THESIS

 

 

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dissertation entitled
Measurement of the Diphoton Differential Cross-Section in
pp-bar Collisions at sqrt s = 1.96 TeV
presented by
(D
E
E Eb- 3‘ Joshua Marc Dyer
‘< c g
(U
8'5 9-?-
fi—J _c: :5) has been accepted towards fulfillment
; ' g of the requirements for the
L____, Ph.D. degree in Physics

 

 

 

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MEASUREMENT OF THE DIPHOTON DIFFERENTIAL
CROSS-SECTION IN pp COLLISIONS AT y; = 1.96 TeV

By

Joshua Marc Dyer

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of
DOCTOR OF PHILOSOPHY
Department of Physics and Astronomy

2007

ABSTRACT

MEASUREMENT OF THE DIPHOTON DIFFERENTIAL CROSS-SECTION IN

pp COLLISIONS AT \/§ 2 1.96 TeV
By

Joshua Marc Dyer

The diphoton differential cross—section as a function of mass up to 300 GeV/c2, qT
up to 100 Gel~’/c, and opening angle over a range of 0 to 7: radians is measured. The
measurement. is performed using 1046.19 pl)"1 of data collected at Fermi National
Accelerator Laboratory using the D0 detector. This analysis considers all direct

diphoton states but attempts to suppress contributions due to fragmentation.

Copyright © by
Joshua Marc Dyer

2007

To my family

iv

ACKNOWLEDGMENTS

Many peOple have my gratitude in supporting me throughout my graduate ed-
ucation. First I need to thank my family and friends. To my bride, Kimberly, for
her enduring love, attention, and strength; I could not have done it without you. To
my parents for their encouragement and love. To Kimberly’s parents for their assis-
tance and enjoyment of MSU sports. To my brothers for their humor and support.
To Richard, Aaron R, and Todd for their friendship after undergrad and providing

plenty of comedy.

Thanks to the GEU for providing me with a community to which I could con-
tribute and better many students’ lives with what little free time I had, as well as
for introducing me to Kimberly. To the Drew students for giving me an avenue to
nurture my love of teaching and for helping me to see the world through others’ life

experiences.

Thanks to my friends at MSU including Russ, Nate, Heather, Andrew, Steve, and
Gene...f0r all of the study sessions, games, and much needed breaks from physics.
Thanks to the MSU group at Fermilab: Josh K., Adam, Joe, Rahmi, Joel, Reiner
and Reinhard for orienting me to Level 2, the D0 packages, and every other bit of

service work involved at the lab as well as Friday tradition and softball. Go DOnuts!

Special thanks to Jodi Wittlin and Suyong Choi for taking me under their wing
and being my surrogate post-docs. They encouraged my progress in research, helped
me contribute to the Higgs group, and assisted me in growing as a scientist. They were
always there for me when I had questions, hit a wall, or had C++ problems...and
Jodi arranged lunches at East China Inn. Also to Alex Melnitchouk and Oleksiy
Atramentov for always helping whenever I had questions about photons.

To the office staff at MSU for making everything run so smoothly behind the
scenes; thanks Brenda and Debbie. Thanks also to the other grads in the office Aous,
Mohammed, Brian, Barath, Stefano, and Chen for helping with random questions as
they occurred.

Thanks to the theory guys that provided comparison predictions. To C-P Yuan for
RESBOS and some theory discussions, Jean-Philippe Guillet for running the DIPHOX
code and providing the result for me, and Carl Schmidt for providing the gluon—gluon
box contribution for addition to DIPHOX.

Finally, to my advisor, Bernard Pepe, for his wisdom, guidance, and support.
Thank you for helping me to navigate Fermilab, high energy, and finding my place in

the physics community.

vi

TABLE OF CONTENTS

LIST OF TABLES ix
LIST OF FIGURES x
1 Introduction 1
2 Theory 3
2.1 The Standard Model ........................... 3
2.2 QCD and Higgs Searches ......................... 6
2.2.1 QCD and the Requirement of Color ............... 6

2.2.2 The Higgs Boson ......................... 7

2.3 Direct Diphotons ............................. 7

3 Fermi National Accelerator Laboratory and the D0 Experiment 11
3.1 Fermilab .................................. 11
3.2 Accelerator and Antiproton (1‘)) Production ............... 12
3.3 The D0 Detector ............................. 15
3.4 Coordinate System and Variables .................... 15
3.5 Tracking System ............................. 18
3.5.1 Silicon Microstrip Tracker .................... 18

3.5.2 The Central Fiber Tracker ................... 21

3.6 Preshower ................................. 22
3.7 Calorimeter ................................ 24
3.8 Muon System ............................... 30
3.9 Luminosity Monitor (LM) ........................ 30
3.10 Trigger System and DAQ ......................... 31
3.10.1 Level 1 Trigger .......................... 33

3.10.2 Level 2 Trigger .......................... 33

3.10.3 Level 3 Trigger .......................... 34

3.10.4 Data Acquisition (DAQ) ..................... 34

3.11 DORECO and CAF ............................ 36

vii

4 Dataset and Monte Carlo
4.1 Trigger ...................................
4.2 Trigger Efficiencies ............................
4.3 Dataset ..................................
4.3.1 Data Quality ...........................
4.4 Monte Carlo ................................

5 Photon ID and Background Study

5.1 Reconstruction Algorithms ........................
5.2 Particle Signatures ............................
5.2.1 Photons ..............................
5.2.2 Electrons .............................
5.2.3 Jets ................................
5.2.4 Muons ...............................
5.3 Signal Variables ..............................
5.4 Background ................................
5.5 Analysis Cuts and Efficiencies ......................
5.5.1 Analysis Cuts ...........................
5.5.2 Cut Efficiencies ..........................

6 Cross-Section Analysis

6.1 Matrix Inversion Method .........................
6.2 Efficiency Data Samples .........................
6.3 Discrimination Variables .........................
6.3.1 Phi Width ............................
6.3.2 CPS_RMS .............................
6.3.3 CPSRMS Squared ........................
6.4 Result of Matrix Inversion ........................
6.5 Cross-Section ...............................

7 Conclusions

BIBLIOGRAPHY

viii

37
37
40
43
44
46

47
47
48
48
48
49
49
49
51
53
53
56

63
63
64
66
66
66
69
69
75

81

83

2.1

2.2

2.3

3.1

4.1

4.2

4.3

LIST OF TABLES

Standard Model Quarks [2]. ....................... 3
Standard Model Leptons [2] ........................ 4
Standard Model Gauge Bosons [2, 3] ................... 5
Depths of the calorimeter layers ...................... 28
Triggers by trigger list ........................... 38
Summary of trigger efficiencies. ..................... 42
Total integrated luminosity by trigger list. ............... 43

ix

LIST OF FIGURES

Images in this dissertation are presented in color.

2.1 Branching ratios of the dominant decay modes of the Standard Model

Higgs boson ................................. 8
2.2 Leading order (LO) Feynman diagrams for direct diphoton production

in QED, QCD, and mixed ......................... 9
2.3 Radiative corrections to the LO Feynman diagrams ........... 10
3.1 Layout of Fermilab’s accelerators [9]. .................. 14
3.2 The D0 Detector [11] ............................ 16
3.3 Cross-section of the D0 tracking system [11] ............... 19
3.4 Barrel/ Disk design of the SMT [11] .................... 19
3.5 Cross sectional view of the SMT [11]. .................. 20
3.6 Positioning of two fiber ribbons to form a doublet [11]. ........ 21
3.7 Cross sectional view of the OFT and associated waveguides [11]. . . . 23

3.8 Schematics of the CPS and FPS detectors. The top right shows the .

CPS geometry, and the bottom right shows the FPS geometry [11]. . 25
3.9 D0 calorimeter [11] ............................. 27
3.10 Calorimeter unit cell [17]. ........................ 28

3.11 Pseudo-projective geometry and segmentation pattern of the calorimeter. 29

3.12 Designed D0 trigger scheme[l7] ...................... 32
3.13 L1 and L2 trigger flow [17]. ....................... 35
4.1 'IYigger turn-on curves for OR’d single EM triggers [23] ......... 41

t'

4.2 Eta vs. Phi lego plot illustrating hot cells. ............... 4o

5.1

5.2

5.3

5.4
5.5
5.6
5.7
5.8

6.1
6.2

6.3

6.4

6.6

6.7

6.8

6.9

6.10

6.11

Distributions of signal variables Pt (top), EMF (middle), and iso (bot-
tom) .....................................

Distributions of the analysis cuts Pt (t0p), EMF (middle), and iso
(bottom). .................................

Phi_fiducial acceptances as a function of W in diphoton MC (tOp) and
data (bottom). ..............................

Di—EM Mass Spectrum ...........................
Di—EM Mass Spectrum after analysis cuts. ...............
Distribution of diphoton Monte Carlo overlayed with data. ......
pp distribution of single photons from diphoton Monte Carlo ......

Analysis Cut Efficiencies as a function of Mass (top), qT (middle), and
Adi.” (bottom). ..............................

Histogram of the Z-mass from the data ..................

Distributions of the Phi Width variable in electrons (top), MC photons
(middle), and jets (bottom). .......................

Efficiencies of electrons (t0p) and jets (bottom) of the Phi Width dis-
crimination variable as a function of pr. ................

Distributions of the CPS_RMS variable in electrons (top), MC photons
(middle), and jets (bottom). .......................

Efficiencies of electrons (tep) and jets (bottom) of the CPS-RMS dis-
crimination variable as a function of m. ................

Distributions of the CPSBMSSQ variable in electrons (top), MC pho—
tons (middle), and jets (bottom). ....................

Efficiencies of electrons (top) and jets (bottom) of the CPS-RMSSQ
discrimination variable as a function of pT ................

Diphoton events determined by matrix inversion of discrimination vari-
able efficiencies as a function of mass. .................

Diphoton events determined by matrix inversion of discrimination vari-
able efficiencies as a function of transverse momentum. ........

Diphoton events determined by matrix inversion of discrimination vari-

able efficiencies as a function of opening angle between the two photons.

Differential diphoton cross-section as a function of mass. .......

xi

52

54

55
57
58
59
60

61
65

67

68

7O

71

72

73

74

74

75
77

6.12 Differential diphoton cross-section as a function of qT .......... 78

6.13 Differential diphoton cross-section as a function of opening angle. . . 79

xii

CHAPTER 1

Introduction

The information provided by this dissertation attempts to extend the knowledge base
of the particle physics community. This thesis presents research into the very tiny

world of particles and fundamental forces, but focuses on particles that are massless.

Photons are occasionally produced in pp collisions. Direct photon production
refers to processes in which the final state photons are produced directly from the
hard scattering of incoming quarks and gluons, and not from secondary decays. It
is particularly interesting to study photons since their energies and angles are well
defined, unlike those of a jet, so that important information can be extracted regarding
the underlying fundamental processes. A particularly useful process to examine is
that of double photon production, or diphotons. Diphoton production has long been
recognized as an important process for testing the parton model, the dynamics of
quarks and gluons, and their interactions. In addition, the postulated Higgs boson is
theorized to decay into two photons and thus an accurate measurement of the QCD
diphoton background is important for any Higgs search.

This analysis presents a measurement of direct diphotons produced at D0. The
rate at which direct diphotons occur in proton-antiproton collisions as a function of
invariant mass, the diphoton’s transverse momentum, and the opening angle between

the two photons is revealed. These measurements are performed at higher energies

1

and with a larger dataset than has ever previously been available. As such, the
measurements are made with greater precision and with a larger mass range than in
previous analyses.

