electrons ddoc and the distance between the electron tracks and the corresponding
cluster in the electromagnetic calorimeter dtc . Their values are listed in Tab. 3.5.
No cut on the transverse momentum of the electrons was applied because the
average pt of electrons coming from a J/ψ is far lower than that of those created
by a Drell Yan process.
As easily seen, the amount of likesign data relative to the unlikesign sample is
cut criterium
clone removal
E/p
track fit χ2 / ndf
Svv
ddoc
dtc
cut value
n.a.
0.88 < E/p < 1.18
< 2.5
< 3.0
< 0.013 cm
< 2.0 cm
Table 3.5: Preliminary cuts used in the dielectron analysis. Their
values were chosen to maximize signal over background of J/ψ ,
which has the same experimental signature as a Drell Yan event.
much lower than in the dimuon case and almost none of it remains after the loose
selection criteria listed above. This is due to the fact that the dielectron trigger
asks for at least one positive and one negative electron per event. This is a much
more stringent selection compared to the muon trigger and was necessary to keep
the trigger rate of electron pairs under control. The few likesign electron events
in the data are thus caused by three or more trigger electrons in one event. This
makes using the likesign electron data as a background simulation to Drell Yan
unusable.
Without a likesign electron pair data sample, the only option to simulate the
background that remains is event mixing. After it became obvious that event
mixing is unable to simulate the background due to the intrinsic nonconservation
of momentum, the analysis of the dielectron data was discontinued.
80
x10
77
2
unlikesign data
70
likesign data
60
50
40
counts per 333 MeV
counts per 33 MeV
3.6. ELECTRON DATA
unlikesign data
likesign data
10
10
3
2
30
20
10
10
0
2.7
2.8
2.9
3
3.1
3.2
4
3.3 3.4 3.5
M ee [GeV]
5
6
(a)
8
9
10 11 12
M ee [GeV]
(b)
2
35
unlikesign data
likesign data
30
25
20
counts per 333 MeV
counts per 33 MeV
x10
7
10
3
unlikesign data
likesign data
10
2
10
15
10
1
5
0
2.7
2.8
2.9
3
(c)
3.1
3.2
3.3 3.4 3.5
M ee [GeV]
4
5
6
7
8
9
10 11 12
M ee [GeV]
(d)
Figure 3.29: Distribution of the dielectron mass. (a) and (c) show
the mass distribution around the J/ψ mass, (b) and (d) the mass
range used in the Drell Yan analysis with no cuts or a full set of
preliminary cuts applied, respectively. After cuts no likesign data
remains.
78
CHAPTER 3. DATA SELECTION & BACKGROUND SUBTRACTION
Chapter 4
Determination of Cross Sections
In this chapter the measured differential cross sections of the Drell Yan process
are presented. Two steps are still necessary to calculate these cross sections.
First, the luminosity of the data used in the analysis is determined. Since the
luminosity of the lepton triggered runs is not available, it has to be determined
indirectly via the yield of a process with a known cross section. As a cross check,
the luminosity determined in the first section is also used to calculate the cross
section of Υ production, which is compared to the result of a dedicated Υ analysis at HERA-b. Second, the acceptance of the detector is given as a function of
several kinematic variables as determined from Drell Yan Monte Carlo.
From the differential cross sections of the Drell Yan process, the nuclear suppression factor α is determined and the parameters of the Lam Tung relation
are extracted. Finally, selected results are compared to measurements from the
experiments E772 and NA50 and a study of systematic effects is presented.
4.1
Luminosity Determination
At HERA-b, the luminosity is only known for runs which use the minimum bias
trigger1 ([Bru05]). For dilepton triggered runs, the luminosity has to be determined indirectly via a known cross section of a second process. By comparing
the number of observed J/ψ → µ+ µ− events NJ/ψ in the same data sample that
was also used for the Drell Yan analysis to the known J/ψ cross section σJ/ψ , the
luminosity of the triggered data L can be calculated as:
L=
σJ/ψ ·
Aα
NJ/ψ
,
· Br(J/ψ → µ+ µ− ) · εJ/ψ
1
(4.1)
The minimum bias trigger is a trigger that randomly selects events containing an interaction
during datataking, as opposed to the dimuon or dielectron trigger, which requires two muons
or electrons to be present in an event.
79
80
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
where A is the mass number of the target nucleus, α the target mass dependance of the cross section, Br(J/ψ → µ+ µ− ) the branching ratio and εJ/ψ the
detector acceptance for the observed decay J/ψ → µ+ µ− . Since the data consists of interactions with wires of different materials, the number of events has to
be determined separately for each of the wire materials Tungsten, Carbon and
Titanium:
LW =
LC =
LTi =
W
NJ/ψ
σJ/ψ · AW α · Br(J/ψ → µ+ µ− ) · εJ/ψ
C
NJ/ψ
σJ/ψ · AC α · Br(J/ψ → µ+ µ− ) · εJ/ψ
Ti
NJ/ψ
σJ/ψ · ATi α · Br(J/ψ → µ+ µ− ) · εJ/ψ
(4.2)
(4.3)
(4.4)
To calculate the number of J/ψ events NJ/ψ , the reconstructed invariant mass
distribution of data around the J/ψ mass peak is fitted with a function consisting
of three separate parts,
fJ/ψ = c0 · fgauss + c1 · frad + fbg ,
(4.5)
where fgauss is a double gaussian in which both gauss functions have the same
mean µ, a radiation tail frad ([Spi04]) and a sum of two exponentials as background fbg . A second gauss function is necessary to account for events which
suffered from multiple scattering in the detector, see also ([Hus05]), as these
events have a lower mass resolution. The radiation tail is caused by the radiative
decay J/ψ → µ+ µ− γ. Thus, the formulas for these functions are:
"
2 !
2 !#
1 M −µ
1 M −µ
fgauss = (1 − c2 ) · exp −
+ c2 · exp −
2
σ0
2
σ1
frad = 12 · exp [c3 (M − µ)] · (M − µ)2 · |c3 |3
fbg = exp [c4 + c5 M ] + exp [c6 + c7 M ]
The signal part of the function is then integrated over the mass range of the J/ψ
peak to derive the number of observed J/ψ :
Z
Z
NJ/ψ = c0 fgauss dM + c1 frad dM
(4.6)
As already discussed in Sec. 3.4 the transverse momentum of the J/ψ is not
simulated properly. Thus, the J/ψ Monte Carlo simulation suffers from the same
problem as the Drell Yan Monte Carlo simulation. The discrepancy between data
and simulation can be seen in 4.1. As the transverse momentum is not directly
used in the luminosity determination, a bin by bin correction was applied to
reweight the simulation to match the data distribution. After the reweighting,
counts per 120 MeV
4.1. LUMINOSITY DETERMINATION
10
x10
81
3
J/ ψ data
J/ ψ MC, not reweighted
8
6
4
2
0
0
1
2
3
4
5
6
p t µµ [GeV]
Figure 4.1: Distribution of the transverse momentum of the J/ψ
in data and in the Monte Carlo simulation before reweighting.
the reconstructed and generated J/ψ Monte Carlo can be used to calculate the
acceptance for J/ψ → µ+ µ− , εJ/ψ .
To improve the signal to noise of the J/ψ peak, a loose set of cuts is applied
before fitting the signal peak in the invariant mass distribution. These are given
in Tab. 4.1.
The result of these cuts can be seen in Fig. 4.2(a) to 4.2(c), separated according
to the material of the target wire. Also shown in each plot is the total fit function
and separately the radiation tail and background components of the fit. The
results of the fits are given in Tab. 4.2, together with the other variables used in
the luminosity calculation. This leads to a total luminosity of the data used in
the Drell Yan analysis of:
LW = (1320 ± 140) nb−1
LC = (32000 ± 3000) nb−1
LTi = (36 ± 5) nb−1
(4.7)
(4.8)
(4.9)
The error on the luminosity is dominated by the uncertainity of the J/ψ
cross section of roughly 10%. Studies on the systematical effect of the kinematic
selection given in Tab. 4.1 and the shape of the fit function 4.5 on the total error
have shown that their influence is smaller than the statistical error of NJ/ψ , which
is about 1%. The systematic error is thus negligible in comparison to the error
on the J/ψ cross section and the total error of the luminosity.
82
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
cut criterium
clone removal
fiducial cuts
hits per track
in muon system
track fit χ2 / ndf
Svv
ddoc
Lµ (µ1 ) · Lµ (µ2 )
max(LK (µ1,2 ))
cut value
n.a.
n.a.
>4
< 2.5
< 3.0
< 0.02 cm
> 0.2
< 0.99
Table 4.1: Cuts used in J/ψ selection. The selection variables are
the same as those listed in Tab. 3.4 and explained in Sec. 3.5.
NJ/ψ
A
σJ/ψ ([Bar05])
α ([Lei00])
Br(J/ψ → µ+ µ− )([Pdg06])
εJ/ψ
Tungsten
Carbon
Titanium
36771 ± 509 65095 ± 586 273 ± 26
183.84
12.0107
47.867
501 ± 44 nb/nucleon
0.96 ± 0.01
0.0593 ± 0.0006
0.732 % ± 0.008 %
Table 4.2: Values used in luminosity calculation.
