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THESIS

Illllllll'illllllllllllllllllillllllll

31293 01716 3522

This is to certify that the

dissertation entitled

INCLUSIVE DIRECI‘ PHUION PRODUCTION IN THE

CENTRAL AND EDWARD RAPIDITY REGIONS IN

PROI’ON:ANI'IPROION COLLISIONS AT A CENTER
OF MASS ENERGY OF 1800 (EV

presented by

Steven A. Jerger

has been accepted towards fulﬁllment
of the requirements for

 

Ph 1) degree in maize—

ﬂewzciée.

 

Majgr professor

Date [0 /Zq [Cr]

v

MSU is an Afﬂrmatiw Action/Equal Opportunity Institution

0-12771

 

LIBRARY

Michigan State
University

 

 

 

PLACE IN RETURN BOX
to remove this checkout from your record.
TO AVOID FINE return on or before date due.

 

DATE DUE DATE Due DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

mo Wow-p.14

INCLUSIVE DIRECT PHOTON PRODUCTION IN THE
CENTRAL AND FORWARD RAPIDITY REGIONS IN
PROTON-ANTIPROTON COLLISIONS AT A CENTER
OF MASS ENERGY OF 1800 GEV
By

Steven A. Jerger

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

1 997

ABSTRACT
INCLUSIVE DIRECT PHOTON PRODUCTION IN THE
CENTRAL AND FORWARD RAPIDITY REGIONS IN
PROTON-ANTIPROTON COLLISIONS AT A CENTER
OF MASS ENERGY OF 1800 GEV
By

Steven A. Jerger

A study of isolated direct photon production in proton-antiproton collisions at a center of

mass energy 5/} = 1800 GeV is reported, as measured at the DO Detector at the
Fermilab Tevatron. Cross sections for the central (OS Inl $0.9) and forward
(1.6SI'nI $2.5) rapidity regions are presented as a function of photon ET
(15 GeV S ET S 150 GeV ), and compared with a next-to—leading order QCD calculation.

In the central region, the data and theory are consistent in both shape and normalization;
however, in the forward region the data are consistently above the theory, especially in the

ET region below ~ 30 GeV. A preliminary measurement of the correlation between the

rapidity of the photon and that of the leading jet in the event shows qualitative agreement

between the data and the theoretical prediction.

To David and Janice Jerger

iii

ACKNOWLEDGEMENTS

My thanks to my friends: Gian, Kate, Terry, etc... there are too many people who have
helped me get through life to make a long list and risk leaving someone out. If you think
your name belongs here, past or present, it does. Thanks.

Thanks to Anne Keman, Steve Wimpenny, and John Ellison at UC Riverside for
giving me the chance to get started down this path as an undergraduate, and to Dave,
Kevin, and Mike for their teachings which helped me through grad school (and life).

Thanks to Chip, Scotty, Packy, Dean, Bruce, and especially all the kids of the
Waubonsie Valley and Neuqua Valley bands - you gave me another home where I could go
for a little sanity or insanity, whichever I needed. Hope this explains protons &... stuff.

Thanks to the direct photon group, especially Sal Fahey, who paved the road and
looked out for me; and Steve Linn for reminding me I am allowed to sit at the big table
with the grownups. Most of all I thank John Womersley, for his guidance and endless
patience - while I doubt I could ever match it, he has always deﬁned for me the level of
excellence for which I should strive.

Finally, I give my appreciation to my advisor, Bernard (1 Pope, for his wisdom and his
uncanny ability to remind me of what’s really important. I will always remember a big
green shamrock on my desk one stressful morning, a symbol of the unfailing support he

has given me through thick and thin times for both of us. Thanks, Bernard.

iv

TABLE OF CONTENTS

LIST OF TABLES ix
LIST OF FIGURES xi
1 Introduction 1
2 Theory 3
2.1 The Standard Model ............................................... 3

2.2 QCD Interactions ................................................. 7

2.3 Direct Photon Theory ............................................. 13
2.3.1 Direct Photon Diagrams ..................... . ................ 13

2.3.2 Bremsstrahlung Component and Isolation ....................... 14

2.4 Variables for Hadron Collider Physics ................................ 17

3 Experimental Apparatus 20
3.1 Accelerator ..................................................... 20

3.2 Detector ........................................................ 23
3.2.1 Tracking ................................................. 25

3.2.2 Calorimetry ............................................... 34

3.2.3 The Muon System .......................................... 39

3.3 Data Acquisition and Processing ....................................
3.3.1 The Trigger System ........................................

3.3.2 Event Reconstruction .......................................

4 Event Selection and Efﬁciencies
4.1 Data Set and Monte Carlo ..........................................
4.1.1 Direct Photon Triggers ......................................
4.1.2 Candidate Sample ..........................................
4.1.3 DOGEANT Monte Carlo ....................................
4.2 Acceptance .....................................................
4.3 Cut Efficiencies ..................................................
4.3.1 Tracking Considerations .....................................

4.3.2 Selection Cuts .............................................

5 Background Estimation
5.1 Introduction .....................................................
5.2 Background Estimation Techniques ..................................
5.2.1 Method ..................................................
5.2.2 Background Monte Carlo ....................................
5.2.3 EMl Calibration ...........................................

5.3 Purity Calculation ................................................

6 Cross Sections and Theoretical Comparisons

6.1 Cross Section Calculation ..........................................

vi

40

40

43

48

49

49

50

52

55

59

59

59

63

63

65

65

67

69

71

79

79

6.2 Comparison with Theory .......................................... 84

7 Photon + Jet Rapidity Correlations 93
7.1 Introduction ..................................................... 93
7.2 Rapidity Correlation Measurement ................................... 94

7.2.1 Motivation ................................................ 94
7.2.2 Data Selection ............................................. 95
7.2.3 Technique and Candidate Sample Behavior ...................... 97
7.2.4 Background Behavior ....................................... 97
7.2.5 Theoretical Prediction and Comparisons ........................ 99
7.3 Conclusions .................................................... 102

8 Conclusions 106

A Triggers and Luminosity 108
A.1 Triggering .................................................... 109

A.1.l Level 1 and Level 2 Requirements ........................... 109
A.1.2 Trigger Tum-On and Efﬁciency ............................. 111
A2 Integrated Luminosity Determination ............................... 117

B Tracking Considerations 121
3.1 The Tracking Efﬁciency ......................................... 122
B.2 Track Overlap Probabilities ....................................... 128

B.2.1 Golden Overlap Method .................................... 128
B.2.2 Z Overlap Method ........................................ 131

vii

B.3 Overall Efﬁciency ..............................................

C EMl Calibration
C.1 Offset Estimation and Origins .....................................
C.2 Cross Checks of the Offset Estimate ................................
C.3 Effects of Pre-EMl Material in the Monte Carlo .......................
C.4 Final Calibration Determination ...................................

C.5 Summary .....................................................

D Comparison with Run 1A Results
D.1 Corrections to the 1A Analysis ....................................
D.2 Effects of Changes in Background Modeling .........................

D.3 Conclusions ...................................................

E Purity Fits

F Monte Carlo Composites

REFERENCES

viii

132

133

133

135

136

140

143

144

144

147

150

152

160

173

2.1

2.2

2.3

4.1

4.2

5.1

5.2

5.3

6.1

6.2

6.3

A.1

A2

A3

B.1

B.2

B.3

LIST OF TABLES
The three generations of leptons ......................................... 4
The three generations of quarks. ........................................ 4
Vector bosons and the forces they mediate. ............................... 5
Description of triggers and associated integrated luminosities. ............... 50
Number of events surviving the application of photon cuts ................... 54
Neutral meson decays to photon states ................................... 64
CC Purity points, variations, and errors. ................................. 74
EC Purity points, variations and errors ................................... 74
Central region cross section points and errors. ............................ 82
Forward region cross section points and errors. ........................... 83

Contributions to the total systematic error on the 39-42 GeV cross

section bins. ...................................................... 84
Description of triggers and associated ﬁlters ............................. 109
Integrated Luminosities for the four single photon ﬁlters ................... 118

Comparison of luminosities calculated using Equation A.4 with those

taken from the Production database .................................... 120
Tracking efﬁciencies and errors in the central and forward regions. .......... 126
Tracking efﬁciencies at different instantaneous luminosities. ............... 127
Overlap probabilities from golden candidate sample ....................... 129

ix

B.4 Variation of the overlap probability with isolation and golden cuts, varied
independently using the EM1_GIS_HIGH trigger. ....................... 130

CI Additive constants used to calibrate the Monte Carlo log(EMl/E)

distributions ...................................................... 143

2.1

2.2

2.3

2.4

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

3.10

4.1

4.2

LIST OF FIGURES
Diagram picturing different aspects of a QCD interaction. ................... 9
Leading order diagrams for direct photon production ....................... 13
Examples of higher order direct photon diagrams .......................... 15
Photon production through Bremsstrahlung .............................. 16
The Fermilab Tevatron Collider. ...................................... 21
The DO Detector. .................................................. 24
The D0 Tracking System ............................................. 25
Side schematic of the DO Vertex Detector. .............................. 27
Cross section of the ﬁrst TRD layer. ................................... 30
End view of a section of the Central Drift Chamber ........................ 31
An exploded view of the Forward Drift Chamber .......................... 33
The DO Calorimeter (cutaway view) .................................... 34
Diagram of the layers within a calorimeter cell ............................ 36
Side view of a calorimeter quadrant. Lines of pseudorapidity are shown to

demonstrate the projective tower geometry ............................... 37
H-matrix x2 distributions from test beam electrons, test beam pions,

and electrons from W decays .......................................... 53

Comparison of data (points) and Monte Carlo (histograms) W electrons
in the central region ................................................. 56

xi

4.3

4.4

4.5

4.6

5.1

5.2

5.3

5.4

5.5

5.6

6.1

6.2

6.3

6.4

6.5

6.6

7.1

Comparison of data (points) and Monte Carlo (histograms) W electrons
in the forward region ................................................ 57

The Run 18 vertex 2 distribution ....................................... 58

Selection cut efficiencies measured using PYTHIA Monte Carlo photons, and
corresponding ﬁts. ................................................. 6O

Instantaneous Luminosity proﬁles for the EM1_GIS (left) and EM1_GIS_HIGH
(right) ﬁlters ....................................................... 61

Comparison of EMl energy fraction left by 10 GeV MC photons and Ito’s ...... 66

Log(EMllE) distributions for W electrons from data (points) and Monte Carlo
(histograms) ....................................................... 7O

Log(EMllE) for Monte Carlo and data between 33—39 GeV in the central
region. The solid line is the MINUIT ﬁt, which results in a measured purity
of 0.467 (P2). ..................................................... 72

Purity vs. ET for the central (left) and forward (right) regions. ............... 75

Variations in the CC (left) and EC (right) purity ﬁts, using the nominal (solid),
exponential (dotted) and straight line (dashed) ﬁt functions .................. 76

Effect of a plus 16 (dotted) and minus 16 (dashed) shift in the EC EMl offset,
relative to the nominal (solid) purity curve ............................... 78

Inclusive isolated photon cross sections in the central (top) and forward

(bottom) regions. .................................................. 81
(Data-Theory)/Theory for the central (top) and forward (bottom) regions ...... 86
(Data-Theory)/Theory using purity determination bins ...................... 87

Variation of the theoretical prediction with a change in scale for the central
(top) and forward (bottom) regions ..................................... 89

Comparison of the theoretical prediction with CTEQ2M and CTEQ4M
PDFS. ........................................................... 91

Change in the theoretical cross sections from that used in Run 1A. ........... 92

Diagram of the ﬁnal state topology when colliding partons have similar (left)
or very dissimilar (right) momentum fractions ............................ 94

xii

7.2

7.3

7.4

7.5

7.6

A.1

A2

A3

A4

A.5

8.1

B]

B.2

C.1

C2

C3

C4

Signed If“ distribution of the leading jet for golden photon candidates. The

shaded band indicates the rapidity bin of the photon; shown at left are the

mean values of signed 11’“ in each bin. ................................. 98
Signed 11"" distribution of the leading jet for background (electromagnetic jet)
candidates. ...................................................... 100
Signed 11"“ distribution of the leading jet in a NLL QCD prediction from

Owens, et al ...................................................... 101

Mean signed If“ versus mean InYI for candidate, background, and theory

samples. ........................................................ 103

Mean signed nie’ versus mean mill for candidate, background, and dijet

samples with E]- between 45 and 55 GeV ............................... 104
7 GeV Level 1 Trigger efficiency for the central and forward regions. ....... 112
6 GeV Level 2 Filter efﬁciency for the central and forward regions .......... 113
14 GeV Level 2 Filter efﬁciency for the central and forward regions ......... 114
25 GeV Level 2 Filter efﬁciency for the central and forward regions ......... 115
40 GeV Level 2 Filter efﬁciency for the central and forward regions ......... 116

Matching of luminosity-corrected ﬁlters (CC only). ...................... 119
Z mass distributions before and after track requirement .................... 125
Log(EMI/E) distributions for Z electrons. Note that 1% EMl corresponds

to -2.0 on this scale. ............................................... 129
Values of EC EM] offset produced by the purity ﬁtting routine for

several Er bins .................................................... 136
Offset measured from W electrons versus ET, using a) full W Monte Carlo;

b) single particle Monte Carlo ....................................... 137
Fraction of energy deposited in each EM layer for several pre—EM] estimates
(simple model), data, and Monte Carlo ................................. 139
Change in percent of total energy in each layer between different material

estimates, and between data and Monte Carlo ............................ 140

xiii

C.5

D.1

D2

D3

D4

E.1

B.2

E3

E4

E5

E6

E7

F.1

F2

R3

R4

F.5

Values of EC EMl offset produced by the purity ﬁtting routine for EC North
(top) and South (bottom) samples ..................................... 142

Ratio of the Run 1A inclusive cross sections to the Run 1B results in the
central (top) and forward (bottom) regions .............................. 145

Effect of reﬁtting the Run 1A central region Purity/Efﬁciency to allow for the
proper maximum value at higher ET values. ............................ 147

Left: Run 1A CC purity points and resulting fit (solid line), along with the
1B CC purity fit (dashed line). Right: 1A purity points and ﬁt (solid line) using
the 1B Monte Carlo, along with the 1A ﬁt (dashed line, same as solid line

on left) .......................................................... 149
Ratio of the “corrected” Run 1A inclusive cross sections to the Run 1B

results in the central (top) and forward (bottom) regions. .................. 151
CC purity ﬁts for ET bins of 10-12, 12-15, 15-21, and 21-25 GeV. .......... 153
CC purity ﬁts for ET bins of 25-30, 30-33, 33-39, and 39—54 GeV. .......... 154
CC purity ﬁts for ET bins of 54-60, 60-70, 70-88, and 88-100 GeV. ......... 155
CC purity ﬁts for the ET bin of 100-150 GeV ............................ 156
EC purity ﬁts for ET bins of 10-13, 13-21, 21-25, and 25-30 GeV ............ 157
EC purity ﬁts for ET bins of 30-33, 33-39, 39-54, and 54-60 GeV ............ 158
EC purity ﬁts for ET bins of 60-75, 75—90, 90-150 GeV .................... 159

Comparison of data (points) and composite Monte Carlo (histogram)
EM fraction distributions in the central region. .......................... 161

Comparison of data (points) and composite Monte Carlo (histogram)
Hmatrix x2 distributions in the central region ............................ 163

Comparison of data (points) and composite Monte Carlo (histogram)
isolation ET distributions in the central region. .......................... 165

Comparison of data (points) and composite Monte Carlo (histogram)
EM fraction distributions in the forward region. ......................... 167

Comparison of data (points) and composite Monte Carlo (histogram)
Hmatrix x2 distributions in the forward region ........................... 169

xiv

F .6 Comparison of data (points) and composite Monte Carlo (histogram)
isolation ET distributions in the forward region. ......................... 171

XV

Chapter 1

Introduction

This thesis presents a measurement of the production of direct photons in proton-
antiproton collisions, using the DO Detector at the Fermilab Tevatron collider. The rate at
which single, isolated photons are produced in such collisions is considered over a range
of photon energies, and for two separate ranges of photon polar angle. In addition, the
structure of direct photon events is considered by measuring the angular correlation
between the photon and the other particles in the event. In both cases, the experimental
results are compared with theoretical predictions. Direct photon measurements have
historically played a role in the modeling of the Strong force which binds nuclei together
(for a review of early direct photon experiments, see [1]), and this thesis continues that
tradition by extending the measurement to the highest photon energies available in the
world. As such, this thesis serves as an extension to and improvement upon previous DO
direct photon measurements [2][3].

The structure of the thesis is as follows: in Chapter 2, an introduction to basic particle

2

physics is given, along with a brief explanation of the theory of the Strong force and of the
theoretical calculation of direct photon production. Chapter 3 describes the DO Detector,
while Chapter 4 describes the way photons are identiﬁed in the detector, as well as the
efﬁciencies with which photons are identified. Chapter 5 presents a discussion of the
backgrounds to the direct photon signal, and describes the method by which the level of
photon signal was determined. Finally, Chapter 6 presents the results of the measurement
of the direct photon production rate, while Chapter 7 presents results from a study of direct
photon event structure. The results are summarized in Chapter 8.

The reader will note that extensive use is made of Appendices. This is done in order to
avoid excessive detail during the description of the measurement; however, it also serves
to partition detailed subjects, so that the Appendices may be more useful to those who may

use this thesis as a reference.

Chapter 2

Theory

2.1 The Standard Model

In order to set the framework to which the study of direct photons contributes, we brieﬂy
consider the known elementary particles and the forces which govern their interactions.
This set of particles, their antiparticle counterparts, and the physical laws they obey are
known as the Standard Model. As its name implies, the Standard Model is a stable and
consistent structure which has developed over time, and which explains most of the
fundamental behavior of particles and forces quite well.

In the Standard Model, all matter is composed of point-like particles which have half-
integer values of spin. These are classiﬁed as fermions, and can be further divided into the
lepton (Table 2.1) and quark families (Table 2.2) [4]. Both the lepton and quark families
can be grouped into three “generations,” each generation having identical properties

except for mass. The reason for these generations is still unknown - most matter in the

4

Table 2.1: The three generations of leptons.

 

 

 

 

 

 

 

 

 

 

 

Particle Symbol Charge Mass (MeV/cz)
electron e -1 0.51 1
electron neutrino v, 0 < 5.10 E-6
muon It -1 105.6
muon neutrino v1; 0 < 0.17
tau 1: -1 1777
tau neutrino v.t 0 < 24

 

 

 

 

 

Table 2.2: The three generations of quarks.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Particle Symbol Charge Mass (MeV/cz)
up u +2/3 2-8
down d -1/3 5-15
charm c +2/3 1000-1600
strange s - 1/3 100-300
top I +2/3 180000
bottom b -1/3 4100-4500

 

universe appears to be composed of particles from the ﬁrst generation: up and down
quarks combine to form protons (uud) and neutrons (uud) that make up the nuclei of
atoms; and electrons orbit the nuclei, giving atoms their chemical and material properties.
Governing how these particles interact are the four known forces: the Electromagnetic,
Weak, and Strong forces and the Gravitational force. Each of these forces is mediated by a

spin 1 particle, classiﬁed as a boson; the bosons are listed in Table 2.3. Particles with

5

Table 2.3: Vector bosons and the forces they mediate.

 

 

 

 

 

 

 

Boson Symbol Force Charge (M12377?)
photon 'y Electromagnetic 0 0
W W Weak :|:l 80300
Z Z Weak 0 91187
gluon g Strong 0 0
graviton ? Gravity ? ?

 

 

 

 

 

 

 

electric charge interact through the Electromagnetic force and its carrier, the photon; Weak
interactions proceed through exchange of W or Z bosons. In very high energy interactions,
where the mass of the W or Z becomes negligible, the Electromagnetic and Weak force are
actually the same; therefore, the two forces are treated theoretically as two aspects of one
Electroweak force. While the Gravitational force was known before any of the other
forces, there is as yet no well-developed quantum theory of Gravity, and therefore no
standard Gravitational boson.

The Strong force acts between quarks - for example, it is the Strong force which holds
the nucleus of an atom together. The Strong force is mediated by the gluon, and introduces
a new type of quantum number called color, analogous to Electromagnetic charge but with
three facets rather than the one of electromagnetism. Thus, quarks can be “red”, “green” or
“blue” (or antired, antigreen, or antiblue), and gluons carry these characteristics in color-
anticolor pairs in order to exchange color between two quarks. Note that this is markedly

different than in Electromagnetism, where photons do not carry charge themselves. Also,

6

only colorless particles are allowed to exist free in nature - therefore, quarks only exist in
quark-antiquark states called mesons (in which color charges cancel) and in three quark
states (such as protons or neutrons) called baryons (in which red, green, and blue form a
colorless combination). Note that these groupings also eliminate the possibility of states
with fractional charge. The more general term hadron is used to refer to any particle
composed of quarks, whether meson or baryon.

Historically, the framework of the Standard Model was laid out during the 1960’s and
1970’s [5], with experimental evidence accumulating in the following decades which

conﬁrmed the model [6]:

0 experimental evidence of point-like scattering centers inside nucleons, which led

to the association with quarks (1969) [7]

0 observation of weak interactions through the exchange of a Z boson (1973) [8]

0 observation of the charm and bottom quarks (1974, 1977) [9]

0 observation of jet structure and gluon radiation (1979) [10]

0 direct observation of the W and Z bosons (1983) [11]

0 observation of the top quark (1995) [12]

Increasingly precise measurements of particle properties and interactions have followed
these discoveries, as physicists seek not only to conﬁrm the building blocks of the model,

but also to reﬁne and extend our understanding of how those building blocks interact.

2.2 QCD Interactions

While the theory of the Electromagnetic force, known as Quantum Electrodynamics
(QED), is now well understood and well tested experimentally, the equivalent theory for
the Strong force, Quantum Chromodynamics (QCD), is less completely understood, and is
thus a very active theoretical ﬁeld. This thesis studies the production of direct photons in
proton-antiproton (i.e., hadron-hadron) collisions - interactions involving the Strong force.
Thus it is important to consider the workings of QCD in more detail.