Chapter 2 provides background and some highlights of particle physics as well as
an indication of the importance of this analysis. Chapter 3 briefly describes the Fermi
National Accelerator Laboratory’s proton-antiproton collider and the D0 detector and
some of its intricacies. Chapter 4 gives a description of the dataset and Monte Carlo
programs used in this analysis. Chapter 5 explains the identification of photons,
electrons, and jets and discusses the analysis cuts, their respective efficiencies, and
background suppression. Chapter 6 describes the final steps of the analysis which use
a matrix inversion technique. The resulting cross-sections are also presented in this

chapter.

CHAPTER 2

Theory

2.1 The Standard Model

The Standard Model is a theory that describes most particles and forces quite well.
It is widely accepted and used by the physics community. The Standard Model de-
scribes all matter as being composed of point-like elementary particles called fermions.
Fermions have half-integer spin and both quarks and leptons are of this type. Quarks

and leptons come in families of three generations each and are listed in Table 2.1 and

Table 2.2, respectively.

 

 

 

 

 

 

 

 

 

Generation Particle (symbol) Charge (e) Mass (GeV)
1 Up (u) + 2/3 0.0015-0004
Down ((1) — 1/3 0004—0008
2 Charm (c) + 2/3 1.15-1.35
Strange (s) - 1/3 0.80-0.130
3 Top (t) + 2/3 178.1
Bottom (b) - 1/3 4.1-4.4

 

Table 2.1: Standard Model Quarks [2].

 

 

 

 

 

 

 

 

 

 

 

Generation Particle Charge (e) Mass (MeV)
1 Electron (e) -1 0.511
Electron Neutrino (11,.) 0 < 2 x 10’6
2 Muon (,u) -1 105.66
Muon Neutrino (11),) 0 < 0.19
3 Tau (T) -1 1776.99
Tau Neutrino (VT) 0 < 18.2

 

Table 2.2: Standard Model Leptons [2].

Quarks are the particles that have fractional charge and make up protons and
neutrons. They come in six flavors: up, down, strange, charm, top, and bottom.
Particles made of quarks are called hadrons, which are further divided into baryons
(containing three quarks) and mesons (containing two quarks). Leptons are particles
that have integer charge and do not interact via the strong force. The charged leptons
are the electron, muon, and tau, each having a corresponding uncharged neutrino
called the electron neutrino, muon neutrino, and tau neutrino. All particles have an
antiparticle that has the same characteristics except for reversed charge, and anti-

fermions have Opposite parity from fermions.

The four fundamental forces, electromagnetic, strong, weak, and gravity, are all
mediated or “carried” by particles called vector bosons which have integer spin. The

bosons’ characteristics are listed in Table 2.3.

 

 

 

 

 

 

Interaction Mediating Particle Rel. Strength Range (m) Charge (e) Mass (GeV)
Strong Gluon (g) 1 10‘15 0 0
Electroweak:
Electromagnetic Photon (7) 10‘2 oo 0 0
Weak Wi 10-5 10-18 11 80.425
Z0 0 91.1876
Gravity Graviton 10‘39 co ? ?

 

 

 

 

 

Table 2.3: Standard Model Gauge Bosons [2, 3].

Particles with electric charge interact via the electromagnetic force, which is me-
diated by the photon. The weak force is carried by exchange of the W and Z bosons.
The W and Z bosons have large masses compared to the others, and work over short
distances. Gravity is theorized to be mediated by the graviton, but no well-developed
quantum theory of gravity has yet been proposed, and no evidence of the graviton has
yet been discovered. The strong force acts between quarks, works to form baryons,
mesons, and holds the nucleus of the atom together. This force is mediated by the
gluon. Gluons are chargeless and massless, but do have a different quantum num-
ber called color or color-charge. Quarks come in three colors, red, green, and blue,
while antiquarks come in cyan (antired), and magenta (antigreen), yellow (antiblue).
Only particles whose elementary particle color combinations are white or colorless
are allowed to freely exist. As such, particles containing three quarks are composed
of quarks where each has a different color (i.e. red, green, and blue) and particles

containing two quarks are composed of a quark color—anticolor pair.

Although the Standard Model is not complete, a completely new theory is not ex-
pected. Due to much experimental testing confirming its predictions, only extensions

of it are expected.

 

2.2 QCD and Higgs Searches

2.2.1 QCD and the Requirement of Color

Quantum Chromodynamics (QCD) is the theory that predicts interactions due to
the strong force. This thesis studies events containing direct diphotons in proton-
antiproton collisions, and are a direct result of the strong force interaction. Basically,
protons and antiprotons are each a container of three quarks. These quarks exchange
gluons as necessary to maintain a bound, stable state. Since gluons and quarks carry
color, they can couple to themselves and can emit gluons. One feature of the strong
force is that as the energy of a collision increases, the interaction strength of the
strong force gets weaker and minimizes the chance of quarks and gluons to radiate.
As such, a collision between proton and antiproton containers is considered to be an
interaction between just one constituent (quark or gluon) of each. Given, however,
that hundreds of particles can be formed by these collisions, a cross-section (a) is
often calculated as a measurement of how likely a particular interaction will occur,
such as a quark and an antiquark producing two photons.

Color is often a new and strange concept for most and can seem completely con-
trived. Several physical instances actually mandate its existence, however, and a brief
overview is provided here. It is not the case that if you grouped millions of red up
quarks together that the human eye would see them as red. Color is instead merely
a characteristic held by quarks and gluons whose interaction happens to mirror the
color theory of light. This characteristic is, however, necessary to resolve the issues of
spin and statistics in baryon spectroscopy [4]. For instance, consider the A++(1232),
which has spin %. This particle is the bound, ground state system of mm and should
have a totally symmetric wavefunction under exchange of up quark pairs. However,
since this particle has spin %, the wavefunction is required to be antisymmetric under

exchange of up quark pairs, which is a problem since spin, space, and flavor consid-

6

erations do not produce an antisymmetric wavefunction. This issue is resolved if the
color parameter is introduced as it provides an antisymmetric wavefunction. Other

examples exist, including experimental data on e+e‘ annihilations [4].

2.2.2 The Higgs Boson

The Higgs Boson is a particle that is theorized to couple to any particle with mass.
This boson comes from the Higgs mechanism, which introduces a field, called the
Higgs field, and has a non-zero vacuum expectation value. This mechanism predicts
three massive vector bosons (Z 0, Wi), one scalar boson (H), and also gives mass to
the quarks and leptons. The discovery of spontaneous symmetry breaking and the
Higgs mechanism were a major breakthrough toward unifying the electromagnetic
and weak forces. The formal mathematics can be found in [4].

The theory of the Higgs mechanism is very successful, but for the theory to con-
tinue, the Higgs boson must be discovered. Higgs searches are ongoing at D0 and
GDP at Fermilab and will also be performed at the Large Hadron Collider (LHC)
being built at CERN in Switzerland. The Higgs is theorized to have a number of
decay modes, and their branching ratios are shown in Figure 2.1. One of the decay
modes is that of two photons, making this analysis interesting not only as a QCD

measurement, but also for measuring the 77 background for future Higgs searches.

2.3 Direct Diphotons

While the Higgs boson is expected to have a two photon decay channel, two photons
may also be directly produced in a number of other interactions as shown in Figure
2.2. Direct diphotons and the mechanisms by which they are produced are sensitive
to the gluon distribution of the proton and are an excellent method for testing both

perturbative and non-perturbative QCD. This thesis includes events from all direct

7

 

 

 

 

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90 100 200 300 400 '
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Figure 2.1. Branching ratios of the dominant decay modes of the Standard Model
Higgs boson.

 

Figure 2.2. Leading order (L0) Feynman diagrams for direct diphoton production in
QED, QCD, and mixed.

diphoton processes. The contributions shown in Figure 2.2, are only the leading
order processes for direct diphoton production, and therefore the radiative corrections
should also be mentioned, and are shown in Figure 2.3. In the Feynham diagrams, the
straight lines represent quarks, the wavy lines represent photons, and the curly lines
represent gluons. A few other diagrams that include photons due to fragmentation
do exist and are sometimes included in theory calculations [6], but the cuts used in

this analysis inevitably suppress those contributions.

 

Figure 2.3. Radiative corrections to the LO Feynman diagrams.

10

CHAPTER 3

Fermi National Accelerator

Laboratory and the D0 Experiment

This chapter will provide a brief description of Fermi National Accelerator Laboratory
(Fermilab or FN AL) , the D0 detector, giving more emphasis to the detector subsys-
tems that are pertinent to this analysis, as well as the trigger and data acquisition

(DAQ) systems.

3. 1 Fermilab

Fermilab is the site of the world’s, currently, highest energy particle accelerator, the
Tevatron, and also is home to a few high energy physics experiments including D0,
CDF, and MINOS. Fermilab was commissioned by the US. Atomic Energy Commis-
sion on November 21, 1967. It is located in Batavia, IL, 40 miles west of Chicago, on
what used to be the village of Weston and covers 6800 acres of farmland [7]. Origi-
nally named the National Accelerator Laboratory, it was renamed in 1974 in honor of
Enrico Fermi, the 1938 Nobel Prize recipient for his work on the artificial radioactiv-
ity produced by neutrons, and for nuclear reactions brought about by slow neutrons

[8]. Fermilab also holds facilities for cancer treatment, science outreach, and a herd

11

of American bison that produces calves each year — always a popular attraction for
visitors. The Tevatron itself is a particle accelerator ring that has a circumference of
4 miles, and collides protons and anti—protons at a center-of-mass energy of \/§ = 1.96
TeV. The Tevatron Collider has been run for two major periods of operation, referred
to as Run I and Run II. Run I lasted from 1992 to 1996, at which time the Tevatron
was shut down for upgrades to both the Tevatron itself and to the detectors that it
serves. The data presented in this analysis are from the Run II portion of the D0

experiment which started recording data in March 2001.

3.2 Accelerator and Antiproton (19') Production

Fermilab uses a series of accelerators to generate the proton and antiproton beams
that are collided. The information about the accelerator process is based on [9] and
[10]. This process starts with tanks of hydrogen gas and the Cockcroft-Walton pre-
accelerator. The hydrogen, consisting of one electron and one proton, is ionized to
have two electrons, and then accelerated to 750 keV. The H ‘ ions then enter the
500 ft. linear accelerator (or LINAC) and are accelerated to 400 MeV using quickly
oscillating electric fields that also cause the protons to be grouped into bunches. Once
the ions are accelerated, they pass through a carbon foil that strips off the electrons,
leaving only protons to continue to the next stage. These protons then travel 20 feet
below the surface to the Booster (a synchrotron), where magnets force them to travel
in a circle and accelerate them up to 8 GeV, where they are then passed to the Main
Injector.

The Main Injector accelerates these protons to 120 GeV. A few of these continue
to be accelerated to 150 GeV and injected into the Tevatron, while the rest are
sent to the antiproton source. Those that are sent to the anti-proton source collide

with a fixed nickel target where a wide variety of particles are produced, one of

12

which is the antiproton. For every million protons that hit the target, about 20
antiprotons are produced. The antiprotons that are produced are focused into a
beam using a lithium lens, and passed through a pulsed magnet, acting as a charge-
mass spectrometer, that removes the particles that are not antiprotons. Now, since
the protons strike the nickel target at the same time the antiprotons that are produced
have a small variation (or width) in time, but a large width in energy since they can
be produced at different energies. So, these are now sent to the Debuncher where
radio-frequency (or RF) cavities are used to exchange the energy and time widths,
creating a continuous (instead of bunched) beam of antiprotons of similar energy.
This antiproton beam is diffuse due to the different, random angles at which they
are produced. This randomness can be likened to temperature. It is important to
remove the diffuseness and focus the beam in order to increase the probability of
producing rare particles in the collider. To accomplish this, the beam is “cooled”
using a method called Stochastic Cooling. The beam is then sent to the Accumulator
where the beam is further focused and the antiprotons are stored and re—bunched.
Once enough antiprotons are produced (which takes several hours), they are sent back
to the Main Injector, accelerated to 150 GeV, and injected into the Tevatron in the
Opposite direction of the protons signaling a new “store” of 36 bunches of protons

and 36 bunches of antiprotons.