4.1. LUMINOSITY DETERMINATION
83
×103
unlikesign data
total fit
background fit
radiation tail fit
6
5
counts
counts
×103
unlikesign data
total fit
background fit
radiation tail fit
10
8
4
6
3
4
2
2
1
0
2.7 2.8 2.9
3
0
2.7 2.8 2.9
3.1 3.2 3.3 3.4 3.5
Mµµ [GeV]
60
unlikesign data
total fit
background fit
radiation tail fit
50
40
3.1 3.2 3.3 3.4 3.5
Mµµ [GeV]
(b) Mass distribution from Carbon target
x10
counts
counts
(a) Mass distribution from Tungsten target
3
2
14
12
10
8
30
6
20
4
2
10
0
2.7 2.8 2.9
3
3.1 3.2 3.3 3.4 3.5
Mµµ [GeV]
(c) Mass distribution from Titanium target
0
2.7
2.8
2.9
3
3.1
3.2
3.3 3.4 3.5
M J/ψ [GeV]
(d) Reconstructed J/ψ Monte Carlo
Figure 4.2: Invariant mass distribution of the reconstructed muon
pair at the J/ψ mass. (a) shows the distribution of unlikesign data
from the Tungsten wire including a fit to the J/ψ peak, (b) from
Carbon and (c) from a Titanium target wire. (d) shows the distribution of a reconstructed J/ψ Monte Carlo simulation. The fits to
the data distributions are according to Eqn. (4.5).
84
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
4.2
Υ(1S) Cross Section
During the event selection (Sec. 3.5), a cut on the invariant mass of the muon
pair of 4 GeV < Mµµ < 9 GeV was applied to remove muon pairs generated by
decays of J/ψ and Υ. Fig. 4.3(a) shows the invariant mass distribution above 8.6
GeV without this cut. A clear Υ(1S) signal can be seen. With the Υ(1S) Monte
Carlo simulation shown in Fig. 4.3(b) and the luminosity calculated in Sec. 4.1
it is possible to determine the cross section, which is calculated as follows:
σΥ =
NΥ
,
L · Aα · Br(Υ → µ+ µ− ) · εΥ
(4.10)
χ2 / ndf
10
7.792 / 16
Prob
c0
0.9548
5.519 ± 1.894
mean MΥ (1S)
9.475 ± 0.066
c1
7.57 ± 3.07
c2
-0.835 ± 0.570
counts
counts
where Br(Υ → µ+ µ− ) is the branching ratio of the decay into two muons, NΥ is
the number of Υ events seen, A is the mass number of the target nuclei, α the
target mass dependance of the cross section and εΥ the detector efficiency which
is calculated from the reconstructed and the generated Υ Monte Carlo simulation.
The mass distribution was fitted between 8 and 11 GeV with three gaussians and
400
350
300
250
200
1
150
100
50
10-18
9
10
(a)
11
Mµµ [GeV]
0
8
9
10
11
MΥ (1S) [GeV]
(b)
Figure 4.3: Invariant mass distribution of the reconstructed muon
pair above 8.6 GeV. (a) shows the distribution of unlikesign data
and a fit (4.12), (b) shows the distribution of a reconstructed Υ(1S)
Monte Carlo simulation.
an exponential distribution. The mean values of the two higher mass gauss peaks
were fixed with respect to the lower gauss peak according to the mass values of
the Υ states (1S), (2S) and (3S) as given in [Pdg06]. Their relative size was also
fixed according to results from E605 ([Mor91]):
N (1S) : N(2S) : N(3S) = (70 ± 3) : (20 ± 2) : (10 ± 1)
(4.11)
4.2. Υ(1S) CROSS SECTION
85
The width of the gauss distributions is also fixed. For the first peak corresponding
to the (1S) state it is set to 159 MeV/c2 , the expected muon momentum resolution
gained by extrapolating from the resolution measured in J/ψ decays ([Abt06]); for
the two peaks corresponding to the higher mass states (2S) and (3S) the widths
are scaled up proportional to their mass as given in [Pdg06]. The fit function is
then given by:
"
1 (Mµµ − MΥ(1S) )2
N (MΥ ) = c0 0.7 · exp −
+
2 (159 MeV/c2 )2
1 (Mµµ − MΥ(2S) )2
(4.12)
0.2 · exp −
+
2 (168 MeV/c2 )2
#
1 (Mµµ − MΥ(3S) )2
+
exp
c
+
c
·
M
0.1 · exp −
2
3
Υ(2S)
2 (174 MeV/c2 )2
The mass of the Υ(1S) MΥ , the overall number of Υ c0 and the two parameters
of the exponential background, c1 and c2 , are the four free parameters.
The fit shown in Fig. 4.3(a) returns NΥ(1S) = 15.4 ± 5.3, NΥ(2S) = 4.6 ±
1.6 and NΥ(3S) = 2.4 ± 0.8 events. As the mass of the Υ(1S) state, a value
of 9.47 ± 0.07 GeV is determined. This agrees well with the PDG value of
9.46030 ± 0.00026 GeV.
Inserting the total number of Υ, NΥ = 22.4 ± 5.6, the luminosity (4.7) and the
Υ detector efficiency εΥ = 0.74 ± 0.02% into (4.10) yields:
σΥ = 225 ± 64 pb/nucleon
(4.13)
√
at a center-of-mass energy of s = 41.6 GeV and within the acceptance of HERAb of −0.45 < xF < 0.05. A dedicated analysis searching for Υ at HERA-b
([Abt06]) published an Υ → µ+ µ− cross section of
Br(Υ → µ+ µ− ) ·
dσ
NΥ
1
pb
|y=0 (Υ) =
·
= 4.0 ± 1.0
, (4.14)
α
dy
L · A · εΥ ∆yeff
nucleon
Υ(1S)
Υ(1S)
Υ(1S)
N
15.4 ± 5.3 4.6 ± 1.6 2.4 ± 0.8
N (Υ)
22.4 ± 5.6
εΥ
0.74% ± 0.02%
∆yeff
1.14 ± 0.12stat
L · Aα
546 ± 381/pb
+ −
Br(Υ → µ µ ) ([Pdg06])
2.48 ± 0.05%
Table 4.3: Values used in the determination of the Υ cross section.
86
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
where ∆yeff = 1.14 ± 0.12syst is a factor connecting full and differential cross
sections at mid rapidity. Calculating the same value using the measurement from
above results in:
Br(Υ → µ+ µ− ) ·
dσ
pb
|y=0 (Υ) = (4.9 ± 1.4)
,
dy
nucleon
which is in good agreement with the value published in [Abt06].
(4.15)
4.3. DETECTOR ACCEPTANCES
4.3
87
Detector Acceptances
The detector acceptance as a function of kinematic variables is calculated from
generated and reconstructed Drell Yan Monte Carlo events. The kinematic selection chosen in Sec. 3.5 is applied to the reconstructed Drell Yan Monte Carlo
dataset for this calculation. Fig. 4.4 shows these acceptances as a function of the
reconstructed
the Feynman x
√ mass (4.4(a)), the transverse momentum (4.4(b)),
xF = 2pz / s (4.4(c)) and the pseudorapidity η = − ln tan 2θ (4.4(d)) of the
muon pair for outbending and inbending muon pairs. In Fig. 4.4(e) and 4.4(f),
the acceptance is plotted as a function of cos(θCS ) and φCS of the positive muon.
The index CS here implies that the angles are calculated in the Collins Soper
([Col77]) frame (see Sec. 2.3 for a definition of the Collins Soper frame).
As expected from the effects of the charge combination of the muon tracks explained in Fig. 3.8, the acceptance of outbending muon pairs is larger than that
of inbending ones. While the acceptance is relatively flat in the reconstructed
mass and transverse momentum of the muon pair, the other distributions show a
significant dependance on their kinematic variances. In xF , the detector limits the
detectable range to −0.45 < xF < 0.05, with outbending muon pairs having a
slightly more positive average xF value than inbending muon pairs. The difference
between out- and inbending muon pairs is especially pronounced in Fig. 4.4(f)
showing depencance of acceptance on the φCS of the positive muon. Outbending
muon pairs are only detected if the positive muon has a |φCS | < 1.8. For inbending muon pairs, the requirement on φCS is just the opposite: |φCS | > 1.2.
acceptance
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
acceptance
88
outbending events
inbending events
10
10
-2
inbending events
10
-3
4
5
6
7
8
9
acceptance
acceptance
inbending events
10
10
-2
-3
-4
-0
10
0.1
xF
outbending events
inbending events
10
10
10
-4
0
2
3
4
5
6
p t [GeV]
0.5
cos( θ CS)
(e) cos θCS of positve muon
-1
outbending events
-2
-3
-4
-8
-6
-4
-2
0
2
η
4
inbending events
10
-3
-0.5
1
outbending events
10
-2
-1
0
(d) Pseudorapidity of muon pair
acceptance
-1
-3
inbending events
10
(c) Feynman x (xF ) of muon pair
10
10
10
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1
-2
(b) Transverse momentum of muon
pair
outbending events
10
10
10 11 12
M µµ [GeV]
(a) Mass of muon pair
acceptance
outbending events
1
10
-2
-3
-4
-3
-2
-1
0
1
(f) φCS of positive muon
Figure 4.4: Detector acceptance as a function of reconstructed
mass (a), transverse momentum (b), xF (c) and pseudorapidity η
(d) of the muon pair. (e) and (f ) show the acceptance as depending
on cos(θCS ) and φCS of the positive muon. All distributions were
calculated by dividing distributions from reconstructed DYMC by
those from generated DYMC.