If we consider a proton-antiproton collision, we might imagine a very complicated
picture. We have essentially a bag of three quarks interacting with another bag of three
(anti)quarks, all the while exchanging gluons as necessary for the quarks to stay bound
together. While these gluons generally have only a small amount of the momentum of the
proton, they are plentiful. In addition, because of the quantum nature of QCD, some
number of quark-antiquark pairs (called sea quarks) are being created and then annihilated
from the vacuum in addition to the 3 valence quarks. How do we keep track of all that
goes on between all these different particles?

The answer lies in one of the more curious aspects of the Strong force. Because the
gluons carry color, and thus couple to themselves, the strength of the Strong force

(expressed as the coupling constant of the Strong force, us) actually gets weaker as the

energy of the collision gets higher (or alternatively, the distance scale gets shorter). This is
the reverse of everyday experience, such as in Electromagnetism or Gravity where
increased energy (shorter distance) means a stronger effect. This can be roughly imagined

by considering that since the gluons can couple to themselves, they can emit other gluons

8

which increase the color force. Thus the quicker and shorter the interaction, the less
chance there is for gluons to radiate, and the smaller the strength of the ﬁeld.

Using this fact, known as asymptotic freedom, we are therefore free to consider the
collision between a proton and an antiproton as an interaction between one component
quark or gluon (generically called a parton) of each. Also, we can use the methods of

perturbation theory to calculate the interaction in orders of us, since at higher energies as

becomes small enough to decrease the importance of higher orders. Generally we
calculate a cross section (0'), measured in units of area, which indicates how likely it is
that a given interaction will occur; this is analogous to the classical cross section, where a
larger surface area with which to collide means a larger chance of a collision.

In order to give an overview of the process, consider the sample interaction shown in
Figure 2.1, in which a quark and a gluon (or more generally, two partons) collide to
produce a photon and a quark (or parton). Looking ﬁrst at the center of the ﬁgure, we see
the “hard scattering” part of the calculation. Here we consider just the two partons
scattering off each other - to calculate the cross section for photon production
perturbatively, we consider all the possible outcomes involving a photon and partons. To
leading order, this is simply a photon plus a Single parton. Notice, however, that we might
also have a gluon radiated off the ﬁnal state parton (shown as “jet 2”); this requires

another strong interaction, and hence another factor of as. We must continue to sum such

possible higher order terms, as well as sum over all the different quark/gluon types which
the “partons” might speciﬁcally be, and integrate over all possible parton momenta in
order to produce a total cross section.

However, because of the complexity of the calculation, it is not possible to sum to all

Bp—9 y+lot+X

   
      

ee-

Parton Distributions Hard scattering
Non-perturbative, must be High momentum transfer
experimentally determined, Perturbative QCD

but are universal

noon

Q's-f: '. \
was

-. ,< . r ' " 1.. .1 ll .
, u l -‘, ..‘. , ‘
wk '.‘

| r
i. v"

photon

no fragmentation —)
direct probe of the hard
scattering process

jet2

let 1

Fragmentation
(quark, gluon) —> jet

Figure 2.1: Diagram picturing different aspects of a QCD interaction.

10

orders - as a result, inﬁnities in the momentum integration no longer cancel, leading to
unphysical results. To resolve this problem, a mathematical method known as
renormalization is used, which neatly removes the inﬁnities, but at the price of

introducing an arbitrary momentum scale ”R (the renormalization scale). It is important to
note that 11R is an artiﬁcial, non-physical parameter which appears in the result of the

calculation only because we cannot complete the calculation to all orders. We choose this
scale to be roughly the order of the produced photon momentum, representative of the

scale of the interaction; however, we expect that the dependence of our result on uR will

be minimized if we have carried the calculation to high enough order.

Given this method of calculating the hard scattering, we can expand our consideration
to the left side of Figure 2.1 - namely, if we collide a proton and antiproton, what iS the
likelihood that two partons of a given momentum will be available to interact? These
directly affect the perturbative calculation, since we need to know how often each parton
combination that we enumerated above might occur. Also, we need to know what fraction
x of the proton’s momentum each of these partons is likely to have, so that we can
integrate over momentum properly. Unfortunately, these are exactly the quantities which
we cannot calculate in perturbative QCD, as they deal with the relatively low energy
structure of the proton.

In order to continue the calculation, then, we must make one further assumption. We
assume that the part of the calculation which speciﬁes the parton densities and momenta
can be separated from the hard scattering part - this is known as factorization. Given this

assumption, we can replace the non-perturbative portion of the theory with experimentally

ll

determined functions which describe the quark and gluon content of the proton - the
parton distribution functions (PDFS). These PDFS can then be considered universal - they
can be applied to any process which requires knowledge of the content of the proton.
However, to implement this separation in the calculation, we must use a mathematical
method similar to that used in renormalization - hence we introduce another (unphysical)

factorization scale up, on which the PDFS are dependent. As in the case of ”R, we choose
up approximately equal to the photon momentum to set the scale of the interaction;

however, it is important to note that the two scales need not be exactly the same, as they
have independent origins.

With an understanding of the PDFS and the perturbative hard scattering, we can ﬁnally
consider the right side of Figure 2.1. In enumerating the outcomes of a hard scattering, we
must consider what happens to the outgoing partons, as we know they cannot remain free
because they are not colorless. Here again the nature of the Strong force comes into play:
because the Strong force grows stronger with distance, as the outgoing parton gets farther
away from the interaction the color force between it and the parent hadron increases.
Ultimately, enough energy builds up to create one or more quark-antiquark pairs from the
vacuum - these quarks then combine to form colorless hadrons. This process is called
hadronization or fragmentation, and it results in a collimated “jet” of particles being
observed as the ﬁnal signature of an outgoing parton. Because of this fragmentation
process, there is a ﬁnite probability of obtaining any given particle from a parton
fragmentation which can be expressed in terms of fragmentation functions; these
functions are also not calculable in perturbative QCD and therefore must be modeled

using experimental data. However, like the PDFS, they can be considered universal, and

12

independent of the nature of the hard scattering process.
Combining these aspects of the calculation, then, we can express the QCD cross
section for the process A + B —> C + X (where X indicates that we do not explicitly keep

track of what, other than C, is produced) with the following expression:

om + B —> C + X) = 2 [dxadxbdcha/Aoa, uF)Fb/B(xb, #1:ch /C(zc) (2.1)
ach

X Gab —) cX(xa, xb: NR9 lip)

where a and b are the partons which interact from hadrons A and B; c is the parton which
gives rise to C; the F are the parton distribution functions which describe the likelihood of

getting a and b (with momentum fractions xa and xb) from A and B; D is the fragmentation

function which describes the probability of getting C from c with some fraction 26 of c’s

momentum; and 6' is the partonic hard scattering cross section, implicitly summed to
some order in as.
Note that in the speciﬁc case of photon production (as illustrated in Figure 2.1), the

ﬁnal state photon is free of the complication of fragmentation (D c H = l ). The photon is

seen in the ﬁnal state exactly as it was produced, directly from the parton level interaction.
This is an important advantage of the study of direct photon production. In contrast, the
study of jet production suffers from ambiguities in reconstructing a parton from the spray
of hadrons; also, because of the ﬂuctuations in hadronization, the measured energy of jets

can be uncertain because the exact particle composition of any given jet is not known.

13

2.3 Direct Photon Theory

The study of direct photons thus provides experimentalists with a unique and useful tool
with which to test QCD. The mechanisms by which they are produced, as described by
QCD theory, imply a direct sensitivity to the gluon distribution of the proton. Also, the
characteristics of the ﬁnal state particles that emerge in a direct photon event, including
the ease and precision with which one can identify and measure a photon experimentally,

provide a practical advantage.

2.3.1 Direct Photon Diagrams

Consider the examples of leading order direct photon production shown in Figure 2.2. We

GLUON COMPTON SCATTERING QUARK-ANTIQUARK ANNIHILATION
9 q 5 r
q 7 q 9

Figure 2.2: Leading order diagrams for direct photon production.

14

see that photons can be produced in quark-antiquark annihilation, in which the direct
photon is produced along with an outgoing gluon. Another process is the QCD analogue to
Compton scattering, in which a quark scatters from a gluon, producing a photon in the

ﬁnal state along with the scattered quark. Because of the relative abundance of low x
gluons in the proton, this process is the dominant form of direct photon production for EV T

below ~ 100 GeV; above this, the (typically) larger momentum fractions of quarks are
necessary to produce such an energetic photon, and the annihilation diagram becomes
more prominent. Because of the Compton dominance, we expect a measurement of direct
photon production to have sensitivity to the gluon content of the proton.

Some examples of higher order photon production diagrams are shown in Figure 2.3.
These typically involve additional gluon radiations, and result in characteristic signatures

of a photon plus two or more jets. Current direct photon QCD calculations include only up
to the two jet level (order (132), known as next-to-leading order (NLO), whereas the

experimental measurement includes all orders unless an explicit cut is made, and is
therefore termed inclusive. However, if terms beyond NLO are small, the NLO prediction

should be a good approximation to the inclusive cross section.

2.3.2 Bremsstrahlung Component and Isolation

As shown in Figure 2.4, there is another source of single photons: bremsstrahlung from an
outgoing quark in a dijet event. In this case, the photon is not produced directly from the
interaction vertex, and is therefore not really a “direct” photon - however, the existence of

this production method affects the way direct photons are measured and modeled

Figure 2.3: Examples of higher order direct photon diagrams.

l6

BREMSSTRAHLUNG

DI
-0|

Figure 2.4: Photon production through Bremsstrahlung

theoretically, as described in the next section. This method of production can be described
using the probability that a quark fragments primarily to a photon - D q H.

In order to reduce the occurrence of the bremsstrahlung case, an isolation criterion is
imposed on the photon: typically, a cone around the photon is examined and required to
have less than a certain amount of energy. Since a photon produced through
bremsstrahlung tends to be very collinear with the quark it radiates from (and thus the jet
resulting from the quark’s subsequent fragmentation), the requirement that the photon be
isolated removes all but the very largest angle radiations. In the theoretical model, a
bremsstrahlung/fragmentation component is added into the calculation and then (partially)
removed by the imposition of an isolation requirement matching that of experiment. This
component contributes a large (up to 50%) fraction of the total (um-isolated) rate, and

remains signiﬁcant in the ET region below ~ 25 GeV even after the isolation Criterion is

applied [13][14].

17

Another important reason to include an isolation criterion is the possibility that a jet
might be misidentiﬁed as a photon. In the process by which a parton fragments into

observable particles, if most of the parton energy remains with a Single particle (for

0

example, a 1: meson) and that particle produces photons as its decay products (e.g.,

no -—) w), the multiple photons can be indistinguishable from a single photon. While only

one in 103-104 jets fragments in this way, the dijet production cross section is 103-104
times larger than the photon cross section; therefore this background to the direct photon
signal is of the same magnitude as the signal itself. The experimental challenges and
solutions involved in removing this background are a major part of any direct photon

analysis, and are described in Chapter 5.
2.4 Variables for Hadron Collider Physics

It is necessary to deﬁne a set of quantities which are used in the study of high energy

hadron-hadron collisions. While the standard phase space variables of energy (E),

9
momentum (p), polar angle (0), and azimuthal angle (4)) can be used, the nature of hadron
colliders makes the introduction of additional quantities necessary.
An important feature of hadron colliders is that while the hadrons can be given equal

and opposite momenta, there is inherent uncertainty in the momenta of the partons which

interact. Unlike positron-electron (e+e') colliders, where the two colliding particles and
their momenta can be exactly deﬁned, the quark and gluon substructure of the proton

implies that we cannot predetermine which partons will interact, and what momentum

18

they will have (as discussed in Section 2.2). Therefore in the lab (detector) frame, the
momenta along the beam axis (deﬁned to be the z direction) will usually not sum to zero,
and the system will be Lorentz boosted.

In the transverse (x-y) plane, however, we expect that the ﬁnal state momenta will
cancel, as the initial state transverse momenta are negligible. Therefore, we deﬁne the

transverse momentum and energy:

’ 2 2

pTE px +py (2'2)
2 2

ET; /E —pz (2.3)

which become important variables for collider physics. Note that if the particle mass
m « E , or for massless particles such as the photon,

ET = pT = EsinO (2.4)

The Lorentz boost also motivates an alternative to the polar angle 0, which is not

Lorentz invariant. Instead, we deﬁne the rapidity (y):

1 E +pz
2]n(E-pz) (2.5)

 

y

which transforms under a Lorentz boost as y —-> y + [constant], thereby preserving the

shape of the rapidity distribution under the boost. Again, if a particle’s mass is much less

than its energy, we can simplify to form the pseudorapidity (11):

n = —ln tang) (2.6)

Thus a pseudorapidity of n = 0 corresponds to 0 = 90° from the beam (2) direction,

19

increasing to oo (—oo) as the angle grows nearer to the +z (-z) direction. Since the

condition m « E is a good approximation for high energy jets and photons, the
pseudorapidity is used almost exclusively, and is often referred to as simply the rapidity.
Finally, since we are interested in measuring a cross section, we consider the rate (R)
at which events with a cross section 0' ( with units of area) occur:
R = OL (2.7)
where L is the luminosity in units of inverse area per second. The luminosity is a measure
of beam ﬂux, and is tied to the performance of the accelerator and its ability to focus the

colliding beams densely enough to achieve signiﬁcant event rates for high energy physics

0-24

processes. Cross sections are typically measured in barns (1 barn = 1 cm2), with rare

events having cross sections of several picobarns (pb) or less; therefore, modern colliders

such as the Fermilab Tevatron provide luminosities of up to ~1031 cm'zs’l. Integrating
over the amount of time the accelerator makes this luminosity available to experiments
gives a useful measure of how much data has been taken - the integrated luminosity. For

the 1994-1995 Tevatron Run 1B, from which the data in this analysis was taken, a total of

~ 100 pb—1 of data was accumulated.

Chapter 3

Experimental Apparatus

3.1 Accelerator

The Fermilab Tevatron Collider, located in Batavia, IL, accelerates protons and
antiprotons to energies of 900 GeV, making a total of 1.8 TeV of energy available as the
particles collide. This makes the Tevatron the most powerful accelerator in the world, and
thus, in the particle physics tradition of giving Nature as much energy as possible to see
what She will create from it, the premier facility at which to study elementary particles
and the forces by which they interact.

While the Fermilab accelerator might be described simply as a huge ring of magnets
almost 4 miles in circumference, there are actually several different, increasingly

sophisticated stages of acceleration which make the ﬁnal collision possible (Figure 3.1).

Cockroft-Walton generators produce H' ions which have a small initial kinetic energy;

these are then fed into a series of accelerating electric ﬁelds known as a linear accelerator,

20

21

   

TARGET HALL

ANTIPROTON
SOURCE

 

Figure 3.1: The Fermilab Tevatron Collider.

and then stripped of their electrons. The remaining protons are then accelerated further in
a small “booster” synchrotron, consisting of a ring of accelerating cavities alternated with
magnets to bend the particles, which are also grouped into bunches at this stage. The
bunches of protons, by now at an energy of 8 GeV, are then extracted into the Main Ring,
so named because it was once itself the ﬁnal stage of acceleration, giving the protons an
energy of 150 GeV. Housed in the same underground tunnel as the Main Ring, however, is
its successor the Tevatron, which uses superconducting magnets to produce a magnetic
ﬁeld strong enough to bend even particles of 900 GeV kinetic energy into the necessary

circle.

22

The production of antiprotons takes place by directing some of the protons circulating
in the main ring into a target, which produces (among other particles) a small amount of
antiprotons. These are carefully selected out, condensed into bunches, stored in a small
“accumulator” accelerator, and ﬁnally, when a sufﬁcient number have been produced,
injected into the Main Ring to circulate in the opposite direction to the protons. This points
out a major advantage of colliding protons with antiprotons: the same apparatus can be
used to accelerate both sides of the collision, since the two particles are identical but for
the opposite charge, which will draw the particles in opposite directions in an
electromagnetic ﬁeld. The two bunches of particles pass through each other without
collisions because of the low density of particles within the bunches.

The antiproton bunches are then fed into the Tevatron and ramped up in energy to 900
GeV. The Tevatron operated during Runs 1A (1992-93) and Run 1B (1994-95) with six
bunches of each particle circulating within the accelerator, with collisions occurring at two
separate interaction points corresponding to the locations of the two detectors (DO and its
sister experiment CDF). At the collision points, focusing magnets are used to squeeze the
particle beams down to densities which make collisions sufﬁciently likely (and thus
produce a useful luminosity). The arrangement of particles into bunches means that the
collisions take place at deﬁnite time intervals as the bunches cross each other - this allows
the detector to synchronize with this time cycle so that the readout electronics have
sufﬁcient and uniform time intervals to process one bunch crossing and prepare for the
next. During Run 1 this time between beam crossings was 3.5 us; the average number of
collisions per bunch crossing varied as a function of the luminosity from ~05 to over 3.0

interactions/crossing.

23

In practice, the accelerator runs in cycles called “stores” - at the beginning of each
store, the particles are injected into the Tevatron bunch by bunch, the beam is “scraped”
(particles with very off-center orbits are removed), and collisions begin. At this point the
luminosity of the collider is at its highest - as the store progresses, luminosity decreases as
particles are lost by attrition from collisions and unstable orbits. After about 8-15 hours
the available luminosity is too low to be useful, and the store is ended by dumping the

particles into a “beam stop,” and a new store is readied.

3.2 Detector

The DO detector is a multi-purpose apparatus, designed with the physics possibilities of

the Tevatron in mind. The goal of studying high-PT phenomena and high-mass states such

as the W and Z bosons, as well as the search for the top quark, led to design emphasis on

electron and muon identiﬁcation and measurement; high-PT jet energy measurement; and

accurate accounting of missing transverse energy.

The detector is shown in Figure 3.2. It consists of three main sections: the central
tracking detectors, which lie close to the bearnline and detect ionization left by particles as
they travel from the interaction point outward; the liquid argon sampling calorimeter,
which stops most particles and measures their deposited energy; and the muon detection
system, which surrounds the calorimeter and provides identiﬁcation and momentum
measurement of muons. A full description of these systems can be found in [15]; a brief
description is presented below, with particular emphasis on the tracking detectors and

calorimeter, which are the systems used in this analysis.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.2: The DO Detector.

25
3.2.1 'h'acking

The DO Tracking System (Figure 3.3) consists of three subsystems, each providing

[EH m M
@ I 1“ ﬂ
ii All

(I) O

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

Central Drift Vertex Drift Transition Forward Drift
Chamber Chamber Radiation Chamber
Detector

Figure 3.3: The D0 Tracking System.

different information as the distance from the interaction point increases. The Vertex
Detector (VTX), which surrounds the beampipc over the range -2.0 < n < 2.0 , provides
ﬁne resolution of tracks very close to the interaction point. The Transition Radiation

Detector (TRD) surrounds the vertex detector, covering the range -1.2 < T] < 1.2, and

26

provides discrimination between electrons and charged pions. The Central and Forward
Drift Chambers (CDC/FDC) give a measurement of charged tracks further away from the
interaction point, where they are more physically separated; the CDC surrounds the TRD,

while the FDC extends the tracking coverage down to n = 3.1.
The Vertex Chamber

The DO Vertex Detector, like the CDC and FDC, is a drift chamber, designed to detect the
ionization left behind as a high-energy charged particle passes through a medium and
Coulomb scatters with atomic electrons. As the name implies, this type of detector
consists of a “chamber” containing a medium to be ionized (usually a gas, which allows
for easy movement of the ionized electrons), and a scheme by which an electromagnetic
ﬁeld is applied to the medium in order to “drift” the ionized electrons to collection points,
these points being organized to provide spatial information on the path of the charged
particle.

The Vertex detector (Figure 3.4) consists of 3 cylindrical chambers, concentrically
layered such that the inner radius of the ﬁrst layer is just outside of the beampipc at r = 3.7
cm, and the outer radius of the last layer is at 16.2 cm. The actual walls between each
chamber are constructed of carbon ﬁber support tubes, and the chambers are ﬁlled with a
mixture of carbon dioxide (95%) and ethane (5%). Each of the layers is segmented in
azimuthal angle (p, with the inner layer segmented into 16 cells and the outer layers
segmented into 32. As seen in Figure 3.4, the cells are deﬁned by rows of wires, which run
the length of the cylinder (in the z direction) under tension, and which provide the

carefully shaped electric ﬁeld. Traces on the carbon ﬁber tubes provide a cathode which

27

 

Figure 3.4: Side schematic of the DO Vertex Detector.

28

coarsely shapes the ﬁeld; ﬁne Shaping is provided by the cathode wires, and the grounded
grid wires serve as anodes to attract ionized electrons to the adjacent sense wires, which
read out the accumulated charge. Note that the cell positions in the three layers are
staggered in order to improve resolution in the r-(i) plane, which is typically ~50 um.

The track position can be determined in the z coordinate by comparing the amount of
charge read out at either end of the sense wires, obtaining a z coordinate via charge
division. Measuring the 2 position of tracks is crucial to reconstructing the location of the
primary interaction vertex, as well as any secondary vertices due to multiple interactions;
knowledge of these vertex positions is used to ﬁx the exact direction of ﬁnal state particles
and therefore measure their production angles and transverse energy components. While
the Vertex Detector was designed to achieve a 2 resolution of ~1 cm, the high track
multiplicity environment near the interaction point at Tevatron luminosities has hampered
this performance. As a result, the position of the primary vertex is determined with the aid

of the Central Drift Chamber.
The Transition Radiation Detector

The Transition Radiation Detector relies on the fact that a charged particle moving at
highly relativistic speeds will radiate photons (as X-rays) when it transits between regions
with different dielectric constants. The amount of radiation emitted depends on the speed

of the particle, which in turn will depend on the energy and mass of the particle. For
example, an electron at a certain energy will travel much faster than a 1t+ meson with the

identical energy, since the 1t+ is almost three hundred times more massive than an electron

- and as a result the electron will on average emit more transition radiation. It is this

29

difference which the TRD is designed to exploit.

The TRD, like the VTX chamber, is made up of 3 separate cylindrical units. Each
contains foils of polypropylene, 18 pm thick, separated by 150 pm in a volume of nitrogen
gas (Figure 3.5). Since the probability of radiation is about 1% per boundary interface [4],
there are 393 foils in each unit to insure maximum efﬁciency. After the foils in each unit
there is a drift chamber, which serves to convert the X-rays and read out the ionization

signal. Since the drift chamber uses a Xe(9l%)/CH4(7%)/C2H6(2%) gas mixture, the drift

chamber in each unit is separated from the nitrogen environment of the foil layers by two

layers of mylar, between which dry C02 gas is circulated to prevent any leakage of gases

between the two volumes.