Once in the Tevatron, the proton and antiproton beams are accelerated to almost
1 TeV, and have a speed nearly that of light. The beams are kept in a helical orbit
around the ring by a 4.2 T magnetic field created using about 1000 superconducting
magnets cooled, using liquid helium, to 4.3 K. The beams are then steered so the
bunches cross each other every 396 ns producing collisions at two interaction locations,

one of which is centered in the D0 detector.

13

 

           

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ZOS<>>FuO¢UxUOO

ZO¢h<>mh

   

"-0.5552— 222‘ f/Mm-..mi\

Z~<IU mOH<mmAmUU< mb<d2mmm

Figure 3.1. Layout of Fermilab’s accelerators [9].

14

3.3 The D0 Detector

Most of the collisions that happen every 396 ns are glancing collisions that produce
uninteresting results. Sometimes, however, a head-on collision or hard scatter occurs
between one parton of the proton (a part of the proton which is either a quark or
gluon) and one parton of the antiproton. In these collisions, the partons not in the
collision travel down the uninstrumented beam pipe, but the two that did collide can
annihilate and produce new particles that travel through the D0 detector and are
studied.

The D0 detector, pictured in Figure 3.2, is a nearly-hermetic, 47r detector [11].
Portions of the detector are completely new with respect to Run I, whereas other
portions have been recycled and are again being used in Run II. The detector consists
of several subdetectors that are layered like an onion or parfait. These subdetectors

are each designed to measure different traits of particles.

3.4 Coordinate System and Variables

The D0 detector uses a right-handed coordinate system with the origin at its geometric
center. The positive z-axis is defined to be in the direction of the protons, and the
positive y-axis is upward. The angles 6, and 45, are the polar and azimuthal angles,
respectively, with the 6 = 0 defined along the beam line and (25 = 0 along the x-axis
[12].

For relativistic particles, it is natural instead of using 6, to use the Lorentz invari-

ant variable rapidity, y, defined as

 

_l
”—2

In (23:) (3.1)

for finite angles in the limit that lim :g. —> 0 [12]. This variable is more convenient to

15

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0 0 0 0 0 0 0 0 0 0
...u.n.u.vu...anovvvvvwvx
.p....O.O-OLO.OIO.6.O.O.O.O>O..-.\9.

                

il-r . ,VA‘L

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n“§“§§§h§h§§§\fidflflflfllflfidflflflfifi 3‘0N&&E§§§\§§§KE

 

 

0

10.00040

 

Figure 3.2. The D0 Detector [11].
16

2233 \ 5% Es

$35.
:8: .2338

9.28:.
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‘eeogmo
0:23....
8::

 

use when approximated by the pseudorapidity, 17, defined as
0

Pseudorapidity calculated from the origin to a position in the detector is called detec-
tor 17, or met, whereas the pseudorapidity calculated using the point of the collision,
or primary vertex, is the physics 77, or simply n. This distinction is made since the
primary vertex does not always occur at the origin.

While the proton-antiproton collisions occur at a fixed center-of-mass energy («3),
these protons and antiprotons have a parton structure due to their constitution of
a number of subatomic particles. This parton structure prohibits the use of total
conservation of energy principles in the analysis since the individual partons only
carry a fraction of the proton/antiproton’s total energy, with the rest of the energy
escaping down the beam pipe with the other partons [13]. Instead, conservation of
momentum and conservation of energy are applied in the transverse plane (or the
plane perpendicular to the beam pipe). This may be used since the transverse energy
and momentum balance prior to the collision are zero. Consequently, useful variables

are defined:

0 Transverse Energy, ET 2 E sin 0

0 Transverse Momentum, pr = pSiDQ = VPE: + P3

0 Missing Transverse Energy, ET.

ET occurs when a particle, such as a neutrino, is produced in the collision but not
found by the detector, and thus carries away some amount of energy. When energy
conservation in the transverse plane is performed, the total does not sum to zero

revealing this missing transverse energy.

17

3.5 Tracking System

The tracking system of the detector, pictured in Figure 3.3, is completely new for Run
II and is designed to detect charged particles as well as locate the primary vertex with
a precision of 35pm. The tracking system consists of the Silicon Microstrip Tracker
(SMT), the Central Fiber Tracker (CFT), and is surrounded by a solenoidal magnet
with magnetic field strength of 2T [11]. The magnetic field will cause a charged
particle’s path to deflect in a circle allowing its momentum to be measured. The

equation that predicts this phenomenon is
r = E (3.3)

where r is the radius of curvature, 1971 is the transverse momentum, q is the charge,

and B is the magnetic field strength.

3.5.1 Silicon Microstrip Tracker

The SMT provides tracking and vertexing information over a pseudorapidity range
of -3 < 17 < 3. Given that the primary vertex does not always occur at the origin and
some particles decay after a short distance creating secondary vertices, a combination
barrel-disk design for the SMT, pictured in Figure 3.4, was employed. In this design,
the barrel portions and the OFT detect particles of low 17, and the disks detect particles
with high 7). The SMT consists of six barrels, and each barrel has four silicon readout
layers. Each layer is composed of silicon modules known as ladders. The ladders
are mechanical support structures made of silicon with beryllium strips that aid in
alignment with carbon-boron fiber/Rohacell rails that bridge the beryllium strips.
All of the barrels use p-type axial sensors and n-type stereo silicon sensors. Layers

one and three of the four inside barrels use 90° stereo, double-sided silicon sensors,

18

Interayostat
Delador

Genital Fiber kaer

 

Figure 3.3. Cross-section of the D0 tracking system [11].

 

(forward, high-n)

Figure 3.4. Barrel/Disk design of the SMT [11].

19

while the outer two barrels use single-sided sensors in these layers. Layers two and
four of all of the barrels use double-sided silicon sensors but only have a 2° stereo

offset. The centers of the barrels are located at |z| = 6.2, 19.0, and 31.8 cm.

Each barrel is capped with an F-disk composed of 12 double-sided, trapezoidal
shaped, wedge detectors built in a planar arrangement, and three more F-disks are
placed at each end of the barrel-disk assembly. The F-disks are located at |z| = 12.5,
25.3, 38.2, 43.1, 48.1, and 53.1 cm. Next, four H-disks composed of 24 single-sided
wedge detectors, also built in a planar arrangement, are located at |z| = 100.4 and

121.0 cm for high 17 coverage. Finally, all of this is supported by beryllium bulkheads.

 

 

 

Figure 3.5. Cross sectional view of the SMT [11].

20

 

 

Figure 3.6. Positioning of two fiber ribbons to form a doublet [11].

These bulkheads are designed to support the ladders and disks as shown in Figure 3.5,
as well as allow support for signal readout cables and coolant. All of these detectors

operate at a temperature below 5° C [11].

3.5.2 The Central Fiber Tracker

The CF T is the second portion of the tracking system and surrounds the SMT. The
CFT is composed of about 77,000 scintillating fibers positioned on eight concentric
cylinders (made with a core of Rohacell and coated with linear carbon fibers impreg-
nated with 40% resin) and fills the space from 20-52 cm from the center of the beam
line. The inner two cylinders are only 1.66 m long to allow space for the SMT H-disks,
while the other six cylinders are 2.52 m long.

The scintillating fibers are arranged into ribbons of 128 fibers each. Two of these
ribbons are formed into a doublet by positioning the second layer in the interstitial
spaces of the first, pictured in Figure 3.6. Each cylinder contains one axial doublet
ribbon oriented along the beam path and one stereo doublet ribbon of either 11 or v
oriented at i3°. These stereo layers start on the inner cylinder with a u layer, and
alternate for each cylinder. The scintillating fibers are 835 microns in diameter. This
small diameter provides a doublet resolution of 100 microns. The fibers are made
of polystyrene doped with fluorescent dyes of 1% paraterphenyl that emits light at
340 nm, and, due to paraterphenyl’s low mean free path in polystyrene, a secondary

wave-shifter dye of 3-hydroxyfiavone at 1500 ppm that absorbs the 340 nm light and

21

emits 530 nm light that transmits well through the polystyrene. These fibers are
then doubly clad with polymethylmethacrylate and then fluoro—acrylic. The dual
claddings provide for both better optical and mechanical performance. One end of
the fibers is capped with an aluminum coating that provides a reflectivity of 90%.
The other end is connected to waveguides pictured in Figure 3.7, whose composition is
the same as the fibers except for the dyes, which pipe out the light from the detector
for readout [11]. The waveguides are connected to Visible Light Photon Counter
(VLPCs) cassettes that are immersed in a liquid helium cryostat and turn the light
from the OFT into electrical signals. The VLPCs Operate at 9 K, have a quantum
efficiency of > 75%, a gain of 22,000 to 65,000, and are able to detect single photons

[11]. The pp resolution at me, = 0 of the entire tracking system can be parameterized

 

as OPT/m = \/0.00152 + (0.0014107)2 [11].

3.6 Preshower

The preshower detectors, also new for Run II, are the next layer of the detector after
the SMT, CFT, and the magnetic field producing solenoid. The preshower is de-
signed to improve photon and electron identification, enhance tracking and calorime-
try matching, and help correct electromagnetic energy measurement offline due to
the uninstrumented solenoid, a lead radiator (which, combined, is about two radia-
tion lengths in thickness), and other material such as structural support and readout
cabling. It is divided into three portions, the central preshower (CPS) and the two
forward preshower (FPS) detectors. Both the CPS and FPS are made of triangular
strips of scintillator with a wavelength-shifting fiber in the center and then coated
with two layers of mylar to increase light yield. The fibers are read out by VLPCs
similar to the CFT. The triangular strips are arranged so that no dead space exists

between them. The CPS and FPS detectors are made from the same material, but

22

256-channel fiber
OFT Of CPS flaw Central calovimeter
waveguide bundle ‘ “VOW W3"

 

Strain
'9'“ Clearance
'1 ll for FPS
(not shown)
lenoid
services
Solenoid _
OU‘BI' OHITIGIBI'
well support

Figure 3.7. Cross sectional view of the CF T and associated waveguides [11].

23

their geometries, pictured in Figure 3.8, are a little diflerent.

The CPS detector is composed of three layers of the scintillating strips and is
positioned in the 5 cm gap between the solenoid and the central calorimeter. The
three layers are in an axial, u, and v geometry with the u-layer at a stereo angle of
23.774° and the v-layer at a stereo angle of 24.016°, and have 1280 strips each [11].

The two FPS detectors are positioned on the heads of the calorimeter endcaps.
Each FPS detector is made of two layers of the triangular strips, a two radiation
length thick layer of lead-stainless-steel absorber, and two more layers of triangular
strips. The inner layers are called the MIP (minimum-ionizing particle) layers and
the outer layers are called the shower layers. This is due to the inner layers typically
detecting charged MIPS, and the outer layer also detecting particle showers produced

in the absorber. These detectors are also read out using the VLPCs.