2
3
φ CS
4.4. ACCEPTANCE CORRECTED KINEMATIC DISTRIBUTIONS
4.4
89
Acceptance corrected Kinematic Distributions
Using the luminosity calculated in Sec. 4.1 and the detector acceptance distributions from Sec. 4.3 it is now possible to calculate differential cross sections. At
other experiments, it is usually assumed that the Drell Yan cross section depends
linearly on the mass number of the target material. [Ale06] published a value of
α = 0.98 ± 0.02. Fig 4.5(a) and Fig 4.5(b) show the distribution of data, corrected for acceptance and luminosity as a function of the transverse momentum
of the muon pair, separated for the two target materials Tungsten and Carbon.
No corrections for target material have been applied yet. Fig 4.5(c) shows a ratio
of the two distributions, with a constant function fitted to the ratio. Using the
mass numbers of Tungsten and Carbon, one can calculate the A dependance of
the Drell Yan cross section from this constant fit: α = 1.03 ± 0.03, which is also
compatible with 1.
For the calculations of the Drell Yan differential cross sections a value of α = 1 is
used. Four differential cross sections are shown in Fig. 4.6, as a function of invariant mass (4.6(a)), the square of the transverse momentum (4.6(b)), xF (4.6(c))
and the pseudorapidity of the muon pair from the Drell Yan process. The mass
distribution again shows a deficit around 6.2 GeV, which will be examined in the
dσ
next section. The differential cross section dM
as shown in Fig. 4.6(a) is fitted
µµ
with the phenomenological function:
dσ
−c
∝ Mµµ
.
dMµµ
(4.16)
This function was derived from the distribution of the dimuon mass in generated
Drell Yan Monte Carlo. The fit value for the exponent c is c = 5.52 ± 0.31.
The low probability of the fit is caused by the bin at 6.2 GeV. Excluding this bin
from the fit yields a value of c = 5.18 ± 0.26 with a reduced χ2 of 13.2/12 and
a fit probability of 35%.
Fig. 4.6(b) shows the differential Drell Yan cross section as a function of p2t of
the muon pair. The fit is an exponential function. No significant deviation from
an exponential decrease is visible.
The xF distribution (Fig. 4.6(c)) is fitted with the empirical function
dσ
∝ (1 − |xF − x0 |)C ,
dxF
(4.17)
which gives a value of C = 4.18 ± 0.47 for the exponent. The mean of the
distribution is compatible with zero at x0 = −0.0002 ± 0.0228. This is the
first measurement of the differential Drell Yan cross section in the negative xF
range. The shape of the distribution is as expected. A more detailed comparison
to measurements from the experiment E772 at Fermilab will follow in Sec. 4.7.1.
90
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
The total cross section measured
in the the mass range of 4 GeV to 9 GeV at a
√
center-of-mass energy of s = 41.6 GeV and within the xF range seen at HERA-b
of −0.45 < xF < 0.05 is gained by integrating over the xF distribution:
σDYxf →µµ = (172 ± 10) pb/nucleon.
(4.18)
The cross section over the full range of xf can be calculated by integrating the
function (4.17). The result is
σDY→µµ = (289 ± 35) pb/nucleon.
(4.19)
The differential cross section dσ/dη as seen in Fig. 4.6(d) shows a flat behavior
at small values of the pseudorapidity and a sharp drop between −2 and −4. The
corresponding behavior in the positive range cannot be seen as it is just outside
the acceptance of HERA-b.
acc. corr. events
16
14
12
10
0.6
0.5
0.4
6
0.3
4
0.2
2
0.1
0
0
1
2
3
4
91
0.7
8
0
0
5
6
p t [GeV]
(a) pt of muon pairs from Tungsten wire
ratio
acc. corr. events
4.4. ACCEPTANCE CORRECTED KINEMATIC DISTRIBUTIONS
1
2
3
4
5
6
p t [GeV]
(b) pt of muon pairs from Carbon wire
60
χ2 / ndf
Prob
p0
50
9.912 / 14
0.7686
16.55 ± 1.22
40
30
20
10
0
0
1
2
3
4
5
6
pt [GeV]
(c) Ratio of pt distributions
Figure 4.5: (a + b): Acceptance corrected pt distributions of data,
separated according to target material. (c): Ratio of distributions
(a) and (b), fitted with a constant function.
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
d σ/dMµµ [nb/(GeV nucleon)]
χ2 / ndf
37 / 13
Prob
p0
10-1
0.0004137
507.1 ± 268.1
-5.518 ± 0.313
p1
d σ/dpt2 [nb/(GeV2 nucleon)]
92
10-3
0.07452
p0
-2.159 ± 0.080
p1
-0.5321 ± 0.0346
10-3
4
5
6
7
8
9
Prob
7.922 / 11
10
0.7203
c0
0.749 ± 0.073
x0
-0.0001977 ± 0.0227995
C
4.184 ± 0.467
1
2
3
4
5
6
7
8 9 10
p2t [GeV2]
(b) Squared transverse momentum of muon
pair
d σ/d η [nb/nucleon]
χ2 / ndf
0
10 11 12
Mµµ [GeV]
(a) Mass of muon pair
dσ/dxF [nb/nucleon]
27.24 / 18
Prob
10
10-2
10-2
1
χ2 / ndf
-1
10
-1
-2
10-1
10
10-2
-0.6 -0.5 -0.4 -0.3 -0.2 -0.1
-0
(c) Feynman x (xF ) of muon pair
0.1
xF
-3
-8
-6
-4
-2
0
2
(d) Pseudorapidity of muon pair
Figure 4.6: Differential cross sections of Drell Yan depending on
the reconstructed mass (a), the square of the transverse momentum
(b), the Feynman x (xF ) (c) and the pseudorapidity (d) of the muon
pair.
η
4
4.5. SYSTEMATIC CHECKS OF THE MASS DISTRIBUTION
Systematic Checks of the Mass Distribution
unlike-like data (signal): 921 evts
Drell Yan rec. MC, reweighted
10
2
counts per 333 MeV
counts per 333 MeV
4.5
10
10
1
10
4
93
5
6
7
8
9
10 11 12
M µµ [GeV]
(a) Before acceptance correction
acceptance corr. data signal
Drell Yan generated MC
4
3
4
5
6
7
8
9
10 11 12
M µµ [GeV]
(b) After acceptance correction
Figure 4.7: Mass distribution (a) of data after background subtraction and reconstructed MC, (b) of acceptance corrected data and
generated Drell Yan Monte Carlo. The “dip” in the distribution
around 6.2 GeV is evident in both plots.
As already seen in Fig. 3.28 in the last chapter and again in greater detail
in Fig. 4.7 and 4.8, the measured Drell Yan signal differs from the Monte Carlo
signal in the mass region between 6.1 and 6.3 GeV. This difference remains after
acceptance corrections (Fig. 4.6(a)) when compared to generated Drell Yan Monte
Carlo distribution.
A χ2 test to determine if the discrepancy between data and Drell Yan Monte
Carlo simulation can be explained by a statistical fluctuation returns a χ2 /ndf =
41.0/15 and a probability of 0.03%. Excluding the bin at 6.2 GeV in Fig. 3.28, the
test gives a χ2 /ndf = 18.4/14 and a probability of 18.9%. A statistical fluctuation
is unlikely to be the explanation.
Also, the effect of the chosen kinematic and fiducial cuts was examined to
further exclude a problem with the analysis. No change in cuts was able to
remove the discrepancy, though it is less apparent with softer cuts. Since the
data deficit is already present before the background subtraction in unlikesign
data (see Fig. 3.26), the reweighting applied on the likesign background cannot
be the reason.
A similar effect was already seen in the reconstructed muon pair mass distribution
published in ([Abt06]). This distribution is shown in Fig. 4.9. The “dip”, which
is marked by the red circle, is less pronounced here as the cuts used in the Υ
analysis are less stringent than the ones used in the search for Drell Yan. The
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
counts per 100 MeV
94
102
data signal
Drell Yan rec. MC
10
1
5
5.5
6
6.5
7
Mµµ [GeV]
Figure 4.8: Zoomed mass distribution of reconstructed Drell Yan
Monte Carlo and data after background subtraction. The vertical
lines indicate the three regions of which x − y muon track distributions in the magnet focal plane and in station MU3 are plotted
separately in Fig. 4.10 and 4.11.
fact that this discrepancy is seen in two independant analyses points to a detector
inefficiency not included in the Monte Carlo simulation.