While this analysis does not explicitly use the information read out from the TRD, its
presence affects the detection of direct photons. At normal incidence (0 = 90°) the TRD
presents 8.1% of a radiation length to a photon; this is most of the material which lies
between the interaction point and the calorimeter. As a result, some fraction of photons
will convert to an electron-positron pair, and will thereafter leave a pair of ionization
tracks. Averaged over the region 09 S. n S 0.9, the probability for such a conversion is
roughly 10%, while in the regions corresponding to 1.6 S lnl S 2.5, where non-normal
incidence on the TRD results in greater material depth and the endplates of the VTX and
TRD present additional material, the probability rises to about 38% [16]. Therefore, a

Signiﬁcant fraction of real photons and jets decaying to photons will convert before the

CDC/FDC, and will behave as an e+e' pair thereafter.

30

CROSS-SECTION 0F TRD LAYER 1

OUTER CHAMBER SHELL
70pm GRID WIRE
ALUMINIZED MYLAR ./

   

 

 

 

65mm
2 o
______ _}_.__ __———o——. ———
0 4mm
2
21r/256 mmt. o
J o
______ — — — — — — — — o— — ..4 _ _
o
RADIATOR STACK CONVERSION .
STAGE 0]

N2
30pm ANODE WIRE]

/ 100nm POTENTIAL WIRE
23am MYLAR WINDOWS

HELICAL CATHODE STRIPS

Figure 3.5: Cross section of the ﬁrst TRD layer.

 

 

3 1
The Central Drift Chamber

Surrounding the TRD is the Central Drift Chamber, which like the VTX and TRD has a

cylindrical shape. As seen in Figure 3.6, the CDC is segmented in azimuthal angle (32

 

 

 

 

 

Figure 3.6: End view of a section of the Central Drift Chamber.

cells in all) and is four layers deep, with alternating layers staggered for better coverage.
While the physical construction of the cells differs from that of the VTX, with Kapton-
covered Rohacell “shelves” deﬁning the physical cell borders, the conﬁguration of sense
wires centered in the cell along with surrounding grounded guard wires is similar. In

addition to the sense and guard wires, two Teﬂon coated delay lines run in grooves cut into

32

the inner and outer shelves of each cell. Signals induced in the delay lines by the nearest
sense wires are read out at each end of the CDC, and the comparison of arrival times at the
two ends yields a measurement of the 2 position of the ionization track. The CDC uses an

Ar(92.5%)/CH4(4%)/COZ(3%) gas mixture.

The Forward Drift Chambers

At smaller angles (closer to the beamline), rather than extending the central detectors, it
becomes advantageous to place separate detectors perpendicular to the bearnline, so that
particles will again impact normally on the detector surface and the z direction extent of
the detector can be minimized. The Forward Drift Chambers thus have a different
geometry than the CDC: each detector (one on each side of the central region) consists of
three disk-like layers (Figure 3.7) oriented perpendicular to the beamline. The ﬁrst and
third layer are constructed of four quadrants of Six stacked rectangular cells each, so that
each cell covers a different range of angle 0. These two “O” layers are rotated by 45° with
respect to each other. The middle layer is very different, composed of 36 cells which are
like pie wedges, providing discrimination in azimuthal angle q). As in the CDC, though,
both “8” and “4)” layers utilize multiple anode and sense wires running along the long
dimension of each cell, and several deep in z, to detect the ionization signal. The gas
mixture used is also the same as in the CDC. Also, in the “O” layers, a single delay line
similar to those in the CDC provides a determination of the location of the track along the

length of the rectangular cell.

34
3.2.2 Calorimetry

The DO Calorimeter System (Figure 3.8) measures the energy of most particles by

   
 
 
 
  
  
 
   
  
  

END CALORIMETER
Outer Hadronic
(Coarse)

Middle Hadronic
(Fine & Coarse)

I

.\ ,\
\.
'.§? 4

.
3%;

\\
”F

///
”Ix

/

l \ ' CENTRAL
" CALORIMETER
\ . ’ 7' Electromagnetic

r‘~

v“-
eff/t

§

Inner Hadronic ' Fine Hadronic

(Fine a Coarse) Coarse Hadronic

Electromagnetic

Figure 3.8: The DO Calorimeter (cutaway view).

Stopping them completely within the calorimeter volume, thus transferring the (kinetic)
energy of the incident particle to the material in the calorimeter. Accordingly, the
calorimeter contains layers of very dense materials (plates of uranium and Steel), within

which the particles shed their kinetic energy, interspersed with layers of an ionizing

35

medium from which a signal can be easily measured (liquid Argon). This is therefore a
“sampling calorimeter” - since only the ionization left within the Argon layers is read out,
only some fraction of the energy (about 10%) is sampled. The total energy deposition is
then inferred from this sample by calibrating with particles of known energy in a test
beam, and deriving "sampling weights" which multiply the raw energy read out in each
layer so that the sum exactly represents the true particle energy. We further expect that
readout charge will be proportional to particle energy, so that the calorimeter response will
remain linear with increasing energy.

Practically, this layering is achieved by enclosing the dense plates within a cryostatic
vessel ﬁlled with liquid Argon, so that the Argon-ﬁlled gaps between plates become the
readout layers. An example of a calorimeter cell implemented this way is shown in Figure
3.9.

As can be seen in Figure 3.8, the calorimeter is separated into one Central and two
Endcap sections (North and South), housed in separate cryostats to allow easier access to
the interior of the detector. The Central Calorimeter (CC) covers roughly the range
Inl S 1.0 and the Endcap Calorimeters (EC) extend the coverage to Inl z 4.

The CC is further segmented radially into 3 sections (Figure 3.10). The
Electromagnetic (EM) calorimeter is the section closest to the interaction, and it is read
out in 4 separate layers (EMl-EM4) which correspond to 2.0, 2.0, 6.8, and 9.8 radiation
lengths, respectively. Most electromagnetic showers from photons and electrons are
contained almost completely within these 4 layers, and thus it is the most important part of
the calorimeter for this analysis. Beyond the last EM layer, and designed to stop the more

penetrating hadronic showers, are the three layers of the Fine Hadronic (FH) section

3

O\

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

( Absorber Plate Pad Resistive Coat Liquid Argon D
N 010 Insulator JL 1 Gap—
7/ \. 7/ / i
% __ _ _/// _L
c <-——- U3_it_0_e_li —--> o

 

 

Figure 3.9: Diagram of the layers within a calorimeter cell.

which include 1.3, 1.0, and 0.9 nuclear interaction lengths. Finally, the Coarse Hadronic
(CH) section, which uses copper as an absorber rather than uranium, provides one more
depth segment of 3.2 nuclear interaction lengths to contain the few hadronic Showers
which penetrate beyond the EM and FH sections.

The depth segmentation of the EC is similar to that of the CC, with the difference that
the hadronic calorimetry is actually broken up into 3 separate sections (concentric about
the beampipc) called the Inner (IH), Middle (MI-I), and Outer (OH) sections, with the 1H
and MH sections containing both ﬁne (uranium) and coarse (stainless steel) layers of
depth sirrrilar to the PH and CH in the central region. The OH section contains only coarse

layers of stainless steel, as it lies in a region of overlapping coverage with the FH section

37

0.0
IETA

Erik-366mm,». n o

 

Figure 3.10: Side view of a calorimeter quadrant. Lines of pseudorapidity are
shown to demonstrate the projective tower geomeU'y.

of the Central Calorimeter, and thus serves essentially as an extension of the Central
Coarse Hadronic layers. Also, the EC EM layers have slightly different thicknesses than in
the CC, comprising 2.0, 20,79, and 9.3 electromagnetic radiation lengths.

Figure 3.10 also shows that the individual cells of the calorimeter are arranged
projectively in towers of An XAO = 0.1 x0.l so that their centers point back to the
midpoint of the detector, which allows good shower Shape resolution. In addition, to

provide better measurement of electromagnetic shower position, the third layer of the EM

38

calorimeter (EM3), where EM showers typically leave the majority of their energy, is
more ﬁnely segmented (An x Ari) = 0.05 x 0.05 ).

To calibrate the calorimeter modules, sections of CC and EC calorimeter assemblies
were studied in a test beam [17][18]. Electrons and charged pions with well-measured
energies ranging from 2 to 150 GeV were scanned across the modules to Simulate various

angles of incidence. These studies found that the response of the calorimeter was linear

above ~ 10 GeV, with a resolution for electrons of 15%/(JE), and 50%/(JE) for

pions. To ﬁnely calibrate the EM calorimeter, calorimeter response was measured in situ

by reconstructing the decays Z —) e+e' , J/\|t —> e+e' , and Ito —> w [19]. Since the masses
of these particles are well established (91.187 GeV, 3.096 GeV, and 134.97 MeV,

respectively) and their decay products span a large energy range, exact calibration of the

response versus energy is possible.
The Intercryostat Region

To accurately measure energy deposited in the gap between central and end cryostats, two
additional detector systems are installed. The ﬁrst, termed massless gaps, consist of single
calorimeter readout cells placed in the region between the cryostat wall and the edge of the
PH calorimeter section (in the CC) or the MH and OH sections (in the EC). These
essentially make the regions between the calorimeter modules and the cryostat walls into
an extra readout cell, albeit with very little mass to stop particles. In addition to the
massless gaps, scintillating counter arrays called the Intercryostat Detectors (ICD) are

mounted in the space between the central and endcap cryostats. Each ICD array consists of

39
384 tiles of An x All) = 0.1 x 0.1 , read out by phototubes, and covering an area on the
inside face of the EC cryostats roughly corresponding to the MH and OH sections. While
they are of no aid in identifying electromagnetic showers, the ICD and massless gaps
provide enough information on hadronic showering between calorimeters to assist in the

proper reconstruction of energy deposition between cryostats.

3.2.3 The Muon System

While the calorimeter stops and absorbs most particles within its volume, there are two
particles it will not contain: neutrinos and muons. Neutrinos, due to their extremely small
cross section for interaction with matter, cannot be detected at all, and the presence of a
neutrino in an event must be inferred by summing the energies in the detector and

determining the amount and direction of “missing” transverse energy (ET ) needed to

make the total transverse energy sum vectorially to zero. Muons, however, will leave a
trace of their passage via ionization - thus the outermost component of the D0 detector, the
Muon System, is designed to identify muons and measure their momenta and position.
The Muon System consists of three sets of proportional drift tube chambers (PDTS)
along with a toroidal iron magnet, implemented in 5 separate pieces, maintaining ﬁelds of
~2 T. The ﬁrst set of PDTS, called the A layer, is mounted before the toroid and consists of
four planes of PDTs; the B and C layers are mounted outside of the toroid, and consist of
three planes of PDTS each, with the two layers separated by 1m. The A layer, with its extra
plane of PDTS, detects muon hits and allows them to be associated with tracks in the

Central Tracking Chambers; the B and C layers track the muon trajectory after it has been

40

bent by the magnetic ﬁeld in the toroid, and thus allow the momentum of the muon to be

determined from the magnitude of the bend.
3.3 Data Acquisition and Processing

3.3.1 The Trigger System

Since the accelerator produces beam crossings every 3.5 1.1.5, the detector must evaluate a
possibly interesting collision 285,000 times per second. At the other end of the timescale
is the rate at which a complete readout of the detector - close to 150,000 channels - can be
written to tape for storage: this is limited to 2-5 Hz. Condensing 285 kHz of potential
collisions down to 2-5 Hz of interesting events which comprise the ﬁnal data sample is

done using the DO Trigger System, which consists of three successive levels.
The Level 0 Trigger

The ﬁrst level of triggering is the Level 0 Trigger, which signals that an inelastic collision
occured in the beam crossing and this event is therefore worth examining by the higher
levels of the trigger. The Level 0 system consists of two planes of rectangular scintillation
counters, mounted 90° relative to each other to form a checkerboard-like pattern of
coverage; one such pair is mounted on the front surface of each of the endcap
calorimeters. When both counters register hits after a beam crossing, there is a >99%
probability that an inelastic collision occurred; the rate of coincident bits is also an
independent measure of the beam luminosity, and can provide feedback to accelerator

operations. The timing difference between the two counters can be used to give a rough

41

measurement of the z of the interaction vertex, and can also indicate the presence of

multiple interactions - all of this information can be utilized in the higher trigger levels.
The Level 1 Hardware Trigger

Once it is established that a collision has occurred, the Level 1 triggering system examines
the calorimeter and the muon system for evidence of signiﬁcant energy deposition. In
order to do this within the 3.5 us deadline, the Level 1 system uses fast, hardware-based
algorithms to evaluate the event.

In the Muon system, 200 electronic readout boards known as Module Address Cards
(MACS) receive from their assigned subset of muon chambers a list of cells from all
planes which registered hits. These hits are processed by the MACS into a single “coarse
centroid,” representing the best quick estimate of the muon position. Centroids output by
the MAC cards are then combined over the A, B, and C layers to give a rough momentum
measurement; this information is then used by the Level 1 system to compare with trigger
requirements for position and minimum momentum within 3.5 its of the interaction. If
needed, the system can initiate additional processing known as the Level 1.5 muon trigger
system: this uses “ﬁne centroids” generated by the MACS and can produce a more
accurate measurement of the transverse momentum, but requires another 3.5 us and thus
incurs a deadtime penalty for the entire detector.

In the Calorimeter, a fast readout samples the rising edge of each cell’s signal pulse,
and sums these signals into An = All) = 0.2 trigger towers, keeping separate account of EM
and hadronic energies. Using lookup memories and the 2 position from Level 0, these

tower energies are processed to provide the Level 1 system with EM, hadronic, and total

42
ET values for each tower, as well as the missing ET resulting from a sum over all towers.
These quantities are then compared against the trigger requirements. The average rate of

events passing at Level 1 is about 100 Hz.
The Level 2 Software Digger

The ﬁnal level of triggering is provided by the Level 2 system, which consists of 50
VAXstation 4000 computers (termed “nodes”) connected to the rest of the system by high
speed data cables. Events which pass the Level 1 system initiate a complete digitization
and readout of the detector, and this information is sent to the ﬁrst available Level 2 node,
which then runs software-based algorithms to evaluate the event in much more detail than
at Level 1. This digitization and processing requires about 200ms; however, this is well
under the average time between events sent to a node from Level 1. To increase the speed
of the readout, calorimeter cells are subjected to zero suppression, in which cells with less
than 20' ﬂuctuations in energy from their normal, quiescent readout level are zeroed and
suppressed, therefore saving the need to read out an energy value.

In practice, the three levels of triggering are carefully tuned and matched to each other
to produce an optimum output stream of events. The Level 1 trigger system, having
received a positive Level 0 result, can evaluate up to 32 separate sets of requirements
(termed “triggers”) on energy in one or more towers, and the position of those towers.
These triggers are carefully selected to correspond to general types of physics events.
Should any Of these requirements be met, the event is passed on to a Level 2 node, where
up to 128 sets of requirements (termed “ﬁlters”) can be made. Each ﬁlter is matched to a

Speciﬁc Level 1 trigger, and serves to identify a more detailed and Speciﬁc type of ﬁnal

43

state. In addition, each trigger and each filter can be “prescaled” to pass only 1 of N events
identiﬁed as matching its requirement - in this way, the passing rates can be kept within
limits, and triggers/ﬁlters corresponding to common event types can be controlled to

ensure that rarer triggers/ﬁlters are not lost to bandwidth limitations.

3.3.2 Event Reconstruction

Once the event has passed the online event selection system, it is then stored on 8mm
tapes. However, in its raw form it consists of only the signals read out from each detector
cell, information from the triggering process, and information about running conditions at
the time it was taken. To put the data in a useful form for physics analysis, the DO

Reconstruction program (DORECO) was developed to serve three main functions:
0 Apply calibration information to the raw data to correct all detector hits

0 Apply algorithms to the detector hits to identify and describe objects within the

detector: photons, jets, muons, etc.
0 Reduce the event to a manageable size for later storage and analysis

Reconstruction of the raw data was done using a farm of SGI and IBM Unix machines,
though the program can be run on multiple platforms and can be rerun on processed data
in order to apply new techniques or calculate new quantities. The DORECO program itself
is a large assembly of code packages which perform all the necessary functions of
calibrating and interpreting the output of each detector; the relevant sections for this

analysis are described below. The output of the program is a ﬁle using the ZEBRA data

44

structure, in which information is organized in “banks” which are referenced by pointer,
and the ultimate size of the output ﬁle can be controlled by which banks are written to the
ﬁle. DO maintains several levels of dataﬁles, each carrying successively less information

but allowing successively more case in processing and disk storage.
The Z TRAKS package

This package is reponsible for the reconstruction of tracks within the tracking chambers;
however, it also includes the determination of the event vertex using tracks reconstructed
in the CDC.

Tracks are found in the CDC by reconstructing hits in the r—(i) plane and aligning them
ﬁrst within each layer, forming what are called “segments.” Starting with the outer layer,
these segments are then compared, and if 3 of the 4 layer segments are sufﬁciently aligned
a track is conﬁrmed, after which the entire track is refit, a 2 position calculated, and a ﬁnal
cut made on the quality of the track.

Tracks in the FDC are determined in a similar way; however, because the forward
region tends to have many more tracks from the breakup of the colliding particles, full
reconstruction of the entire FDC is very time-consuming and is usually not done. Instead,
only the region between the vertices and physics objects such as electrons or photons is
reconstructed - the tracking “road,” which is usually A0 x All) = 0.2 x 0.2.

To determine the vertex, reconstructed tracks within the CDC are pointed back to their
z-intercept point, and the points from all such intercepts are put into a histogram. A cluster
ﬁnding algorithm is run to identify clusters of points, and those with at least three points

are resolved into separate vertices, with the primary vertex assigned as the one with the

45

most points. The mean and error of the points in each cluster are then taken as the mean
and error on the vertex position. If there is only one cluster, even with only one point, it is
taken as the vertex; if there are no CDC tracks (perhaps 5% of the time), the FDC is used
instead, in which case the entire FDC is reconstructed. The error on the vertex position can
range from 6mm for an event with many tracks, to 2 cm for an event with only one CDC
track, to 10cm if the FDC tracks must be used. For each found vertex a ﬁt is then done
using only those tracks pointing to that vertex and constraining them to originate from a
single point, resulting in the ﬁnal mean and error of the vertex 2 position. Note that
determination of the x-y coordinate of the vertex is done using VTX readings during data-
taking - the x-y dimensions of the beamspot are small and usually vary only a few microns

from run to run, so that an average value can be used over a certain run period.
The CAHI TS package

The CAI-[ITS package is responsible for the bookkeeping of all the energies of each
calorimeter cell, the application of calibration corrections, and the mapping of cells to
physics coordinates. Its output, basically a corrected bank of all cells in the calorimeter, is
then used by object ﬁnding packages such as those relevant to this analysis, CAPHEL and

CAJETS.
The CAPHEL package

As implied by its name, this package searches the calorimeter to find photons and
electrons. It employs a clustering algorithm which ﬁnds towers ( 0.1 X 0.1 ) in the EM

calorimeter above a certain ET threshold, then associates neighboring towers with this

46

tower until no neighboring towers above a 50 MeV threshold are found. The package then
calculates quantities for this cluster (such as its total energy, position, etc.), making several
ZEBRA banks full of information, and also associates with it any tracks coming from the
primary vertex within the tracking road between the vertex and the cluster, making links to

the corresponding tracking ZEBRA banks.
The CAJE TS package

The CAJETS package is Similar to the CAPHEL package, in that it must search the
calorimeter to ﬁnd jets. Since the deﬁnition of a jet, and which particles in the event
should be associated with it, is somewhat ambiguous, several different algorithms are
used. The one relevant to this analysis is the ﬁxed cone deﬁnition, using a radius of 0.7 in
An x Ad) Space.

In the ﬁrst stage of the algorithm, a “precluster” is found similarly to the
electron/photon case: the cell with the highest ET in the calorimeter is used as a starting
point, and cells with ET greater than 1 GeV and within 0.3 in n or (i) are grouped together
around it; these cells are then removed from consideration and the remaining highest cell
has a precluster built around it; and so on until all cells with more than 1 GeV ET are in a
precluster.

Then for each precluster, cone clustering is applied: starting with the highest ET

precluster, the ET weighted centroid of the cluster is found, and all towers within a radius

of 0.7 in An x All) are assigned to the jet. The jet axis is recalculated using these towers,

and the process is then iterated until the jet axis becomes stable. If the resulting jet has

47

ET> 8 GeV it is kept, and it is compared against other jets found for any Shared towers.

Should any two jets share towers, an algorithm is run which either splits them, assigning

contested cells to the nearest jet, or merges them, depending on how much ET is shared

between the two. Split or merged jets then have their axis recalculated a ﬁnal time.

Chapter 4

Event Selection and Efﬁciencies

In order to measure the cross section for direct photon production, we must ﬁrst deﬁne
what we expect a direct photon to look like in our detector, and place requirements on all
photon candidates in order to select these characteristic events and reject non-signal
events. AS outlined in Chapter 3, this can be done at the trigger level, selecting events
which look like direct photon events, and then reﬁned further using ofﬂine cuts to impose
even stricter requirements. The goal of background rejection may lead to cuts harsh
enough to reject even some real direct photon events; therefore, we must also estimate the
number of direct photon events lost so that the total number measured can be corrected to

equal the total number produced.

48

49
4.1 Data Set and Monte Carlo

4.1.1 Direct Photon Triggers

Because the direct photon production rate falls steeply with ET, multiple triggers/ﬁlters
must be used to acquire data in each ET region and prescaled accordingly to achieve
comparable statistics over the measurable ET range. The direct photon candidate sample

was obtained using the four Single photon triggers and ﬁlters summarized in Table 4.1.

The two lowest ET ﬁlters, GAM_6_ISO_GAM and GAM_14_ISO_GAM, were taken in

Special runs, when the lurrrinosity and event rate were lower and the full bandwidth of the
trigger system was devoted solely to photon triggers; therefore, usually only the 6 Gev
ﬁlter was prescaled. The two highest ﬁlters, EM1_GIS and EM1_GIS_HIGH, were taken
as part of global running, where only a part of the bandwidth was devoted to photons. The
EM1_GIS filter was therefore prescaled, with the EM1_GIS_HIGH ﬁlter also prescaled at
very high luminosity running where high event rates taxed the trigger system’s capability.
Total integrated luminosities for each ﬁlter are also shown in Table 4.1, and carry a 5.4%
uncertainty.