3.7 Calorimeter

The D0 calorimeter system, shown in Figure 3.9, is unchanged from Run 1. It is de-
signed to provide very accurate energy measurements for electrons, photons, and jets.
It is a compensating- sampling calorimeter that consists of three portions, the central
calorimeter (CC), and two endcap calorimeters (EC). (It is called a. “compensating-
sampling” because the calorimeter collects only a sample of a particle’s energy, but
is considered compensating since uranium releases extra energy by fast neutron fis-
sion during a particle’s shower.) The CC covers Indetl < 1.2 and the ECs extend the
coverage up to |ndet| z 4. In the ¢-dimension, the calorimeter consists of 32 sepa—
rate modules with unavoidable gaps between them. These gaps, often referred to as
phi-cracks, make it possible for particles to both escape through them, and be mis-
measured if their position is too close to the edge of the modules. All three portions of

the calorimeter are made of three distinct sections: an electromagnetic (EM) section,

24

a fine hadronic (FH) section, and a coarse hadronic (CH) section made of plates of
metal to act as absorbers. The EM section of the CC uses 3 mm thick and the EC
uses 4 mm thick plates of pure depleted uranium, 238U. The fine hadronic sections are
made of 6 mm thick plates of uranium-niobium (2%) alloy, and the coarse hadronic
sections use 46.5 mm thick plates of copper in the CC and stainless steel in the EC.
The calorimeter uses liquid argon at a temperature of 90 K as the active material

that fills the space between the plates.

The absorbers cause particles produced from the collision to shower into secondary
particles at a geometric rate as they interact with the absorber atoms. Electromag-
netic objects, namely photons and electrons, lose energy by traveling through matter
primarily by two shower processes: bremsstrahlung (e —> 67) (literally braking ra-
diation) and pair production (7 —> e+e‘). As these showers occur, the secondary
particles ionize the argon atoms which are collected and provide a measurement of

the original particle’s energy, given that

E(a:) 2 E079??? (3.4)

where x is the distance traveled, and X0 is the radiation length of the material
through which it travels. X0 is defined for electrons as the mean distance over which
the electron will lose ,1; of its energy through the bremsstrahlung process, and defined
for photons as the thickness of material through which a photon travels so that the
probability of its converting to an electron-positron pair is equal to 7/ 9, provided that
the energy of the photon is of order 1 GeV [14]. The radiation length for uranium
is approximately 0.34 cm [16]. Due to the nature of EM objects, the calorimeter is

designed with four layers of uranium plates aptly called EM], EM2, EM3, and EM4

26

 

Figure 3.9. D0 calorimeter [11].

which extend radially outward from the beam pipe where these objects will deposit

most of their energy in a narrow shower.

Hadrons (particles often present in jets), however, interact differently than EM
objects. Hadrons interact with the uranium nuclei through the strong force and have
an associated quantity similar to radiation length, called nuclear interaction length,
A. Nuclear interaction length is defined as the mean free path between inelastic
interactions, and is calculated by

“’3' 01'

A IAEAJ'

 

(3.5)

where N A is Avogadro’s number and 111,- is the weight fraction of the jth element in

the element [16]. These hadrons typically break up into other particles as well as

27

 

( Absorber Plate Pad Resistive Coat Liquid Argon
\ GIO Insulator Gap

\1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

c <—— Unithll -———> J

 

Figure 3.10. Calorimeter unit cell [17].

causing the uranium atoms to fission. This leads to larger showers in both width and
length in the calorimeter. Layer depths for the EM, FH, and CH, are shown in Table
3.1.

 

EM FH CH

 

 

CC depth 1.4, 2.0, 6.8, 9.8Xo 1.3, 1.0, 0.76/\ 3.2/\

 

EMdepth 1.6, 2.6, 7.9, 9.3x0 1.1,1.1,1.1,1.1,\ 3.2x

 

 

 

 

 

 

Table 3.1: Depths of the calorimeter layers.

All of these layers are instrumented to create readout cells of size 0.1 x 0.1 in
eta-phi space, with the exception of the EM3 layer. This layer is further divided into
0.05 x 0.05 to increase EM shower precision in position.

Each cell, pictured in Figure 3.10, is made of an absorber plate, a gap filled
with liquid argon, a G-10 sheet coated with copper and then by an insulating epoxy,
another gap of liquid argon, another absorber plate, and so on. As each particle

passes through the detector, it starts a shower of particles inside the absorber plate

28

 

Figure 3.11. Pseudo-projective geometry and segmentation pattern of the calorimeter.

producing many secondary particles. The secondary particles proceed to ionize the
liquid argon. The ionized electrons are then attracted to the G-10 sheet due to an
electric field generated by grounding the absorber plates, and placing a positive high
voltage on the G—10 sheets. The electron drift time across the 2.3 mm liquid argon
gap is about 450 MS [11]. The drifting electrons induce an image charge on the copper

which is read out as the signal.

The cells of each layer are aligned and grouped to form pseudo-projective towers,
as shown in Figure 3.11. These are considered pseudo-projective because the centers
of the cells lie on rays projecting from the center of the calorimeter, but the cell
edges are perpendicular to the absorber plates. These towers are also aligned in the

approximate direction of shower development.

29

3.8 Muon System

Muons are much more massive than electrons and most of their energy loss comes from
interaction with the detector material rather than from bremsstrahlung like electrons.
Because of this behavior, muons above 2. 3.5 GeV typically pass through the entire
calorimeter, which is why the muon system is the outermost layer of the detector and
is well protected from debris from the hadronic and electromagnetic showers in the
calorimeter. The D0 muon system is intended to identify muons and independently
measure their momenta in a toroidal magnetic field. The muon system is comprised

of three main components:

0 Wide Angle MUon Spectrometer (WAMUS) covering [77] < 1
0 Forward Angle MUon Spectrometer (FAMUS) covering 1 < [nl < 2

o Solid-iron magnet forming a toroidal field of 1.8 T.

The WAMUS has three layers of proportional drift tubes and two layers of plate
scintillation counters that help with triggering and removal of background muons
from cosmic rays. The FAMUS has three layers of mini-drift tubes and three layers
of scintillation pixel counters that help with triggering [18]. More information on this

system can be found in [11] and [18].

3.9 Luminosity Monitor (LM)

D0 has two luminosity detectors mounted at z = i140 cm on the outer surface of the
endcaps and are positioned in the area between the beam pipe and the FPS (pictured
in Figure 3.3). These detectors monitor the luminosity at the D0 interaction region
by detecting inelastic p13 collisions [11]. The LM detectors constitute two arrays of

scintillation counters, are 15 cm long, and cover 2.7 < [7}] < 4.4. Luminosity is a

30

quantity that can be described to the layperson as the amount of data recorded. To
the physicist, however, luminosity, E, is given by

1‘le M

L = f (3-6)

 

OLM

where NLM is the average number of inelastic collisions per beam crossing, f is the

beam crossing frequency, and oLM is the effective cross section.

3.10 Trigger System and DAQ

As stated previously, the proton and anti-proton beams cross every 396 ns which
equates to 2.5 million crossings every second (2.5 MHz). Most of these events consist
of glancing collisions and are considered uninteresting by today’s standards. Con-
sidering this and the amount of data space required per event, it would be wildly
inefficient to record every event. This is where the Trigger System and the Data
Acquisition come into play by saving and writing to tape only the events that are

deemed interesting.

The D0 trigger has three distinct levels of decision and, overall, was designed
to reduce 7 MHz of input rate to 50 Hz written to tape, as illustrated in Figure
3.12. The trigger decisions are made looking for certain signatures in the detector
that correspond to different objects or events. Each level allows fewer events to pass
than the previous by examining events in more detail and consequently taking a little
more time. For example, an EM event trigger might require two detector sections (or
towers) with at least 6 GeV deposited in each tower’s EM layers at Level 1, require
one of those detector towers and its neighboring towers (or cluster) to have at least a
total of 15 GeV deposited in the EM layers at Level 2, and require that cluster to be

completely reconstructed to an EM physics object of at least 35 GeV at Level 3, but.

31

— 7 MHz:
J Lum = 2 x 1032cm'2s;1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

‘ ~ 396 ns +132 ns crossing time
L1 «r— — — — 9] FRAMEWORK
4-2 “3 L1: HARDWARE [,4
1"
5-10 kHz ,x’
128 bits J
L2
100 us L2: HARDWARE
1 kHz
128 bits
L3
100 ms

0 Maintain low- & high-p, physics 50 nodes L3: SOFTWARE
| Implement fast algorithms,

 

 

 

 

 

 

parallel processing, pipelininglbuffering 50 HZ\ [.83ng 3

o Trigger Deadtime < 5%

 

Figure 3.12. Designed D0 trigger scheme[l7].

32

veto on events containing hadronic objects and events with only one EM object.

3.10.1 Level 1 Trigger

The first level (L1) is composed of a hardware trigger consisting of Field Pro-
grammable Gate Arrays (FPGAs) holding short algorithms in order to make quick
decisions since it must do so for every beam crossing. These algorithms view the de-
tector in a very coarse fashion only using calorimeter towers, for example, instead of
actual physics objects. At L1, only the calorimeter, CFT, muon system, and luminos-
ity monitor portions of the detector are used. The information from these detectors
is read into the trigger framework, and based on a maximum of 128 different And/Or
trigger terms, or trigger hits, the event is either rejected and dumped, or it is passed

onto level 2.

3.10.2 Level 2 Trigger

The second level (L2) consists of preprocessors for each detector subsystem that
combine signals from the system into physics objects. It no longer views information
in terms of calorimeter towers and hits in the tracker, but rather electromagnetic
objects and tracks. L2 also contains global processors (L2Global) that can look at
these objects on an event wide basis. This level contains both hardware and software
algorithms referred to as firmware. L2 was designed to take up to 10 kHz input with

a maximum acceptance rate of 1 kHz.

Level 2 Global

L2Global is responsible for making trigger decisions based on the physics objects cre-
ated by each subsystem’s preprocessors. These decisions can be made based solely

on the objects themselves or by combining objects from different systems. For exam-

33

ple, it can make a decision based on a muon object itself, or it can decide based on
whether a muon object has a spatially matched track object as well.

The decision process begins by examining which of the 128 bits fired in L1. Each
L1 bit has an associated L2 script that contains a number of filters and a minimum
number of global objects to pass each filter. These global objects are made from tools.
Tools are specific C++ classes that build objects based on selection criteria that decide
which from the list of L2 preprocessor objects should be made into global objects.
These tools are also where objects from different preprocessors can be combined into
a single global physics object. An example of a script requires two EM objects greater
than 7 GeV with matched STT tracks and one EM object with isolation less than

0.2. If any L2 script passes, the event is passed to level 3.

3.10.3 Level 3 Trigger

The third level (L3) is a completely programmable software trigger that is designed
to reduce 1 kHz of input rate to 50 Hz to be recorded to tape for offline analysis. This
trigger is run on a collection of Linux based computers, or Linux farm, that processes
the events in parallel [11]. At L3, the software constructs the physics objects into
photons, electrons, muons, taus, jets, vertices, and missing energy, as well as the
relationships between them like azimuthal angle and invariant mass. One or more L3
scripts each containing filters are assigned to each L2 bit that fires and is compared

to a programmable trigger list. If the event is accepted, it is then written to tape.

3.10.4 Data Acquisition (DAQ)

There are a great many detectors and electronic systems in this experiment, as pre-
viously outlined. A program called COOR controls the systems and is used for DAQ.

COOR performs everything from calibration to synchronizing the systems to actually

34

[ETECTOR

L1
i ? iTR’GGER

510m: ;~—————

i r— LZTRIGGER j
‘ '7 m“!