To check if a detector inefficiency missing in the simulation is the reason, the
positions of muon tracks in the detector are examined. For this events with an
invariant muon pair mass in the affected region and in regions slightly below and
slightly above it were plotted separately both for data and for Drell Yan Monte
Carlo simulated events. The three mass regions are indicated by vertical lines
in Fig. 4.8. Fig. 4.10 shows the position of tracks coming from muon pairs with
invariant masses below (5.7 GeV < Mµµ < 6.0 GeV), in (6.0 GeV < Mµµ <
6.3 GeV) and above (6.3 GeV < Mµµ < 6.6 GeV) the problematic mass region
at the magnet focal plane. Fig. 4.11 shows the track position in the station MU3
for the same mass regions. All distributions are plotted separately for in- and
outbending muon pairs.
This method suffers from the low statistics, especially in the problematic region
for the data. The data distributions have too few entries to be able to find
problematic detector regions. Some differences are visible in the distributions of
Drell Yan Monte Carlo simulated data. In the distributions showing the x − y
position of tracks at the station MU3, one can see that below (Fig. 4.11(d)) and
above (Fig. 4.11(f)) the problematic mass region, tracks are distributed evenly to
the left and the right of the Inner Tracker area, while in the problematic mass
region (Fig. 4.11(e)), there are more tracks on the left side of the detector. Also,
4.5. SYSTEMATIC CHECKS OF THE MASS DISTRIBUTION
95
Figure 4.9: Distribution of reconstructed invariant mass of muon
pairs as published in [Abt06]. The red circle marks the “dip” in the
mass range of 6.1 to 6.3 GeV. Since the cuts used in the Υ analysis are less strict than those used in this analysis, the discrepancy
between data and Monte Carlo is less pronounced. The plot also
shows the combinatorical background (dotted line) and Drell Yan
(dashed line) in addition to a fit to the Υ signal.
in this middle mass bin, the tracks are concentrated in a smaller area than in the
bins above and below.
In the inbending muon pair distributions at station MU3 (Fig. 4.11), the situation
is reversed. Both Fig. 4.11(j) and 4.11(l) show more tracks on the left detector
side, while Fig. 4.11(k) shows a more even distribution. Considering that the data
distributions before background subtraction (see Fig. 3.26) show a larger “dip”
in the inbending distributions, this might be the cause. On the other hand, the
distributions showing track positions at the magnet focal plane (Fig. 4.10) show
no visible differences.
While there are differences in the distribution of tracks in the three mass regions,
no significant differences that would explain the missing events can be seen, the
cause remains unknown.
2
20
0
2.5
40
2
20
1.5
-20
3
60
0
1
-40
0.5
-80
-80 -60 -40 -20
0
20
40 60 80
x magnet [cm]
2
0
1
1.5
1
-40
0.5
-60
0
2.5
40
-20
-40
-60
3
60
20
1.5
-20
80
counts
2.5
40
80
y magnet [cm]
3
60
counts
80
y magnet [cm]
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
counts
y magnet [cm]
96
-80
-80 -60 -40 -20
0
20
0
40 60 80
x magnet [cm]
0.5
-60
-80
-80 -60 -40 -20
0
20
40 60 80
x magnet [cm]
0
20
0
-20
-40
-60
-80
-80 -60 -40 -20
0
20
40 60 80
x magnet [cm]
220
200
180
160
140
120
100
80
60
40
20
0
60
40
20
0
-20
-40
-60
-80
-80 -60 -40 -20
0
20
40 60 80
x magnet [cm]
80
140
60
counts
80
y magnet [cm]
40
240
220
200
180
160
140
120
100
80
60
40
20
0
counts
60
y magnet [cm]
80
counts
y magnet [cm]
(a) 5.7GeV < Mµµ < 6.0GeV, (b) 6.0GeV < Mµµ < 6.3GeV, (c) 6.3GeV < Mµµ < 6.6GeV,
outbending
outbending
outbending
120
40
100
20
80
0
-20
60
-40
40
-60
20
-80
-80 -60 -40 -20
0
20
40 60 80
x magnet [cm]
0
1.6
40
1.4
20
1.2
0
1
60
0.9
0.8
0.6
-40
-80
-80 -60 -40 -20
0
20
40
60 80
x magnet [cm]
1.8
20
0
0.5
0
-20
0.4
-20
0.3
0.2
-60
0
-80
-80 -60 -40 -20
20
40
60 80
x magnet [cm]
1.4
1.2
1
0.8
0.6
-40
0.2
0
1.6
40
0.6
-40
0.4
-60
0.7
2
60
20
1
-20
0.8
40
80
counts
80
y magnet [cm]
1.8
counts
2
60
y magnet [cm]
80
counts
y magnet [cm]
(d) 5.7GeV < Mµµ < 6.0GeV, (e) 6.0GeV < Mµµ < 6.3GeV, (f) 6.3GeV < Mµµ < 6.6GeV,
outbending
outbending
outbending
0.4
0.1
-60
0
-80
-80 -60 -40 -20
0.2
0
20
40
60 80
x magnet [cm]
0
40
80
20
100
40
80
20
60
0
-20
40
-40
0
20
40 60 80
x magnet [cm]
60
20
50
0
40
-20
40
-20
30
-40
20
-60
10
20
-60
0
70
40
60
20
-80
-80 -60 -40 -20
80
60
0
-40
-60
80
-80
-80 -60 -40 -20
counts
60
counts
80
yMU3 [cm]
100
60
counts
80
y magnet [cm]
y magnet [cm]
(g) 5.7GeV < Mµµ < 6.0GeV, (h) 6.0GeV < Mµµ < 6.3GeV, (i) 6.3GeV < Mµµ < 6.6GeV,
inbending
inbending
inbending
0
20
40 60 80
x magnet [cm]
0
-80
-80 -60 -40 -20
0
20
40 60 80
x MU3 [cm]
0
(j) 5.7GeV < Mµµ < 6.0GeV, (k) 6.0GeV < Mµµ < 6.3GeV, (l) 6.3GeV < Mµµ < 6.6GeV,
inbending
inbending
inbending
Figure 4.10: Position of tracks in the magnet focal plane belonging
to out- and inbending muon pairs for both data and reconstructed
Drell Yan Monte Carlo.
1.8
1.6
100
2
50
0
1.5
-50
0.5
-150
-200
-200 -150 -100 -50
0
50 100 150 200
x MU3 [cm]
0
0
50 100 150 200
x MU3 [cm]
1
0.8
0.6
-100
0.4
-200
-200 -150 -100 -50
1.2
-50
0.6
-150
1.4
0
0.8
-100
1.6
50
1
-50
1
1.8
1.2
0
-100
2
150
100
1.4
50
200
counts
2
150
97
y MU3 [cm]
2.5
100
200
counts
150
y MU3 [cm]
3
y MU3 [cm]
200
counts
4.5. SYSTEMATIC CHECKS OF THE MASS DISTRIBUTION
0.4
0.2
-150
0
-200
-200 -150 -100 -50
0.2
0
50 100 150 200
x MU3 [cm]
0
30
-50
20
-100
-150
10
-150
0
-200
-200 -150 -100 -50
0
50 100 150 200
x MU3 [cm]
counts
40
50
60
-100
-200
-200 -150 -100 -50
100
0
30
-50
20
0
40
-50
50
150
50
50
0
200
80
100
60
50
100
150
y MU3 [cm]
70
100
200
counts
80
150
y MU3 [cm]
y MU3 [cm]
200
counts
(a) 5.7GeV < Mµµ < 6.0GeV, (b) 6.0GeV < Mµµ < 6.3GeV, (c) 6.3GeV < Mµµ < 6.6GeV,
outbending
outbending
outbending
40
-100
20
10
-150
0
50 100 150 200
x MU3 [cm]
0
-200
-200 -150 -100 -50
0
50 100 150 200
x MU3 [cm]
0
100
1.2
0
0.8
0.6
-100
-150
-200
-200 -150 -100 -50
0
50 100 150 200
x MU3 [cm]
0.8
0.9
0.8
100
0.7
0.7
0.6
50
0.6
0
0.5
0
0.5
-50
0.4
-50
0.4
0.3
-100
0.4
1
150
50
1
-50
200
0.2
-150
0
-200
-200 -150 -100 -50
0
50 100 150 200
x MU3 [cm]
0.3
-100
0.2
counts
0.9
100
1.4
50
1
150
y MU3 [cm]
1.6
200
counts
1.8
y MU3 [cm]
2
150
y MU3 [cm]
200
counts
(d) 5.7GeV < Mµµ < 6.0GeV, (e) 6.0GeV < Mµµ < 6.3GeV, (f) 6.3GeV < Mµµ < 6.6GeV,
outbending
outbending
outbending
0.2
0.1
-150
0
-200
-200 -150 -100 -50
0.1
0
50 100 150 200
x MU3 [cm]
0
50
50
150
40
100
200
40
150
counts
100
200
counts
60
yMU3 [cm]
150
yMU3 [cm]
yMU3 [cm]
200
counts
(g) 5.7GeV < Mµµ < 6.0GeV, (h) 6.0GeV < Mµµ < 6.3GeV, (i) 6.3GeV < Mµµ < 6.6GeV,
inbending
inbending
inbending
35
100
30
50
40
0
50
30
0
50
25
0
20
30
-50
20
-50
20
-100
-100
10
-150
-200
-200 -150 -100 -50
0
-200
-200 -150 -100 -50
50 100 150 200
x MU3 [cm]
15
-100
10
-150
5
10
-150
0
-50
0
50 100 150 200
x MU3 [cm]
0
-200
-200 -150 -100 -50
0
50 100 150 200
x MU3 [cm]
0
(j) 5.7GeV < Mµµ < 6.0GeV, (k) 6.0GeV < Mµµ < 6.3GeV, (l) 6.3GeV < Mµµ < 6.6GeV,
inbending
inbending
inbending
Figure 4.11: Position of tracks in station MU3 belonging to outand inbending muon pairs for both data and reconstructed Drell Yan
Monte Carlo.