Inefﬁciencies due to triggering do occur; however, to avoid this complication, ﬁlters
were used in the cross section measurement only where fully efﬁcient. Detailed
descriptions of the triggering algorithms, triggering efﬁciencies and the determination of

integrated luminosity for each ﬁlter are included in Appendix A.

50

Table 4.1: Description of triggers and associated integrated luminosities.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L1 L2 L . i
Level 1 Trigger Threshold Level 2 Filter Threshold “31:9: ‘3'
(GeV) (GeV)
EM_1_2_GAM 2.5 GAM_6_ISO_GAM 6 13.644
EM_1_7_GAM 7 GAM_14_ISO_GAM 14 225.29
EM_1_HIGH 14 EM1_GIS 25 14577
EM1_GIS_HIGH 40 94657

 

4.1.2 Candidate Sample

The standard cuts applied ofﬂine to deﬁne a good photon candidate are :

0 0 S Inl S 0.9 (1.6 S Inl S 2.5) in the central (forward) regions. These cuts define

the region of phase space which will be measured in the cross sections.

0 0 < IIETAI S 9 (16 S IIETAI S 25) in the central (forward) regions. The quantity
IETA is the integer index of each 0.1 x 0.1 calorimeter tower in pseudorapidity

(see Figure 3.10). This cut restricts the candidates to be well within calorimeter

boundaries.

- vertex 2 position IZm

| < 50 cm to retain the beneﬁts of projective geometry.

0 Exclude candidates within 10% of a module edge in 4) (CC only). Energy

reconstruction near these edges is not well understood.

51

no track pointing to the candidate from any found vertex.

EEM
E

 

> 0.96 , where EEM (Em) is deﬁned as the EM (EM + hadronic) energy in a

tot
core cone of 0.2 around the candidate. This rejects hadron showers, which leave

signiﬁcant energy past the electromagnetic layers of the calorimeter.

[ET-(R = 0.4) —ET(R = 0.2)] < 2 GeV where R = A/Ar]2 + A1112 and the ET
within a cone of radius R refers to the sum of EM and hadronic layers. This

isolation requirement rejects most neutral mesons, which are typically part of a jet

and therefore are accompanied by additional energetic particles.

H-matrix 12 < 150. The H-matrix algorithm is a measure of shower shape in the

calorimeter, and uses the total energy, energy deposition in each layer, each energy
in a 6x6 array of cells in EM3, and the vertex 2 position as 41 separate,

characteristic observables of a Shower. These are combined in a covariance matrix

N
1 ,, - ,, _
Mij = IT, 2 (x, -xi)(xj -xj) (4.1)

n=l

where x? is the value of observable i for candidate n and 3c,- is the mean value of

the observable i for a sample of “idea ” electromagnetic showers (test beam and

52

Monte Carlo electrons were used to tune the matrix). A x2 distribution

x2 = 2(xf—£,)H,j(xf—ij) (4.2)
it

(H = M.1 ) can then be formed to measure how well each candidate compares to
the expected shower shape. An illustration of the H-matrix discriminating power
between 25 GeV test beam electrons and pions is Shown in Figure 4.1 [20]; the

distribution for electrons from a sample of W—r ev decays (~ 25-40 GeV) is

included for comparison. Figure 4.1 demonstrates the effectiveness of a cut at

x2: 150 in selecting electromagnetic showers.

The ﬁrst four requirements are classiﬁed as acceptance cuts; the last 3 are known as the
photon selection cuts, as they provide the bulk of the photon identiﬁcation and
discrimination from backgrounds.

To illustrate the effect of each of these cuts on the data sample, and to Show the
number of events each ﬁlter contributed to the analysis, the number of raw events

satisfying the physics 1] requirement in each region is shown in Table 4.2.

4.1.3 DOGEANT Monte Carlo

In order to calculate cut efﬁciencies and estimate background from neutral mesons,
several different types of simulated (Monte Carlo) events were generated [21] using the

PYTHIA event generator [22]. These were generated including PYTHIA modeling of the

number of events

53

100

 

 

 

 

electrons

80 pions

O w-9ev

 

60

 

40

20

 

Figure 4.1: H-matrix x2 distributions from test beam electrons, test beam pions,
and electrons from W decays.

Table 4.2: Number of events surviving the application of photon cuts.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Filter # before cuts # after # after 8:13;“
(after 11 cut) acceptance track cut cuts
CC 28878 20087 11850 4628
GAM_6
EC 25370 21264 6214 2777
CC 5820 4170 2327 1346
GAM_14
EC 6839 5579 1485 890
CC 79469 56558 27622 13823
GIS
EC 82091 68580 15036 7496
CC 79499 57490 26988 12283
GIS_HIGH
EC 58602 5057 l 9323 3861

 

 

spectator event, and simulated using a DO-Speciﬁc implementation [23] of the GEANT
detector simulation package [24] with fully detailed geometry. In order to model uranium
noise effects, multiple interactions, and “pile-up” (which occurs when a cell is read out
before the calorimeter electronics are fully recovered from energy deposition in a previous
beam crossing) the Monte Carlo was merged with non-zero suppressed zero bias data,
taken without any trigger requirement at Level 0 or above. The combined ﬁles were then
zero suppressed and reconstructed as in the data. The Monte Carlo was put through several
iterations of this overlay process to produce 5-10 times the number of ﬁnal events; this
smooths the effects of noise and multiple interactions for a given number of Monte Carlo
showers. Since the statistical power of the Monte Carlo sample is limited by the number of

actual PYTHIA events generated, however, statistical errors were kept equal to that due to

55

the actual number generated before the overlay process.

Single photon events were generated over the range 10-200 GeV (segmented into four
parts for roughly equal statistics in each), resulting in a falling ET spectrum closely
resembling the data. A large sample was generated for background studies (Chapter 5) in
which only the region around the photon was simulated in DOGEANT to save processing
time; a smaller sample in which the entire event was Simulated was used for efﬁciency and
physics studies. A sample of full W and Z events was also generated for comparison to
data.

As a check on the ability of the Monte Carlo to model the data, a sample of electrons
from Monte Carlo W -—) ev events was compared to electron candidates from data
W—) ev events taken from the direct photon trigger sample. The results are shown in
Figure 4.2 (CC) and Figure 4.3 (EC). Shown are the EM fraction, the H-matrix x2, and the
isolation ET; the Monte Carlo (histograms) Show good agreement with the data (points),
though the isolation ET distribution has a slightly larger tail in the data than in the Monte

Carlo.

4.2 Acceptance

The acceptance A corrects for the effects of the IETA, vertex position, and o module cuts
on events with physics 1] in the central or forward range.

The Run 18 vertex 2 distribution is shown in Figure 4.4. This distribution was found to
be stable during Run 1B and between different photon triggers, and is described by a

Gaussian peak of mean -0.3 cm and width 28.5 cm. The vertex position acceptance was

56

 

 

 

 

 

 

 

 

 

 

 

 

 

£1 _ £1 —
§ — E :
or: iii L
E; E;
'- 111411111 _ ...- L*:‘:_:Jllll
0.94 0.96 0.98 1 1.02 0 50 100 150 200
EMFraction x'
i
m .
a: T
E : i
z P—
L +++
r
r + ++
.— +
L- lll11111l111111111111
—1 0 1 2 3 4
lsolatiorrli1

Figure 4.2: Comparison of data (points) and Monte Carlo
(histograms) W electrons in the central region.

57

 

 

 

 

 

 

 

 

3 : 3
§ L 5’
111 E m
‘g :— ii
2 §_ 2
0.94 o 50 100 150 200
x)
3
a
>
In
:3
E
O
2

 

 

 

11JJIILLL

— 1 0 1 2 3 4
Isolation IiT

 

Figure 4.3: Comparison of data (points) and Monte Carlo
(histograms) W electrons in the forward region.

58

 

Events

_IIIlllllIl—LIFTIIIIFIIIllllllII—IT

 

 

 

lllllllillllllll ll

— 100 —50 O 50 100
Vertexz (cm)

 

Figure 4.4: The Run 1B vertex 2 distribution.

determined simply by measuring the number of events lost from the vertex distribution
after the cut. This was measured separately for all four ﬁlters, and was found to be very
consistent; the acceptance for this cut using all four ﬁlters is 0.913 with a negligible error.

The IETA acceptance was measured using the Owens, et.al. Monte Carlo program [25]
to generate photons with the theoretically modelled 1] distribution in each region. Each
event was smeared with a Gaussian vertex distribution to mimic the data distribution, a
50 cm cut was placed on the vertex position, and the calorimeter IETA of the resulting
candidates was calculated geometrically. While this should give the appropriate
acceptance for real photons, the calculation was also done assuming a ﬂat distribution in

physics 1], and the difference taken as a systematic error. The resulting IETA acceptance is

0.917 i 0.007 (0.930 :1: 0.007) in the CC (EC).

59

Combining the vertex and IETA acceptances with the exact 11) module acceptance of

0.80 in the CC, the total acceptance is then A = 0.670 i 0.007 (0.849 i 0.007 ).

4.3 Cut Efﬁciencies

4.3.1 Tracking Considerations

By vetoing candidates with a track, real photon candidates are lost in two ways:

' A photon might convert to an e+e' pair in the material in front of the CDC/FDC;

the fraction of such conversions whose track is accurately reconstructed will be

removed from the sample.

0 A charged track produced as part of the underlying event might overlap the photon
closely enough to lie within the tracking road, in which case the photon will be

removed from the sample.

The effect of the charged track cut is considered in detail in Appendix B; the total

efﬁciency due to both sources is found to be e k = 0.828 i 0.013 (0.554 1: 0.030).

[70C

4.3.2 Selection Cuts

Selection cut efﬁciencies were determined using full Monte Carlo photon events which
were put through the trigger simulator, and are shown in Figure 4.5. The efficiency dips at

very low ET due to the Hmatrix and EM fraction cuts, as the Shower shape changes and the

60

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a .
C1, 1' ............................................................................................................
g _ 0;868 -; 0 0002E,-exp— (0 24E,— 0 008)
t 1 ,_... .......................................................
LIJ '- 3
r- . . . . E . . . .
0.9 ... ........ l ..,- ........ .§,,,,. .......... ,,.,. .......... :, ..........
Z ‘ “LI—LC " 3- I‘ i :ﬁ—ii E E
_ - 1T2! 21* 737 a w : : :——
0.8 p”... _..........a_...........}..........: ..... +..:...........:\..........g ........... : .......... 3 ..........
r- ! ' ' E I I p—jy—4 I
0.7 L ...... ...L .......... ..........
C ‘ ' §CC Cut Efficiency;
0'5 ..‘- .......... ..........
" I 2 2 I I Z Z 2 3 I
i- 1 . - . .
0.51-11l111111111L11L11111111111111111l11111
0 20 40 60 80 100 120 140 160 180 200
<E,> (GeV)
5‘
r: 1.1
.93
.9
t 1
LL!
0.9
0.6
0.7
0.6
t- . . . .
0_5b11111g1111111111111111111111l
O 20 4O 50 80 100 120 140
<E,> (GeV)

Figure 4.5: Selection cut efﬁciencies measured using PYTHIA Monte Carlo
photons, and corresponding ﬁts.

roughly constant contribution of noise from the PH] layer becomes an increasingly larger
fraction of the total energy. The isolation cut causes a fairly linear decrease with

increasing ET, as outlying edges of the shower become more energetic relative to the ﬁxed

2 GeV cut. The selection cut efﬁciencies were thus ﬁt to the form

—- bE
a—e( ”Chara, (4.3)

with the values of the parameters a, b,c, and d as shown in Figure 4.5.

61

Because the global running data were taken over a range of instantaneous luminosities,
the effect of instantaneous luminosity on the selection cut efﬁciencies was studied using
full event Monte Carlo overlaid with SE30 and 19E30 zero bias data. Initial studies using
Monte Carlo W electrons overlaid with SE30, 14E30, and 19E30 zero bias data indicated
that the selection cut efﬁciency dropped linearly with increasing instantaneous luminosity,
resulting in a 10-20% lower efﬁciency at the highest luminosities. Since the instantaneous

luminosity of the data set was peaked at ~ 6E30, however (Figure 4.6), with only a small

 

 

 

 

 

 
  
  

 

 

 

 

 

 

 
 

 

 

£9 -— Mean 6.861 :3 I Mean 7.669
5 : RMS 2.526 5 : nus 3.548
> _ > .T'
Lu _ m :

:— EM1_GIS E— EM1_GIS_HIGH

:_ E-

: E

g :

' 1 4 1 1 1 1 1 1 1 1 1 1 J 1 : 1 1 1 1 1 1 1 1 I 1 1 L 1 1 1 1

O 5 10 15 20 O 5 10 15 20

Instantaneous L (xE30) Instantaneous L (x1330)

Figure 4.6: Instantaneous Luminosity proﬁles for the EM1_GIS (left) and
EM1_GIS_HIGH (right) ﬁlters.

tail extending to the highest luminosities, the average efﬁciency was expected to be close

62

to that at SE30, allowing selection cut efﬁciencies to be determined using Monte Carlo
with only the SE30 overlay.

This expectation was checked using the photon Monte Carlo: for several ET bins
above 30 GeV, the 5E30 and 19E30 efﬁciencies were measured and used to deﬁne a linear
parametrization of the efﬁciency vs. luminosity. Using the instantaneous luminosity
proﬁles of the EM1_GIS ﬁlter (or EM1_GIS_HIGH, depending on the ET of the bin), a
weighted efﬁciency was then constructed for each ET bin by summing over the luminosity
bins, weighting each with the parametrized value of 838,. The resulting weighted
efﬁciencies were found to agree with those derived from the SE30 Monte Carlo to within
2.5% or less; an uncertainty of 2.5% is therefore placed on the ﬁtted selection cut
efﬁciencies derived from the 5E30 Monte Carlo.

To cross-check these efﬁciencies, a sample of Z events was selected and a
background—subtracted selection cut efficiency calculated for Z electrons between 30-50
GeV. The resulting efﬁciencies were 0.865 i0.011 (0.902 i0.018) for electrons with

mean ET of 42.7 (36.4) GeV. The ﬁtted efﬁciencies evaluated at these points,

0.859 :t 0.021 (0.880 i 0.022) , are in good agreement with the Z efﬁciencies.

Chapter 5

Background Estimation

5.1 Introduction

The main background to the direct photon signal comes from jet ﬂuctuations. While most

jets consist of many particles, and are thus easily distinguishable from a single photon, a

small fraction (10'3 - 10'4) fragment such that a single particle carries most of the
momentum of the parent parton. Several neutral mesons decay to produce two or more

photons, including the lightest (and therefore most commonly produced) neutral meson,

the no, which decays to two photons with a branching ratio of 99% [4]. Thus non-direct

photons are common in hadronic collisions, and because jet production rates are a factor

of 103 larger than that of direct photons, the number of jets which fragment to a single
meson and then decay to photons - referred to as electromagnetic (EM) jets - are
comparable to the level of direct photon signal. Because of this, the level of background in

the direct photon data sample must be carefully measured and subtracted.

63

64

Table 5.1: Neutral meson decays to photon states.

 

 

 

 

 

 

 

 

 

Particle (($37?) decay products branching ratio
1:0 0.135 w 0.99
11 0.547 w 0.39
11 0.547 31:0 0.32
n 0.547 n°n+1r 0.23
KOL 0.494 211° 0.31
(0 0.781 1107 0.09

 

 

 

 

 

Further complicating matters is the fact that, at the energies considered in this analysis
(above ~10 GeV), the individual photons from meson decays cannot be separately
identiﬁed given the spatial resolution of the D0 calorimeter - the decay products coalesce

into a single shower which is difﬁcult to distinguish from a single photon. This can be

seen by considering that the two photons arising from a 1:0 decay have an opening angle

distribution peaked at the minimum [26]
0 - = — (5 .1)

which for a 10 GeV 1:0 results in a minimum separation of 2.5 cm at the ﬁrst layer of the

D0 calorimeter. Since a typical cell size in the calorimeter is ~7 cm, it is clear that most no

decays will not be identiﬁable as two distinct photons.

While Table 5.1 identiﬁes several neutral mesons which decay to photons, the no and
11 are the main particles considered in this analysis, as they are the two neutral mesons

which are most commonly produced. Other backgrounds are expected to be further

65

suppressed in the data sample due to small branching ratios (e.g., the (1)) as well as the

photon selection cuts. For example, while a signiﬁcant fraction (~30%) of K? mesons

decay to 216’, at lower values of ET the four resulting photons are sufficiently spread out

that they usually fail the photon selection cuts. At higher ET the showers coalesce and the

passing rate is higher; however, due to the long lifetime of the K2 ,

at higher E;- a

signiﬁcant fraction do not decay before they reach the EM calorimeter, and thus create a
hadronic shower which also fails the photon cuts. As a result, the expected ratio of K? to

11:0 in the data sample is less than 5%.
5.2 Background Estimation Techniques

5.2.1 Method

While background subtraction on an event-by-event basis is impossible, there is a
statistical method which exploits the difference between single photons and multiple
photon clusters as they traverse the detector. At the energies considered in this analysis,

photons begin showering in the calorimeter by converting to an electron-positron pair

(7 —-) e+e') near a nucleus. The probability for this to occur is dependent on the amount of

material the photon passes through; the deeper into the calorimeter the photon gets, the

more likely a conversion becomes.

Consider the probability PZ—m that a single photon will convert in or before the ﬁrst

66
calorimeter layer. For a no meson decaying to two photons, the probability that at least one

of the photons will convert is then greater than in the single photon case:
2
PTEIMI = ZPIYE‘MI -(PIIM1) (5-2)
In other words, multiple photon showers are more likely to begin earlier in the calorimeter,

since there are more independent chances for a photon to convert early. As an example of

this, consider Figure 5.1 [2], which shows the clear difference in the fraction of total

 

350 H —— MC Photons
........... MC Pizeros

300 -*

250 ~

200 ;

 

 

.
......

 

 

O 1 J 1 l 1 1 1 l 1 l 1 l 1 l 1 I 1 l
O 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25
EM 1 / E

 

Figure 5.1: Comparison of EM] energy fraction left by 10 GeV MC photons and

0

1: ’s.

67

energy left in the ﬁrst electromagnetic calorimeter layer (EMl) by single Monte Carlo
photons and no’s. While a signiﬁcant fraction of photons leave little or no energy in BM],

relatively few no’s do so.

This difference provides discriminating power with which to estimate the fraction of
background present in the direct photon candidate sample. The data distributions can be
compared to those of Monte Carlo photons and neutral mesons to determine the relative
fraction of each present in the data.

As a discriminant variable, we use the logarithm of the fractional EM] energy

E
log(EMl/E) = loglO(EE—MI) (5.3)
total
with the denominator Em“, calculated as the sum of the layers:
5
Em = 2 E. (5.4)

n = l
(where n = 5 represents the PH] layer). This quantity emphasizes the region of small

fractional EM] energy where the greatest difference between photons and mesons is seen.

5.2.2 Background Monte Carlo

Previous analyses [16] [2] used single 11:0 and 11 mesons, generated at discrete energies,

D¢GEAN Ted, and with the appr0priate noln production ratio, as a model of the EM jet
background. While this model provided the primary constituent of an EM jet, and
reproduced the data EM] distributions fairly well, it was found that the single particles did

not recreate some other distributions such as the isolation ET [16]. In general, the Monte

68

Carlo mesons were found to be more isolated than data showers, which is to be expected
since real jets produce a spectrum of particles, and in EM jets, the meson that carries most

of the momentum is usually accompanied by softer particles. Further evidence that a more
detailed background model was desirable came from the fact that when considering the n0

and 11 backgrounds separately, comparison to data favored the 1] even though the n0 is

expected to be produced and selected more often. Since the 11 Monte Carlo included the

3n0 and n0n+n' decay states as well as the W state, this indicated a preference for more
complex, multi-particle showers.
In order to provide a better background model for this analysis, a large number of

PYTHIA QCD dijet events were generated in a falling ET spectrum over a range similar to
the Monte Carlo photons (Section 4.1.3). Just as in the data, these events were then

“ﬁltered” to ﬁnd EM-ﬂuctuated jets: at the particle level, n0 and n mesons were selected

by requiring

. [ET(R = 0.4) —ET(R = 0.2)] < 2 GeV where R = Janz + 11112 around the

meson
0 No charged particle within a cone of R = 0.2

0 Energy within a cone of R = 0.2 > 60% of parent parton energy

Only events passing this ﬁlter (~0.l-0.01%) were then run through DGGEANT; in

addition, only a cone of R = 1.0 around the parent meson was simulated to save

69

processing time.

It is important to note that even with the particle level filter, a major constraint on
Monte Carlo production was the availability of processing power. This has also been a
factor in the past, and is in fact one reason why previous analyses were limited to single
particle Monte Carlo. The Monte Carlo events used in this analysis were generated on a
farm of DEC 3000/400 Alpha workstations at the Supercomputer Computations Research
Institute in Tallahassee, FL; a fully detailed DﬂGEANT event required approximately one
hour of CPU time to generate. Also, while the particle level ﬁlter was intended to avoid
unnecessary simulation of events which would fail the offline cuts, it was necessarily
loose enough to ensure a reasonably realistic EM jet sample. As a result, the fraction of
DQGEANTed EM jets which passed the photon cuts (and could therefore be used in
modeling the data sample) was still only about 30%.

As in the case of the photon Monte Carlo, events were overlaid with non-zero

suppressed zero bias data to add detector and multiple event effects.

5.2.3 EMl Calibration

Because this method of background estimation relies on accurate modeling of the data by
Monte Carlo, it is important to verify that the Monte Carlo reproduces the data
distributions. Such agreement was demonstrated in Section 4.1.3; however, the
log(EMl/E) distributions must also be examined.