  
  

 

 

._-__.__—___
l

 

 

Global Jam
. .L2 , (Software)

 

 

     

 

 

 

 

 

 

 

 

 

 

 

L2: Combines
Ll: ET towers. tracks objects into c. [Lj
consistent with c, it. j (multi-detcctor correlations)

 

 

 

 

Figure 3.13. L1 and L2 trigger flow [17].

35

recording the data. All of these detector systems also have monitoring systems to
ensure that they are running properly and the data are not compromised. The mon-
itoring systems and COOR are controlled by physicists around-the—clock on a shift

schedule whenever a store of protons and anti-protons is in the Tevatron.

3.11 DORECO and CAF

After an event is written to tape, the entire event is reconstructed for use in analysis.
This is done by the DORECO program on many farms of computers. DORECO uses
all of the information from the detector not only to reconstruct all of the particles
detected in an event, but also to trim down their associated variables to a bare-
bones format called thumbnails (or TMBs) for ease in handling and hard-drive space
considerations for the analyst. The specifics of the reconstruction algorithms relevant
to this analysis are discussed later in Section 5.1. These TMBs are stored in the
sequential access via metadata (SAM) data handling system. All of the data are then
skimmed by the Common Samples Group (CSG) at D0 into separate datasets that
group similar events together. Examples of this would be events that contain two
electromagnetic objects of high pr, or events that contain 3 jets. The events are also
processed into a format that is designed to be universal for all collaborators at D0
called CAF (Common Analysis Format).

CAF is a set of C++ classes and scripts that allow the users to create a ROOT-
based file to access all the variables they need including likelihoods and matrix al-
gorithms designed by other users [19]. This allows for users to share their work so
that everyone does not have to design their own methods. It also, however, provides
the ability to access only the variables they need, thus, writing only the variables
of interest. For example, this analysis is principally concerned with photons, and

therefore, does not require information regarding the muons.

36

CHAPTER 4

Dataset and Monte Carlo

This chapter will explain the triggers used to collect the data used in this analysis,
and the Monte Carlo samples used to simulate expected results. It will also describe
the size of the data sample and the method that was used to skim the data into

different dataset definitions.

4. 1 Trigger

The events used in this analysis were selected using a number of triggers that fire due
to high-p7» electromagnetic objects. This allows for examination of a small subset of all
the data collected with the D0 Detector. The triggers used are listed in Table 4.1, and
are broken down by trigger list version. Fermilab is continually making improvements
to the Tevatron in an attempt to increase the instantaneous luminosity delivered to
its experiments by increasing the number of bunches of particles in the ring and
by increasing the number of particles per bunch. As these improvements are made,
tighter triggers must be employed to keep the recording rate within acceptable limits.
For this reason, as well as to make use of better algorithms that collaborators design,
D0 must periodically alter the triggers, thus creating different trigger list versions.

Each trigger list version has the suite of triggers logically “OR’d” together.

37

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Trigger List Trigger L1 L2 L3
v8-v1 1 EM_HI CEM( 1,10) - ELELOOSE(1,30)
EM_HI_SH CEM(1,10) - ELELOOSESH.T(1,20)
EMMX CEM(1,15) — ELELOOSE( 1,30)
EM_MX_SH CEM(1,15) - ELELOOSESH_T(1,20)
EM_HI_2EM5_SH CEM(2,5) - ELELOOSESH-T(1,20)
v12 E1 _SHT20 CEM(1,11) - ELE_NLV.SHT(1 ,20)
E2_SHT20 CEM (2,6) - ELE_NLV_SHT(1,20)
E3_SHT20 CEM(2,3) - ELE.NLV.SHT(1,20)
CEM(1,9)
E1_SH30 CEM( 1,11) - ELE_N LV_SH( 1,30)
v13 ELSHT22 CEM(1,11) L2CALEM(15,x) ELE.NLV_SHT(1,22)
E2.SHT22 CEM(2,6) L2CALEM(15,x) ELE_NLV_SHT(1 ,22)
E3_SHT22 CEM(2,3) L2CALEM(15,x) ELE.NLV_SHT(1 ,22)
CEM( 1,9)
E1_SH30 CEM(1,1 1) L2CALEM(15,x) ELE.NLV_SH (1,30)
v14 E1.SHT25 CEM(1,12) L2CALEM(15,x) ELE_NLV_SHT(1,25)
E3.SHT25 CEM(1,12) L2CALEM(x,11,0.2) ELE_NLV_SHT(1,25)
E1_SH35 CEM(1,12) L2CALEM(15,x) ELE.NLV_SH(1,35)
E3_SH35 CEM(1,12) L2CALEM(x,1 1,0.2) ELE_NLV_SH(1,35)
ELISHT22 CEM(1,12) L2CALEM(15,x) ELE_NLV_SHT ( 1,22)
IsoEleSHT(1,22)
E3_ISHT22 CEM(1,12) L2CALEM(x,11,0.2) ELE_NLV_SHT(1,22)
IsoEle_SHT(1,22)
ELISHBO CEM(1,12) L2CALEM(15,x) ELE_NLV_SH(1,30)
IsoEle_SH (l ,30)
E3JSH30 CEM(1,12) L2CALEM(x,11,0.2) ELE.NLV_SH(1,30)

 

 

 

 

IsoEleSH(1,30)

 

Table 4.1: Triggers by trigger list.

 

The notation in Table 4.1, is described by the following:

CEM(n,x) represents the number of EM trigger towers, n, with energy of at least x

(GeV).
EM(1,12) requires one EM candidate with energy of at least 12 GeV.
L2CALEM(15,x) represents an L2 cluster with at least 15 GeV.

L2CALEM(x,E,0.2) requires a single tower EM object with isolation less than 0.2

and energy of at least E (GeV).

L2CALDIEM(18) requires the sum of the two highest EM towers to be at least 18
GeV.

ELELOOSE(n,x) represents the number of loose electron candidates, n, with energy
of at least x (GeV).

ELE_LOOSE_SH_T(n,x) represents the number of loose electron candidates, n, with
energy of at least x (GeV), satisfying transverse shower shape require-

ments.

ELE_NLV(n,x) represents the number of loose electron candidates, n, with energy of

at least x (GeV).

ELE_NLV_SH(n,x) represents the number of loose electron candidates, n, with energy

of at least x (GeV), satisfying loose shower shape requirements.

ELE_NLV_SHT(n,x) represents the number of loose electron candidates, n, with en-

ergy of at least x (GeV), satisfying tight shower shape requirements.

IsoEleSHT(1,22) represents one isolated electron candidate satisfying tight shower

shape requirements and at least 22 GeV.

39

IsoEle_SH(1,30) represents one isolated electron candidate satisfying loose shower

shape requirements and at least 30 GeV.

In the cases like CEM(2,3)CEM(1,9), the trigger bits are “AND’d” together, so in
this instance, the event will pass the trigger if two trigger towers contain at least 3
GeV, and one of those contains at least 9 GeV. More information on triggers can be

found in the trigger database [20].

4.2 Trigger Efficiencies

All of the events in this analysis are required to have fired an unprescaled trigger
from its respective trigger version listed above. These triggers and their respective
efficiencies, including their “OR’d” response, have been studied by the Electron ID
group and used in other analyses at D0 [21, 22, 23], and only highlights will be
presented here.

The trigger efficiencies were measured using a tag-and-probe method where Z —>
e+e‘ events were used by requiring two electron candidates with an invariant mass
> 65 GeV, or near that of the Z boson [24]. One of the candidates becomes the
“tag” and must pass tight electron identification cuts, while the other candidate,
the “probe”, is used to measure the trigger efficiency. The “OR’d” response of these
triggers was studied, and while flat in met and did“, the response has a pp dependence,
often referred to as turn-on, and is shown in Figure 4.1. Their parameterizations can
be found elsewhere [22].

Due to the changes in triggers and trigger list versions, an average trigger efficiency
must be calculated. This efficiency is weighted by the percentage of total integrated
luminosity collected by each trigger version and is shown in Table 4.2. The estimated

trigger efficiency for the diphoton process is 0.99 :t 0.05.

40

 

 

 

 

 

 

 

 

 

 

Auk/000 a 0m . 0— 0
1 . . . — . A.
:fiTwAfiYfiM—Wmu.» .mmd
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.8 5.8. a 1,.
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m

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m

     

 

N0

00

  

 

seesaw swath _ 22>.

Figure 4.1. Trigger turn-on curves for OR’d single EM triggers [23].

41

 

 

 

 

 

 

 

 

Trigger Version Efficiency Trigger Lum. Weighted Efficiency
v8-v11 0.975 0.102 0.099
v12 0.996 0.221 0.220
v13 0.984 0.359 0353
V14 0.987 0.318 0.314
Total 1.0 0.986

 

 

 

 

Table 4.2: Summary of trigger efficiencies.

42

 

4.3 Dataset

The data used in this analysis were recorded between October 2002 and February
2006. These data were reconstructed using DORECO production release 17 (p17)
and use trigger lists v8-v14. These data amount to a total integrated luminosity of

1046.19 pb‘lzt 6%, and are broken up by trigger version in Table 4.3.

 

 

 

 

 

 

 

 

 

 

Trigger List f£(pb-l)

v8 5.81
v9 24.78
v10 10.75
v11 65.24
v12 230.96
v13 375.55
v14 333.11

Total 1046.19

 

 

 

 

Table 4.3: Total integrated luminosity by trigger list.

The datasets used here come from two different CSG skims. The first is the
2EMhighpt skim and is comprised of two data definitions. The first definition
is CSG_CAF2EMhighpt_PASS3-p17.09.03, and contains data from runs 165973-
210437. The second definition is CSG_CAF_2EMhighpt.PASS2_p17.09.01, and con-
tains data from runs 210442-215670. The two data definitions were broken up this
way due to a mistake found in the hadronic calibration and fixed before processing
runs 210442-215670. The 2EMhighpt skim requires two EM objects of [ID] = 10,
11 and pr > 12 GeV. The second skim is the QCD skim and, for the same rea-

son as above, also has two definitions which are CSG-CAF_QCD_PASSB_p17.09.03

43

and CSG_CAF_QCD_PASS2_p17.09.01. The QCD skim requires one of the follow-
ing jet triggers to fire: JT_125TT, JT_95TT, JT_65TT, CJT5, JT_8TT, JT-15TT,
JT_25TT_NG, JT_45TT, JT_L3M225, JT_L3M250, JT_L3M380, JT_L3M430. Both
skims are further skimmed down using a copy of the photon_id_tools CAF package
similar to [25] and stored into ROOT-tuples, a ROOT-based [26] data format.

4.3.1 Data Quality

Not all the data collected at D0 are used in this analysis. Some data are rendered
useless due to issues like malfunctioning detectors or problems with electronics read-
out. These problems are tracked and studied by the Data Quality group and released
to the collaboration. The results are linked in CAF and remove runs of bad data and
bad luminosity blocks.

A run of data is defined as the data recorded from when the DAQ software starts
recording to when it is stops. Every time the DAQ software is started and stopped,
a unique run number is assigned to that run of data. If a detector subsystem shifter
observes a malfunction during a particular run of data, they will mark that run as
bad according to their detector sub-system. Also, if the Data Quality group finds a
problem during offline examination, they will also mark it as bad. All of these are
recorded in the bad runs list.