98
4.6
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
Angular Distributions
As seen in chapter 2.3, the double differential cross section d cos θdσcs dφcs is of special interest. The theoretical prediction including leading order QCD processes is:
1 dσ
3 1
ν
=
1 + λ cos2 θ + µ sin 2θ cos φ + sin2 θ cos 2φ ,
σ dΩ
4π λ + 3
2
(4.20)
where θ is the polar angle of the positive muon in the rest frame of the virtual
photon, and φ is the azimuthal angle. λ, µ and ν are variables independant of
the angles which take the role of structure functions. If the mass of the virtual
photon is small compared to the Z0 mass, the middle term disappears, µ = 0.
The parameters λ and ν are connected by the Lam Tung relation ([Lam80])
1 − λ − 2ν = 0
(4.21)
While first order QCD corrections have no influence on the Lam Tung relation,
higher order corrections point to a slightly positive value of 1 − λ − 2ν.
A two dimensional fit of equation (4.20) to data yields λ = 0.04 ± 0.45 and
ν = 0.09 ± 0.16. This gives for the Lam Tung relation a value of 0.78 ± 0.50.
The data available at HERA-b is not sufficient for a two dimensional fit. Also, the
fit function does not describe the data very well, the fit probability is only 1.7%
and χ2 /ndf = 58/37 = 1.55. Because of this, the one dimensional distributions
of cos θCS and φCS were also fitted. The distributions and the corresponding fits
are shown in Fig. 4.12.
For the fit of the cos θCS distribution, Eqn. (4.20) was integrated over φ in the
range from −π to +π. The fit result is λ = 0.60 ± 0.58. Integrating Eqn. (4.20)
over cos θCS in the acceptance range of HERA-b and using the result for λ from
the first fit, one gets a value of ν = 0.14 ± 0.14 from a fit to the φCS distribution.
The Lam Tung relation then is 1 − λ − 2ν = 0.12 ± 0.61.
Within the large errors, the value of λ is compatible with one, while both the
value of ν and the resulting value of the Lam Tung relation is compatible with
zero.
Unfortunately the amount of data available does not allow a measurement of the
dependance of the coefficients λ and ν on the transverse momentum of the muon
pair, which would be necessary to help distinguish between the two theoretical
models for the quark correlation presented in Sec. 2.4.2.
0.2
χ2 / ndf
0.18
Prob
c0
0.16
λ
99
10.51 / 11
0.4855
0.08997 ± 0.00624
0.6025 ± 0.5841
0.14
χ / ndf
2
0.06
d σ/d φ [nb/nucleon]
d σ/dcosθ [nb/nucleon]
4.6. ANGULAR DISTRIBUTIONS
32.6 / 18
Prob
0.01865
0.02855 ± 0.001494
c0
0.05
λ
0.6025 ±
ν
0
0.142 ± 0.1439
0.04
0.12
0.1
0.03
0.08
0.02
0.06
0.04
0.01
0.02
0
-1
-0.5
0
(a)
0.5
1
cos(θCS)
0
-3
-2
-1
0
1
2
(b)
Figure 4.12: One dimensional angular differential cross sections.
(a) shows d cosdσθ , (b) φdσ
cs
cs
3
φ CS
100
4.7
4.7.1
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
Comparisons with other Experiments
E772
HERA-b is unique compared to other measurements of Drell Yan with respect
to the covered xF range. The sensitive region extends from −0.45 to 0.05, which
corresponds to a back scattering of the incident quark. The experiment E772
([McG94]) at Fermilab measured the dependance of the Drell Yan cross section
on mass and xF with a mass range of 4.5 GeV < MDY < 13.5 GeV and an xF
range of 0.0 < xF < 0.7. Since the Drell Yan cross section exhibits scaling in
the variable τ = M 2 /s and the center-of-mass energies at E772 (38.8 GeV) and
HERA-b (41.6 GeV) differ, the mass values of HERA-b were adjusted by the
ratio of the center-of-mass energies to be able to compare the cross sections. The
comparisons are shown in Fig. 4.13.
A problem can be seen in Fig. 4.13(c), where the measurement from HERA-b is
below that of E772. This discrepancy is caused by the problematic mass bin at
6.2 GeV which was described in Sec. 4.5. Apart from this problem, the distributions match very well and extend the measurement performed by E772 into the
negative xF range.
40
M µ3 µ d 2σ/dM µµdx F
M µ3 µ d 2σ/dM µµdx F
4.7. COMPARISONS WITH OTHER EXPERIMENTS
HERAb data
E772 data
35
30
25
101
25
HERAb data
E772 data
20
15
20
10
15
10
5
5
0
-0.6
-0.4
-0.2
0
0.2
0.4
0
-0.6
0.6
xF
HERAb data
E772 data
12
-0.2
0
0.2
0.4
0.6
xF
(b) 4.5GeV < mass < 5.5GeV
M µ3µ d 2σ/dM µµdx F
14
10
8
20
HERAb data
E772 data
18
16
14
12
10
6
8
6
4
4
2
0
-0.6
2
-0.4
-0.2
0
0.2
0.4
0
-0.6
0.6
xF
(c) 5.5GeV < mass < 6.5GeV
M µ3 µ d 2σ/dM µµdx F
M µ3µ d 2σ/dM µµdx F
(a) 3.7GeV < mass < 4.5GeV
-0.4
-0.4
-0.2
0
0.2
0.4
(d) 6.5GeV < mass < 7.5GeV
14
HERAb data
E772 data
12
10
8
6
4
2
0
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
xF
(e) 7.5GeV < mass < 8.5GeV
Figure 4.13: xF distribution of data from E772 and HERA-b.
The data is divided in mass bins, the mass measured at HERA-b
was adjusted to the center-of-mass energy of E772. The deviation
between data from E772 and HERA-b in plot (c) is caused by the
problematic mass bin described in Sec. 4.5.
0.6
xF
102
4.7.2
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
NA50
The experiment NA50 at CERN is a muon spectrometer situated at the SPS.
Here, protons with a beam energy of 450 GeV hit a fixed target of different materials. A dimuon trigger selects events containing bottonium and the Drell Yan
process. A recent publication√([Ale06]) gives transverse momentum distributions
of high mass (> 6 GeV at s = 29.1 GeV) Drell Yan events. The paper uses
the following function to fit the differential cross section dependance on pt :
dσ
pt
∝
6
dpt
1 + (pt /p0 )2
(4.22)
The fitted value of p0 , the average transverse momentum hpt i and the average
transverse momentum squared hp2t i are compared for different target materials.
The pt distributions of the data taken at HERA-b are shown in Fig. 4.14, for all
data and separately for two of the three target materials. The Titanium data
sample taken at HERA-b is too small to be fitted by function (4.22) as it consists
of only three Drell Yan events after the data selection.
The result of the fit to the three distributions as well as the average transverse
momentum values are given in Tab. 4.4. Also given as a comparison are the
values from NA50 for a Tungsten target. The measurements agree within their
errors, showing no dependancy on the target material.
Target
A
p0 ,
All data
2.99
W
183.84 2.96
C
12.0107 2.94
W @ NA50 183.84 2.80
[GeV]
± 0.05
± 0.08
± 0.08
± 0.03
hpt i, [GeV]
1.31 ± 0.05
1.35 ± 0.10
1.27 ± 0.08
1.20 ± 0.01
hp2t i,
1.49
1.75
1.68
1.96
[GeV2 ]
± 0.22
± 0.23
± 0.19
± 0.04
Table 4.4: Fit results of p0 (as defined in Eq. (4.22)), hpt i and
hp2t i of Drell Yan events in data depending on mass number of the
target wire. Also given are the values measured with a Tungsten
target at NA50 ([Ale06]).
10
10
10
d σ/dp t [nb/(GeV nucleon)]
d σ/dp t [nb/(GeV nucleon)]
4.7. COMPARISONS WITH OTHER EXPERIMENTS
10
-1
-2
10
-3
10
0
1
2
3
4
5
6
p t [GeV]
103
-1
-2
-3
0
1
2
3
4
5
6
p t [GeV]
d σ/dp t [nb/(GeV nucleon)]
(a) Drell Yan originating from a Tungsten wire (b) Drell Yan originating from a Carbon wire
10
10
10
-1
-2
-3
0
1
2
3
4
5
6
p t [GeV]
(c) All Drell Yan data
Figure 4.14: Differential cross sections of Drell Yan depending
on the transverse momentum of the muon pair. The distributions
are fitted with function (4.22). The data sample originating from a
Titanium wire is too small to be used.