These distributions are shown in Figure 5.2 for W electrons from data and from Monte
Carlo. While the central region Monte Carlo (left) shows good agreement in shape and

peak with the data, the forward region (right) shows a slight offset - the Monte Carlo

70

 

 

CC + EC

Normalized Events

llllllllllllllllllllllTTlllllllllllllllllllllll

Normalized Events

llIlTrlllIIIIIITTTIIIIIIIIllllllllllllll

 

 

 

 

 

 

 

l l L I I l l 1 cl.“ 1 1 1 1 1 1 l
- 4 -— 3 —- 2 — 1 0 - 2 — 1 0
log(EMl/ETOT) log(EMl/ETOT)

llllllll

 

I
4:.
I
(A

Figure 5.2: Log(EMllE) distributions for W electrons from data (points) and
Monte Carlo (histograms).

showers have a slightly smaller fraction of energy deposited in BM] than the data. This
difference directly affects the background estimation, since a shift in the Monte Carlo
distributions represents a shift in the position of the data between the extremes of the
Monte Carlo jet and photon behavior. To ensure that the Monte Carlo best models the data,
this offset must be corrected.

The reasons for the difference are considered in detail in Appendix C, where it is
determined that the offset is consistent with a difference in EMl sampling weight between
the Monte Carlo and the data. Since the sampling weight is simply a multiplicative factor
applied to the raw energies read out from EM], the Monte Carlo can be properly

calibrated by applying another multiplicative factor to the EM] energy, or equivalently an

71

additive offset to the log(EMl/E) distributions. Using the W electron data, the offsets were

derived separately for the North and South endcap calorimeters, and were found to be
0.147 i 0.013 (North), and 0.094 :1: 0.013 (South) in the log(EMl/E) variable. For

completeness, a very small central region offset (0.014 i 0.005) was also applied.

5.3 Purity Calculation

An example of the log(EMl/E) distributions for central region data, Monte Carlo photons,
and Monte Carlo EM jets between 33 and 39 GeV is shown in Figure 5.3. The Monte
Carlo distributions are binned in 50 bins across the range —4.0 <log(EM1/E)< 0.0 , and
are normalized to the data so that they may be directly compared. Note that in the
log(EMl/E) variable, a value of ~10 indicates 10% of the shower energy deposited in
EMl, a value of -2.0 indicates 1%, etc. The difference in single and multi-photon behavior
is seen in the larger tail of the photon Monte Carlo at left (smaller values of EMl/E), and

the sharper peak in the jet distribution which occurs at larger values of EMl/E.
Using the CERNLIB MINUIT program, a x2 minimization was performed to ﬁt the
data log(EMl/E) distribution as a sum of the photon and background distributions:
Fdam(P, x) = PDy(x) + (1 — P)Dje,(x) (5.5)
where P is the purity of the photon sample (the single parameter of the ﬁt), and x is the
range of log(EMl/E). Fits were performed for 13 separate ET bins in the central region,

and for 10 bins in the forward region. The resulting ﬁt for the central region between 33

and 39 GeV is shown in Figure 5.3; a complete set of ﬁts for both regions is included as

72

 

 

 

 

.3 “711612795 / 45
2 P1 35.6321: 0.0000E+OO
Id 432 0.4671 :1: 0.1566E—O1 ..
5 o 7887 00 data &.... .0.
° : o 6703 CC MC vs 4111' . .-
e r E] 2884 CC MC jets . O . .
Z .0 , D .
F 0"”: D
: ..' [pa '
E ' w B ¢
C] I
~ 0 T F3513] ¢
0.. D +
0 C13
- El

 

 

 

 

 

log(EllEm)

Figure 5.3: Log(EMllE) for Monte Carlo and data between 33-39 GeV in the
central region. The solid line is the MINUIT ﬁt, which results in a measured purity
of 0.467 (P2).

Appendix E.
Prior to ﬁtting, the Monte Carlo distributions were smoothed to reduce statistical

effects. In order to ensure that the data and MC were comparable in E7- across each bin, the
Monte Carlo ET spectra were weighted to match the data E7- spectrum. This had a

negligible effect except in bins where the Monte Carlo was not matched well to the ET bin

73

edges (e.g., near the Monte Carlo generation ET bin thresholds), and in ET bins where
statistics were limited, in which cases it resulted in small (less than ~ 6%) corrections to
the ﬁt result.

The events in the data with large EM I/E (seen at the right edge of the distribution in
Figure 5.3), which are not accurately modeled by the Monte Carlo, are due in part to a
small fraction of candidates which had a track pointing beyond the allowed vertex
reconstruction region, and which impacted on the calorimeter at a far steeper angle than
modeled in the MC. The effect of these events was investigated by ﬁtting the distributions
over only the range from -4.0 to -0.8; no signiﬁcant difference was observed.

For each purity point, the statistical error on the ﬁt given by MINUIT was inﬂated by

Jag—2 of the ﬁt in order to estimate the combined statistical and systematic error on the ﬁt
to the smoothed MC distributions for each point. The change in purity when calculated
with unsmoothed distributions was also added in quadrature to the error on each point, in
order to estimate the effect of limited MC statistics (which are not explicitly included in
the MINUIT error). The purity points, errors, and variation with smoothing and ET
weighting are summarized in Table 5.2 and Table 5.3.

The purity versus ET for the central and forward regions is shown in Figure 5.4. It is

important to note that the purity should be a continuous distribution in E7; it is therefore

reasonable to ﬁt the measured purity points to a functional form. The function

P _ l

— ——Tb (5.6)
1 + a(ET)

was selected, as it satisfies the evident boundary conditions of low purity at low ET and

74

Table 5.2: CC Purity points, variations, and errors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

((5:2) Purity #3::3. Aunsmoothed Ano Et correct 53:31.
10.9 0.1 12 0.307 -0.021 0.065 0.308
13.2 0. 144 0.062 -0.025 0.008 0.067
17.1 0.245 0.148 —0.151 0.001 0.211
22.7 0.395 0.051 -0.048 0.006 0.070
27.2 0.350 0.070 -0.072 0.006 0.101
31.4 0.372 0.043 -0.127 -0.007 0.134
35.6 0.467 0.039 -0.066 0.056 0.077
44.5 0.460 0.044 -0.040 -0.001 0.059
56.8 0.558 0.045 0.001 -0.007 0.045
64.3 0.644 0.052 0.037 0.016 0.063
77.4 0.726 0.042 -0.003 0.025 0.042
93.4 0.826 0.060 0.046 0.005 0.076
1 15.7 0.789 0.040 -0.030 -0.002 0.050

Table 5.3: EC Purity points, variations and errors.

(GEg‘Ir) Purity gﬁﬂggr Aunsmoothed Ano Et correct 53::
15.3 0.482 0.056 -0.023 0.025 0.061
22.7 0.520 0.060 -0.092 0.016 0.1 10
27.1 0.603 0.078 0.017 0.006 0.080
31.4 0.614 0.032 -0.012 0.010 0.034
35.6 0.571 0.032 -0.022 0.013 0.039
44.0 0.606 0.032 -0.013 0.023 0.034
56.7 0.695 0.037 -0.031 0.029 0.049
65.6 0.812 0.041 0.030 0.024 0.051
80.5 0.886 0.052 0.005 0.022 0.053
101.8 0.957 0.123 0.092 -0.043 0.153

 

 

 

 

 

 

 

75

 

 

 

 

 

 

 

 

 

9.3 _ .2 _
E 1 '
h
5"- 31 F-
0.0 1- 0.0:-
p .
D L .
0.0 — 0.6:- ’y/
0.4 ~ 0.4:-
0.2 ~ —— 0.2;
b A .
/
0 " o 1—
I
11 1 1 .11#111 111.1 . 1 1.1...1
6 7 0910 20 30 40 50607000100 5 7 5910 20 30 40 50507030100
mew) mew)

Figure 5.4: Purity vs. ET for the central (left) and forward (right) regions.

high purity at high ET. Further, one would expect the data set to be a sum of two falling

cross sections (photon and EM jet) of rough form a(ET)_b. The purity is then the ratio of

the photon cross section to the sum, as described by Equation 5.6. The result of the ﬁt is
shown along with the points in Figure 5.4.

While this choice of function is reasonable and physically motivated, and describes the
data well, it remains an estimate of the shape of the purity curve. In order to estimate the
uncertainty due to the choice of function, the alternate forms

—(aET+ b)
e

P = 1 — (5-7)

76

( the form used in the Run 1A analysis) and

P = a + blogET (5.8)

(a straight line fit) were studied. Each gave a very similar xZ/dof to the nominal form,
and resulted in a similar curve through most of the ET region, but varied signiﬁcantly at

the extremes of ET (see Figure 5 .5). The total uncertainty on the purity ﬁt was calculated

 

 

   

 

 

 

 

 

 

.9 1 — .b 1 — _

E I .> E 1-
8 ~ 8 1
4: T— .r: I.
m 0.6 _ but 06 _
0.4 ‘- 0.4 l
1— 1—
0.2 :- 02 :_
- r

O —4111’ l 1 1111111 0 11111 1 11111111
10 102 10 102
ET(GeV) El.(GeV)

Figure 5.5: Variations in the CC (left) and EC (right) purity ﬁts, using the nominal
(solid), exponential (dotted) and straight line (dashed) fit functions.

as the error on the fit to the nominal form, augmented in quadrature by the difference

between the nominal and the two alternate forms. However, because this ﬁt dependence

77

affects the lowest ET points by a large fraction of their value, and because the low ET
region suffers from a lack of well determined purity points, it is difﬁcult to extrapolate
into this region. We therefore restrict the use of the purity to values of ET above 15 GeV,
corresponding to the first measured point in the EC and the ﬁrst statistically signiﬁcant
point in the CC.

Additionally, for the forward region, the uncertainty due to the EMI offset was
estimated by varying the nominal North & South offsets by i1 0 , and ﬁtting the purity for
each case. Since an increase or decrease in the offset directly shifts the purity points up or

down, this results in an overall shift of the purity function (Figure 5.6). The uncertainty

due to the offset was calculated as

P —P + P —P
Goff“; = I +10 nomlzl nom -lol (59)

 

where the P are the purity functions (as in Equation 5.6) for each case. This was then
added in quadrature with the other uncertainties to arrive at the ﬁnal uncertainty in the

forward region.

78

 

.0
on

Photon Purity

.0
\1

0.5

0.4

0.3

O
O)
IIIUIIYIIIT'IIIUIIIIT‘TYUII'YIIIYYIIII

 

.‘h. "
..‘. o
0 2 v '
, . ‘a
a

0.1

VWTIYIHF.
‘.

 

 

0 l 1 1 l l l I 1 I 1 l l l l

6 7 8 910 20 30 40 50 60 7080 100

Edam

 

Figure 5.6: Effect of a plus 16 (dotted) and minus 10' (dashed) shift in the EC EMl
offset, relative to the nominal (solid) purity curve.

Chapter 6

Cross Sections and Theoretical Com-
parisons

6.1 Cross Section Calculation

The differential cross section for isolated direct photon production (measured as a function

of photon ET, for speciﬁc regions of photon rapidity), is given by

do _ NP
dE _ LAETAnAesele

 

 

(6.1)

8

trig track

where

0 N is the number of photon candidates in each bin of ET and 11

0 P is the photon purity (as determined in Chapter 5)

0 L is the integrated luminosity over which the data were taken

79

80

° AET is the transverse energy range spanned by each bin

0 AT] is the rapidity range spanned by each bin (both the central (0 S Inl S 0.9) and

forward (1.6 S In] S 2.5 ) region measurements cover a range of An = 1.8)
0 A is the geometric acceptance for photons (as calculated in Chapter 4)

0 838, is the efﬁciency of the photon selection cuts (as calculated in Chapter 4)
am“ is the efﬁciency of the charged track veto (as calculated in Chapter 4)

Note that there is an uncertainty associated with the ET binning due to the
electromagnetic energy scale, which has a measured uncertainty in the central region of
approximately 0.2% [19]. Since the direct photon falls steeply (of order ET'S), the
resulting error on the central region cross section is taken as 1%. While the forward
calorimeter is expected to perform equally well, its calibration has not yet been veriﬁed to

the same precision, resulting in a 4% energy scale uncertainty on the forward cross

section.

Using the components of Equation 6.1 as described previously, we can form the
central and forward region cross sections; these are plotted versus photon ET in Figure 6.1.
The data points and errors are summarized for the central region in Table 6.1 and for the

forward region in Table 6.2. Statistical errors on each point were calculated as the Poisson

error J1?! . Systematic uncertainties from each component were added in quadrature to

arrive at a total systematic uncertainty (plotted on each point in Figure 6.1 as horizontal

81

 

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20 40 60 80 100 120

f 40
E, (GeV)

Figure 6.1: Inclusive isolated photon cross sections in the central (top) and forward
(bottom) regions.

82

Table 6.1: Central region cross section points and errors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ET bin Mean E Cross Section Statistical Purity Systematic
(GeV) T (pb'l) Error (%) Error (%) Error (%)
15-18 16.3 0.161E+04 6.2 22.3 23.3
18-21 19.3 O.779E+03 9.7 18.3 19.6
21-24 22.4 O.343E+03 3.8 15.5 16.9
24-27 25.4 O.198E+03 5.4 13.2 14.8
27-30 28.4 O.133E+03 6.9 11.2 13.1
30-33 31.3 O.775E+02 9.4 9.7 11.9
33-36 34.4 0.539E+02 1.5 8.4 10.8
36-39 37.4 O.388E+02 1.8 7.4 10.0
3942 40.4 O.27OE+02 2.2 6.5 9.4
4245 43.4 O.206E+02 2.6 5.9 9.0
45-48 46.4 0.150E+02 3.1 5.4 8.6
48-51 49.4 0110sz 3.7 4.9 8.4
51-54 52.4 O.824E+01 4.3 4.6 8.2
54-60 56.8 O.550E+01 1.5 4.2 8.0
60-65 62.3 0.37213+01 2.0 3.9 7.8
65-70 67.4 O.244E+01 2.6 3.7 7.7
70-75 72.4 0.171E+01 3.1 3.6 7.7
75—80 77.4 0.125E+01 3.7 3.6 7.7
80-85 82.5 O.967E+OO 4.3 3.7 7.7
85-90 87.4 O.731E+00 5.0 3.9 7.8
90105 97.0 0.444E+00 3.8 4.4 8.1
105-120 111.4 O.209E+OO 5.6 5.4 8.7
120-150 132.3 0.829E-Ol 6.5 7.0 9.8

 

 

 

 

 

 

 

Table 6.2: Forward region cross section points and errors.

83

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E T bin Mean Cross Section Statistical Purity Systematic
(GeV) ET (pb'l) Error (%) ”123' Error (%)
15-18 16.3 O.217E+04 8.0 16.2 18.7
18-21 19.2 O.961E+03 12.6 14.0 16.8
21-24 22.3 0.461E+O3 4.6 12.3 15.4
24-27 25.3 O.243E+03 6.6 11.0 14.4
27-30 28.4 O.139E+03 9.0 9.9 13.6
30-33 31.5 O.865E+02 11.6 8.9 12.9
33-36 34.4 0.510E+02 1.9 8.2 12.4
36-39 37 .4 0341sz 2.4 7.5 12.0
39-42 40.4 0235sz 2.9 7 .0 11.7
42-45 43.4 O.165E+02 3.5 6.6 1 1 .4
45-48 46.4 0.107E+02 4.4 6.3 11.3
48-51 49.4 0.656E+01 5.7 6.1 11.2
51-54 52.4 0.533E+01 6.4 6.1 11.1
54-60 56.7 0.318E+01 2.3 6.1 11.2
60-66 62.7 O.164E+01 3.3 6.4 11.3
66-72 68.8 O.907E+OO 4.5 6.8 11.6
72-7 8 74.9 O.493E+OO 6.2 7 .4 11.9
78-84 80.8 0.325E+00 7 .7 7.9 12.3
84-93 88.1 O.137E+00 9.9 8.6 12.8
93-102 97.2 0.713E-01 13.9 9.5 13.3
102-120 109.0 0.305E-01 15.2 10.5 14.1
120-150 129.9 0.447E-02 31.6 11.9 15.2

 

 

 

 

 

 

 

84

bars); as an example, the systematic errors on the central and forward 39-42 GeV bins are

shown in Table 6.3.

Table 6.3: Contributions to the total systematic error on the 39-42 GeV cross section bins.

 

 

 

 

 

E scale
41%) (.70) 2.41%) 8%" L(%) P(%) Totat(%)
CC 1.0 1.0 3.5 1.6 5.4 6.5 9.4
EC 0.8 4.0 3.4 5.4 5.4 7.0 11.7

 

 

 

 

 

 

 

 

 

It should also be noted that the results of this analysis differ from those found in
previous D0 analyses [16][2][3]. The differences, which are mainly due to improvements

in the modeling of the detector and the EM jet backgrounds, are discussed in Appendix D.
6.2 Comparison with Theory

Also shown in Figure 6.1 is a next-to-leading order prediction from Baer, Ohnemus, and
Owens [25] using the CTEQ4M parton distributions [31]. For this calculation both the

renormalization and factorization scales were set to the ET of the photon. The Dﬂ photon
and jet energy resolution functions were applied to the theory; this resulted in a negligible

change. Also, an isolation cut was applied at the parton level to match that applied to the

data.

85

In order to show more clearly the comparison between data and theory, the quantity

Data — Theory
Theory

 

(6.2)

is plotted in Figure 6.2; statistical errors are indicated on the points. The grey band
indicates the combined systematic errors, some elements of which (such as the luminosity)

are correlated across the ET range.

In the central region, the data lie slightly above the theoretical prediction, but are
consistent given the systematic error. In particular, the overall shape of the distribution
agrees well, although a slight increase in cross section is seen in the very lowest points.

Since the systematic error (mainly from the purity) becomes large at low ET, this shape

deviation is not necessarily signiﬁcant.
In the forward region, the data are consistently higher than the theoretical prediction,

especially in the lowest ET bins where the data are almost a factor of two above the

prediction. Also, a difference in shape between data and theory is evident in the region
below ~ 40 GeV.

In order to check the effect of ﬁtting the purity points to a functional form, the cross
sections were also calculated using the same coarse binning as in the purity determination
- each cross section point was then adjusted by the corresponding purity value for that bin,
rather than the ﬁtted value. The resulting (Data-Theory)/Theory plots are shown in Figure
6.3. The systematic and statistical uncertainties are plotted separately on each point; the
systematic uncertainty is the error on the purity in each bin (see Figure 5.4), augmented in
the forward region by the EMI offset uncertainty (Equation 5.9). A comparison of Figure

6.2 and Figure 6.3 indicates no signiﬁcant difference in shape, and in particular

86

 

 

 

 

 

 

 

 

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Figure 6.2: (Data-Theory)/I‘heory for the central (top) and forward (bottom)
regions

—O.5

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-1

Figure 6.3: (Data-Theory)/'I'heory using purity detemiination bins.

87

 

 

 

 

 

 

 

 

t I11|_<0-9 DQPreliminary
: NLO QCD, CTEQ4M, u=E¥

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88

demonstrates that the low ET excess in the forward region is not an artifact of the purity ﬁt.

A low ET increase in cross section over that predicted by theory has been seen by the
CDF collaboration [32] in a measurement limited to the central region only
(0 S Inl S 0.9 ). The CTEQ collaboration, in an analysis of direct photon results from that
and past experiments [33], concluded that there is a shape difference between experiment
and theory which cannot easily be accounted for in the parton distribution functions.
Recent theoretical work has included attempts to account for this apparent excess through
soft gluon emission [34].

On the other hand, some theorists argue that the current theory is compatible with
experiment given the uncertainty due to the choice of theoretical parameters [13], or that
theoretical problems in implementing the isolation criteria may play a role [35]. In Figure
6.4 we show the variation of the theoretical cross section with a reasonable change of the
renormalization and factorization scales, to that of twice or one half the value of the

photon ET. The resulting shift in the cross section is less than 10%, and is ﬂat over the ET

range; however, it must be pointed out that the two scales were varied in tandem, while
some of the effects noted in [13] arise from separate variation of the scales. It should also
be noted that the imposition of an isolation requirement must be matched to the particular
experiment to which the theory is compared - therefore, theoretical problems in
implementing the cut may have different effects when comparing to different experiments.

While it is beyond the scope of this thesis to present a detailed examination of these
and other theoretical issues, it is important when comparing data and theory to consider

that the theoretical treatment of direct photons is an area of much current debate and

89

 

 

 

 

 

 

 

 

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Figure 6.4: Variation of the theoretical prediction with a change in scale for
the central (top) and forward (bottom) regions.

90

effort. To illustrate this, we consider the effect which the more recent CTEQ4M parton
distribution functions have on the theoretical prediction, compared to the CTEQ2M
distributions which were used in comparing previous DO results to theory. The difference

in cross sections is shown in Figure 6.5, plotted as

Theory(CI'EQ4M) — Theory(CFEQ2M)
Theory(CTEQ2M)

 

(6.3)

and it is evident that the newer PDFS have some effect on both the shape and

normalization of the cross section, increasing it signiﬁcantly at low ET. In addition, since

the version of the Baer, Ohnemus, and Owens program used in this analysis has different

heavy quark contributions and uses a different method of determining as than in the

version used in previous comparisons [36], we consider in Figure 6.6 the total change in
the calculation (PDFS and version) from that used to compare to the DO Run 1A result,

plotted as

Theory(new) — Theory(old)
Theory(old)

 

(6.4)

A shift of ~ 15% is observed fairly uniformly across the ET spectrum. While these changes

are clearly the result of reﬁnements of the theoretical calculation, they indicate the level of
precision currently achievable in our effort to measure direct photon production and derive

thereby a better understanding of strong interactions.

91

 

 

 

 

 

 

 

 

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_O.5 E 1 1 1 I 1 1 1 I 1 1 1 I 1 1 1 I 1 1 J I 1 1 1 I 1 1 l I 1
0 20 40 60 80 100 120 140

8,? (GeV)

Figure 6.5: Comparison of the theoretical prediction with CTEQ2M and
CTEQ4M PDFS.

92

 

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0
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O
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Figure 6.6: Change in the theoretical cross sections from that used in Run
1A.

Chapter 7

Photon + Jet Rapidity Correlations

7 .1 Introduction

The preceding chapters have described a detailed analysis of the Run 1B direct photon
sample, including the sample’s purity. Following this analysis comes the ability to use the
sample to investigate more than simply the total rate of direct photon production. Of
particular interest is the content of the rest of the event: how many jets are produced? How
are they distributed kinematically? The advantages inherent to the inclusive direct photon
measurement - an unambiguous ﬁnal particle, measured extremely well - also provide a
good anchor against which to compare the rest of the event. Unlike dijet production, for
example, in which jet measurement uncertainties cause ambiguities regarding which was

the leading (highest ET) jet (thereby muddying the associated kinematics), direct photon

events have a clearly identiﬁed object against which are balanced one or more jets,

typically in the opposite hemisphere of the event.