Sometimes small malfunctions occur during the course of a run that only require
a small piece to be discarded. Since runs can sometimes last a few hours, it is better
to discard only the problematic data rather than the entire run. This can be done by
recording the luminosity block number (LBN) and marking it. as bad. A luminosity
block is the basic unit of time for a luminosity measurement. Each block has a unique
number assigned to it and corresponds to a separate raw data file. These luminosity
blocks are incremented for every start of data recording, every initialization of the

trigger framework, or every 60 seconds [11]. If a problem occurs, these LBNs can be

44

 

  
 
     

    

 

‘1]
III
1

I" ‘ -
.ll' ._
I

in [in
' I|"l||||||l|l| lllll1

will]. ..

 

    
 

 

Figure 4.2. Eta vs. Phi lego plot illustrating hot cells.

vetoed without biasing the luminosity calculation. These bad LBNs are tabulated by

the Data Quality group.

Certain run numbers were noted to contain an excess of events with two EM
candidates that continually occur at the same location in eta-phi space, as can be
seen in Figure 4.2. Due to the extremely low probability of this occurring naturally,
these runs are believed to contain hot cells in the calorimeter, and, consequently, were

manually discarded from this analysis and accounted for in the luminosity calculation.

45

4.4 Monte Carlo

While this analysis is primarily data driven, some computer simulated events are
used as a means to predict the response of the D0 detector and to compare results to
theoretical predictions. These simulated events are produced by generators known as
Monte Carlo. The diphoton samples used in this analysis are generated using Pythia
6.3 [27], CTEQ6L1 PDF’s [28], and GEANT3 [29]. These packages simulate the pp"
interaction from collision and hard scatter to fragmentation to detection, including
effects of the D0 detector materials and magnetic field, to reconstruction. This Monte
Carlo was produced in three mass ranges with 98250 events of range M7,, = 50 - 130
GeV, 51500 events of range M.” = 130 - 250 GeV, and 26750 events of range M7,, =
250 - 500 GeV.

RESBOS [30] and DIPHOX [31] theoretical predictions are also used in this anal-
ysis. The RESBOS prediction comes from [32], and is a theoretical prediction that
includes all-orders soft-gluon resummation and is valid to next-to—next-to—leading
logrithmic accuracy. The DIPHOX Monte Carlo, [33], is an event generator at the
parton level designed to calculate the hadroproduction of two photons. It provides a
prediction up to NLO, but does not include gluon box contributions at NLO. Since
the DIPHOX prediction does not include gluon box diagram components at NLO,
and will be added from another source, the LO gluon box component was removed
from the DIPHOX calculation. Both the LO and NLO were then calculated from [34]
and added into the DIPHOX prediction. Since there are inheirent differences in these

theory calculations, some differences are expected between the predictions.

46

CHAPTER 5

Photon ID and Background Study

This chapter will discuss the variables and search techniques for identifying photons
in a hadron collider. It will describe the reconstruction algorithms that RECO uses
to identify photon-like objects and the analysis cuts used to fully identify photons.
The sources of background and specifically how the analysis cuts reject much of this

background and the associated cut efficiencies will also be presented here.

5.1 Reconstruction Algorithms

As previously stated in Section 3.11, after an event passes the different trigger levels,
it is written to tape. Then, offline, the DORECO software, using various algorithms,
reconstructs all of the particles detected in the event and stores them in a TMB.
Photons and electrons (electrons are taken to mean both electrons and positrons) are

reconstructed as follows: A group of calorimeter towers in a cone of R = 0.4, where

R = i/Ani’ + M2 (5.1)

centered around a calorimeter tower of high energy content is identified as an EM
cluster. This cluster must have a minimum transverse energy of 1.5 GeV, and an

electromagnetic fraction, as defined in Section 5.2, of EMF > 0.9. If a track exists

47

within
Induster —' 77track| < 005 and [$cluster — ¢trackl < 0.05

this cluster will be assigned [I D[ = 11, and if not, the cluster will be assigned ID = 10.
An EM cluster with [I D[ = 10 or 11 is considered a loose EM candidate, or a potential
photon or electron. The DORECO software also accounts for a number of other
corrections due to geometrical effects, non-linearities in electronics, hot cells, and

calorimeter noise [37, 38].

5.2 Particle Signatures

There are many particles that can be produced in proton+anti-proton collisions. In
order to distinguish between these difl'erent particles, it is important to know what

characteristics each one has so that one can distinguish between them.

5.2.1 Photons

A photon (or gamma particle) is simply a particle of light. It is massless, charge-
less, and is entirely electromagnetic in nature. As a result, one can exploit these
characteristics to distinguish photons from other particles.

When a photon travels through the D0 detector, it leaves a signature of:

o a narrow electromagnetic shower in the calorimeter

o no tracks matched to the electromagnetic shower

5.2.2 Electrons

Electrons are particles that are also electromagnetic in nature. As such, electron

signatures are very similar to those of photons. Electrons have a key difference,

48

however, in that they carry an electric charge that will not only cause a deflected
trajectory in the magnetic field of the detector, but also leave a matched track in the

detector.

5.2.3 Jets

A jet is a relatively localized spray of particles that can consist of both electromag-
netic and hadronic particles. Because jets contain many particles, the showers that
deve10p in the calorimeter are often much wider than those of electrons and photons,
the showers often deve10p much deeper in the detector into the hadronic sections,
which does not happen with electrons and photons, and the particles can leave many

associated tracks.

5.2.4 Muons

Muons are particles that typically pass through the calorimeter without depositing
any significant amount of energy. These particles are, however, detected in the muon
system described in Section 3.8. Since this analysis is not concerned with muons,

further detail will not be given here.

5.3 Signal Variables

Due to these characteristics of photons, electrons, and jets, some variables are de-
fined to better distinguish these particles: electromagnetic fraction, isolation, track
probability, track isolation, and missing ET.

Electromagnetic fraction (EMF) is defined as

 

EMF 2 EB” (5.2)
Etotal

49

where EEM is the energy deposited in the electromagnetic layers of the calorimeter, as
described in Section 3.7, and Em“, is the total energy deposited in the the calorimeter.
A high EMF (value > 0.9) corresponds to an object that deposits most of its energy
in the EM layers of the calorimeter, such as a photon or an electron.

Isolation (iso) is defined as

_ Etotal (R < 0.4) — EEM(R < 0.2)
_ EEM(R < 0.2)

 

iso (5.3)
where EMMR < 0.4) is the total energy deposited in the calorimeter in a cone
of radius 0.4 and EEM(R < 0.2) is the energy deposited in the EM portion of the
calorimeter in a cone of radius 0.2. 130 is a measure of how isolated an electromagnetic
object is in the calorimeter. A small isolation (iso < 0.2) corresponds to a single
electromagnetic object where no other particles traveled through the detector close-
by. If another particle were to travel through the detector nearby (within AR < 0.4),
it would cause a larger value.

Track matches are done using a probability. First, the tracks are reconstructed by
extrapolating them from their origin to the EM3 layer (the most segmented calorime-
ter layer). Next, the position of the EM object and the track are compared using the

equation

<><>

where 617 is the difference in 17 between the track and the EM object, (it!) is the
difference in (1) between the track and the EM object, and 0,, and 04, are the root-
mean—square (RMS) values of n and d), respectively, determined by experimental
distributions [36]. A spatial track match of x2 > 0.01 is considered to be a track
match with a 77% efficiency [36].

Track isolation (IsoHC4) is defined as the 197 sum of all tracks within a hollow

50

cone. This hollow cone is of size 0.05 < AR < 0.4, and the sum must be below 2
GeV/c. This variable is used to remove particles that have any kind of activity in the
tracking portion of the detector, since photons’ signatures do not contain a track.

Missing transverse energy, ET , as described in Section 3.4, is found by performing
a total energy conservation in the transverse plane, and returning a non-zero value.
ET is produced when either energy is added to the event by an outside source, or,
the more likely instance, by undetected particles such as neutrinos, which cannot be
directly detected with the D0 detector. Cosmic rays are continually bombarding the
earth and the D0 detector, and while the odds are quite small, it is possible for a
cosmic ray to be detected in the calorimeter and leaving a photon-like signature. As
such, a cut of ET < 30 GeV is employed as a precautionary measure, and removes
only 2.5% of the events.

Some distributions of these variables in the dataset are shown in Figure 5.1.

5.4 Background

A number of event topologies do exist that contain objects whose signature resembles
that of a photon. These t0pologies are referred to as background, and need to be
minimized as much as possible. The main source of background is a jet that leaves
a signature that is similar to a photon, called a fake-photon. This can occur, for
example, if the jet contains a neutral pion (no or pizero) that carries most of the jet’s
associated momentum. Pizeros typically decay to two photons (more than 98% of
the time [35]), and due to the pizero being energetic and of low mass (134.97MeV/c2
[35]), the Opening angle between the two photons is very small. This angle is so
small, in fact, that the two photons can appear as one in the detector. They can,
however, have a wider shower shape in the detector than the average photon, and

the probability of one of these two photons beginning its shower in the preshower

51

 

45 000

30000

 

 

0 20 40 60 80 PT (Gch)

 

900000 ’ H
600000

300000

0. i.._.T"T"TJ-F‘:L.

0.9 0.92 0.94 0.90 0.98

 

 

 

 

EMF

 

 

 

 

 

 

200000 7
I
I
>-
I’
I
h..-
E
”30000 _-
b
E'
I."
I
0 p A AM 1 A A A L‘ J A .L j j l A A A L l_ A. .A. L
0 0.05 DJ 0.15 Isolation

Figure 5.1. Distributions of signal variables Pt (t0p), EMF (middle), and iso (bot-
tom).

52

detectors is enhanced compared with a single photon.

While these features can also be exploited to remove some of these events, some
will still remain as irreducible background. At that point, all that can be done
is to statistically estimate how much of this background is present in the overall

measurement.

5.5 Analysis Cuts and Efficiencies

5.5.1 Analysis Cuts

As this analysis is concerned with measuring the diphoton cross-section, background
suppression is a key component to an accurate measurement. As such, some tight
cuts are applied to the above variables that will appropriately remove much of the
QCD fake-photon contribution. The cuts used here are EMF > 0.95, iso < 0.07,
trkprb < 0.001, I soH C4 < 2.0 GeV/c, and ET < 30 GeV. Some of the distributions
relating to the cuts are shown in Figure 5.2. In addition to these cuts, a couple of
geometric cuts are also applied.

The D0 detector phi-cracks as mentioned in Section 3.7, require some careful
analysis. In order to minimize the effect of these cracks in particle measurements, a
cut is employed, referred to as a phi-fiducial cut, to remove events that have particles
near these cracks. This phi-fiducial cut is not well-modeled in the MC, and cuts
out approximately 9% more events than it should. This discrepancy is accounted
for when determining the analysis cut efficiencies, and is shown in Figure 5.3. The
average acceptance in the MC is 70.81%, while the average acceptance in the data is

77.78%.

Also, the detector, as pictured in Figure 3.11, has large gaps between the cen-

tral calorimeter and the end-caps. These inter-cryostat detector (ICD) regions are

53

 

1600

1200

800

 

 

'V'r'VUIUVTTVFTT'VUIYVIIUT'IUUI‘VVTT

 

 

 

400
0 L... LL“ “Himmluulun Al --1--M
0 20 40 60 80 PT(GcV/c)

 

30000

30000

10000

 

 

 

TY‘I—TT'TV—U'TIU'IYVV‘I'VT"I‘VVV'IITVIF

 

‘LlJ—ALL4 l Adi-ILL

0.92 0.94 0.96 0.98 EMF

0
y

 

53
~o

 

8000

6000

4000

2000

 

 

Y'TrIYTYF'UUIIIIWI'YT’IIUII’V'UTI"! VIII

 

ALALlLimlennnmfinan

0 0.5 0.l 0.15 Isolation

D
l-
L
p

 

Figure 5.2. Distributions of the analysis cuts Pt (top), EMF (middle), and iso (bot-
tom).