104
4.8
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
Systematic effects
To study systematic influences on the results, the analysis was repeated several
times with changed input parameters. Four sources of systematic errors were
identified:
• The reweighting procedure of the likesign data. To check the influence of
the Single Track Monte Carlo weights, the binning of the efficiency matrix
was changed from 20 × 10 to 19 × 11. A new efficiency matrix was then
calculated and used to reweight the likesign data (“stmc” in Tab. 4.5).
• The reweighting of the Drell Yan Monte Carlo to match the distribution
of transverse momentum of the muon pair found in data. The function
used to fit the Monte Carlo Mµµ vs. p2t distribution was modified slightly
by removing the third exponential term (3.15) and using the remaining
function to reweight the Drell Yan Monte Carlo (“dymc” in Tab. 4.5).
• The kinematic selection. This influence was checked in two different ways.
First, all six cuts applied to data were tightened by 5% each (“hard”),
then loosened again by 5% (“soft”). Second, the two cuts with the largest
influence on data, the cut on the reduced χ2 of the track fit and on the
transverse track momentum were changed up and down by 5% individually
(“pt hard”, “pt soft”,“χ2 hard” and “χ2 soft”).
• The determination of the luminosity. As already described in Sec. 4.1, the
systematic influence of the fit function used to fit the J/ψ peak and the
choice of cuts is negligible compared to the error on the value of the J/ψ
cross section from literature.
In Tab. 4.5 the results of the systematic changes above are given. “n.c.” stands
for no change and represents the unchanged analysis presented in the last chapters. The systematic influence of the changed Single Track Monte Carlo and the
kinematic selection are correlated, as the cuts are also applied to the reweighted
likesign distributions. To examine this correlation, the hard and soft cut selection was also applied simultaneously with the STMC change (“hard stmc”
and “soft stmc”). The last column gives the events in the data sample. Especially the hard and soft cut selections change the size of the sample. This
change p
introduces an additional statistical error, which can be calculated by
∆stat = |Nnew − Nold |/Nnew . Since this value is in no sample larger than 2%, it
is not sufficient to explain the deviations, which thus are real systematic effects.
It can also be seen easily that the changed Drell Yan Monte Carlo reweight function has almost no influence on the results.
Due to the correlations between the samples, the deviations cannot simply be
added to get the total systematic error. Some of the correlations are positive, e.g.
in the case of ν, where the combined error of STMC reweighting and changed
4.8. SYSTEMATIC EFFECTS
105
kinematic selection is larger than the individual contributions. Others are negative as that between STMC reweighting and kinematic selection for the value of
λ. Here, the combined deviation of the measurement is smaller than the individual ones. Thus, the largest deviation from the measurement was chosen as the
systematical error. The chosen value is marked in bold in Tab. 4.5.
The results of the analysis including statistical and systematic errors are summarized in Tab. 4.6. Except for two values, the systematic errors are smaller than
the statistical ones. The first of these is ν. As one can see from Fig. 4.12(b), the
fit does not describe the data very well. Small changes of the fitted distribution
can easily lead to large changes in the fit. The second value is p0 (W), which is
the result from the fit in Fig. 4.14(a). In this distribution the shape of the fit
does not quite match the shape of the distribution, which also leads to a larger
systematic error.
106
n.c.
dymc
stmc
hard
soft
hard
stmc
soft
stmc
pt
hard
pt
soft
χ2
hard
χ2
soft
CHAPTER 4. DETERMINATION OF CROSS SECTIONS
hptW i
[GeV]
1.35
0.00
0.00
-0.03
0.02
hp2tW i
[GeV2 ]
2.20
0.00
0.00
-0.11
0.02
p0 C
[GeV]
2.93
0.00
-0.02
-0.01
0.01
hptC i
[GeV]
1.27
0.00
0.00
0.01
0.02
hp2tC i
[GeV2 ]
1.94
0.00
0.00
-0.01
0.05
α
#evts
0.14
0.00
-0.04
-0.09
-0.04
p0 W
[GeV]
2.93
0.00
-0.01
-0.02
0.13
1.03
0.00
-0.01
-0.01
0.03
921
921
924
733
1022
-0.21
-0.16
-0.01
-0.03
-0.11
-0.01
0.01
0.00
-0.02
767
2
-0.27
-0.10
0.13
0.02
0.03
0.00
0.02
0.05
0.03
1074
-3
-0.20
-0.05
-0.02
-0.02
-0.05
-0.01
0.01
0.00
-0.01
979
-4
-0.47
-0.06
0.14
0.02
0.02
0.00
0.01
0.04
0.02
787
-11
-0.01
0.03
0.00
0.01
0.01
0.01
0.00
0.01
-0.01
909
+5
-0.12
0.02
0.01
-0.01
-0.03
0.00
-0.01
-0.02
0.00
934
σDY
[pb/n]
289
0
0
-11
-12
λ
ν
0.60
-0.02
-0.21
-0.35
-0.35
1
Table 4.5: Influence of systematic effects on analysis results.
Given are the deviations from the default analysis values listed in
the first row. The top row names the value given below, the left column indicates the change applied to the analysis. The abbreviations
of the changes are explained in the text.
α
σDY
λ
ν
p0 (W)
hpt i(W)
hp2t i(W)
p0 (C)
hpt i(C)
hp2t i(C)
1.03 ± 0.03stat ± 0.03syst
(289 ± 35stat ± 12syst )
0.60 ± 0.58stat ± 0.47syst
0.14 ± 0.14stat ± 0.16syst
(2.96 ± 0.08stat ± 0.13syst )
(1.35 ± 0.10stat ± 0.03syst )
(1.75 ± 0.23stat ± 0.11syst )
(2.94 ± 0.08stat ± 0.02syst )
(1.27 ± 0.08stat ± 0.02syst )
(1.68 ± 0.19stat ± 0.05syst )
pb/nucl.
GeV
GeV
GeV2
GeV
GeV
GeV2
Table 4.6: Analysis results including systematic errors.
Chapter 5
Conclusions
In this thesis, the cross section of the Drell Yan process was measured. The data
used was gathered at the HERA-b detector, one of the four experiments at the
HERA storage ring at DESY in Hamburg, Germany. Unlike other experiments
dedicated to measure muon pair production, there is no absorbing material between interaction point and detector at HERA-b. Because of this open geometry
the level of background is much higher and presents a difficult challenge. Due to
the large background and the low number of events taken during the short data
taking period in 2002/2003, the main difficulty was to extract and conserve the
Drell Yan events by applying a kinematic selection and subtracting the remaining background. The cross section of the Drell Yan process was determined to
be σDY→µµ = (289 ± 35stat ± 12syst ) pb/nucleon in the mass range of 4 GeV to
9 GeV. Using the same selection, the Υ cross section was also measured. The
result is Br(Υ → µ+ µ− ) · dσ
| (Υ) = (4.9 ± 1.4) pb/nucleon.
dy y=0
Due to the requirement of electrons with opposite charge in the HERA-b dielectron trigger, the extension of the search for Drell Yan to include the dielectron
data set was not possible.
After the background subtraction, a difference between measurement and expectation was observed: a significant deviation of Monte Carlo and data was found
in the distribution of reconstructed mass of the muon pair. This deviation is
also visible in an independant analysis of the same dataset presented in [Abt06].
While no conclusive reason for this discrepancy was found, it is likely that unknown detector inefficiencies are the cause.
The measurement of the double differential cross section dσ/dMµµ dxF performed
at the Fermilab experiment E772 ([McG94]) was extended for the first time into
the negative xF range. Except for the mass bin containing the mass deviation
mentioned above, the data between the two experiments agree very well.
The distribution of transverse momentum of the muon pair was compared with
measurements performed by the NA50 collaboration ([Ale06]). A fit to the pt
distribution and the average pt and p2t agree within errors. No dependance on
the mass number of the target material was found.
107
108
CHAPTER 5. CONCLUSIONS
A measurement of the A dependance of the Drell Yan cross section σ ∝ A−α
yielded the result α = 1.03 ± 0.03stat ± 0.03syst , which is compatible with one as
expected from other Drell Yan measurements, e.g. [Ale06].
Unfortunately, the number of Drell Yan events remaining after the kinematic
selection was not sufficient to perform a significant measurement of the angular
distributions. The statistical errors of the parameters λ and ν are too large to
yield a conclusive result for the Lam Tung relation.
List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Overview of the HERA accelerator complex. . . . .
Schematic overview of HERA-b. . . . . . . . . . . .
Schematic view of VDS and Target. . . . . . . . . .
Schematic drawing of a GEM MSGC. . . . . . . . .
Illustration of the honeycomb structure of the OTR.
Cross section of the RICH. . . . . . . . . . . . . . .
Overview of the ECAL and drawing of a single cell.
Cutout illustration of the muon system. . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
7
9
10
12
13
14
15
16
Feynman graph of the Drell Yan process at parton level. . . . . .
Factorisation model of the Drell Yan Process. . . . . . . . . . . .
QCD corrections to the Drell Yan process. . . . . . . . . . . . . .