93

94

The following analysis investigates the event structure of direct photon events using a
subset of the Run 1B data. While limited in scope, it indicates the type of study which can

be done more precisely using the techniques and experience from the Run 1B inclusive

analysis.

7 .2 Rapidity Correlation Measurement

7 .2.1 Motivation

As the dominant method of direct photon production at the Tevatron is that of qg —-) q'y
(QCD Compton Scattering), one expects that the gluon distribution of the proton will
affect not only the rate of direct photon production, but the associated kinematics. This
effect can be appreciated in the following way: consider the collision of two partons which

create the leading order signal of one photon and one jet (Figure 7.1). If the partons are of

Figure 7.1: Diagram of the ﬁnal state topology when colliding partons have similar
(left) or very dissimilar (right) momentum fractions.

95

equal momenta, the system retains its center of mass back-to-back nature. If one parton is
of much greater momenta than the other, the system is boosted, as the more energetic
parton overwhelms the softer one, and the ﬁnal state objects tend to the same side of the
event. When one ﬁxes the angle of the photon, then, one can probe a range of parton
momentum fraction combinations by looking at the relative distribution of the leading jet.
Since gluons typically carry much less of the momentum of the proton than do quarks, one
expects that in direct photon production unequal momentum combinations will dominate,
and the ﬁnal state system will tend to be boosted in the direction of the incoming quark.
Also, one might expect that beyond leading order, the production of additional jets
may restrict the phase space available to the leading jet, affecting its angle. Similarly, the
production of soft gluons from fragmentation or color coherence effects may affect the
phase space of the leading jet. It is therefore interesting to examine the correlation in
rapidity between the photon and the leading jet, in order to conﬁrm the expected event

structure and to test the precision with which NLO can model it.

7.2.2 Data Selection

A sample of photon candidates was selected using the EM1_GIS_HIGH filter, and the

standard photon cuts were applied, along with an additional cut on missing ET:

|Zm| < 50 cm

0 Exclude candidates with 10 S IIETAI S 15

0 Exclude candidates within 10% of a module edge in 6 (CC only).

96

0 Missing ET< 20 GeV

0 no track from any found vertex

EM

 

> 0.96

to!

- isolation cut: [ET(R = 0.4) — ET(R = 0.2 )1 < 2 GeV

H-matrix x2 < 150

The photons were required to have ET above 45 GeV in order to select a region where the

photon purity is enhanced. The sample was further subjected to the “golden” photon cut,
which requires less than 1% of energy deposited in the EMI layer, and which is expected
to increase the purity of the photon sample since multi-photon backgrounds are, on
average, expected to shower earlier than direct photons. In addition to the above cuts on

the photon, standard jet quality cuts were applied to the leading jet:

0 E9“ > 2OGeV

0 At least 5% but not more than 95% of jet energy in the EM layers

0 No more than 40% of jet energy in the coarse hadronic layers (to prevent lost

energy due to punch-through)

- Ratio of highest to next highest energy calorimeter cell < 10 (to eliminate the

97

effects of spurious signals)

7 .2.3 Technique and Candidate Sample Behavior

The sample was binned in 5 regions of the photon pseudorapidity lnYI (0.0-0.3, 0.3-

0.6, 0.6-0.9, 1.5-2.0, 2.0-2.5). The "signed nie’" of the leading jet in the event was then

formed:
Signed 11"“ = Signmy) . nj" (7.1)
This quantity indicates the degree to which the leading jet is on the same side of the ﬁnal

state (in rapidity) as the photon. The signed ni“ distribution for the candidate sample is
plotted in Figure 7.2. The data show a tendency for the leading jet to follow the photon

candidate forward (though not fully), Conﬁrming the expected behavior. Also shown in

Figure 7.2 are the mean values of the signed nj“ distribution for each bin.

7 .2.4 Background Behavior

Since the candidate sample is not background subtracted, it is important to gauge the
effect of the jet component of the distribution. To investigate this, candidates in the raw
photon sample were anti-selected - i.e., selected especially to fail the photon cuts. This

was done by requiring:

EEM]
E

 

> 0.01 (anti-golden)

to!

0 [ET-(R = 0.4) — ET(R = 0.2)] > 2 GeV (anti-isolated)

DO Preliminary

Mean 17,,

0.07

0.19

0.26

0.59

0.61

98

 

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Figure 7.2: Signed 11"“ distribution of the leading jet for golden photon candidates.
The shaded band indicates the rapidity bin of the photon; shown at left are the

mean values of signed If“ in each bin.

99

as well as one or more of the following characteristics which are indicative of

electromagnetic jets:

- Two or more tracks pointing to the candidate

EEM
E

 

< 0.96 (higher hadronic activity)

tot

0 H—matrix x2 > 150 (poor shower shape)

with the acceptance and missing Er cuts retained as in the golden photon case. While there

is a limit to how "bad" a candidate can get, due to the trigger and reconstruction quality

cuts already placed on raw photon candidates, this "bad" photon sample is expected to be

mostly composed of jets which have ﬂuctuated to electromagnetic energy. The signed If“
distributions for this sample are shown in Figure 7.3, and indicate a much smaller

tendency for the leading jet to follow the "bad" photon forward. This is expected, since

dijet production reﬂects processes such as g g —> gg , in which the interacting partons tend

to have similar average momenta.

7 .25 Theoretical Prediction and Comparisons

Using the Monte Carlo program of Baer, Ohnemus, and Owens, a NLL QCD
prediction for the leading jet behavior in direct photon events was obtained (Figure 7.4).
Energy resolution smearing and a photon isolation cut matching that used on the data were

applied to the prediction, which used the CTEQ2M parton distributions. Note that the

00 Preliminary

Mean 77,.

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101

 

 

 

 

 

 

 

 

 

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771

0.0<l77,|<0.3

0.3<|77,l<0.6

0.6<m,1<0.9

1.5<|17,|<2.0

2.0<m,1<2.5

Figure 7.4: Signed 'qje‘ distribution of the leading jet in a NLL QCD prediction
from Owens, et a1.

102

trend and appearance of the QCD prediction are similar to that of the golden photon

candidate sample.

The means of the signed nie‘ distributions for the candidate, background, and theory

samples are plotted versus mean photon rapidity in Figure 7.5; errors are statistical only,
calculated as the R.M.S. of the distribution divided by 717 . While the means do not fully

describe the distributions, they provide a measure of the trend in signed nje‘, and illustrate
the evident difference between the signal and background behavior. Also, the signal-
enhanced sample is seen to be qualitatively consistent with the theoretical prediction,
though a fully background-subtracted comparison of distributions would be necessary to
draw stronger conclusions.

To ensure that the electromagnetic jet sample has a negligible amount of direct photon

signal, the behavior of this sample was cross-checked against an unbiased dijet sample.
Events in the golden and background photon sample with 45 GeV < ET< 55 GeV were
compared to a sample in the same range measured as part of the inclusive dijet triple
differential cross section [37]. The two samples were found to give consistent results with

respect to the behavior of the leading jet (Figure 7.6), which indicates that the

electromagnetic jet event sample behaves similarly to that of normal jets.

7 .3 Conclusions

The analysis presented above demonstrates the utility of direct photon events in studying

event structure. Future work, building on the work contained within this thesis, might be

Signed m,

0.8

0.6

0.4

0.2

103

00 Preliminary

 

—
~-
7'
p—

O
p—
b—
p

p—

 

- Errors are statistical only

Photon Candidates (No Background Subtraction)
Electromagnetic Jets
QCD NLL (J. Owens, et al) CTEQZM, p=P,

 

 

_ O

— 1- 1-

’ O

_ 15

‘— t v

P V

... * Y

'- 1 1 1 1 I 1 1 1 1 1 1 1 1 I 1 J 1 1 I 1 1 1 1 I 1 1 1 1
0.5 1 1.5 2 2.5

I77,l

Figure 7.5: Mean signed If" versus mean mil for candidate, background, and

theory samples.

Signed 77,,

0.8

0.6

0.4

0.2

Dﬂ Preliminary

104

45—55 GeV Jet Comparisons

 

" V Electromagnetic Jets

P =3" Inclusive Dijets

_ Errors are statistical only

1.-

l

p—

4<}=—I—

 

—-I Golden Photon Candidates (No Background Subtraction)

4533
4'33

 

I777!

Figure 7.6: Mean signed 117“ versus mean mill for candidate, background, and
dijet samples with E7» between 45 and 55 GeV.

 

105
expected to extract the pure direct photon signed 11"“ behavior using the knowledge of the
background behavior, along with a purity calculation in each region of InYI as performed
in Chapter 5. Studies of the ratio of events with the leading jet on the same/opposite side
as the photon (essentially the ratio of events on the positive/negative sides of Figure 7.2)
are currently in progress within the collaboration.

Ultimately, it can be recognized that this analysis is essentially an uncorrected,

unnormalized triple differential photon cross-section, (da3)/(dn7dnje'dET) , integrated
over the ET region above 45 GeV. The formation of the full cross section will allow not

only the comparison of event shape between data and theory, but also of absolute
production rate as a function of that shape. Further, it will be informative to form the cross
section in bins of ET, extending down to lower ET where increased effects of gluons (as
colliding partons and as initial/ﬁnal state radiation) might be seen; however, it is apparent

from the inclusive cross section measurement that the useful range of photon ET will be

dictated by the uncertainty in the photon purity.

Chapter 8

Conclusions

This thesis has presented a detailed analysis of direct photon production at the Dﬂ
Detector, using the large statistics available during the Fermilab Tevatron Run 1B.

The analysis has relied on the excellent capabilities of the D0 Detector in measuring
electromagnetic objects over a large range in rapidity, as well as its ability to trigger
effectively on direct photons over a wide range of photon energies.

The ability of the DQ Calorimeter to reject the copious backgrounds from jet
production enabled a signal to noise ratio of up to ~ 10. Measurement of the purity of the
remaining sample was made possible by a detailed Monte Carlo simulation;
improvements in the calibration of the Monte Carlo, as well as a more realistic
background modeling, enabled a better understanding of the photon purity compared to
previous Dﬂ analyses.

The cross section for direct photon production has been measured, and is in mixed

agreement with the QCD prediction. While the central region (0 S. In] S 0.9) cross section

106

107
shows consistent agreement with the prediction within errors, the forward region

(1.65 Inl S 2.5) cross section is consistently higher than the prediction, and further

exhibits a shape difference in the lower ET region which may indicate a need for a more

complete theoretical treatment.

In addition, the structure of direct photon events was investigated by comparing the
rapidity distribution of the leading jet in the event to that of the photon. Here the data and
theory qualitatively agree; however, we anticipate that future analyses such as the triply
differential direct photon cross section will provide a more detailed and quantitative
measure of the level of agreement. We expect that this thesis will provide a useful
reference for such future analyses, and hope that continued improvement in our ability to
measure direct photon production will accompany the progress of the theoretical

community in predicting it.

APPENDICES

Appendix A

Triggers and Luminosity

In order to make proper account of the number of direct photon events produced and
recorded during data acquisition, and hence of the cross section for production of such
events, the triggering process must be understood. The purpose of this appendix is to:
outline in more detail the requirements which were made at Level 1 and Level 2 to select
EM showers within the calorimeter; present efﬁciency measurements which determine at

which ET each trigger and filter becomes completely efﬁcient at ﬁnding photons; and

discuss the calculation of luminosities for each of the ﬁlters, including cross checks which

determine how well the separately triggered regions of ET match once corrected for

luminosity.

108

109

A.1 Triggering

A.1.l Level 1 and Level 2 Requirements

The Run 1B direct photon data set was collected using four separate Level 2 ﬁlters fed

from three separate Level 1 triggers - these are listed in Table A. 1. At Level 1, the triggers

Table A. 1: Description of triggers and associated ﬁlters.

 

 

 

 

 

 

 

 

Level 1 L1 L2
Trigger Threshold Level 2 Filter Threshold Requirements
(GeV) (GeV)

EM_1_2_GAM 2.5 GAM_6_ISO_GAM 6 shape, iso(30%)
EM_1_7_GAM 7 GAM_14_ISO_GAM 14 shape, iso(15%)
EM1_GIS 25 shape, iso(15%)

EM_1_HIGH 14 .
EM1_GIS_HIGH 40 shape, 1so(15%)

 

 

 

 

 

 

merely required one trigger tower (An x A4) = 0.2 )2 0.2) to have more than 2.5, 7, and
14 GeV, respectively.

While each Level 2 filter also had a different ET threshold, they shared the same
algorithm used to identify photon-like showers [38]. This algorithm ﬁrst ﬁnds the most

energetic EM3 cell (or “seed”) in the trigger tower ﬁred at Level 1, then forms a simple

cluster by summing the cells within a An X Atl) = 0.3 X 0.3 window around the seed in

 

110

the EM and FHl layers. Several requirements are then imposed on this cluster:

Energy in the FBI layer must be less than 10% of total shower energy.

Energy in the EM3 layer must be between 10% and 90% of total shower energy.

The positions of all EM3 cells in a 5 X 5 array centered on the shower are energy-
weighted and summed, forming a measure of the “sprea ” of the energy from the
center. The same sum is made for a 3 X 3 array, and subtracted from the 5 X 5
sum, producing a quantity which should be small for electromagnetic showers; too
large a value would indicate signiﬁcant energy deposited further away from
shower center. The actual cuts used were determined from test beam electron

studies, and vary as a function of n.

The cluster is required to have little energy in the region around it, deﬁned by

ER = 0.4 _ Ecluster
Ecluster

 

(f (A.1)

where ER = 0'4 is the energy (including the cluster energy) within a cone of

R = «lAn2 + A432 centered around the cluster. The isolation fraction f was 15%
for all triggers except GAM_6_ISO_GAM, for which it was loosened to 30% in

order to ensure that it was less restrictive than the 2 GeV ofﬂine isolation cut.

11 1
A.1.2 Trigger Turn-On and Efﬁciency

Because the D12) Level 1 Calorimeter Trigger looks for energy in ﬁxed towers, it should be

expected that its ability to ﬁnd all EM showers with a minimum amount of ET will be

impaired when the shower occurs near a tower boundary - some fraction of the energy will
be split between two (or more) towers and neither tower may pass the trigger. This

inefficiency should diminish for increasing candidate ET , until, for candidates with twice

the E;- of the trigger requirement, even sharing between towers leaves at least one tower

above threshold.
While the Level 2 system is able to perform rudimentary clustering and thus avoids

this problem, its ET resolution does suffer somewhat from the limited vertex position

information available at Level 2. There should also be an inefﬁciency at Level 2, then,
which diminishes faster than at Level 1.
When using a speciﬁc ﬁlter to measure a cross section, it is desirable to determine the

ET above which that ﬁlter and its parent trigger are fully efﬁcient - in this way, trigger

efﬁciencies can be neglected in the cross section. It is important to note that for the direct
photon analyses, trigger efﬁciencies are deﬁned as the efﬁciency for real direct photons to
pass the trigger, since we only care how many real photons might be left out of our
measurement due to a trigger inefﬁciency. Thus the efﬁciency is studied only for events
which pass all ofﬂine candidate selection cuts, and we expect the efﬁciency to be unity

above some ET threshold since the ofﬂine shape and quality cuts are stricter than those
imposed at Level 2.

Efﬁciencies were measured using the DOLibrary L2BIT_TRIED and L2BIT_PASSED

112

routines - the efﬁciency is deﬁned as

N tried and passed (A 2)

trig = N:

 

8
ried

The 7 GeV Level 1 trigger efficiency was evaluated by using special run events which

passed the 2.5 GeV Level 1 trigger; the trigger efﬁciency is shown in Figure A.1. This

 

.l..'........i............ ....

 

Efficiency

 

.0
on

 

0.5 L..."
'- 3 O 0.0 .S. 1) SE 0.9

I 1.6§n!§2.5

 

0.4

 

0.2

 

 

 

 

 

 

 

 

Figure A. l: 7 GeV Level 1 Trigger efﬁciency for the central and forward regions.

113
trigger is seen to be fully efﬁcient by 15 GeV. The 2.5 GeV and 12 GeV trigger

efﬁciencies were not explicitly evaluated; however, it is expected that they will likewise
become fully efﬁcient at about twice the threshold energy, well before the ET at which

their daughter ﬁlters become efﬁcient.

Efﬁciencies for the four Level 2 ﬁlters are shown in Figures A.2 - A5. The 6 GeV

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

>\
0
C
.22
.2 1 I I": c o . ......
1....
H—
” l
0.8 is
l.
0.6
o 0.0 s n a; 0.9
. > I
I 1.6 s 17 :E 2.5
0.4
0.2
0 1 l +L 1 1 l
o 5 10 15 20 25

Er

Figure A2: 6 GeV Level 2 Filter efﬁciency for the central and forward regions.

114

 

 

 

Efficiency

_._..
'01
—O—
I
I

 

 

t l
0.6
r T O 0.Cl§n§09

 

0.4

 

0.2

 

 

 

 

 

 

 

 

 

 

 

Er

Figure A3: 14 GeV Level 2 Filter efﬁciency for the central and forward regions.

trigger efﬁciency was evaluated using a special “mark-and-pass” run in which the photon
special run ﬁlters were set to pass all events regardless of the ﬁlter evaluation. In this way
an unbiased source of candidates was obtained; however, in such a sample the number
which pass ofﬂine selection cuts is very small, and the trigger efﬁciency determination
suffers from low statistics.

Efﬁciencies for the 14 GeV filter were determined using events which passed the 6
GeV ﬁlter, since it is fully efﬁcient by 14 GeV and provides a sample of events which

should pass the 14 GeV ﬁlter. The 25 GeV ﬁlter efﬁciencies were determined from the 14

115

 

 

 

Efficiency
5

 

 

0.8 I
0.6
t ooosnsos
l16§n§25
0.4

 

 

 

0.2 +

 

 

 

 

 

 

 

Figure AA: 25 GeV Level 2 Filter efﬁciency for the central and forward regions.

GeV ﬁlter in the same way, making use of a special run ﬁlter which is identical to the 25
GeV EM1_GIS ﬁlter used in global running. The 40 GeV ﬁlter efﬁciency was determined
using global data, checking the outcome of the 40 GeV ﬁlter on events which passed the
25 GeV ﬁlter.

Inspecting these efﬁciency curves, the ET above which each trigger is completely
efﬁcient was determined to be 10 GeV for GAM_6_ISO_GAM, 21 GeV for

GAM_14_ISO_GAM, 33 GeV for EM1_GIS, and 54 GeV for EM1_GIS_HIGH.

116

 

 

Efficiency

d
I T

 

 

06
- C) OJ)§17§(19 1J

 

 

 

  
 

 

 

 

 

 

 

 

 

 

i ll 1|i§17§12‘i l
0A
02
l
O Illl llll llll lﬁlillll Llll llll l
O 10 20 30 4O 50 60 70
E:

Figure A.5: 40 GeV Level 2 Filter efﬁciency for the central and forward regions.

117

A.2 Integrated Luminosity Determination

The integrated luminosity for each filter was determined using the D0 Production
Database, which stores information on beam and trigger conditions for each run. The

instantaneous luminosity L is determined as

RLO
measured = 6:0 (A3)

L

where RLO is the rate at which the Level 0 Trigger indicates inelastic collisions, and
GL0 is the cross section subtended by the Level 0 counters. Further adjustments are made

to account for multiple interactions and other effects; the ﬁnal luminosity calculation has
an overall uncertainty of 5.4% [39]. Production Database utilities integrate the
instantaneous luminosity readings during each run and adjust appropriately for any trigger
prescales in effect for that run in order to arrive at the proper total luminosity for which the
ﬁlter was active. This luminosity calculation is only valid for events which had a Level 0
vertex found within 100 cm. of the center of the detector; therefore a cut was imposed on
the direct photon events to enforce this requirement (less than 2% of the events were
removed due to this cut).

Luminosities for each ﬁlter were calculated for each run used in this analysis; for the
two lowest ﬁlters this represents approximately 30 dedicated special runs, while for the
two higher ﬁlters this spans the thousands of runs collected during 1994-1995. The
resulting total integrated luminosities are shown in Table A.2.

The spectrum of good (passing all photon cuts) photon candidates passing each of the

ﬁlters, corrected only by the relevant integrated luminosities and without any background

118

Table A.2: Integrated Luminosities for the four single photon ﬁlters.

 

 

 

 

 

 

ﬁlter Luminosity (nb'l)
GAM_6_ISO_GAM 13.644
GAM_14_ISO_GAM 225.29
EM1_GIS 14577
EM1_GIS_HIGH 94657

 

 

 

 

subtraction, is shown in Figure 8.1 (CC only shown). It is expected that each of the ﬁlters
should line up with the next, since correcting for the calculated luminosity and prescales
should reconstruct the equivalent of a single ﬁlter allowed to populate the entire ET
region. The agreement appears good; however, a more quantitative check of this can be
obtained by comparing the number of events observed by one ﬁlter to that of the next

higher in an ET region where both ﬁlters are fully efﬁcient. We would then expect that

Nlower X Lhigher
Nhigher

 

Lzower = (AA)

The results of such a comparison are shown in Table A3 and conﬁrm that the trigger

regions agree given the statistical uncertainties.

O
u

dN/LdndP,
O

10

119

 

I IIIIIIU

l

 

I Tillllll

l IIIIIIII
D
9

O
O
O
o 0 gam 6 iso gam
o A gam 14 iso gam
o 0 eml gis
°o * em1 gis high
:- o
: O
' A
" A
: 3"
_ . “if
A

I I IIIIII
a
3+

 

 

.ﬁ
.
§_ :1 , Kn
— i
: O . N
. , l?

, <3 t ﬂy
llllllllllllllllll‘llllllllllllllllIIIWIIIJJI
O 10 20 3O 4O 50 6O 70 80 90

ET

Figure 8.1: Matching of luminosity-corrected ﬁlters (CC only).

120

from the Production database.