54

 

[diphotonMC Phi_Fidu Acceptance]

g 1

0.9

 

Accept-

;i system“

0.2

Illlllllll]I11I'I1ITTT1TVIIIIIIIIIIIIllIIIIII

0.1

 

 

 

a
TUFT

oJ‘J-llllllnllllllllllllllll‘lllLlll‘l
v- v-

20 30 40 50 00 70
PT (GeVIc)

| 251i big—hptdata P_ercent Pli—LFidu— Accepted |

 

0.9
0.8
0.?

Acceptance

0.6
05
0.4
0.3
0.2
0.1

:l'l'llll]lrllllll|IIIII'IllllllIIIllllllllll‘lll

 

I I I I I J I I I I I I I l I l I I I I l I I I I
‘F 16 an so 40 so so 7 70
P, (Ger)

 

BC

I

'i

1..

‘L
.—

 

Figure 5.3. Phi_fiducial acceptances as a function of pr in diphoton MC (top) and
data (bottom).

55

problematic and are not well-understood. In addition, the tracking efficiency in the
end—caps is slightly worse than in the central calorimeter, as well as the complimen-
tary algorithms for the preshower detectors of the CC are not available in the EC.
Thus, a pseudorapidity cut of Indetl < 1.1 is applied to the data to remove these

concerns.

Finally, the pT threshold is raised on the highest energy photon to 21 GeV while
the threshold on the second highest energy photon is set at 20 GeV. These p7» cuts
were selected to improve the trigger efficiency as well as to prOperly compare our

result to theories that prefer asymmetric transverse momentum cuts.

The distribution of di-EM events as a function of mass prior to these cuts is shown

in Figure 5.4.

Note the presence of a peak due to the process Z ——> 6+6”. The result of these

cuts on the dataset is presented in Figure 5.5 as a function of mass.

5.5.2 Cut Efficiencies

The efficiencies of the above cuts have been measured using a diphoton MC as de-

scribed in Section 4.4, and have distributions presented in Figures 5.6 and 5.7.

The efficiencies are defined as

 

Flair <59
where 8 is the efficiency, Nfight is the number of events satisfying the tight analysis
cuts, and NMC is the number of input Monte Carlo events. The efficiencies are
measured on a bin-by—bin basis and as a function of Mass, qT, and A05”. These
efliciencies are then used on a bin-by-bin basis and are presented in Figure 5.8. For

masses below 50 GeV/c2, the efficiency is extrapolated.

56

 

10000

16”
14000
12000

1W0

 

 

Illllljjllll —l1.lJllllLl

50 100 150 200

Figure 5.4. Di-EM Mass Spectrum.

57

 

250 300
lnv. Mass (cevm’)

 

[2EMhighptdata LogMass tight cuts CCCCI 52:9

counts

 

 

 

 

 

 

Underflow
: Overflow
10‘ .-.r i-—i
E i—t
- i--t
103 5—
: H—i i—D—l
L“ l—-!—-l
2 :- H—1
10 5 I i
: i—I—i
10 E— } f
1 L I L 1 I I I I I I l I I J I I J I I I I I M] .L 1 j I
0 100 150 200 250 300
Mass (GeV/c2)

Figure 5.5. Di-EM Mass Spectrum after analysis cuts.

58

 

[ZEMhighEtdata Mass tight cuts CCCCI

 

 

 

O
310‘ HH - Diphoton Data
0 '— I I l D'phot MC
A I On
3
‘0 H—l
l—I-i I—H
l—H
H—t

F—I—I
‘°’ “13::

%
10 "

 

 

.4
1 I t I If 1 I I I Ll I I I J l I I M I I I I I I l 1 1M I
0 so 100 150 200 250 300
Mass(GeVlcz)

Figure 5.6. Distribution of diphoton Monte Carlo overlayed with data.

59

[DiphotonMC Single Photon Pt |

TWO

0 10

 

lIIIIll[IIIIIITTIFTITIIIT‘TII1IIIII

 

Illllllll

 

 

 

 

 

UIJJIIILLIIIILIIIIIILII

 

2030405060

70

80

 

90 100
P, (GeVlc)

Figure 5.7. pr distribution of single photons from diphoton Monte Carlo.

60

 

W

 

 

 

 

 

 

 

 

 

 

 

 

330.8
0.6
0.4 WW+++++++
0.2
0 wuttiti ”LLL200UM;sl(G-e\llc2)
Wacnbnotonemonl
530.8
0.6
”Pap“?
- ”lifts +
+ +
.W
0 20 40 60 80 QfiGeV/c)
[Dtptieionucntpnoionerumfl
:13
mos
0.6 +
'i‘
0.4 + +++rfflfi '~
[flee
0 1.0 2.0 Acwtrad)

Figure 5.8. Analysis Cut Efficiencies as a function of Mass (top), qT (middle), and
A057, (bottom).

61

Data Smearing

The calorimeter has a particular energy resolution that can cause energy measure-
ments to be slightly above or below the actual value, an effect known as smearing.
Due to the relative shape of these histograms, this smearing can cause an excess of
events in the neighboring histogram bin. This smearing has been modeled in the
computer simulated detector, and is accounted for in these efficiencies, as the Nag,“
is considered to be a detector smeared value, and the NMC is an unsmeared input
value. The application of the efficiencies in Figure 5.8 will effectively unsmear the
data and yield the true cross-section measurement.

The efficiencies shown here shall be applied to the data in the following chapter.

62

CHAPTER 6

Cross—Section Analysis

This chapter will explain the method used to separate the diphoton signal from back-
ground events, thus yielding a final cross-section. The variables used will be described,
the mathematics involved will be explained, and the final cross-section measurement

including efficiencies and associated errors will be presented.

6.1 Matrix Inversion Method

As mentioned in Section 5.4, even though the analysis cuts have exploited the dif-
ference in particle signatures in the detector to remove events that do not contain
diphotons, some background events remain. Now, a statistical method must be em-
ployed to separate the portion of true gamma-gamma events from gamma-jet and

jet-jet events where the jets have signatures similar to that of a photon.

This statistical method requires a discrimination variable, a variable that shows
a different response to photons and jets. When a cut is then placed on this variable,
there will be efficiencies, 5,, for a photon to pass this cut, (1 — 5,), for a photon to fail
this cut, 5,, for a photon-like jet to pass this cut, and (1 — 5,), for a photon-like jet

to fail this cut. Given that the events in this analysis contain two photonic objects,

63

combinatorics suggests the following three equations:

Npp = 5?,N77 + €7€jN7j + 5;“?ij (6-1)

NpF = 257(1 — 5,)NW + [5,(1 — 53') + (1 — 5,)53-[N7j + 25,-(1 — 5,)ij (6.2)

NFF = (1 — ’57)?va + (1 - €7)(1 — 53')N513' + (1 - 52')?ij (63)

where Npp is the number of events where both objects pass the cut, Npp is the
number of events where one object passes and one object fails the cut, Npp is the
number of events where both objects fail the cut, N7, is the number of events that
contain a diphoton, N7,- is the number of events that contain a photon + jet, and M,-
is the number of events that contain a jet + jet. Taking the coefficients of equations

6.1, 6.2, and 6.3, a matrix equation can be formed

Npp 8.2, 8753‘ 5? [Vin
Npp 2 287(1— 87) 57(1 — Ej)+(1— 57)?) 2€j(1 — Ej) N7‘ (64)
NW (1 '— 57)? (1 - 80(1- 53') (1 — 5:12 Ne“

When the 3x3 matrix is inverted, N77, N71, and 1ij are determined, thus yielding

the true diphoton signal.

6.2 Efficiency Data Samples

A pure set of photons should be examined using a discrimination variable, but no cur-

rently discovered particle of reasonably high energy and relatively high production

64

[2EMhighEtdata Mass tight cuts 0000' an” 1::

Underline 0
2200 Overflow 12
2... [

1&0
1&0
1400
1200
1”

 

 

 

 

 

 

IFIITIIIIUIIIIIIIIllll'lllllll[IITIITIlIIIII

§§§§

 

 

IJJLL‘I'MIIIlJJLI|IIII

so 100 150 200 250 300
Mass (GeV/c2)

 

0°
r.

Figure 6.1. Histogram of the Z-mass from the data.

decays into photons, preventing the use of photons from data to tune the discrim-
ination variable cut. Electrons, however, basically shower identically to photons in
the detector, save for a matched track, and are often produced by a decaying Z bo-
son. Since the Z boson has a well-known mass, a relatively high production rate,
and decays into high energy electrons, it is possible to get a pure sample of electrons
that will model a photon’s response in the detector by selecting events in data that
contain two electrons and possess a reconstructed invariant mass within the Z boson
mass window. The Z-mass peak is presented in Figure 61.

Pure photon Monte Carlo samples could be used in lieu of this electron substitu-
tion, however, there are some observable differences between Monte Carlo and data

that will be avoided by keeping this analysis data driven.

A pure set of photon-like jets in data is a little easier to obtain. The QCD dataset

65

detailed in section 4.3 is used, requiring in the event one good jet, an EM—object
that passes the analysis cuts from section 5.5.1, and ET < 10 GeV to remove event
topologies such as W —-> 511 that would naturally contain a jet and an electron and
bias the efficiency. A good jet is defined in [39].

The efficiencies of the electrons or photon-like jets to pass the discrimination cut

are measured as a function of pp, and are determined by

IVPass
N Pass + N Fail

 

(6.5)

57/1 =

6.3 Discrimination Variables

Presented in the following subsections are three variables that do show a difference
between photons and jets and will be used as the discrimination variables in this

analysis.

6.3.1 Phi Width

Phi Width is a measure of the width squared of the object’s shower measured by
the EM3 layer of the calorimeter. The larger the value, the wider the shower the
object created in the calorimeter. Histograms of the phi width of photons in MC,
electrons in data, and EM-jets in data are shown in Figure 6.2, and show that large
values correspond to jets, while smaller values correspond to electrons and photons.
In agreement with the D0 Photon-ID group, a cut is placed at Phi Width < 14 cm2

[40]. The related efficiencies of this cut are shown in Figure 6.3 as a function of pr.

6.3.2 CPS_RMS

The CPS_RMS variable is an energy weighted root-mean-square of the difference in

each strip’s phi position with that of the EM3 layer’s phi position. This is done for

66

 

16000_
12000:
8000:

4000:

 

 

 

 

UJJJAAALIALIII I'LL

0 20 40 ”'60. ‘60” 1100
Phi Width2 at EM3 (cmz)

‘llll

 

 

4000
3000
2000

1000 r

 

 

0 20 40 60 80 100
Phi Width2 at EM3 (emf)

 

4000

3000

2000

 

1000

 

 

_ Ulll'll[UrillII‘I"IIIUIIIII'UIIFIVIII'TIlllT'

O
F—

 

. l—l-ll-ll-IJIUJLLL

0 ”‘90 40‘ 60 80 100
Phi Width: at EM3 (cm?)

 

Figure 6.2. Distributions of the Phi Width variable in electrons (top), MC photons
(middle), and jets (bottom).

67

 

[2EMhighptdata Eff. Phi Width(Pt) in col

 

Y

 

 

1% —' 1_1

Efficient:

0.8

0.6

0.4

0.2

IIIIITIIITIIIIIIIII

 

 

 

I I I I I l I I I ' I I I l I I I l I
60 80 100

h
F
p
1-
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co
8.
S

140
P1, (cove)

 

[OCDdata Eff. Phi Width(Pt) in col

> 0.9

 

0.8

 

Ettlclenc

0.7
0.6
0.5
0.4
0.3
0.2

0.1

IIIIIIIIIIITIIIlllllllll‘llrl'llIIIIIIIIIITII

 

 

 

I I I I I I I I .I I I I J I I I I I I I I I I I I I I

20 40 60 80 100 120 140
Pt (GeWc)

 

0

Figure 6.3. Efficiencies of electrons (top) and jets (bottom) of the Phi Width dis-
crimination variable as a function of m.

68

every strip in a CPS cluster and the result is the sum of each layer. Large values
correspond to particles with large widths in the CPS detector, such as jets, whereas
small values correspond to particles such as photons and electrons. Distributions of
this variable for photons in MC, electrons in data, and jets in data are shown in
Figure 6.4. A cut is placed at CPS_RMS < 0.003, and the efficiencies for this cut are
shown in Figure 6.5 as a function of pr. More information on how this variable is

determined can be found in [41].

6.3.3 CPS_RMS Squared

The CPS_RMSSQ variable is similar to the CPS-RMS variable except that the weight-
ing is done by the energy of the strip squared. This is done in an effort to magnify
the result when two objects pass through the CPS with a very small opening angle
between them, such as a pizero that has decayed to two photons. Again, small values
correspond to electrons and photons, whereas large values correspond to jets. This

can be seen in the distributions presented in Figure 6.6.

A cut on this variable is placed at CPS_RMSSQ < 0.0012, and the resulting

efficiencies are shown in Figure 6.7 as a function of pT.

More information on how this variable is calculated can also be found in [41].

6.4 Result of Matrix Inversion

Using the efliciencies in the plots presented, a matrix is produced and inverted for
each pr bin. The result for each discrimination variable is determined independently,

overlayed on each other, and shown in Figures 6.8, 6.9, and 6.10.

The matrix inversion is applied to the mass distribution on a bin-by-bin basis

69

 

3000

2000

1000

[Ill1"Illlll'llllll1ll'l1

  

 

 

 

I 0006 C'stiivts

 

400

llflllllll’l

200 —

 

 

I...LI....1L._.LI-...I.. I I

0.006 CPS_RMS

 

 

600

  

llIl’rlllllII‘llIIlllllIll

 

200

 

 

O -....1

....l....
0 0.002

l....l....

 

1...il....l....l...il....
0.006 CPS_RMS

Figure 6.4. Distributions of the CPS_RMS variable in electrons (top), MC photons
(middle), and jets (bottom).

70

 

[2EMhighptdata Efl. CPS(Pt) in CC]
1

 

Efficiency

0.8

0.6

0.4

0.2

IIIIIIITIIIIIIIIIII

 

 

 

 

o I I I I I I I I 1 I I I I I I I I I I I n I l I I I I I
I 20 40 60 80 100 140
PT (GeV/c)

 

[QCDdata 1511. CPS(Pt) in cc]

 

o
in

llllrllIrllj‘rlllllllllfi[

Etflclency

0.4

0.3

0.2

0.1

 

 

 

A I I I 1 I I f I I I I I I n I I I I I I I l I I I L I I
“0 20 40 00 so 100 120 140
I"T (GeVlc)

 

Figure 6.5. Efliciencies of electrons (top) and jets (bottom) of the CPS_RMS discrim-
ination variable as a function of m.

71

 

4WD

2000

 

0
0 0.002 0.004 0.006 CPS_RMSSQ

 

l 200

800

400

 

0 .
0 0.002 0.004 0.006 CPS_RMSSQ

 

1200

400:

 

 

 

1111

0” I... ...r
0 0.00:: 0.004 0.000 CPS__ _MSSQ

All I‘llAluLlllHill-AAI.JJIA1LLII'L

 

Figure 6.6. Distributions of the CPS_RMSSQ variable in electrons (top), MC photons
(middle), and jets (bottom).

72

 

Izmhlghgtdata Eff. CPS SQPQ In CC]

)4

30.9

'5 03
0.7
0-5

 

0.5
0.4
0.3
0.2

0.1

IIIIITUUTIIIIIIIIIIIIIIIIIITTIITTIIIWFIIITUIIT

 

 

 

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b
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b
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b
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-
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s
3
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§
§

 

IGCDdata Eff. CPS SQPQ in CC I

4:: an

0.3

 

 

 

 

0.25

0.2

0.15

0.1

0.05

ITIIIIUlIITTTIIIIIIIIIIIIIIIUIITIIIIIIII

 

 

 

ljlllLlJlLllllLJLJJLILAIL

'20 40 so so 100 120 140
P, (Ge‘Wc)

 

O
G
I

Figure 6.7. Efficiencies of electrons (top) and jets (bottom) of the CPS-RMSSQ
discrimination variable as a function of pT.

73

 

d
9.

 

g E I Phi Width

0’: 3 I CPS_RMS

5 ' A CPS_RMS_SQ
'—

g3

10’

r' ”Hull
1

ti
4%

I I IIIIIII

I I A

 

 

 

 

1
49+

'250 0
Mass (GeV/c2)

Figure 6.8. Diphoton events determined by matrix inversion of discrimination variable
efficiencies as a function of mass.

 

 

m l l

g o PhIWIdlh

I?! I CPS_RMS

S 3 A CPS_RMS_SQ
z 10 _

10

  

 

1
0 80 qT GeV/cs)o

Figure 6.9. Diphoton events determined by matrix inversion of discrimination variable
efficiencies as a function of transverse momentum.

74

 

    

 

 

 

3104
E
“E
S
3
210 g m
: FIE!
: H-l—l-i
02 0+1
1 :— n—z—a
E hi-i “"3;an
: “11343: $ '"vb'm
f “ C? +
_ cit}. _.
1 v '1 LJ J l:_-L" I'LEJ' l l l l I l I I I I l I l l 1 L I l J
c 0.5 1 1.5 2 2.5 3
A¢W(rad)

Figure 6.10. Diphoton events determined by matrix inversion of discrimination vari-
able efficiencies as a function of opening angle between the two photons.

using the good approximation that

MW
2

7 N
PT~

 

(6.6)

For the distributions of transverse momentum of the diphoton and the opening angle
between the two photons, an average efficiency across all pp is used for the matrix
inversion. These distributions show good agreement, and will provide a method of

determining the systematic errors involved with this matrix inversion method.

6.5 Cross-Section

Given the equation,

N77 : OWL: (6-7)

75

where NT, is the number of direct diphoton events found in a dataset containing
luminosity, C, the cross-section of the direct diphoton process, a”, can now be cal-
culated. The cross-section is calculated as a function of mass, qT, and opening angle
by averaging the three separate results of the matrix inversion, dividing by the lu-
minosity from Section 4.3, and applying the efficiencies from the previous sections.
Application of the efficiencies will account for true diphoton events removed by the
analysis cuts, thus correcting N77 to its true value. Figures 6.11, 6.12, and 6.13 show
the differential cross—section for direct diphoton production as a function of invariant
mass of the diphoton, the qq» of the diphoton, and the Opening angle between the two

photons, respectively.

The dotted line at the bottom of each plot is a nominal line, while the solid
curve around it expresses the systematic error on the data. The systematic errors
on the mass plot range from 4.9% at the mass peak to 160% at high masses, the
systematic errors on the qT plot are 6.4% at low qTand 2.5% at high qT, and the
systematic errors on the A057, plot are 360% at small opening angles and 3.2% near
77 (i.e. back-to—back). The two continuous curves in the figures correspond to two
different theoretical predictions. The solid line represents the RESBOS prediction,
and the dotted line represents the DIPHOX with the addition of the gluon-gluon box
contribution at L0 and NLO. The bin widths change as statistics allow for better
mapping of the cross-section. Figure 6.11 shows a fall off in the cross-section at low
masses. This is due to the transverse momentum cut on each photon. Above an
invariant mass of about 50 GeV/c2 it is seen that the cross-section falls smoothly as
a function of mass as predicted by both theoretical curves. Figure 6.12 also shows
the cross-section falling with increasing qT in general agreement with the theories,
but it is noted that the DIPHOX prediction is significantly higher than the data at
low qT. Figure 6.13 also shows essential agreement between the data and the two

theoretical predictions, indicating that most diphoton states are produced back-to-

76

 

IAve Diphoton Mass Cross-Section]

A

 

 

 

 

 

 

 

 

 

n1; _ - . mom
3104 5r
3 E
3 _
r
210'2 5'
'2 E
'8 :
10“
10“
10's L I I J I I I I I I I I I I I I J I I l I I I I I I
0 50 1% 150 200 250 90
M.”(GeV/c )

Figure 6.11. Differential diphoton cross-section as a function of mass.

 

[Ave Diphoton Qt Cross-Section]

 

 

 

:6 , \ Q Ave.an
E I. “ 0m
\ '- wx
V \
3 1 X -—-—nesaos
e 10 9;: ~
‘ ‘—

P
U' \
E ’9 k
b ‘
1: ". ~.

10’2 ‘ "Q

“‘1
10-3 ~.

 

 

10 20 30 40 50 60 70 80 ngfGeV/gp

Figure 6.12. Differential diphoton cross-section as a function of (17‘-

78

 

IAve Diphoton Phi Cross-Section I

 

 

 

dold A4)" (pb/rad)

 

10’2

 

 

 

 

Figure 6.13. Differential diphoton cross-section as a function of opening angle.

79

back (A037.7 ~ 7r). When A457, is far from 7r, the cross-section arises from the extra
jet produced in the NLO calculations and is very sensitive to the isolation cuts made
in this analysis. The theory predictions are also not well modeled in this region due

to uncertainty in fragmentation function parameters.

80

CHAPTER 7

Conclusions

The differential cross-section of the direct diphoton process as a function of mass,
qT, and Opening angle at \/§ = 1.96 TeV has been measured using 1046.19 pb’l of
luminosity collected with the D0 detector between October 2002 and February 2006.
The results shown are in good agreement with theory.

This measurement of the diphoton production at the Tevatron can be used to
predict the QCD production at the upcoming LHC at CERN, which is scheduled to
start within the next couple of years. This in turn will be useful in predicting the
irreducible background to Higgs searches at LHC.

CDF has previously attempted this analysis in Run II with one-fifth of the data
[42]. They are currently updating their analysis to include more statistics.

An alternative approach to the matrix inversion technique used here would be
to cut on any or all of the three discrimination variables. This would increase the
purity of the final sample which could then be used to study other aspects of the
diphoton production (e.g. associated particle production). This method, however,
would involve much larger inefficiencies and an unknown background contamination.
It would also likely suffer from low statistics.

The cross-sections presented in Figures 6.1], 6.12, and 6.13 are the average of the

cross-sections resulting from the application of each of the discrimination variables in

81

the matrix inversion technique. This averaging is likely not to be strictly accurate,
especially if the three variables are coupled (as the CPS_RMS and CPS_RMSSQ
variables are likely to be). Future analyses could study the interdependence of these
variables and shed further light on the dynamics of diphoton production.

Further interesting analysis could be performed to study the non-perturbative
QCD aspects of this process by implementing a qT < M77 cut. This cut should remove
events containing perturbative effects such as the Feynman diagrams presented in
Figure 2.3. The result of such a cut would be most pronounced in the opening angle
plots by continuing to slope downward at 1.5 radians instead of leveling off. The
differential cross-sections could also be measured as a function of other kinematic

variables.

82

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85

   

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