Theoretical calculation of the differential Drell Yan cross section. .
Illustration of the Collins Soper reference frame. . . . . . . . . . .
λ, µ and ν as a function of pt , measured at NA10. . . . . . . . . .
λ, µ and ν as a function of pt , measured at E615. . . . . . . . . .
Comparison between measurements of λ, µ and ν from NA10, E615
and E866. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9 Comparison between data from E615 and a Higher Twist simulation.
2.10 Comparison between data from E615 and a vacuum fluctuation
simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.11 Comparison between data from E615 and a simulation using time
reversal (T) odd distribution functions. . . . . . . . . . . . . . . .
19
21
22
23
24
26
27
3.1
3.2
3.3
3.4
3.5
3.6
34
35
37
38
40
3.7
3.8
Fiducial cuts at stations PC1 and MU3. . . . . . . . . . . . . . .
Invariant mass of muon data after preselection. . . . . . . . . . .
p distribution of muons in Drell Yan Monte Carlo. . . . . . . . . .
Comparison of distributions between likesign and event mixing data.
Difference in acceptance between likesign and unlikesign muon pairs.
x position of muon tracks in the focal plane of the magnet after
fiducial cuts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x vs. y position of muon tracks in station PC1 after fiducial cuts.
Detector regions containing data depending on muon charges. . .
109
28
29
31
32
41
41
42
110
LIST OF FIGURES
3.9 Efficiency map of the First Level Trigger. . . . . . . . . . . . . . .
3.10 Distributions of px and py of generated Single Track Monte Carlo
muons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.11 px and py distributions of Single Track Monte Carlo muons accepted by FLT and SLT. . . . . . . . . . . . . . . . . . . . . . . .
3.12 px vs. py distribution of Single Track Monte Carlo muons accepted
by FLT and SLT. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.13 Track position in the magnet focal plane of Single Track Monte
Carlo muons accepted by both triggers. . . . . . . . . . . . . . . .
3.14 Distribution of the weights applied to likesign data. . . . . . . . .
3.15 Mass distribution of the data after fiducial cuts and likesign reweighting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.16 Comparison between the x position of tracks for rec. and reweighted
gen. Drell Yan Monte Carlo. . . . . . . . . . . . . . . . . . . . . .
3.17 Comparison of kinematic distributions of rec. and reweighted gen.
Drell Yan Monte Carlo. . . . . . . . . . . . . . . . . . . . . . . . .
3.18 Distribution of the transverse momentum of the muon pair in data
and Monte Carlo. . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.19 Mass vs. p2t distribution and fit of reconstructed Drell Yan Monte
Carlo events. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.20 Mass vs. p2t distribution and fit of data events. . . . . . . . . . . .
3.21 pt and p2t distribution in data and Monte Carlo simulation after
reweighting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.22 Dependance of signal MC and likesign background on kinematic
variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.23 Effect of the consecutive kinematic cuts. . . . . . . . . . . . . . .
3.24 x position of tracks passing station PC1 left and right of the insensitive inner region. . . . . . . . . . . . . . . . . . . . . . . . . .
3.25 x position of tracks passing station PC1 left and right of the insensitive inner region after additional geometrical cut. . . . . . . .
3.26 Mass distribution of data after cuts and reweighting of likesign
background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.27 Event likelihood distribution for signal and background. . . . . . .
3.28 Mass distribution of signal extracted after cuts and background
subtraction for both selection methods. . . . . . . . . . . . . . . .
3.29 Distribution of the dielectron mass in the J/ψ and Drell Yan mass
region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
4.1
4.2
81
4.3
pt distribution of J/ψ in data and Monte Carlo. . . . . . . . . . .
Invariant mass distribution of the reconstructed muon pair at the
J/ψ mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Invariant mass distribution of the reconstructed muon pair above
8.6 GeV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
47
49
50
51
54
55
58
59
61
62
63
63
68
69
70
71
72
73
75
77
83
84
LIST OF FIGURES
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
111
Detector acceptance as a function of kinematic variables. . . . . . 88
Acceptance corrected pt distributions of data, separated according
to target material. . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Differential cross sections of Drell Yan. . . . . . . . . . . . . . . . 92
Mass distribution of data after before and after acceptance correction. 93
Zoomed mass distribution of reconstructed Drell Yan Monte Carlo
and data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
Distribution of reconstructed invariant mass of muon pairs as published in [Abt06]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Track position in the magnet focal plane below, in and above the
problematic mass region. . . . . . . . . . . . . . . . . . . . . . . . 96
Track position in station MU3 below, in and above the problematic
mass region. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
One dimensional angular distributions. . . . . . . . . . . . . . . . 99
xF distribution of data from E772 and HERA-b, separated in mass
bins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Differential cross sections of Drell Yan depending on pt of the muon
pair, separated for target material. . . . . . . . . . . . . . . . . . 103
112
LIST OF FIGURES
List of Tables
3.1
3.2
3.3
3.4
3.5
Detector regions at the magnet as defined in Fig. 3.8 which contain
data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trigger efficiencies in Single Track Monte Carlo. . . . . . . . . . .
List of Drell Yan Monte Carlo runs used. . . . . . . . . . . . . . .
Cuts used in muon analysis. . . . . . . . . . . . . . . . . . . . . .
Preliminary cuts used in the dielectron analysis. . . . . . . . . . .
4.1
4.2
4.3
4.4
4.5
4.6
Cuts used in J/ψ selection. . . . . . . . . . . . . . . . .
Values used in luminosity calculation. . . . . . . . . . .
Values used in the determination of the Υ cross section.
p0 (as defined in Eq. (4.22)), hpt i and hp2t i of Drell Yan.
Influence of systematic effects on analysis results. . . .
Analysis results including systematic errors. . . . . . .
113
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
44
48
64
67
76
. 82
. 82
. 85
. 102
. 106
. 106
114
LIST OF TABLES
Bibliography
[Abt94] I. Abt et al. (HERA-b Collaboration), An Experiment to Study CP Violation in the B System Using an Internal Target at the HERA Proton Ring,
DESY-PRC-94-02, Hamburg, Germany, 1994.
[Abt06] I. Abt et al., Measurement of the Υ Production Cross Section in 920
GeV Fixed-Target Proton-Nucleus Collisions, hep-ex/0603015, Hamburg,
Germany, March 2006
[Ada05] A. Adametz, Preshower Measurement with the Cherenkov Detector of
the BABAR Experiment, Diploma thesis, Universität Heidelberg, Germany,
2005
[Alb95] H. Albrecht, ARTE. (Analysis and Reconstruction Tool) HERA-b Internal Note 95-065, DESY, Hamburg 1995
[Ale06] B. Alessandro et al. (NA50 Collaboration), Bottonium and Drell-Yan
production in p − A collisions at 450 GeV, Phys. Lett. B 635 (2006), 260-269
[And84] L. Anderson et al. (NA10 Collaboration), A High Resolution Spectrometer for the Study of High Mass Muon Pairs Produced by Intense Hadron
Beams, Nucl. Instr. Meth. A223 (1984), 26
[Ari04] I. Arino et al., The HERA-b Ring Imaging Cherenkov Counter,
Nucl.Instrum.Meth.A516:445-461, 2004
[Bag02] Y. Bagaturia et al., Studies of aging and HV break down problems during development and operation of MSGC and GEM detectors for the inner
tracking system of HERA-b, ICFA Instrum. Bull. 24 (2002), 54–84
[Bal03] V.
Balagura,
Efficiency
/hb/flt/balagura/eff map viewer/viewer
Map
Viewer,
2003,
√
[Bar05] M. Bargiotti et al., J/ψ production cross section at s = 41.6 GeV by
means of NRQCD calculations, HERA-b note 05-015, DESY, Hamburg, 2005
[Bau03] C. Bauer et al., Performance of the HERA-B vertex detector system,
Nucl. Instrum. Meth. A501 (2003), 39-48.