Table A3: Comparison of luminosities calculated using Equation A.4 with those taken

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Filter (CC) LPDB (nb'l) Lea!c (nb'l) Stat. Err
GAM_6_ISO_GAM 13.644 12.43 1.2
GAM_14_ISO_GAM 225.29 222.8 14.3

EM1_GIS 14577 14724 367

Filter (EC) LPDLmb'l) Lglc (nb'l) Stat. Err
GAM_6_ISO_GAM 13.644 14.27 1.3
GAM_14_ISO_GAM 225.29 252.3 23

EM1_GIS 14577 15970 730

 

 

Appendix B

Tracking Considerations

Since the selection of direct photon candidates requires the absence of a matching track in
the CDC/FDC, it is important to determine not only the efﬁciency of these detectors, but
also the ways in which real direct photons might be misidentiﬁed due to tracking

considerations. Speciﬁcally,

" A photon might convert to an e+e‘ pair in the material in front of the CDC/FDC;
only the fraction of such conversions whose track is accurately reconstructed will

be removed from the sample.

’ A charged track produced as part of the underlying event might overlap the photon
closely enough to lie within the tracking road, in which case the photon will be

removed from the sample.

The fFaction snack of real direct photons remaining in the sample after the tracking cut is

121

122

then

8mm], = (1 -Pt)(1 -\II) (B.1)
where p is the probability that a photon will convert before the tracking chambers,
measured at 0.095i0.00985 (038610.041) in the CC (EC) [16]. The tracking
efﬁciency t is the probability that a track present in the detector will be reconstructed. The

track overlap probability w is the probability that a reconstructed track from the
underlying event will be found in the tracking road of a good photon. It should be noted
that in the data set used in this analysis, EM clusters are matched to tracks from any
primary vertex, although this was found to add only 4% (2%) to the number of raw

candidates with tracks.

B.l The Tracking Efﬁciency

The method used to measure the tracking efﬁciency t is similar to that employed in
Previous tracking efﬁciency studies at DC [40][41]. A sample of Z —> e+e' events is

selected as follows:

' Select the EM2_GIS_GAM filter, which requires two EM clusters with ET above
20 GeV at Level 2; one cluster is required to pass shape and isolation cuts, the

other only shape cuts.

' Require 0 jets in the event to avoid electrons which have overlapped a jet; this

123

ensures a similar topology to photon events where the jet is generally in the

opposite hemisphere from the photon.

Require that the reconstructed E7 of both EM clusters be above 25 GeV.

Require that both EM clusters satisfy the direct photon 7], 11"“ cuts to eliminate the

ICD region.

Exclude EM clusters in the central region which are within 10% of a module edge

in (1).

This selects a fairly clean sample of electrons from Z bosons. Both electrons are then

checked against the following strict requirements:

11 < 0.9

at least one track in road

Track match signiﬁcance 0', < 5 (10) in the CC (EC)
EM fraction > 95%

Isolation fraction < 10%

Hmatrix x2 < 100

Passed Level 2 shape, isolation, and ET cuts

124

Those electrons passing these requirements are considered “tagged” as good Z electrons;
the other electron is then considered unbiased and can be used in measuring the tracking
efﬁciency. If both electrons in the event are tagged, then both are used as unbiased.
Standard photon selection cuts (minus the track cut) are then applied to each unbiased
candidate. For each passing candidate, an entry is made into a histogram of the invariant

mass of the two electrons (separately for CC and EC candidates). A further requirement is

then made that candidates in the CC (EC) have a track with 0', < 5 (10) , and two more

histograms are ﬁlled for these candidates - we then have histograms of the mass spectra
for events before and after the tracking cut, for both the central and forward regions
(Figure B. 1).

The tracking efﬁciency can then be determined by calculating how many electrons

from real Z —-) e+e' events were found to have passed the track requirement. To establish

the level of background in the sample, we deﬁne a region S as the signal region, between

86 and 96 GeV/c2 - this region should contain mostly real Z events with some background

events. We deﬁne two equal regions on either side of the mass peak as B] (61 - 71

GeV/c2) and 82 (111 - 121 GeV/c2), which should contain only background events. Using

the technique established in [40][41], we assume a linear background distribution,

approximating the level of background in the signal region S as

NB, +ng2

NB: 2

(B.2)

250

200

150

100

50

300

250

200

150

100

50

125

 

 

10 101

 

 

 

 

 

 

 

 

:— Entries was
__ noon 90.90
_ Rus 3.794 ,
L
LIL-d] l l 1 1 1
60 80 1 00 1 20 1 40
CC candidates passing track cut
-— ID 100
"’ Entries 2396
: than 90.63
.. RMS 9.134
ll
E
l...
V 60 80 100120 140 ‘
CC Candidates before cut

100

80

6O

40

20

140

120

100

80

60

4O

20

 

 

 

 

 

 

 

 

 

:“ game. :37
L
C
C
60 80 100 1 20 1 40
EC candidates passing track cut
g 3.... 3°
_ than 92.71
__ nus 3.535
C
L
’- 1 L11] ml. 1 l l I l .
60 80 1 00 1 20 1 40
EC Candidates before cut

Figure B. 1: Z mass distributions before and after track requirement.

126

in which case the tracking efﬁciency becomes

where the subscript T indicates the number in each region which have been tracked.

t—

_ NTS‘NTB
NS-NB

(B3)

The resulting tracking efﬁciencies are shown in Table B.l, along with estimates of the

background in each sample. Systematic error due to the background estimation is

Table B. 1: Tracking efﬁciencies and errors in the central and forward regions.

 

 

 

 

 

 

 

 

 

. Stat. Sys. Background
Efficrency err Error ( % )
CC 0.830 0.0096 0.0029 2.66 :1: 0.4
EC 0.767 0.016 0.0037 2.54 :1: 0.6

 

 

estimated by taking the difference in efﬁciency with and without background subtraction.

Note that because the deﬁnition of “tracked” applied here includes a cut on the track

match signiﬁcance, the resulting efﬁciencies are lower than in [40] [41]. This is necessary

because, since we are considering the possibility of overlaps separately, we wish to extract

the probability that an existing track which is directly pointing to the cluster (i.e., from

conversions) will be seen by the tracker. Loosening the deﬁnition of “tracked” to mean

simply ﬁnding a track in the tracking road would doubly count the effect of overlapping

tracks.

127

The mean luminosity of the runs used is 6.6X1030cm-zs_l (6.6E30); runs ranged from
0E30 to 20E30. The change in tracking efﬁciency with increasing instantaneous

luminosity is shown in Table B.2; in the central region, the efﬁciency decreases as the

Table B.2: Tracking efﬁciencies at different instantaneous luminosities.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Luminosity . Stat. Sys. Background
Range Efficiency Error Error (%)
CC 0.898 0.028 0.0066 1.7 :1: 1.2
0 - 3E30
EC 0.780 0.059 0.0043 2.0 :1: 2.0
CC 0.860 0.016 0.0022 3.0 :1: 0.8
0 - SE30
EC 0.814 0.026 0.0077 2.8 :1: 1.1
CC 0.822 0.013 0.0064 2.8 :1: 0.5
5 - 10E30
EC 0.742 0.021 0.0009 2.7 :t 0.7
CC 0.792 0.034 0.0040 1.4 :1: 0.6
10 - 15E30
EC 0.786 0.054 0.0067 0.8 :1: 1.0

 

 

luminosity goes up, which is consistent with previous studies and reﬂects the fact that
vertex ﬁnding becomes poorer as the average number of vertices increases, causing the
tracking road to be drawn inaccurately. This effect is less noticeable in the EC, due to the
higher average number of tracks and the larger z region which the tracking road intercepts
at smaller angles. The lowest bin, between 0E30 and 3E30, has a mean luminosity of

2.1E30, which is close to the average luminosity of the photon special runs from which

128
data below 33 GeV are taken.

B.2 Track Overlap Probabilities

B.2.l Golden Overlap Method

In order to estimate the probability w of a random track from the underlying event to
overlap a photon, a “golden” photon sample was selected from candidates which satisﬁed

the standard photon cuts (without applying the no track cut), and which further had less

than 1% of the photon energy in the ﬁrst layer. This golden requirement is > 98%

efﬁcient at rejecting electrons from Z —) e+e' events (Figure B.2), since charged particles

begin depositing energy as soon as they enter the calorimeter, whereas photons must

convert to an e+e' pair ﬁrst. Any tracks in the tracking road pointing to a golden photon
candidate are therefore presumed to be overlaps, rather than a real track associated with
the calorimeter cluster, and the overlap probability is obtained by observing how many
golden candidates have tracks. This is similar to a technique used for the Run 1A analysis.

The results of this method are shown in Table B3. The overlap probabilities obtained
are quite consistent when evaluated for samples obtained from the special runs (6 and 14
GeV Level 2 thresholds), the global EM1_GIS ﬁlter (25 GeV threshold), and the global
EM1_GIS_HIGH ﬁlter (40 GeV threshold).

While this method has the advantage of using a subset of the direct photon sample, and

thus matching the luminosity & trigger proﬁles and E7- range of the overall sample, one

possible source of uncertainty in this method comes from the fact that the sample is not

350
300
250
200
150
100

50

129

 

IIITTTIIIIIIIIIIIIIIIIIIIIIFIIII

 

IIII

 

 

 

CC Z candidates

180
160
140
120
100
80
60
4O
20

 

 

 

 

 

"r

E.

E.

C

E-

:1_Lll_l_.l_L [111111—11

—4 —3 —2 —1 O
log(EMllE)

ECanndidates

Figure B.2: Log(EMllE) distributions for Z electrons. Note that 1% EM]

corresponds to -2.0 on this scale.

Table B.3: Overlap probabilities from golden candidate sample.

 

 

 

 

 

 

 

 

- olden golden Stat
Trigger NTg N w error
CC 169 1558 0.108 0.008

Special Runs

EC 435 2129 0.204 0.009

CC 564 5810 0.0971 0.004

EM1_GIS

EC 1481 7105 0.208 0.005

CC 707 7184 0.0984 0.004

EM1_GIS_HIGH

EC 1408 6485 0.217 0.005

 

 

 

 

 

 

 

 

130

pure photons. While the golden photon cut does boost the purity of the sample by
preferentially selecting single photons over multiple photon backgrounds (which tend to
convert earlier), the remaining background may unfairly add overlaps which are not from
the underlying event but from jet fragmentation, which will not affect real photons. One
might hope that by making the isolation or golden cuts more restrictive, a better purity
might be obtained, and the overlap probabilities would approach a stable value. This was

found not to be the case, as shown in Table 3.4 - requiring progressively less isolation ET

Table B.4: Variation of the overlap probability with isolation and golden cuts, varied
independently using the EM1_GIS_HIGH trigger.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12:33“ W EStat. EMl cut 1! Stat.

(GeV) rror (%) Error

2.0 0.098 0.004 .1 1.0 0.098 0.004

1.5 0.093 0.004 0.8 0.093 0.004

CC 1.0 0.083 0.004 0.5 0.081 0.004
0.5 0.070 0.007 0.3 0.069 0.005

2.0 0.217 0.005 1.0 0.217 0.005

EC 1.5 0.193 0.005 0.8 0.205 0.006
1.0 0.151 0.006 0.5 0.183 0.006

0.5 0.099 0.010 0.3 0.157 0.007

 

or less energy in EMl progressively lowered the overlap probability (and removing the

isolation cut greatly increased the probability). This is understood when it is considered

 

131

that the isolation ET is in fact itself a direct measurement of underlying event activity,
especially when a 2 GeV out has been imposed to reduce the isolation ET to approximately

the level of underlying event. Similarly, the energy in BM] is correlated with the amount
of underlying event overlapping the candidate. The level of overlap is therefore dependent
on the choice of cuts for these two variables. Since the isolation cut used here is the
standard cut used in this analysis, it is clear that it should give the appropriate level of
overlap. The cut on EMl is less obvious; however, the level of electron rejection observed
with a 1% cut appears to be a reasonable balance between allowing real associated
charged tracks and overly minimizing the underlying event effect. As an estimate of the
systematic error arising from these choices, the variation in w from varying the isolation
cut from 2.0 - 1.5 GeV and from varying the EMl cut from 1% to 0.8% were added in
quadrature.

The resulting overlap probability, obtained by averaging the numbers of the two global

triggers and combining systematic and statistical errors in quadrature, is then

0.0978 :1: 0.010 (0.213 t 0.026) for the CC (EC).

13.2.2 2 Overlap Method

As a cross check, an alternative estimate was obtained using the Z —-> e+e' sample.
Using the same method used to determine the tracking efﬁciency t, an efﬁciency was

determined for a Z electron to have an additional track in its tracking road. This

probability was found to be 0.108 i 0.008 (0.261 i 0.018) (errors statistical only). The

analysis was also performed on a sam le of Herwig Z —> e+e' events, usin late-level
P g P

132

GEANT, in order to estimate the probability that a Z electron would produce an extra track

through bremsstrahlung and conversion, etc. After correcting for this effect, the ﬁnal

overlap probability using the Z sample is then 0.107 :l:0.008 (0.244i0.018) with
statistical error only. This agrees well with the result obtained by the primary method

using golden candidates.

B.3 Overall Efﬁciency

Using Equation B.1, we can then construct the overall efﬁciency for photons to be lost due

to tracking considerations:

8 k = 0.828 :1: 0.013 (0.554 :1: 0.030) (B.4)

(me
While this efﬁciency has been calculated using global run data, with a mean instantaneous
luminosity of 6.6E30, substitution of the tracking efﬁciency t calculated in the 0E30-3E30
bin does not change the result within errors. This is due to the stability of the overlap
probability between the global and special runs, and also to the constancy of the
conversion probability p and its dominant error. Therefore the values calculated in

Equation B.4 can be used over the entire range of the photon ET spectrum.

Appendix C

EMl Calibration

The observed offset in log(EMI/E) between EC Monte Carlo and EC data (Figure 5.2)
directly affects the purity measurement, since a Shift in the distribution of the Monte Carlo
represents a shift in the position of the data between the extremes of the Monte Carlo jet
and photon distributions. In order to ensure that the Monte Carlo best models the data, this

offset must therefore be understood and corrected.

C.1 Offset Estimation and Origins

The most direct way to correct the Monte Carlo is to determine the offset between the
Monte Carlo and data W electron peaks, and then apply this additive offset to the Monte
Carlo photon and jet distributions used to estimate the photon purity.

The offset estimated in this way is 0.120 1 0.011 . This additive offset in log(EMI/E)

is equivalent to a multiplicative correction of ~30% to the EMl energy; or more

133

134

accurately, to the sampling weight applied to the uncalibrated energy read out from EM].
The sampling weights for the EC EM layers were determined using electrons in a test
beam study of EC calorimeter modules [18]; a plate level test beam Monte Carlo, the
precursor to the Monte Carlo used in this analysis, was also used in the study. It is

apparent from this study [28] that

0 When different methods were used to determine the sampling weights (in order to
ﬁnd the scheme which optimized the energy resolution), the EMI sampling weight
varied much more than other layer weights. This effect was dismissed as negligible
to the goal of the study, however, since the energy in BM] is a small (~4%)

fraction of the total energy of the shower.

0 The EMl sampling weight varied depending on the amount of material upstream
of the calorimeter. An attempt was made to approximate the amount of material
which would be present in the real detector; however this was modeled only with a

steel plate of uniform thickness.

0 The EMl sampling weight varied up to a factor of 3 between the testbeam data and

testbeam Monte Carlo.

It is also important to note, as pointed out in [29], that the sampling weights determined so
as to optimize energy resolution may in fact not reproduce the exact energy in any given
layer. Because the energies in each layer are correlated, the ideal weight for EMI may
depend on the behavior of EM3, for example. The authors of [29] estimate that this might

cause up to a 100% difference in the EM] energy when comparing Monte Carlo and data.

135

However, one expects that Since the sampling weights are simply multiplicative factors
applied to each layer for all energies, the calibration of the Monte Carlo EMl weights
relative to the data will provide, if not the actual energy in BM], a well-determined
quantity which allows direct comparison of Monte Carlo and data to extract a background

fraction.

C.2 Cross Checks of the Offset Estimate

As a qualitative check, the photon purity fitting routine (described in Section 5.3) was

modiﬁed to allow the signal and background distributions to shift by an offset; the routine
then minimized the x2 to ﬁnd not only the best purity estimate, but also the best offset
estimate in each ET bin. The result is shown in Figure C.l. This method is not exact, as it

relies on the ﬁtter to determine dual quantities and their errors, but it does indicate that the
purity ﬁts prefer the Monte Carlo photon and jet distributions offset by roughly the

amount determined from W electrons, with no obvious ET dependence.

To check more rigorously the possibility that the offset might be ET dependent, the
Monte Carlo and data W samples were binned in ET and compared (Figure C.2a); within
the limited statistics, there appears to be no ET dependence. To provide better statistics, an

alternate sample of plate level Monte Carlo W electrons was obtained. These were
generated using ISAJET as Single particles distributed with W electron kinematics [30],
and therefore cannot be compared with full data events to derive an absolute offset;

however, the dependence of the offset with ET can be studied. The analysis was repeated

with this sample (Figure C.2b), and again no obvious dependence on ET was observed.

136

 

*5 0.3 —
E Z
O 0.2 l d]
0.1 1 Cl C] [3 D D a E3 [#3
0 L
—o.1 :-
L11 1 1 Li 1 1 1 lllgjl 1 ll 1 l I l l I l l l l 1 Lil l l_Ll l
10 20 50 40 50 60

 

 

 

ET(GeV)

Figure C. 1: Values of EC EMl offset produced by the purity ﬁtting routine for
several ET bins.

C.3 Effects of Pre-EMl Material in the Monte Carlo

While the offset appears consistent with a mismatch in sampling weight between data
and Monte Carlo, there is also the possibility that the DOGEANT simulation of the
detector has mismodeled the amount of material in front of the calorimeter. If the amount
of material were greater in the real detector than in the Monte Carlo, electromagnetic
showers would tend to start earlier, develop further by the time they reach EMl, and thus
leave more energy in BM]. The application of the offset in this case would still help

correct the Monte Carlo, but there would be an additional, uncorrected effect on the

probability that a photon converts to e+e' before the EMI layer, which is precisely the

discriminant we hope to exploit.

137

OJ

 

02 '-

Ql —

 

 

 

 

25 30 35 4O 45 50 55

03

 

OJ

 

 

f1 r T I I I I
t T

 

Figure C.2: Offset measured from W electrons versus ET, using a) full W Monte
Carlo; b) single particle Monte Carlo

To examine this possibility, it is necessary to understand how extra material would
affect the longitudinal energy deposition of an electron shower. A model of this energy
deposition was created using the formula [4]

dB (1:1)“ ‘6’”

E = Eob 1"(a) 1 (8.1)
where t is distance in radiation lengths (X0), and a and b are constants determined, in this

case, for 35 GeV electrons passing through uranium. Given the known ECEM layer

138
thicknesses of 2, 2.6, 7.9, and 9.3 X0, we can then integrate Equation 8.1 in each layer,
assuming different initial radiation lengths before EMl, and observe the effect on all

layers. An initial estimate of 2.0 X0 before EMl was taken as a benchmark value (the
design estimate quoted in [18] is 2.31X0). In order to better calibrate the model, a set of

“sampling weights” was derived using the benchmark estimate so that the benchmark

layer proﬁle matched that of the data, and applied to all estimates:

W _ Fndata

n _ (8.2)
1“"20x0

This weighting was meant to add in the effect of “optimized” sampling weights as are
present in the data; however, since the quantities of interest here are relative shifts between
different pre-EMl estimates, the weighting had little effect on the results.

Figure C.3 shows the fractional energy deposited in each layer for several values of
pre-EMl material. Note that an increase in material results in increased energy in the ﬁrst
two layers, and a decrease in layers 3 and 4 (and in layer 5, though this is not
distinguishable in Figure C.3 due to the small fraction of energy deposited there). Also

plotted are the data (identical to the 2.0X0 points) and Monte Carlo fractional energies.

Figure C.4 shows the percent (of the total Shower) change for each layer between several
combinations of pre-EMl estimates, and also between the Monte Carlo and the data. For

example, going from 2.0X0 to 1.5X0 results in a loss of ~1% of the total shower energy
from EM], and a gain of ~1% in EM3. Note that a difference of 0.5X0 results in a change

in EMl fractional energy similar to that seen between the data and the Monte Carlo; this

difference is consistent between assumptions of 1.5-2.0X0 and 3.5-4.0X0 , implying that

139

 

- (material assumed before EMl)
A 4.0x,

.0
\l
l

3.0)(0

[>130-

C]
O 2.0x, / Data
I MC

.0
U!
1

Fractional Energy
7’ ,

 

 

0.4—-
0.3—
0.2—
_ i
C]
e A
0.1— A
: [I]
0” Lil illlLleliiiiliiLJ‘
O 1 2 3 4

 

5
Layer

Figure C.3: Fraction of energy deposited in each EM layer for several pre-EMI
estimates (simple model), data, and Monte Carlo.

the observed changes are fairly stable over the range of realistic pre-EMl estimates. The
data/Monte Carlo EM3 difference, however, is not consistent with a 0.5X0 change, but
with a larger change of ~1.0X0. Most importantly, whereas the model shows that a
decrease in material results in an increase in the EM4 and F111 energies, the data/Monte
Carlo difference shows a decrease in those two layers. While the model in Equation 8.1 is
fairly basic, these results indicate that the difference in EMl is not wholly due to a failure

of the Monte Carlo to account for pre-EMl material correctly. Also, since 0.5X0 is roughly

140

 

 

 

 

50.04 — 13 2.0XOtol.5XO
9 I
8 __ O 4.0X0l0 3.5x° l
50.03 - A 3.0x,1e 2.0xo
g l
A
a:
“0.02 — a Data to MC
.5 o
8 9 U
. 1 ~— 0
E00
0
0 __ ................................................................... 121--
' a
—0.01 — g
: i l
t O
)—
-0.02 —
- A
—0.03 —
-0.04 e
1 l l J 1 1 i L L 1 1 l J l 1 l l t J I l
o 1 2 3

Layer

Figure CA: Change in percent of total energy in each layer between different
material estimates, and between data and Monte Carlo.

20-25% of the expected pre-EMl material, and corresponds to roughly 1cm of steel, it is

unlikely that the DOGEANT simulation would exclude this much material.
C.4 Final Calibration Determination

In order to arrive at a final correction with which to calibrate the Monte Carlo EMl
distributions, the offset was examined separately in the North and South endcap

calorimeters. While the same sampling fractions are applied in both the North and South,

141

in calibration studies the two endcaps have been found to differ by about 2% in total
response, and are separately calibrated ofﬂine. While the Monte Carlo sample was found
to be consistent between the two endcaps, the data W EMl distribution peaks were found

to differ by a statistically signiﬁcant amount, resulting in different offsets in the two

regions: 0.147 :1: 0.013 (North), and 0.094 i 0.013 (South). In order to achieve the best
calibration of the EM] energy deposition, the cryostats were therefore corrected
separately.

This difference was again qualitatively checked by separating the Monte Carlo
photon/jet and data photon candidates into North and South samples, and rerunning the
purity ﬁtter to attempt to ﬁt the offset separately in each cryostat. While the results of the
ﬁts (Figure C.5) show the effects of the reduced statistics, a difference can be seen which
is consistent with a greater offset in the North endcap than in the South. Note that since the
EMI layer energy is such a small fraction of the total energy, the difference in total
response between the two endcaps may, depending on its origin, affect the EM]
signiﬁcantly. Also, while the overall offset seems unlikely to be caused by conversion
material differences, and there is no expected asymmetry in the detector between the
North and South, a slight difference may also contribute to the relative shift.

For completeness, the CC W EMl distributions were examined in similar detail to the
EC, and the data and Monte Carlo peaks were found to differ by only 0.014 i 0.005.
While this is a small difference compared to the EC offset, to maintain a consistent

calibration method the CC Monte Carlo was adjusted by this factor, which resulted in a

slight (~ 5%) increase in the CC cross section.

OJ

—OJ

OJ

-OJ

142

 

 

 

 

 

 

 

:

l.— Ei’ North

I- E:

Z [:1 C.3

2— D D 9

e 4 :1 i

+—

:l i 1 l i l l l l l l 1 l l l l l l l i l l l l i 1 l l 1 i l l l_l I l
10 20 3O 40 50 6O 70 80

ET(GeV)

E- South

C

a i] a 9

D [:1 D ED

; cl- e

b-l I l 1 I l i 1 l l l l l l L L l L L L 1 i l l l l i 1 l l 1 l J_l l I l 1
10 20 30 4O 50 60

ET (GeV)

Figure C.5: Values of EC EMl offset produced by the purity

ﬁtting routine for EC North (top) and South (bottom) samples.

 

 

143

C.5 Summary

The observed offset in log(EMl/E) distributions between Monte Carlo and data W
electrons has been investigated, and was found to be consistent with a variation in EMl
sampling weight between data and Monte Carlo. Also, the offset does not appear to be
consistent with incorrect modeling of pre-EMl material in the Monte Carlo. In order to
calibrate Monte Carlo photons and EM jets for use in determining the photon purity, we

derive from the W electron comparisons a set of additive constants in log(EMl/E)

Table C. l: Additive constants used to calibrate the Monte Carlo log(EMl/E) distributions.

 

 

 

 

 

 

 

 

Calorimeter log(EM llE) correction
CC 0.014 i 0.005
ECN 0.147 :1: 0.013
ECS 0.094 i 0.013

 

(multiplicative constants in BM] energy). These were determined separately for the North,
South, and Central calorimeters (Table C. 1), and applied to the photon and EM jet Monte

Carlo log(EMl/E) distributions.

Appendix D

Comparison with Run 1A Results

To compare this analysis with the Run 1A inclusive photon analysis [3], the cross section
was rebinned to match that of [3] and the ratio of 1A/ 1B was formed (Figure D. 1). In both
the central and the forward regions, the Run 1A results are found to be signiﬁcantly below
the Run 1B measurement. It is therefore important to consider the sources of the

disagreement.

D.1 Corrections to the 1A Analysis

To investigate this difference, the Run 1A analysis was reviewed, and several
discrepancies were found. First, the calculated acceptance for the central region was found
to be higher in the 1A analysis than in the 1B. This was found to be attributable to the
IETA acceptance, which was found in the 1A analysis [16] to be 97.5% compared to the

updated value (Section 4.2) of 91.7% for identical IETA cuts - a difference of 6%. Note

144

145

 

be: r WWWVVV’W
\$8 L
b

1.6 L 18 la systematic error

1.4 -

1.2 >-

 

: O
0.6 —

0.4 F +
: 1A 10 systematic error %

 

 

 

 

0.2 —
7/
0 0 20 40 60 80 100 120 140
13; (GeV)
2 7
ba / / %
‘ r
$8 — é
3 é
1.6 h- 18 la systematic error 5
1.4 -

 

 

TIII

0.6E wﬁmﬁjﬂiﬂ]

1A 10 systematic error

 

 

 

 

 

0.2

IT‘TII

 

\\\.\\\\\\\ ~ .

/

 

 

3 N)"

40 so 80 100 120 140

Elm

Figure D. 1: Ratio of the Run 1A inclusive cross sections to the Run 1B results in
the central (top) and forward (bottom) regions.

146

that while the 1A vertex was more off-center than the IB vertex, in fact this should serve

to lower the acceptance rather than increase it. It was veriﬁed that the actual cut used in
the 1A analysis was 0 < IIETAI S 9; however, the acceptance quoted in the 1A analysis is

more consistent with the looser cut 0< IIETAI S 10, which had been used in earlier
versions of the 1A analysis. Applying the IB acceptance to the 1A cross section would
raise the 1A result and bring it closer to the 1B.

Also, since the Production Database (which stores all run and luminosity information)
has been improved since the 1A analysis was completed, the integrated luminosities for

the triggers and ﬁlters used in the 1A analysis were recalculated. For the lowest ET ﬁlters,

the new numbers are 3.2% greater than those quoted in [3], which is consistent with the
shift expected from a re-analysis of the DO luminosity calculation [39]. The highest ﬁlter,
however, used above ~ 30 GeV, was found to be a factor of 2.7% lower than the old,
implying a 5.9% discrepancy. It was found that luminosity values for a minimum-bias
ﬁlter were used for the 1A analysis rather than those calculated explicitly for the photon
ﬁlters, due to Production Database difﬁculties existing at the time. Correcting the 1A
luminosity would increase the 1A cross section above ~30 GeV by 2.7%, bringing it
closer to the 18 result.

Another discrepancy is related to the fact that the 1A analysis fit a function to the
efﬁciency-corrected purity (purity divided by efﬁciency), rather than simply the purity.
Though the maximum value of the purity/efﬁciency quantity is therefore approximately
1.23, the ﬁt was made assuming a maximum of 1.0, as would apply to the purity alone.

Figure D.2 shows the effect of reﬁtting the 1A central region purity points to allow for the

147

 

Run IA Central Region Purity/Efﬁciency

--------- PRL ﬁt
Reﬁt to max = 1.23

   

 

Photon Purity
r

0.8 —

0.6 -

O.4 -— +
l.
0.2 ‘- {K

1 l I l l l 1 l l 1 l l
6 7 8 910 20 30 4O 50 60 70809000

 

 

 

 

 

E,

Figure D.2: Effect of reﬁtting the Run 1A central region Purity/Efﬁciency to allow
for the proper maximum value at higher ET values.

proper maximum; while only the region of ET > 70 GeV is affected, it is in this region that

the 1A central cross section was found to deviate below the theory by 20-40%. Refitting
the purity in the forward region yields no signiﬁcant change, however, as the forward

purity/efﬁciency was lower and therefore less sensitive to the maximum allowed value.

D.2 Effects of Changes in Background Modeling

The remaining discrepancies are consistent with the change in the jet background

148

modeling between the 1A and 1B analyses, and the statistical improvement in the number
of purity points. In the forward region, of course, the dominant change is the calibration of
the EMI distribution between Monte Carlo and data, which was not performed in the 1A
analysis, and therefore causes the 1A result to be lower than the 1B result. This also
produces a difference in the central region, though much smaller (~ 5%).

It is expected that the “messier” nature of the PYTHIA EM jets compared to the single
particle backgrounds used in the 1A analysis will tend to increase the purity of a given
sample: the messier jets leave slightly more energy in EMl, increasing the difference
between signal and background, as well as data and background. Since the difference
between the data and the signal behavior remains the same, this results in a higher purity.

In the 1A analysis, it was found that when the fitter was allowed to compose the

background sample with no restriction on the 1] to 1:0

ratio, it chose a much higher fraction
of us than than the expected value. This indicated that the ﬁtter preferred more complex,

multiphoton showers when trying to reproduce the data, as the n decay modes include

signiﬁcant 31:0 and 7:01t+1t' states, whereas the 1:0 decays almost exclusively to w. This,

along with examination of quantities such as the single particle isolation ET distributions,

gave evidence that the single particle Monte Carlo did not perfectly approximate EM jet
behavior, and (along with an increase in available processing power) led to the generation
of PYTHIA jets as an improvement for the 1B analysis.

To demonstrate the improvement in background modeling, a “composite” sample was
created by combining the 13 Monte Carlo photon and jet candidates in the fractions

indicated by the 1B purity, and then plotting other quantities of interest (EM fraction, H-

149

matrix x2, and isolation ET) and comparing to the data distributions. These comparisons
are presented in Appendix F; one example of interest is the composite isolation ET

distribution. There is generally good agreement between the Monte Carlo and data; when
compared to a similar study done in the 1A analysis [16], the improvement from the 1A
analysis can be seen.

In another study [43], the Run 1B PYTHIA Monte Carlo was used in place of the Run
1A single particle Monte Carlo to reﬁt the 1A candidate sample and rederive purity points

in the CC. Figure D.3 (left) shows the original 1A purity points (without the efﬁciency

 

 

0.0 '-
0.6 '-
0.4

0.2

V I r ' I r Y V '

 

 

 

 

 

A All I l A A A j
078910 20 30 40 506070801m El- 678910 20 30 40 506070801“) El!

4 A L A I l l A L LL A4 A A A l l

 

 

Figure D.3: Left: Run 1A CC purity points and resulting ﬁt (solid line), along with
the 1B CC purity ﬁt (dashed line). Right: 1A purity points and ﬁt (solid line) using
the 1B Monte Carlo, along with the 1A ﬁt (dashed line, same as solid line on left).

150

correction), along with a ﬁt to these points (solid line) and, for comparison, the 1B purity
ﬁt (dashed line). Figure D.3 (right) shows the new purity points determined using 1A data
with 1B Monte Carlo, along with the resulting ﬁt (solid line). Note that the rederived
purity points and resulting ﬁt are about 10-20% higher than the 1A result (the 1A ﬁt is
plotted again as a dashed line, for reference). This indicates that the single particle Monte
Carlo used in the Run 1A analysis may have underestimated the purity, resulting in a

lower cross section.

D.3 Conclusions

In order to estimate the combined effect of these differences, a rough correction of the
Run 1A cross sections was made by applying the above factors. To estimate the effect of
the EMI calibration on the 1A data, the Run 18 cross section was calculated without the

calibration and a rough parametrization of the difference versus ET was employed. The
resulting ratio of “corrected” 1A to 1B is shown in Figure D.4. While only a reanalysis of

the Run 1A data will provide a more exact comparison, the corrected 1A result and the 1B

result appear consistent.

151

.5 L 18 la systematic error

e
11),)le ..............

_ 9 (5
0.8 :-
0. g. i 1

1A 10 systematic error

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.2 — .,
i 7%
0 0 20 I 40 60 i 80 10 120 140
EINGCV)
2 7 7 '5!
\ ' I x /
$8 " / ‘ /
e / 2
v I %
1.6 Z. 18 la systematic error é
a f
1.4 i— I? :
t e
1 '— """"""""""" quQ--H-E§n# """" """rrtu ----------------
: [389%] in til
0.8 — [:3
0.6 L #1 T
0.4 :- 2
: 1A 10 systematic error /
0.2 ~ 2 // é
. ,l , / / ¢
// r
0 0 20 40 so 80 ' I 100 ' 120 140

E: (GeV)

Figure D.4: Ratio of the “corrected” Run 1A inclusive cross sections to the Run 1B
results in the central (top) and forward (bottom) regions.

Appendix E

Purity Fits

In the purity ﬁts which follow, the mean ET of the sample is given by the ﬁt parameter P1,

the ﬁt purity as the parameter P2. For clarity, statistical errors are not included on the

Monte Carlo points.

152

153

 

 

 

 

 

 

 

 

 

  
  

 

 

 

 

 

 

 

 

 

 

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E-O 5513 CC MC 75 '1 o .1 :0 5848 CC MC 75
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:P1 17.131: 0.0000E+00 PF’l 22.71 :1: 0.0000E+00
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C o 368 cc data :‘o 811 00 data ......“
:0 4333 cc MC'ys "In: E. 8119 cc MC'ys .. .
__ Cl 429 CC MC jets ,' ‘ : El 1608 CC MC jets 1‘ O
f‘r ... F "‘
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W ”W

Figure B]: CC purity ﬁts for ET bins of 10-12, 12-15, 15-21, and 21-25 GeV.

 

 

154

 

 

 

 

 

 

 

 

 

 

   
  
  

 

 

 

 

 

{#1015268 / 37 -x'/n01345.8 / 46
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Figure B.2: CC purity ﬁts for ET bins of 25-30, 30-33, 33-39, and 39-54 GeV.

 

 

155

 

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Figure B.3: CC purity ﬁts for ET bins of 54-60, 60-70, 70-88, and 88-100 GeV.

 

 

 

156

 

 

 

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Figure E.4: CC purity ﬁts for the ET bin of 100-150 GeV.

 

 

157

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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158

 

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159

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Appendix F

Monte Carlo Composites

Following are comparisons of data (points) to a composite of Monte Carlo photons and
jets (histogram) combined using the purity calculated for each bin. Bins are the same as

for the purity calculation in each region.

160

 

161

 

 

 

0 Data 10-12 Ceﬁ o 061012-150ev o 061615-21Cev
- MC MC

 

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I Data 3.3-39 GOV I Data 54-60 GeV

 

 

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P

0.95

   

Figure F. 1: Comparison of data (points) and composite Monte Carlo (histogram)
EM fraction distributions in the central region.

 

162

 

 

 

 

 

 

 

 

 

 

 

 

2 0 Data 60—70 C v : o 0616 70-66 GeV :‘ 0 Data 66-10 v

T— — _

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Figure F.1 (cont’d)

 

 

 

 

_ r o Data10-126ev
p— - MC
1 l l 1 Ii 1 l l I l L
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I Date 21-25 GOV
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I Data 33-39 GOV
- MC

 

163

 

    

 

I Data 12—15 Gev
— MC

 

 

 

 

I Data 25-30 GOV
- MC

 

 

 

O Data 39-54 GOV
— MC

 

 

 

I Data 15-21 Gev
— MC

 

 

 

 

I Data 30-33 GOV

 

 

 

 

I Data 54-60 GOV
— MC

 

 

Figure F2: Comparison of data (points) and composite Monte Carlo (histogram)
Hmatrix x2 distributions in the central region.

164

 

 

I Data 60-70 GeV
- MC

I Data 70—88 GeV
- MC

 
   

 

 

 

 

 

i1 50 100 150 o 50 100 150

 

    

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Figure F2 (cont’d)

 

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165

 

 

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0 1 2

Isolation E, (GeV)

 

Figure F3: Compan'son of data (points) and composite Monte Carlo (histogram)
isolation ET distributions in the central region.

166

 

 

 

    

I Data 60- 7O GOV

I Data 70-88 GOV

IIIIIIIIIITII

 

lLllIllll

 

 

 

     

 

0

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- MC

   

 

 

 

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0.95

 

 

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1— - MC

 

 

 

 

 

167

 

 

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0.

 

 

 

 

0.95

*' I Data 13-21 GeV I Data 21—25 Gev
- 1—
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: — MC
1._.
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I Data 54—60 GeV 1— I Data 60-75 GeV

IIIIIIIIIITTTIIT

 

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Figure F4: Comparison of data (points) and composite Monte Carlo (histogram)
EM fraction distributions in the forward region.

 

168

 

1— 0 Data 75—90 Gev

   

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Figure F.4 (cont’d)

 

 

I Data 25-30 GOV

 

 

 

I Data 39-54 GOV
- MC

 

 

169

 

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1 l

 

I Data 13-21 GOV
- MC

 

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100 150

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- MC

 

 

 

 

I Data 21 -25 GOV
- MC

 

 

50 100 150

Hmatrix);1

 

 

I Data 3.3-59 GOV

 

 

 

I Data 60-75 GOV
— MC

 

 

Figure F5: Comparison of data (points) and composite Monte Carlo (histogram)

Hmatrix x2 distributions in the forward region.

 

170

 

 

I Data 75—90 GOV
- MC

[111

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—
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171

 

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Figure E6: Comparison of data (points) and composite Monte Carlo (histogram)
isolation ET distributions in the forward region.

 

172

 

 

I Data 75-90 GOV —- I Data 90-150 GOV
_ MC ' - MC H

 

 

 

 

 

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Figure F.6 (cont’d)

REFERENCES

REFERENCES

[1] T. Ferbel and W. Molzon, Rev. Mod. Phys. 56, 181 ( 1984)

[2] S. Fahey, Ph.D. Thesis, Michigan State University (unpublished) (1995)

[3] S. Abachi, et al., Phys. Rev. Lett. 77, 5011 (1996)

[4] Review of Particle Properties, Physical Review D54, Part 1 (July, 1996)

[5] S. Glashow, Nucl. Phys. 22, 579 (1961);S. Weinberg, Phys. Rev. Lett. 19, 1264
(1967); A. Salarn, in Elementary Particle Theory, W. Svartholm, ed., Almquist and
Wiksell, Stockholm (1968); J .D. Bjorken, E.A. Paschos, Phys.Rev.185 1975 (1969)

[6] I. Hinchcliffe and J. Womersley, FERMILAB-Conf-96/432

[7] ED. Bloom, et al., Phys. Rev. Lett. 23, 930 (1969); M. Breidenbach et al., Phys.
Rev. Lett. 23, 935 (1969)

[8] F. J. Hasert, et al., Phys. Lett. 46B, 138 (1973)

[9] J .J . Aubert, et al., Phys. Rev. Lett. 33, 1404 (1974); J .E. Augustin, et al., Phys. Rev.
Lett. 33, 1406 (1974); G. Goldhaber, et al., Phys. Rev. Lett. 37, 255 (1976); S.W.
Herb, et al., Phys. Rev. Lett. 29, 252 (1977); D. Andrews, et al., Phys. Rev. Lett. 45,
219 (1980)

[10] R. Brandelik, et al., Phys. Lett. 86B, 243 (1979); DP. Barber, et al., Phys. Rev. Lett.
43, 830 (1979); C. Berger, et al., Phys. Lett. 86B, 418 (1979); W. Bartel, et al., Phys.
Lett. 91B, 142 (1980)

[11] G. Amison, et al., Phys. Lett. 1223, 103 (1983); M. Banner, et al., Phys. Lett. 122B
476 (1983)

173

 

[12]

[13]
[14]
[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

174

S. Abachi, et al., Phys. Rev. Lett. 74, 2632 (1995); F. Abe, et al., Phys. Rev. D52,
2605 ( 1995)

W. Vogelsang and A. Vogt, Nucl. Phys. B453, 334 (1995)
M. Gliick, et al, Phys. Rev. Lett. 73, 388 (1994)
S. Abachi et al, Nucl. Inst. and Meth. A338, 185 (1994)

S. Linn, “The Inclusive Cross Section For Isolated Photons in Run 1A,” DO Internal
Note 2745 (unpublished) (1995)

M. Abolins, et al., Nucl. Inst. and Meth. A280 36 (1989)

A. Spadafora, “Analysis of the Electron Energy Scans from Test Beam Load 1,” DO
Internal Note 1378 (unpublished) (1992)

I. M. Adam, Ph.D. Thesis, Columbia University (unpublished) (1997)

M. N arain, et. al, in Proceedings of the American Physical Society Division of
Particles and Fields Conference, F ermilab, 1992, R. Raja and J. Yoh, ed., World
Scientiﬁc, Singapore (1993)

C. Shaffer, “The Photon Plus One and Two Jets Cross Section,” DO Internal Note
3104 (unpublished) (1997)

T. Sjastrand, Comp. Phys. Comm. 82, 74 (1994)

A. Jonckheere, W. Merritt, “DOGEANT User's Guide,” DO Internal Note 969a
( 1995)

[24] F. Carminati et. al., GEANT Users Guide, CERN Program Library (1991)

[25]
[26]

[27]

[28]

[29]

H.Baer, J. Ohnemus, and IF. Owens, Phys Rev. D42, 61 (1990)
T. Ferbel and W.R. Molzon, Rev.Mod.Phys. 56, 181 (1984)

S. Linn, “The Photon Purity in the Central Rapidity Region,” DO Internal Note 2326
(unpublished) (1994)

A. Spadafora, private communication

A. Peryshkin & R. Raja, “On Sampling Fractions and Electron Shower Shapes,” DO
Internal Note 1215 (unpublished) (1991)

 

175

[30] A. Kotwal, private communication.
[31] H.L. Lai, et al., Phys. Rev. D55, 1280 (1997)

[32] CDF Collaboration, F. Abe et al., Phys. Rev. D48, 2998 (1993); CDF Collaboration,
F. Abe et al., Phys. Rev. Lett. 73, 2662 (1994)

[33] J. Huston et al., Phys. Rev. D51, 6139 (1995)

[34] H.Baer and M. H. Reno, Phys. Rev. D54, 2017 (1996)

[35] E. Berger et al., hep-ph/9610497

[36] S. Linn, private communication.

[37] Nang, F., Ph. D. Thesis, Brown University (unpublished) (1996)

[38] McKinley, J. and Linnemann, 1., “Description of the Level 2 Electromagnetic Filter
Algorithm and Study of the Effects of Shower Generation Method, Zero
Suppression, and Event Generation Method on the Level 2 Electromagnetic Filter

for D0,” DO Internal Note 1354 (unpublished) (1992)

[39] Bantly, J. et al., “DO Luminosity Monitor Constant for the 1994-1996 Tevatron
Run,” Fermilab TM-l995 (1997)

[40] Chopra, 8., Heintz U., and Narain, M., “Comparison of Electron ID Efﬁciencies in
Run 1A and Run 1B,” DO Internal Note 2351 (unpublished) (1994)

[41] Melanson, H., “Electron Efﬁciency Studies,” DO Internal Note (in preparation)

[42] Womersley, 1., “Random Charged Track Overlap Probability in the Central and
Forward Direct Photon Samples,” DO Internal Note 2106 (unpublished) (1994)

[43] S. Linn, private communication