115
116
BIBLIOGRAPHY
[Bii86] C. Biino et al. (E615 Collaboration), An Apparatus to Measure the Structure of the Pion, Nucl. Instr. Meth. A243 (1986), 323
[Boe99] D. Boer, Investigating the Origins of Transverse Spin Asymmetries at
RHIC, Phys. Rev. D60 (1999) 014012
[Boe05] D. Boer, A. Brandenburg, O. Nachtmann and A. Utermann, Factorization, Parton Entanglement and the Drell-Yan Process, Eur. Phys. J. C 40,
55-61 (2005)
[Bra93] A. Brandenburg and O. Nachtmann, Spin Effects and Factorization in
the Drell-Yan Process, Z. Phys. C60 (1993), 697-710
[Bra94] A. Brandenburg, S.J. Brodsky, V.V. Khoze and D. Müller, Angular distributions in the Drell-Yan process: A Closer look at higher twist effects,
Phys. Rev. Lett. 73 (1994), 939-942, hep-ph/9403361
[Brä01] M. Bräuer, Die Alignierung des HERAB Vertexdetektors, Ph.D. thesis,
Universität Heidelberg, Germany, 2001
[Bru02] M. Bruinsma, Performance of the First Level Trigger of Hera-B and Nuclear Effects in J/ψ Production, Ph. D. thesis, Universiteit Utrecht, Netherlands, 2002
[Bru05] M. Bruschi, Luminosity Determination at HERA-b, HERA-b Internal
Note 05-011, DESY, Hamburg, 2005
[Cal69] C.G. Callan and D.J. Gross, High-energy electroproduction and the constitution of the electric current, Phys. Rev. Lett. 22 (1969) 156
[Cer94] CERN, GEANT 3.21 detector description and simulation tool, CERN
Library Long Writeup W5013, CERN, Genève, 1994
[Cha03] Webpage of the Charmonium Analysis Group, http://www-hera-b.
desy.de/subgroup/physics/herab/analysis/cc2003/welcome.html,
2003
[Col77] J.C. Collins, D.E. Soper, Angular distributions of dileptons in high-energy
hadron collisions, Phys. Rev. D16 (1977) 2219
[Col89] J.C. Collins, D.E. Soper and G. Sterman, Factorization of hard processes
in QCD, Pertubative QCD, ed. A.h. Mueller, World Scientific (1989) 1
[Con89] J.S. Conway et al. (E615 Collaboration), Experimental study of muon
pairs produced by 252-GeV pions on tungsten, Phys. Rev. D39 (1989(, 92
[Dam04] M. Dam et al., HERA-b Data Acquisition System, Nucl. Instrum. Meth.
A525:566-581, 2004
BIBLIOGRAPHY
117
[Des00] DESY, Hamburg, Press and Public Relations Department, 2000
[Dre70] S.D. Drell and T.M. Yan, Massive lepton-pair production in hadronhadron collisions at high energies, Phys. Rev. Lett. 25, 316 (1970); Ann.
Phys. (NY) 66, 578 (1971)
[Egb02] K. Egberts, H. Rick, A Background Generator for Muons from Decay in
Flight of Charged PI and K Mesons, HERA-b Internal Note 02-044, 2002
[Fey69] R.P. Feynman, Very high-energy collisions of hadrons, Phys. Rev. Lett.
23 (1969) 1415
[Gle01] T. Glebe, Cluearte 0-42 - The ARTE Interface to BEE, HERA-b Internal
Note 01-110, DESY, Hamburg, 2001
[Gra01] W. Gradl, The Readout System of the HERA-B Inner Tracker and
Prospects of HERA-B in the Field of Drell-Yan Physics, Ph. D. thesis, Universität Heidelberg, Germany, 2001
[Gor03] I. Gorbunov, ITR Performance for Analysis, talk given at Coll. Meeting,
May 12-16th 2003, also HERA-b Internal Note 03-027, DESY, Hamburg,
2003
[Gua88] M. Guanziroli et al. (NA10 Collaboration), Angular distributions of
muon pairs produced by negative pions on deuterium and tungsten, Z. Phys.
C37 (1988), 545
[Har95] E. Hartouni et al. (HERA-b Collaboration), HERA-b – An Experiment to
Study CP Violation in the B System Using an Internal Target at the HERA
Proton Ring, Technical Design Report, DESY-PRC 95/01, January 1995
[Hul02] W. Hulsbergen, A Study of Track Reconstruction and Massive Dielectron
Production in HERA-b, Ph. D. thesis, Universiteit van Amsterdam, Netherlands, 2002
[Hus05] U. Husemann, Measurement of Nuclear Effects in the Production of J/ψ
Mesons with the HERA-B Detector, Ph. D. thesis, Universität Siegen, Germany, 2005
[Kis99] I. Kisel, S. Masiocchi, CATS - A Cellular Automaton for Tracking in
Silicon for the HERA-B Vertex Detector, HERA-b Internal Note 99-242,
1999
[Lam80] C.S. Lam and W.-K. Tung, Parton-model relation without quantumchromodynamic modifications in lepton pair production, Phys. Rev. D21
(1980), 2712
118
BIBLIOGRAPHY
[Lei00] M.J. Leitch et al (E866/NuSea Collaboration), Phys. Rev. Lett. 84 (2000)
3256
[Pdg06] Particle Data Group, Review of Particle Physics, J. Physics G: Nucl.
Part. Phys 33 1., 2006
[Pi92] H. Pi, An event generator for interactions between hadrons and nuclei:
FRITIOF version 7.0, Comput. Phys. Commun. 71 (1992), 173-192
[Mas00] Silvia Masciocchi, Private Communication, May 2000
[McG94] P.L McGaughey et al. (E772 Collaboration), Cross-sections for the production of high mass muon pairs from 800-GeV proton bombardment of H-2,
Phys.Rev.D50:3038-3045, 1994, Erratum-ibid.D60:119903, 1999
[Mor91] G. Moreno et al. (E605 Collaboration), Phys. Rev. D43 (1991) 2815
[Nee92] W. L. van Neerven and E. B. Zijlstra, The O(αs2 ) corrected Drell-Yan
¯ schemes, Nucl. Phys. B 382, 11 (1992)
K-factor in the DIS and MS
[Otr02] Webpage of the HERA-b OTR group, http://www-hera-b.desy.de/
subgroup/detector/tracker/outer/, 2002
[Ric03] H. Rick, private communication, Spring 2004
[Sch01] B. Schwenninger, Das Myon-Pretrigger-System für das HERA-bB Experiment, Ph.D. thesis, Universität Dortmund, Germany, 2001
[Spe04] J. Spengler, HERAB detector components, http://www-hera-b.desy.
de/subgroup/detector/, 2004
[Sjö94] T. Sjöstrand, High-energy physics event generation with PYTHIA 5.7 and
JETSET 7.4, Comput. Phys. Commun. 82 (1994), 74-90
[Spi04] A. Spiridonov, Bremsstrahlung in Leptonic Onia Decays: Effects on Mass
Spectra, HERA-b Internal Note 04-016, 2004
[Web02] J. Webb, Measurement of Continuum Dimuon Production in 800-GeV/c
Proton-Necleon Collisions, New Mexico State University, Sept 2002
[Zhu06] L.Y. Zhu, Measurement of Angular Distributions of Drell-Yan Dimuons
in p + d Interaction at 800 GeV/c, arXiv:hep-ex/0609005, Sept 2006
Danksagung
Zuallererst möchte ich mich bei Herrn Prof. Eisele für die Gelegenheit, beim Experiment HERA-b mitzuarbeiten, bedanken. Nach meiner Diplomarbeit in der
Designphase eines Detektors war es sehr aufregend, an einem laufenden Detektor
mitzuwirken. Außerdem konnte ich jederzeit mit Fragen zu ihm kommen, wenn
mal wieder eine Untergrundbetrachtung im Sande zu verlaufen schien.
Bei Herrn Prof. Knöpfle möchte ich mich für die Bereitschaft, die Zweitkorrektur
dieser Arbeit zu übernehmen und die nette Zusammenarbeit in Hamburg bedanken.
Ich danke meinen ehemaligen Inner Tracker Kollegen Juri Bagaturia, Iouri Gorbounov, Sonja und Wolfgang Gradl, Carsten Krauss, Hartmut Rick, Stefan Rieke,
Roger Wolf und Torsten Zeuner, die mich in die Geheimnisse von ARTE, Rooibostee und BEE einführten, in dieser Reihenfolge.
Meinen Heidelberger Kollegen möchte ich dafür danken, dass sie mir immer
wieder zuhörten und eine sehr angenehme Arbeitsumgebung schafften. Christoph
Werner ertrug die meisten Fragen und gewann den Kampf der Teemauern eindeutig, Matthias Mozer stand immer bei Fragen zu Root und Nethack zur Verfügung. Aleksandra Adametz, Johannes Albrecht, Dr. Stephanie HansmannMenzemer und Stefan Schenk halfen besonders durch ihre Bereitschaft, diese
Arbeit Korrektur zu lesen. Tanja Haas gebührt Dank für ihren unerschöpflichen
Optimismus und ihre gute Laune, die durch das Zusammenschreiben half.
Ohne die ständige Unterstützung, Anteilnahme und Liebe meiner Eltern wäre
weder mein Studium noch diese Arbeit jemals zustande gekommen. Auch wenn
sie dies bereits wissen und mein Vater daher eine Reinkarnation als sein eigener
Sohn plant: Danke für Alles, Ihr seid die Besten.
My American family, the Crowells took an unknown boy into their home, gave
him their love and helped him grow up. It was there that I decided to study
physics. Thanks for all your support and love throughout the years, Mom, Dad
and Grandma.
Meinen Schwiegereltern möchte ich mich für die Aufnahme in ihre Familie und
die Gebete danken.
Meiner Gilde danke ich für den Ausgleich zur Arbeit. Gegenschlawüt!
Mein besonderer Dank gilt meiner Frau Salma, deren Liebe mich durch alle Tiefen
im Laufe dieser Arbeit trug. Enhebek Habibti.
119
Widmen möchte ich diese Arbeit meinen beiden Großmüttern Oma Katrin und
Oma Liesel, die mich im Studium sehr unterstützt haben, dessen Abschluss sie
aber leider nicht mehr miterleben durften.
Was this manual useful for you? yes no
Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertising