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dissertation entitled

Direct Photon Production at sqrt(s) = 1.8 TeV

presented by

Salvatore T. Fahey

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DIRECT PHOTON PRODUCTION AT fl = 1.8 TeV

By

Salvatore T. Fahey

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

1995

ABSTRACT

Direct Photon Production at fl = 1.8 T eV

By

Salvatore T. Fahey

A measurement of direct photon production from proton-antiproton collisions at the
Fermilab Tevatron center of mass energy of J3 = 1.8 TeV is reported. Photons
were detected in a liquid Argon calorimeter, with charged particle rejection provided
by drift chambers. Subtraction of the neutral meson background was done on a
statistical basis using the depth profile of the calorimeter showers which were modeled
by a detailed Monte Carlo simulation. The efficiencies for direct photon detection
were also studied with Monte Carlo. A comparison of the isolated direct photon
cross section in the central pseudorapidity region (I 17 I< 0.9) with 3. Quantum
Chromodynamics prediction is provided. The data and theory are seen to agree well

over a large range of transverse momenta (12 — 100 GeV).

To my parents, Paul and Rosemarie Fahey.

iii

 

 

 

 

 

es;

Tl

Acknowledgements

I greatly appreciate the work and help of my colleagues in the photon group,
especially Steve Linn, Bob Madden, Paul Rubinov, Greg Snow, and John Womersley.
There were many others not directly related to my analysis who also provided much
needed support. I would like to single out Rich Astur, whose patience with new
students is incredible, and Norman Graf, who was always there to nudge the analysis

back on track.

The support of my friends, both at Fermilab and MSU, has been amazing. I
would like to thank Ian Adam, Gian Di Loreto, Tom Fahland, Eric Flattum, Kate
Frame, Elizabeth Gallas, Steve Jerger, Brent May, Andy Milder, Joelle Murray, and
Tom Rockwell; I will miss seeing you hanging around my desk. Gene Gualtieri and
Kristine Marquard deserve a very special thank you. I hope they know what a

wonderful influence they have been on my life.

The lion’s share of credit for this work goes to my advisor, Bernard Pope. It
is impossible to imagine a better mentor. I may have lost him as an advisor by

graduating, but our friendship will remain as strong as ever.

Finally, my debt to my family goes beyond the obvious. My major regret about
choosing this field is that it takes me so far away from them. Thank you Bridget,

Gus, Paul, Mom and Dad.

iv

 

 

 

 

 

 

Ct

Contents

1 Introduction 1
1.1 Brief Introduction to the Standard Model ................ 1
1.2 Variables for Hadron Collider Physics .................. 6
1.3 Theoretical Underpinnings of Direct Photon Production ........ 7

1.3.1 A Brief Introduction to QCD .................. 7
1.3.2 Direct Photon Production in pf) Collisions ........... 9
1.3.3 First Order Processes ....................... 11
1.3.4 Higher Order Processes ...................... 11
1.4 Previous Direct Photon Experiments .................. 14

2 Experimental Apparatus 16
2.1 The Fermilab Tevatron Collider ..................... 16
2.2 The DO Detector ............................. 19

2.2.1 The D0 Tracking System .................... 19

V

 

 

 

 

3I

3

2.2.2 The D0 Calorimeter System ...................

2.2.3 The DC Muon system ......................
2.2.4 The D0 Trigger and Data Acquisition System .........
2.3 A Brief History of the DO Experiment .................

Data Sample

3.1 Triggers ..................................
3.1.1 Level 1 ...............................
3.1.2 Level 2 ...............................

3.2 Offline Processing .............................
3.2.1 The D0 Reconstruction Program ................
3.2.2 Photon Identification .......................

3.3 Efficiency .................................

Background Subtraction

4.1 Longitudinal Shower Profile Method ..................
4.2 Central Drift Chamber Conversion Method ...............
4.2.1 Matrix Formulation ........................

Isolated Direct Photon Cross Section

5.1 The Differential Cross Section Formula .................

26

31

32

34

36

36

37

37

41

41

44

49

55

59

64

69

75

75

 

 

 

 

5.2

5 Che
6.1
6.2

6.3

7c.

5.1.1 The Number of Candidates, N .................. 76

5.1.2 The Photon Fraction, '7 ..................... 78

5.1.3 The Luminosity, .C ........................ 80

5.1.4 The Geometric Acceptance, a .................. 81

5.1.5 The Photon Efficiency, 6., .................... 82

5.1.6 The Bin Size, Am and A17 .................... 82

5.2 Cross Section vs Transverse Energy ................... 82
5.2.1 Comparison with Theory ..................... 83

6 Characteristics of Direct Photon Events 90
6.1 The Golden Photon Sample ....................... 90
6.2 Jet Identification and Efficiency ..................... 93
6.3 Jet production in Direct Photon Events ................. 95

7 Conclusions 99

vii

 

 

List

1.1

 

1.2

1.3

2.1

4.1

4.2

4.3

4.4

5.1

5.2

5.3

List of Tables

1.1

1.2

1.3

1.4

2.1

4.1

4.2

4.3

4.4

5.1

5.2

5.3

The six Standard Model Quarks. .................... 4
The six Standard Model Leptons. .................... 5
Vector Bosons and their respective forces. ............... 5
Previous Direct Photon Experiments ................... 15

Proposals submitted for a detector at the DO interaction region of

the Tevatron. ’[- Withdrawn, 1- Approved ............... 35
Neutral Meson Background. ....................... 57
Photon Fraction from the EMI Method. ................ 64
CDC Conversion Method Parameters ................... 71
Photon Fraction from the CDC Conversion Method ........... 73
Number of Candidates after cut for each trigger ............. 76
Photon Fraction Fit Parameters ..................... 78
Luminosity of the Photon Triggers ................... 81

5.4 Cross Section Points

 

 

List

 

1.1

1.2

1.3

2.1

2.2

List of Figures

1.1

1.2

1.3

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

Schematic of proton-antiproton scattering. ............... 10
First Order Direct Photon Feynman Diagrams .............. 12
Examples of Next-to-leading Order Direct Photon Feynman Diagrams. 13

The Fermilab Tevatron Collider ...................... 17
Cutaway view of the DO detector ..................... 20
The D0 tracking system .......................... 21
The D0 Vertex Detector .......................... 22
Cross sectional view of TRD layer 1. The dashed lines denote one

anode cell .................................. 24
End view of the CDC. .......................... 25
FDC, exploded view. ........................... 26
Cutaway view of the DO Calorimeters. ................. 27
Diagram of a calorimeter cell. ...................... 28

X

 

 

2.10

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4.1

4.2

 

2.10 Side view of one quadrant of the calorimeter showing the projective

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

3.9

4.1

4.2

tower geometry ...............................

Turn-on curve for Level 1 high ET electromagnetic calorimeter trigger.

Turn-on curve for Level 2 high ET trigger. ...............

z vertex position. The average position of the vertex in run Ia was

not zero ...................................

Isolation distributions for Monte Carlo photons and Z —> ee electron

data .....................................
Missing transverse energy distribution from photon candidates. .

x2 distributions from test beam electrons, pions, and electrons from

W —> at! events ...............................

Offline selection cut efficiency measured with Monte Carlo photon

sample ....................................
The efficiency of the missing ET cut vs photon ET. ..........
Trigger efficiency for Monte Carlo photons which have passed offline

selection cuts. ...............................
Width of jet candidates from data. ...................

Electromagnetic fraction of jet candidates from data. Roughly 4 / 1000

jets have an electromagnetic fraction higher than 90% . ........

xi

30

38

40

43

46

47

50

51

52

54

56

4.3 Minimum separation between photons from we and 1] decays at the
first layer of the calorimeter. The horizontal line denotes the cell size

at pseudorapidity of 0. .......................... 58

4.4 Histogram of the fractional energy contained in the first layer of the

calorimeter for 10 GeV Monte Carlo photons and ads. ........ 60

4.5 Fraction of candidates with EM 1 / E < 1% vs transverse energy for

samples of Monte Carlo photons, background, and data. ....... 62

4.6 Photon Fraction vs Transverse Energy for the Longitudinal Shower
Profile Method. The solid line is a fit to the function 1 — a. x e‘bXET
The dashed lines are from varying the parameters a. and b by enough

to change the x2 one unit. ........................ 63
4.7 Comparison between Monte Carlo and data electrons from Z events. . 65

4.8 Photon fraction for different values of the EMl / E discriminant. The

lines are fits to the three sets of data points. .............. 66
4.9 CDC dE/dx distribution .......................... 68
4.10 Comparison of the photon fraction from the two methods. ...... 74

5.1 Raw number of candidates vs transverse energy. The three large peaks
are from the three different trigger thresholds. The small peak a low

ET is from low energy, non-triggered photon candidates. ....... 77

5.2 Error on the Photon Fraction vs Transverse Energy ........... 79

xii

5.3

5.4

5.5

5.6

6.1

6.2

6.3

6.4

6.5

6.6

Photon Cross Section vs Transverse Momentum ............. 85

Comparison of Photon Cross Section with QCD prediction. The
shaded error at the bottom represents the normalization error on the

data due to luminosity uncertainty. ................... 86
Comparison of data and theoretical predictions with different p. scales. 87

Comparison of data and theoretical predictions with different parton

distribution sets. ............................. 88

Side view of a direct photon candidate event. The photon is in the
lower half of the Central Calorimeter and the jet can be seen in the

right Endcap Calorimeter with tracks in the Forward Drift Chambers. 91

Lego plot of the direct photon event. The height of each element

corresponds to the amount of energy deposited in that calorimeter

Number of jets in direct photon events from the golden photon sample. 95
Photon 45 - jet ()5 for golden photon sample events with one jet ..... 96

Photon 4S - summed jet 4) for golden photon sample events with more

than one jet ................................. 97

Photon and jet 1] distributions for golden photon sample events. . . . 98

Chapter 1

Introduction

1.] Brief Introduction to the Standard Model

High Energy Physics (HEP) is simply the study of the most basic constituents of
matter and the interactions between them. The term “High Energy” refers to the
dominant tool used in extracting this information. The foundation of the experimen-
tal methods used in HEP lies in Rutherford’s scattering experiment with a-particles
and gold foil. The distribution of the angles of the scattered a-particles correctly
pointed to the fact that gold atoms were composed of mostly empty space with a
hard compact nucleus in the center. Modern HEP experiments, while far advanced
in technology, still use the same scattering methodology to illuminate the inner
workings of matter. The size of the details that can be resolved depends upon the
wavelength of the scattered object, thus the smaller the scale of interest the higher

the energy of the beam used. The quest for finer and finer detail has become a quest

1

for higher and higher energy scattering beams.

As the energy of the scattering beams increased in the 1940’s and 50’s (whether
in particle accelerators or in cosmic rays) another phenomenon manifested itself.
Interactions at higher energy led to the production of “strange” new particles, which
were not predicted by any viable theory. What had started in 1947 with Rochester
and Butler’s discovery of the K 0 had exploded by 1960 to include as many as 50
“elementary” particles! Clearly high energy physicists were creating more questions

than they were answering.

In 1964 a mathematical shorthand for classifying the elementary particles was
proposed by Gell—Mann and Zweig [1, 2]. Their idea postulated three elementary
particles (six if you want to count their antiparticles), called quarks, from which

the more massive particles could be built. The three quarks were called the up,

_1
3

down, and strange with charges of +§, , and —31,- respectively. The proton, for
example, could be thought of as being composed of two up quarks and one down
quark. Ordinary everyday matter was composed of up and down quarks, while the
third quark, strange, was used to explain all the strange new particles found in the
1950’s. While this model was satisfying from a theoretical standpoint it had one
major experimental drawback: quarks had never been seen. A free quark, with its
fractional charge, would give a clear experimental signal; a simple Millikan oil dr0p
experiment could provide the necessary evidence. The quark model also had a major

theoretical problem. These quarks needed to have spins of %, yet Pauli’s Exclusion

Principle states that two spin i; objects cannot occupy the same state, as seemed to

3

be the case for the three strange quarks in an (2‘.

Greenberg suggested a way out of the Exclusion Principle dilemma by proposing
that quarks have an additional quantum number called color [3]. A A‘H‘, for example,
could be composed of three different colored up quarks: red, blue, and green. A
rule requiring that all naturally occurring particles are colorless limits the number of
particles that can be created to be consistent with what was seen. Colorless particles
are made by combinations of quarks and anti-quarks (eg blue and anti-blue), or all
colors in equal amounts (cg red, blue, and green). This lack of free quarks suggested
an extremely strong color force tying them together. At the time the quark model

was thought of as a convenient mathematical device rather than a picture of reality.

Then the experimental evidence favoring the quark model started to build up.
Data taken at the Stanford Linear Accelerator Center (SLAC) in the late 1960’s of
electron-proton scattering seemed to point toward the proton having three centers
of charge. In 1974 a new heavy neutral particle called the J /‘¢ was discovered at
Brookhaven/SLAC by Ting/ Richter [4]. Its long life, 1000 times longer than the
other meson particles, seemed to point to new physics. It could be explained by the
existence of a fourth quark, called charm. The charm quark explanation correctly
predicted an array of new particles that were soon found, and the quark hypothesis

took on a new air of respectability. Subsequent experiments found a fifth bottom

quark [5], and finally a sixth, called top, in 1995 [6].

The particles that can be explained as combinations of quarks are called hadrons.

But there are many other particles in the subatomic zoo that are not hadrons and are

Table 1.1: The six Standard Model Quarks.

 

 

 

 

 

 

 

 

 

 

 

 

 

[ Charge Mass (MeV/cz)
down — 51,- 5- 15
up g 2-8
strange —% 100-300
charm g 1,000-1 ,600
bottom —§ 4,100-4,500
top g 180,000

 

 

not made of quarks. One class of these are the leptons. The first lepton, the electron,
was discovered as far back as 1897 by J .J . Thompson. The electron neutrino (V8)
was first postulated by Pauli in 1930 to explain the apparent violation of the law
of conservation of energy in beta decay (the easily overlooked He was carrying away
the missing energy). It was seen experimentally by Cowan and Reines in 1956 [7].
Two other electron-like objects, the muon and the tau particle, were discovered in
1937 [8] and 1975 [9] respectively. Each of these has a corresponding neutrino. The
muon neutrino was discovered in 1962 [10], while the tau neutrino has yet to be
experimentally confirmed. The hadrons and leptons are summarized in Tables 1.1

and 1.2 respectively.

The forces between these particles are also well understood in the framework of
the stande model. All interactions between particles are described by the exchange
of another particle which carries the force. The four forces and their respective ex-
change particles are listed in table 1.3. The quantum theory that describes the

Electromagnetic and Weak forces is called Electroweak theory, a recent consolida-

Table 1.2: The six Standard Model Leptons.

 

 

 

 

 

 

 

Charge Mass (M eV/cz)
electron -1 0.511
electron neutrino 0 < 5.1 x 10’6
muon -1 106
muon neutrino 0 < 0.27
tau -1 1,777
tau neutrino 0 < 31

 

 

 

 

 

 

 

 

Table 1.3: Vector Bosons and their respective forces.

 

 

 

 

 

 

Force Charge Mass (M e V/ c2)
photon Electromagnetic 0 0
gluon Strong 0 0
W:t Weak i1 80000
Z Weak 0 9 1000
graviton? Gravity ? ?

 

 

 

 

 

 

 

 

 

tion of the earlier Weak theory and Quantum Electrodynamics (QED). The theory
of the Strong force is called Quantum Chromodynamics (QCD). In QCD the color
quantum number is the basis for all strong interactions much like charge is in elec-
tromagnetic interactions. Unlike the photons of electromagnetic interactions, the
exchanged gluons carry color and thus couple to themselves. There is no standard

quantum theory for Gravity yet.

6

1.2 Variables for Hadron Collider Physics

It is useful to define a. set of quantities that are consistent among experiments so that
results can be compared. A natural variable for describing the scattering process is
called the cross section. In classical physics this is simply the effective area of the
target, while in quantum physics it depends on the details of the interaction. In a
scattering experiment the relationship between the event rate and cross section is
given by:

R = (IE, (1.1)

where R is the rate, a' is the cross section, and L is a measure of the beam flux,

called luminosity. Luminosity is measured in units of inverse area per second.

Different experiments have different detectors and cover various ranges of phase
space, so what is actually measured is a differential cross section. The natural vari-
ables for describing phase space are momentum (13'), energy (E), azimuthal angle
(45), and polar angle (9). In hadron-hadron collisions the colliding partons typically
have different momenta along the beam direction, giving the center of mass frame
a Lorentz boost with respect to the lab frame. This means that in the lab frame
the longitudinal (parallel to the beam) momenta will not necessarily sum to zero.
Since the incoming partons have negligible transverse (perpendicular to the beam)
momenta, the transverse momenta of the outgoing partons will sum to zero. Trans-
verse momenta (p7) is therefore an important quantity in hadron collisions. The

polar angle 0, which is measured from the beam direction, is also not invariant with

respect to Lorentz boost. It is useful to define a new angular variable rapidity, which

is a measure of the object’s fractional momentum along the beam axis:
y = — tanh'1(%) (1.2)

Rapidity tranforms under Lorentz boost as y —-> y + constant. Distributions of

rapidity are unaffected by Lorentz boost.

In the high energy limit where a particle’s mass is much smaller than its energy

the rapidity of a particle becomes equal to its pseudorapidity (17):
9
1] = —lntan(§). (1.3)

Pseudorapidity has an advantage over rapidity in that it can be calculated even when
the particle’s mass is unknown. An additional variable called detector pseudorapidity
(17“) is sometimes used. Detector pseudorapidity assumes an interaction vertex at

the center of the detector.

1.3 Theoretical Underpinnings of Direct Photon

Production

1.3.1 A Brief Introduction to QCD

Direct photons are produced in interactions between quarks and gluons, and under-

standing these interactions involves knowledge of QCD theory. The force between

quarks and gluons is the Strong force, which has a coupling constant called a,. The
probability for a specific process can be classified by the number of interaction ver-
tices, and therefore the number of times a, enters the calculation. QCD calculations
are performed using the mathematical methods of perturbation theory. The theo-
retical prediction for a process of interest (in this case, direct photon production)
can be expanded in powers of 01,. If a, is small the contributions from higher order
terms are negligible, which significantly simplifies the calculation. With large (1,,

higher order terms contribute more to the sum.

As stated in section 1.1, the Strong force must be powerful enough to bind quarks
tightly, and thus its coupling constant must be large. This would seem to make
higher order terms large and render perturbation theory useless. Luckily, QCD
theory is saved by the strange distance behavior of the Strong force. When quarks
are close together the force between them is small and they can be treated as free.
This is called “asymptotic freedom”. As the distance between quarks increases the
force also increases, which gives rise to quark confinement. If the distance between
quarks increases passed a critical value the energy in the Strong field creates a quark-
antiquark pair. This new pair combines with the original to create two new hadrons
which are colorless, and therefore have no force between them. This process is called

“hadronization” .

So a, becomes manageable at short distances and allows perturbation theory
to work. At high energies (short distances) we can treat the quarks and gluons as

essentially free partons.

9

1.3.2 Direct Photon Production in p13 Collisions

The Standard Model describes the proton as consisting of two up quarks and one
down quark. These “valence” quarks are held together by exchanging gluons be-
tween them. In QCD theory a gluon has a non-zero probability of creating a quark-
antiquark pair for a brief period of time. These quark pairs that blink in and out of
existence in the proton are called “sea” quarks. In the Standard Model, therefore,
the proton is made of valence quarks, sea quarks, and gluons. The momentum of

the proton is carried by both quarks and gluons in roughly equal parts.

Proton - antiproton scattering in the Standard Model is shown diagramatically
in Figure 1.1. The process A + B -—) C + D can be broken into three distinct
parts. The first part involves the probability of finding a parton of given momentum
inside the hadron. The probability of finding parton a within hadron A with a
momentum between a: and a: + dz is given by the Parton Distribution Function
(PDF) Ga/A(a:). The second part contains the perturbative hard scattering of the
partons a + b —> c + d. Finally, the probability of obtaining particle C from parton c
with a momentum between 2 and z + dz is described by the fragmentation function
Dc/c(z). The corresponding expression of the cross section for A + B —+ C + X

(where X can be any outgoing particle) is:
a'(AB —> CX) = Z jdzadzbdcha/A(ma)Gb/B(mb)Dc/C(zc) x [7(ab —> cd), (1.4)
abcd

where the caret indicates a parton level cross section. Thus, the probability for

10

Figure 1.1: Schematic of proton-antiproton
scattering.

a final state can be calculated by summing the parton level cross sections, once
the appropriate parton distribution and fragmentation functions are known [11].
Unfortunately, the PDF and fragmentation parts are examples of the low energy
and long distance regime, which cannot be calculated by QCD perturbation theory.

They must be measured in experiment by processes such as direct photon production.

When calculating direct photon production A + B —> 7 + D the fragmentation
function Dc/c(z) can be replaced by 1, since the photon does not fragment and is
detected directly by the experimental apparatus. This means the PDF part can be
directly measured without the additional ambiguity of a fragmentation function. A
further advantage of studying direct photon processes is that the photon energy can

be well measured by the experimental apparatus. The dominant QCD process at

11

Tevatron energies is jet production, where an outgoing parton fragments into a “jet”
of lower energy particles as a result of hadronization. There are ambiguities both in
the definition of a jet and in deciding which particles belong to the original parton. In
addition, the smeared out jet energy contributes to uncertainties in the experimental

measurement. These problems are absent in direct photon measurements.

1.3.3 First Order Processes

The advantage of direct photon physics as a probe of the gluon content of the pro-
ton can be seen by examining the first order production processes. The two first
order Feynman diagrams, called Gluon Compton Scattering and Quark-Antiquark
Annihilation, are shown in Figure 1.2. At low values of the photon p7- the Gluon
Compton Scattering process dominates, which makes the direct photon cross-section
particularly sensitive to gluon distributions. In deep inelastic scattering, where a
high energy electron is used to probe a proton, the gluon only enters as a second

order process.

1.3.4 Higher Order Processes

The number of processes that contribute to direct photon production increases sub-
stantially in second order. Figure 1.3 shows a sampling of the Feynman diagrams
that must be added into the calculation. As can be expected, the number of possible
diagrams increases substantially at higher order. These corrections to leading order

are potentially very small, but the inability to calculate to all orders can create other

12

GLUON COMPTON SCATTERING

    

QUARK-ANTIQUARK ANNIHILATION

ii 7

Figure 1.2: First Order Direct Photon
Feynman Diagrams.

theoretical headaches.

Higher order diagrams can cause infinites in the calculation [12]. Loop diagrams
lead to what are known as ultraviolet divergences. These loops are virtual states
which can violate conservation of energy for a small amount of time. This violation
can be arbitrarily large, which leads to an infinity when the loop is integrated over
momenta. To avoid this disaster the integral is cut off at an arbitrary momentum.
This procedure is called “renormalization” and introduces an arbitrary momentum
scale a. This means that the strong coupling constant becomes dependent upon the
scale factor, a, —> a,(a). If it were possible to calculate the theory to all orders the
dependence on this renormalization scale would vanish. Various schemes for picking

the arbitrary parameter p exist. The scale is set by the interaction, so choices on

13

206%
363%

Figure 1.3: Examples of Next-to-leading Order Direct Photon
Feynman Diagrams.

 

14

the order of the W of the event are common.

The need to separate the theoretical prediction into a calculable part and a set of
parton distribution functions introduces another parameter. This procedure is called
“factorization” and denoted by the parameter A. The PDF’s depend on the choice
of lambda, but can be evolved to other scales via the Gribov-Lipatov-Alterelli-Parisi
(GLAP) evolution equation. As with a, the natural choice of A is on the order of
the momentum of the event. For the theoretical predictions used in this analysis A
is set equal to a. It is important to emphasize that the choice of scale can affect the

theoretical cross section.

1.4 Previous Direct Photon Experiments

The simplicity of first order processes and sensitivity to gluon distributions are ob-
vious theoretical motivations for studying direct photon production. Unfortunately
there are many ways of producing non-direct photons, primarily as the decay of
neutral mesons. This background problem has been handled by the different ex-
periments in one of two ways. The direct method eliminates the meson decays by
reconstructing a mass between the photon decay products. The direct method re-
quires a finely segmented detector to resolve the two photons, and can only be used
at a low pT range (where the photon decay products are well separated spatially).
The conversion method uses the fact that photons convert into electron-positron
pairs in the presence of matter. Double photon clusters have a higher conversion

probability than single photon clusters, so by measuring the conversion rate of the

15

Table 1.4: Previous Direct Photon Experiments.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Beam fl Max. Place Background
+ Target (GeV) p7 Subtraction
R806 1) + p 63 12 ISR Direct
R108 p + p 45,63 12 ISR Conversion
E95 p + Be 19,24 4 Tevatron Direct
E629 p + C, 7r+ + C 19 5 Tevatron Direct
AFS p + p, p + 13 53,63 10 ISR Direct
R110 p + p 63 10 ISR Direct
UAl p + 13 630 80 SppS Conversion
UA2 p + 13 540,630 43 SppS Conversion
UA6 p + p, p + p 24 7 SppS Direct
NA3 p + C, 1ri + C 19 6 SPS Direct
NA24 p + p, 7:"E + p 24 7 SPS Direct
WA70 p + p, 1ri + p 23 7 PS Direct
E705 p + D, «i + D 24 8 Tevatron Direct
E706 p + C, «i + C 41 10 Tevatron Direct
CDF p + p 1800 100 Tevatron Conversion

 

 

 

 

sample the background can be subtracted statistically.

The first experiment to find evidence for direct photon production was at the
CERN ISR in 1976 [14] using the direct method. Since then there have been a
substantial number of direct photon measurement covering a variety of kinematic
ranges [13]. Table 1.4 contains a summary of some of the more modern direct photon

experiments.

Chapter 2

Experimental Apparatus

2.1 The Fermilab Tevatron Collider

The accelerator at the Fermi National Accelerator Laboratory produces the high-
est energy particles in the world. Protons and antiprotons are accelerated to 900
GeV. There are five distinct stages that bring the protons from rest to this high
energy. Stage one is the Cockcroft-Walton which first adds electrons to hydrogen
atoms, and then pulls these negative ions toward a positive voltage. The ions leave
the Cockcroft-Walton with an energy of 750 KeV, about 30 times the energy of

electrons in a television picture tube.

The ions next encounter the linear accelerator, called the LINAC, which consists
of drift tubes of increasing length. An oscillating electric field is applied to the drift
tubes - the positive potential accelerates the negative ions. The negative potential

is timed to coincide with the ions being inside the tubes, and therefore shielded from

16

17

   

\ TARGET HALL
n, esteem"

/

‘ i ’5“, H ‘-

i F / cocxaorawaaron

Figure 2.1: The Fermilab Tevatron Collider.

the field.

After leaving the LIN AC the ions are passed through a carbon foil which strips
them of their electrons. The remaining protons enter the Booster synchrotron for
stage three of the acceleration. The Booster is a ring 500 feet in diameter which
consists of resonant cavities that accelerate the protons and magnets which bend the
particles into a circular path. The beam circulates in the Booster about 20,000 times
before it leaves, pumping the energy up to 8 GeV. The beam, actually a “bunch” of

protons, then enters the Main Ring.

The Main Ring is another synchrotron like the Booster, only 13 times larger,
almost 4 miles in circumference. It lies in a 10 foot wide tunnel buried 20 feet

underground. It consists of 1000 conventional copper-coiled magnets that bend and

18

focus the protons, which are accelerated to an energy of 150 GeV.

The final stage is the Tevatron synchrotron, which occupies the same tunnel as the
main ring. The Tevatron’s magnets are wound with superconducting wire which must
be cooled to a temperature of —450 deg F by liquid helium. The superconducting
magnets are needed to produce the large magnetic field necessary for bending the

beam of protons which now reach an energy of 900 GeV.

Antiprotons are produced by siphoning off some of the protons from the Main
Ring and focussing them onto a target, usually made of nickel. The collisions pro-
duce many secondary particles, some of which are antiprotons. These antiprotons
are selected and transported to the Debuncher ring which sits in a separate antipro-
ton tunnel (a triangular ring 500 ft per side). The Debuncher ring condenses the
antiprotons into a bunch with a small range of constituent proton momenta by a
process known as stochastic cooling. The antiprotons are then stored in the Ac-
cumulator ring which occupies the same tunnel as the Debuncher ring. Then they
are transferred to the Main ring where they circulate in the direction opposite to
the protons. Finally they are injected into the Tevatron ring and ramped up to
an energy of 900 GeV. The counter-clockwise rotating antiprotons collide with the
clockwise rotating protons at two interaction points — BC and DO. During data
run Ia the collider was operated in “six-on-six” mode, six bunches of protons collid-
ing with six bunches of antiprotons. The time between colliding bunches in run Ia
was 3.5 pace. The total integrated luminosity processed by the D0 experiment in

run Ia was 16 pb".

19

2.2 The DC Detector

Surrounding the Tevatron at the DO interaction region is the DO detector [15] (see
Fig 2.2), weighing 5500 tons and standing 40 feet high. It can be separated into three
subsystems — the Tracking, Calorimeter, and Muon detection systems. A particle
travelling outward from the interaction region would first encounter the wires and
chambers of the DO tracking system, which traces the path of all charged parti-
cles. Next the particle would enter the liquid Argon Calorimeter, where electrons
and hadrons would deposit their energy and stop. Muons, which have more mass
than electrons and interact less often than hadrons, are able to punch through the
calorimeter and hit the Muon tracking system. Their paths are bent by the iron
toroid and their tracks seen in the muon chambers. Their momenta can be calcu-

lated by the curvature of their tracks.

The DC detector is thorough enough in its identification of particles over a large
area of phase space to provide for many diverse physics analyses. The particular
analysis discussed in this thesis does not use the full capabilities of this large ma-
chine, but a brief discussion of all major detector subsystems is included below for

completeness.

2.2.1 The D0 Tracking System

The tracking system (see Fig. 2.3) consists of four separate detectors. The

innermost region is covered by the Vertex Detector, which is used to pinpoint

 

 

 

 

 

 

 

 

20
l l
._J L : — ‘ : u
l
l J I
' \ \
i; \
\K‘ \ 2
\ \ .

 

 

 

 

 

D6 Detector

Figure 2.2: Cutaway view of the D0 detector.

 

_‘_r_

P7
;.___
hi:

6“
,_- z) u I

 

 

 

21

l I 7 ll V I I
l l
I In
Ill Ill
lll ll]
(1) 9

Central Drift Vertex Drift TranSitim Forward Drift

Chamber Chamber Radiatim Chamber
Detector

 

F

 

—

 

I—
.—

 

—
.—

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.3: The DC tracking system.

the proton-antiproton interaction vertex (and any possible secondary vertices). It
covers the :i:2.0 region in pseudorapidity. Surrounding it in the central region
(—1.2 < 17“ct < 1.2) is the Transition Radiation Detector which can be used to
discriminate between electrons and pions. Furthest from the beam pipe are the drift
chambers — the Central (—1.2 < 17“ct < 1.2) and Forward (1.4 (I 11““ I< 3.1) Drift
Chambers. They track the path of a. charged particle and can also be used along

with the Vertex Detector to determine the interaction point.

Vertex Detector (VTX)

The proton-antiproton collisions in the D0 interaction region do not always occur

at the same spatial point. In fact, for the 1992-93 data run the vertex position could

22

Sense

Grid

Cathode
Coarse Field
Fine Field

 

I
.........
n 0

Figure 2.4: The DC Vertex Detector.

be described by a Gaussian with a width of 25 cm and offset 8 cm from the center of
the detector. The measurement of the transverse momentum of a particle depends

on the correct determination of the vertex position.

The VTX [16] has an inner radius of 3.7cm, an outer radius of 16.2cm and is
116.8cm long. It consists of three independent concentric layers of drift cells. Each
layer is separated into azimuthal (45) sections — 16 for the inner layer and 32 for the
two outer layers. As a charged particle passes through the VTX cells it ionizes the
C 02 — ethane gas. The freed electrons then drift in an electric field and are collected

on sense wires which provide a measure of the r — ¢ coordinate. The sense wires are

23

read out at both ends to provide a measurement of the position along the beam pipe

(2) using charge division.

Transition Radiation Detector (TRD)

Charged particles radiate photons when passing through boundaries between regions
of different dielectric constants. The energy depends on the Lorentz factor, which
is inversely proportional to the square root of the mass of the particle. Therefore
the amount of radiation from electrons is different from the amount from hadrons
of the same energy. The TRD [17] takes advantage of this with three layers of 393
polypropylene radiator foils and an X-ray detector. The 18 pm thick foils are sepa-
rated by a gap of 150 pm and are housed in an He filled enclosure. The X-ray detector
is mounted just outside the radiator foils and contains a gas of XC(90%)02H6(10%).
The radiated photons ionize the gas in the first few millimeters of the X-ray chamber
and the charge is detected on the sense wires. Figure 2.5 shows a diagram of the first
layer. The radiator and X-ray detector packages are separated by two mylar cylin-
ders, between which dry N2 gas is circulated. This is done to prevent the radiator

helium from contaminating the chamber gas.

Drift Chambers (CDC and FDC)

The Central and Forward Drift Chambers (CDC and FDC) operate on the same
principle as the VTX. Charged particles passing through a gas liberate electrons

which are collected on sense wires. Signals are induced by the sense wires on two

24

CROSS-SECTION OF TRD LAYER 1

OUTER CHAMBER SHELL
70am GRID WIRE
ALUMINIZED MYLAR
8m

15mm . .

  
 
   

  
 

 

 

 

 

 

O
_____ _. _. .. _ _ _ _ _. _
4
2mm’. mm
C O
O
_____ _. _ _ __ _ _ _ __
C
RADIATOR STACK CONVERSION . 0
STAGE 0]
N2
30am ANODE WIRE
/ 100nm POTENTIAL WIRE
23pm MYLAR WINDOWS

HELICAL CATHODE STRIPS

Figure 2.5: Cross sectional view of TRD layer 1. The dashed lines denote one
anode cell.

25

 

 

 

 

 

 

 

Figure 2.6: End view of the CDC.

delay lines which are read out at each end and give the z-direction measurement.

The CDC [18] is divided into four concentric layers parallel to the beam line (see
figure 2.6). Each layer is subdivided into 32 43 cells. There are seven sense wires per

cell and two delay lines. The CDC has an inner radius of 49.5cm and an outer radius

of 75.4cm.

The FDC [19] is a drift chamber like the CDC but with a radically different design.
Whereas the CDC looks like a cylinder parallel to the beam, the FDC resembles a
disk perpendicular to the beam. It is subdivided into three separate disks — two
subdivided in 0 with one in d) sandwiched between (see figure 2.7). The 45 layer is

divided into 36 azimuthal chambers, each with 16 sense wires that extend radially

26

 

 

 

 

 

Figure 2.7: FDC, exploded view.

outward. The two 9 layers are divided into four quadrants. The quadrants consist of
six chambers stacked radially, with eight sense wires per chamber. The two 0 layers

are rotated by 1r / 4 with respect to each other.

2.2.2 The DC Calorimeter System

After passing through the central tracking detectors, a particle will next en-
counter the cryostat wall of the DC calorimeter system [15] (see Fig 2.8). Photons
leave no tracks in drift chambers and never make it to the muon system, making

the calorimeter the main detector system of interest for this work. There are in

27

or LIQUID ARGON CALORIMETER , h.

 
  
  
  
 
   
 
 
 

END CALORIMETER
Outer Hadronic
(Coarse)

Middle Hadronic
(Fine & Coarse) ,

CENTRAL
CALORIMETER
Electromagnetic

Inner Hadronic Fine Hadronic

(Fine & Coarse) Coarse Hadronic

Electromagnetic \ \\_// t

Figure 2.8: Cutaway view of the D0 Calorimeters.

28

Resistive Coat
Absorber Plates —-— G 10
Is I. At Gaps K 7

 

 

 

 

 

 

 

 

/ II t II II II \\

70u Pads

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.9: Diagram of a calorimeter cell.

fact three separate cryostats housing the three separate calorimeters — one Central
Calorimeter (CC) and two Endcap Calorimeters (ECs). The are all liquid Argon
sampling calorimeters. Liquid Argon is the medium ionized by the incident particles
and sampling refers to the fact that only a fraction of the deposited energy is ac-
tually measured (roughly 10 ‘76). The basic design of the calorimeter is a sandwich
of liquid Argon, readout boards, and absorber plates. A particle deposits energy in
the Argon by ionizing, and these electrons are collected and read out by the signal
boards. The absorber plates absorb the particle’s energy and cause it to shower, i.e.

create secondary particles. Figure 2.9 shows a diagram of a calorimeter cell.

The Central Calorimeter covers the pseudorapidity region of | 11““ |< 1.2. It is

29

divided radially into three different sections — the Electromagnetic (EM), the Fine
Hadronic (FH), and the Coarse Hadronic (CH). The EM section is the innermost
region and contains four separate layers. The absorber used is uranium, which is
dense enough to provide good stopping power with a limited volume. Lepton and
photon showers are usually wholly contained in the EM section, which makes it the
most important section for this analysis. It is divided into four depth layers (EM1-4)
with longitudinal segmentation of 2,2,6.8, and 9.8 radiation lengths. The FH section
is next, which also uses uranium as the absorber. There are three FH depth layers.
The bulk of hadronic showers are contained in the FH layers. Farthest from the
beam pipe is the single layer of the CH section, used to contain those rare hadronic
showers that punch through the PH. Copper plates are used as the absorber in the

CH.

The two Endcap Calorimeters cover the region of 1.5 <| 11““ |< 4.5. Like the
CC, they are divided into a EM, FH, CH sections. Unlike the CC, the FH section
is divided into four depth layers rather than three. The absorber used in the CH

section is stainless steel.

Both calorimeters are segmented in projective towers of A1) x A45 = 0.1 X 0.1
which point back to the nominal interaction point (see figure 2.10). The third EM

layer is further subdivided into cells of A17 x A45 = 0.05 x 0.05. This allows for

additional shower shape pattern recognition.

The calorimeters were calibrated and studied at the DC test beam [20]. Mo-

noenergetic beams of electrons and pions from 2 to 150 GeV were aimed at various

30

a)

DIV-POOQCDAN O

 

Figure 2.10: Side view of one quadrant of the calorimeter showing the
projective tower geometry.

31

sections of the calorimeter. The response was found to be linear above 10 GeV.

The resolution for electrons and pions was measured and found to be 15% / x/E and

50% / JD- respectively.

The region between the CC and ECs, 0.8 <| 17““ I< 1.4, consists mostly of
calorimeter support structures and cryostat walls. This creates an area where energy
is not well measured. To correct for this shortcoming two additional calorimetric
devices were added. The first are called Massless Gaps which are mounted onto the
inside of the calorimeter cryostats. They consist of two signal boards which collect
the ionization energy deposited in the liquid Argon near the cryostat wall. A second
type of detector, called the Inner Cryostat Detector (ICD), is mounted between the

cryostats. The ICD consists of 384 scintillator tiles which are read out by phototubes.

2.2.3 The DC Muon system

The DC Muon System consists of five iron toroids and three superlayers of single
wire Proportional Drift Tubes (PDTs). The first layer, called the A layer, consists
of four sublayers of PDTs and is mounted on the inner face of the toroid magnet.
Hits in the A layer are formed into tracks which point back to tracks in the Central
Detectors. The other two superlayers, B and C, are mounted on the outside of the
magnet and each contain three sublayers of PDTs. Tracks in the B and C layers
are matched with the A layer tracks. The muon momenta can be determined by the
amount of deflection caused by the magnetic field in the toroid. The Wide Angle

Muon System (WAMUS) covers the region of | 11““ I< 2.5 and the Small Angle Muon

_ ’7—

32

System (SAMUS) extends the coverage to I 11““ |< 3.6.

2.2.4 The DC Trigger and Data Acquisition System

The time between colliding bunches of protons and antiprotons in Tevatron run Ia
was 3.5asec, or 286,000 bunch crossings per second. While the rate of inelastic colli-
sions (interactions where the proton breaks apart) depends on the beam luminosity,
a typical rate in run Ia was on the order of 200,000 times per second. As can be
imagined, reading the 150,000 channels of information from the detector is not pos-
sible at this rate. A typical event contained on the order of 250 kilobytes of data.
The data was written to magnetic tape at a rate of 2 events per second. The difficult
task of reducing the event rate from 200kHz to 2Hz is handled by the DO Triggering

system.

The DC Trigger system consists of three levels. Each subsequent level is more
restrictive, yet slower and more precise, than the preceeding one. For an event to

make it in to the data stream it must pass the requirements of each level.

Level 0

The first level of triggering is the Level 0 detector [21]. It consists of two scintillator
hodoscopes mounted on the inside faces of each of the EC cryostats, 140cm from
the center of the detector. Each hodoscope has two perpendicular planes of 28

scintillating tiles. They cover the pseudorapidity range of 1.9 <| 17““ |< 4.3.

In the event of an inelastic collision both hodoscopes will fire (with ~ 99% effi-

33

ciency). The vertex 2 position can be determined by timing information. The Level
0 detector can also flag possible multiple interaction events. The trigger can be set
up to require a single vertex, multiple vertices, a 2 position in a specific range, or

any combination thereof.

Level 1, The Hardware Trigger

Events passing the Level 0 requirements are sent to the Level 1 triggering system [22].
The Level 1 trigger provides a decision before the next bunch crossing, but with
limited programmability. The Level 1 system can be programmed with up to 32
different requirements. Each of these separate requirements, called triggers, can be
optimized for a specific physics analysis. Level 1 decisions use information from two

detector systems — the Calorimeter and Muon detectors.

The Calorimeter Level 1 Trigger makes fast hardware sums in trigger towers of
0.217 x 02¢. Each tower has both an electromagnetic sum (using the EM section)
and a total (using the EM and FH sections). Cuts can be applied on the number of
towers above a programmed threshold set, which can specify different thresholds for

each tower.

The Muon Level 1 Trigger counts the number of muon tracks in each region of
the Muon system. If additional processing is required (for example, a cut on the
muon p1) a Level 1.5 decision is requested. This incurs a detector deadtime of one

beam crossing.

34

Level 2, The Software Trigger

The Level 2 system [23] consists of a farm of 50 VAXstation 4000/60 processors
which run Fortran analysis code. When one of the 32 Level 1 triggers has fired
the full detector information is digitized and sent to one of the VAXstations. Each
processor is loaded with the same code, which is modularized into software “tools”.
The processor runs the appropriate tools associated with the Level 1 trigger. There
can be more than one Level 2 trigger associated with each Level 1 trigger. Events
that pass the Level 2 trigger are copied to tape to be analyzed further by an offline

computer farm.

2.3 A Brief History of the D0 Experiment

In 1981 the Fermilab directorate issued a call for expressions of interest in a detector
to be built at the DO interaction point on the Tevatron accelerator ring. The new
detector would take advantage of a Fermilab upgrade which would enable proton and
antiproton collisions at a center-of-momentum energy of 1.8 TeV, the highest in the
world. A detector had already been approved for construction at the B0 crossing
point in 1978. The DC detector was planned to be a smaller and less expensive
complement. The proposals submitted are summarized in table 2.1. By late 1982
some merging of the groups was already taking place. Early 1983 saw the discovery
of the W and Z bosons at CERN and the cancellation of ISABELLE, a proton-proton

collider slated to be built at Brookhaven. With this in mind the Physics Advisory

35

Table 2.1: Proposals submitted for a detector at the DC interaction region of the
Tevatron. '|'- Withdrawn, 1- Approved

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

| # Spokesperson Description Proposed Rejected
709 Longo forward detector 1/ 1 1 / 82 6 / 23 / 82
712 Rappl muon production 2 / 1 / 82 6 / 23 / 82
713 Price heavily ionizing particle search 2 / 5 / 82 7 / 1 / 83
714 Grannis LAPDOG (calorimetric) 2 / 5/ 82 7/ 1 / 83
717 Lach forward detector 3 / 19 / 82 6 / 23/ 82
718 Erwin calorimetric detector 4 / 1 / 82 6 / 23 / 82
722 Kenney streamer chambers 10 / 1 1 / 82 2 / 18 / 82
724 Longo calorimetric detector 10 / 26 / 82 7 / 1 / 83
725 Goulianos diffractive dissociation 1 1 / 1 / 82 7 / 1 / 83
726 Abolins calorimetric detector 11/1/82 7 / 1 / 83
727 Rosen forward calorimeter 11 / 2 / 82 6/16/831
728 Green a production (supersedes 712) l 1/ 1 / 82 7 / 1 / 83
736 Adair free quark search 4 / 1 1 / 83 7 / 1 / 83
740 Grannis D0 9/9/83 8/10/841

 

 

 

 

 

Committee decided to reject all DO proposals and recommend the construction of
a more ambitious detector and asked Paul Grannis to head that effort. The current

DC detector is the result of the merging of proposals 714, 726, and 728.

Chapter 3

Data Sample

3. 1 Triggers

The direct photon event rate decreases quickly with increasing photon transverse
energy. In order to populate the full range of pr, from 10 to 100 GeV, the direct
photon triggers were split into three streams — low, medium, and high. The rate of
events with low pT photons is too large for the D0 DAQ system and only a fraction
of events can be written to tape. This rate reduction is done by statistically ignoring
some events, called prescaling. A prescale rate of 100 means that only one out of
every 100 events is accepted by the DAQ system. The medium photon trigger was
also prescaled for most of run Ia. Prescaling is not needed for the high photon trigger,

because its rate is low enough for the DAQ system to accept every event.

36

37

3.1.1 Level 1

The three Level 1 triggers used involved simple cuts on the electromagnetic energy
in a trigger tower. A trigger tower is a collection of 4 calorimeter readout towers
ganged together, with a transverse width of A17 x Ad = 0.2 X 0.2. The cuts were set
at 2.5, 7, and 12 GeV for the low, medium and high triggers respectively. Often the
energy of a photon candidate is shared between two trigger towers which can cause
the energy in any one tower to be less than threshold. This effect makes a trigger
inefficient for candidates with an energy close to the trigger threshold. This effect
was measured from data by taking events which had passed a lower threshold trigger
and observing the pass rate for a higher threshold trigger (see figure 3.1). Since a
lower efficiency could create a bias in the candidates that passed, only candidates

with an E7» high enough for the trigger to be fully efficient were used in this analysis.

3.1.2 Level 2

The Level 2 trigger used a list of candidate towers from Level 1 as seeds and searched
for the highest energy EM3 cell in the tower. It then clustered the calorimeter energy
in the EM and FHl layers around the peak cell in a window of A1) x Ad = 0.3 x 0.3.

Cuts were applied to the candidate cluster in the following order:

0 The transverse energy of the candidate cluster must be above a specified thresh-

old. The three Level 2 thresholds used in run Ia were 6, 14, and 30 GeV.

38

Level 1 Hiqh Trigger (Er > 10 GeV)

 

l
l
o
I

_o__°.-0—0—0—0-0—0—0—0—0-0—0—0—0—0—O-

Relative Efficiency
3
I

0.6 7" -0-

 

0.4 —

0.2 [- +-

0 l l l 1 1 L L l l l l l l l 1 1 l l l A J I L l I I

10 20 so 40 so so
Candidate Offline Er

 

 

 

Figure 3.1: Turn-on curve for Level 1 high ET electromagnetic calorime-
ter trigger.

 

39

o The hadronic energy of the cluster (is energy in the hadronic section of the

calorimeter) must be less than 10% of the total energy.

0 The energy deposited in the EM3 layer must be greater than 10% and less than

90% of the total.

0 The shower shape in the plane transverse to the particle direction must be
consistent with electron showers from the test beam. This cut defines a lateral
spread variable which is simply the difference between the second moment of
energy in a 0.5 x 0.5 window and the second moment in a 0.3 x 0.3 window.
This number is expected to be low for photon and electron showers. The actual

cut value varies with 17.

o The candidate must pass an isolation cut, defined as

Er=.4 _ Eduster
Eduster

 

< 15%, (3.1)

where r = .4 denotes a cone of radius 0.4 around the candidate with

r = (A)? + ¢2. (3.2)

Turn-on curves were plotted for the Level 2 trigger as well, and data were used only

in the region of 100% efficiency (see Fig. 3.2).

d

Relative Efficiency
.0
m

0.6

0.4

0.2

40

Level 2 Com High Trigger E, > 30 GeV)

 

 

 

 

 

 

 

 

 

- -0-O-0-O-0-0-0-0-0-0-O- -0-0-0-O~ -0-O-0-0-0-
l— 0'
.0.
+—
,. .4).
L -<>-
' -<>-
llllllf§1_l_l%lLJllllll[ALLIIIllllllllLlllll
20 25 30 35 40 45 5O 5 60

5
Candidate Offline E,

Figure 3.2: Turn-on curve for Level 2 high ET trigger.

 

41

3.2 Offline Processing

Events that have satisfied the Level 2 selection criteria were written to 8 mm mag-
netic tape. These tapes were then stored for further processing. Unlike Level 2, the
offline processors are not subject to stringent time constraints and can therefore run
more sophisticated algorithms. A farm of 100 Unix processors is used to run the DO

reconstruction program (DORECO).

3.2.1 The DC Reconstruction Program

The raw detector information is converted to physics information by the DORECO
program. DORECO is a huge program, with over 1 million lines of code, written
primarily in FORTRAN. It is modularized into separate sections which analyze the
data from the separate detector subsystems. There are two primary sections used
for this analysis, called ZTRAKS and CAPHEL. ZTRAKS uses the central tracking
system to identify the 2 position (position along the beam line) of the primary inter-
action vertex. CAPHEL is used to cluster cells of energy deposits in the calorimeter

and identify them as photons or electrons.

ZTRAKS

Since the calorimeter measures energy and not momentum, transverse energy (ET)

becomes the primary quantity of interest. At high energy ET and p7 are roughly

42

equivalent. ET is defined as

ET 2 E X sin(0) (3.3)

where 0 is the polar angle measured from the beam axis.

Measurement of ET therefore depends upon measurement of the coordinate sys—
tem origin or vertex. The beam spot has a small cross section, making the vertex
stable in the a: — 3] plane. As Fig. 3.3 shows, the vertex in the z direction can vary by
as 1 meter from event to event. ZTRAKS works by reconstructing charged particle
tracks in the CDC and projecting them back to a vertex. The track reconstruction

proceeds as follows:

0 Reconstruct tracks in the r — d plane from aligned hits in the drift chambers.

The r — d tracks are then reconstructed in the r — 2 plane.

Project the reconstructed tracks onto the z axis (r = 0). The z-position of

each track is then histogrammed in 2 cm bins.

The histogram bin with the largest number of tracks is combined with its

neighboring bins to form the primary cluster. Smaller clusters form secondary
vertices. If no bin contains more than two tracks, the largest contiguous set of
bins is used to determined the primary vertex. The cluster mean 2 and error

on the mean define the z vertex position and resolution.

0 If there is only one track in the event the z-position at r = 0 from that track

is used for the primary vertex.

43

Vertex; Position
‘2w I. Mean -7.884
RES 25.57

I I f

 

 

o LLLlLJJL+LAllAAllAAlLAllALAlL A A_—A
-100 —60 -60 -‘0 ~20 0 20 ‘0 60 80 100

 

Figure 3.3: 2 vertex position. The average posi-
tion of the vertex in run Ia was not zero.

The resolution of the vertex position depends upon the number of tracks, but is
typically approximately 1cm. Figure 3.3 shows a plot of the reconstructed vertex

for the run Ia direct photon events.

CAPHEL, CAlorimeter PHotons and ELectrons

The CAPHEL reconstruction package creates clusters of calorimeter cells using a
nearest neighbor algorithm. Readout towers (0.1 X 0.1 in r) X d) with more than
1.5 GeV of ET are used as seed towers. Neighboring towers (towers that share a
common border with the seed) are added to the cluster if their ET is above 0.05 GeV.
Then towers bordering this cluster are added. The cluster is expanded in this way

until no neighboring towers above threshold are found.

44

3.2.2 Photon Identification

Photons are uncharged and therefore leave no tracks in the tracking chambers. They
deposit energy in the EM section of the calorimeter in showers with a relatively small
transverse size. The cluster is also expected to be well isolated from othdr activity in
the event, as can be seen from the leading order direct photon Feynman diagrams.
The photon signature is therefore a small cluster of cells in the EM calorimeter
with no associated track. This motivated the Level 2 cuts detailed above, and an
additional stricter set of cuts were applied offline to reduce the number of background
events in the sample. Fiducial cuts were also applied offline to restrict the photon

candidates to an active region of the calorimeter, where the photon energy was well

measured. The fiducial cuts used were:

0 The cluster must be in the Central Calorimeter with a detector 1] (11‘1“) coor-
dinate of less than 1.0 (corresponds to a polar angle between about 40° and

140°). Detector 1] assumes a z-vertex of 0 cm.

0 The cluster must have a physics 1] of less than 0.9. Physics 1] used the z-vertex

position found by ZTRAKS.

o The z-vertex position of the event must be within 50 cm of the nominal inter-

action point (206,,“ = 0).

o The d coordinate of the center of the cluster must be at least 1.125° away from
the detector d cracks. This puts the center of the cluster in the middle 80% of

the detector module.

45

The other cuts applied offline were:

0 The cluster must have no reconstructed CDC track in a road of size A17 X Ad 2

0.1 x 0.1.

o The electromagnetic fraction, defined as

. EM Er=.2
EMFractzon — Total Er=.2 (3.4)

 

of the cluster must be greater than 96%.

0 Less than 2GeV of ET in an isolation cone of radius 0.4 around the cluster (see
figure 3.4):

E}=-4 — E?“ < 2 GeV. (3.5)

Note that the offline isolation cut was independent of photon ET, while the

trigger isolation cut was not.

0 The missing ET in the event was required to be less than 20 GeV (see figure 3.5).
An ET unbalance in the event is typically caused by either a neutrino, which

should not be present in a direct photon event, or a noisy calorimeter cell.

0 The shower shape of the cluster was required to be consistent with the observed

shower shape from electrons in the DO test beam data.

The final cut deserves further explanation. The statistical fluctuations present in
the development of a calorimeter shower make cuts on any single variable inefficient.

A multivariate cut can potentially take these fluctuations into account, raising the

46

 

 

 

 

 

m Isolation Er
€0.16 -
v t'
> .
w P
'80.“ — O electrons from 2 events
% _ Monte Carlo photons
r
€0.12 —
o .
Z .
0.1 -
0.08 -
0.06 —
r
I-
0.04 _
0.02 - + +
. + 4.,
T I I I I ' ‘
0111: [Ill 1111 1L11 11411LJ
—1 0 1 2 3 4 5

(DA r-J
Er " Er

Figure 3.4: Isolation distributions for Monte Carlo pho-
tons and Z —> as electron data.

47

 

1250

1000

750

“IIU‘IU‘UVIYV'YIUVUTIYTII[TUITIIUWTI

 

250

 

 

 

llllllllllllllLlllllAlll L--a4

5101520253035404550
Missing Transverse Energy (GeV

 

OWI'I

Figure 3.5: Missing transverse energy distribution from
photon candidates.

48

background rejection along with the efficiency over any single cut [24]. A covariant

matrix was defined for a sample of N test beam electrons:

1 N n — n -
Mo = NEW '- a=-')(='=,- — 31') (3-6)

71

where a:-

, is the value of observable i for electron n and 2?.- is the mean value of

observable i for the sample. Once the matrix is tuned on a signal sample, a x2 can

be computed for every candidate 1::
X2 = ZOE? - 5.)H.-,-(:cf - 51') (3-7)
to

with

H=M4. mm

Notice that if the off-diagonal elements of the H matrix are zero (i.e. there are no

correlations between the observables), equation 3.7 reduces to the familiar definition

det

of x2. Thirty seven H matrices, one for each 17 readout tower, were tuned on

samples of test beam electrons. Forty one observables were used:

Fractional energy in EM layers 1,2 and 4.

0 Fractional energy in each cell in a 6 X 6 window around the cluster in EM layer

3.

108100”-

Vertex 2 position (z/az).

49

Figure 3.6 shows distributions of this x2 for calorimeter showers from 25 GeV
electrons and pions [25]. Electrons from W events are shown to agree very well with
the test beam electron sample. It can be seen from the plot that requiring the x2 to

be less than 100 provides excellent rejection of pions with good electron efficiency.

3.3 Efficiency

The efficiency for the selection criteria detailed above was measured with simulated
direct photons, called the Monte Carlo sample. These events were created using
CERN’s GEANT[26, 27] package, which tracks the passage of particles through mat-
ter. Data taken with a minimum bias trigger (only a level 0 requirement) were added
to the simulated photon events to create the effect of detector noise and multiple
interactions. The distributions from the Monte Carlo were found to agree with elec-

trons from Z —r ee and W —> eu events (Z and W events yield an unambiguous
signal).

Figure 3.7 shows the offline cut efficiency vs transverse energy for this Monte
Carlo photon sample. The efficiency for each cut is defined as the number of can-
didates that survived the cut divided by the number before the cut. Since the cuts

can be correlated, the individual efficiency of each cut depends upon the order of the

cuts.

The missing ET cut is absent from figure 3.7. This is because the Monte Carlo

sample only simulated the photon in the event; the jet (or jets) balancing the photon

50

El electrons
@ pions

number of events

 

ii

10 102 1

 

Figure 3.6: x2 distributions from test beam electrons, pions, and elec-
trons from W —) an events.

 

51

 

 

 

>s
U
c 1*-
S!
o ' ______ _____________.._.
33 ~ WW -
Lu 7‘?’ ......... *~-~. “'
- n.-.-.. ..... . ----------
I ‘1
0'8- .
I
r- I
I

 

0.6 -

- 0 Track Veto

- I EM F roction cut
0.4 — A Isolation cut

. V Hmctrix cut

- 0 TOTAL
0.2 —

 

 

O llllllllllLlLllllllllllllllJlllllllllllIl

o 10 20 so 40 so so 70 so
Photon Transverse Energy (GeV)

 

Figure 3.7: Offline selection cut efficiency measured with Monte
Carlo photon sample.

 

52

 

 

 

 

   
 

 

 

, 2 Efficigncv of Missing E; Cut v3 Photon El
5" {/mr 42.20 / 44
c A0 1.017
.3 AI -o.issss-02
::
.-
m 1— +

0.3 —

Eff=A,+A.tE.

oer

0.4 -

0.2 >-

o I‘llllLALlLAIIlllljlllllilllllllllllIlllllJlllllA

orozosowsoeoroeosoroo

 

 

 

Transverse Energy (GeV)

Figure 3.8: The efficiency of the missing ET cut vs photon ET.

was not simulated. The large amount of computer time necessary to track all the
particles in a jet made full event simulation impossible. This caused the Monte
Carlo sample to have missing ET which is always equal to the transverse energy
of the photon. The efficiency of the missing ET cut was derived by dividing the
number of candidates which pass all cuts by the number which pass the cuts when
the missing ET cut is not applied. Figure 3.8 shows a plot of this efficiency vs the
transverse energy of the photon candidates. This was then fit to eliminate the effect

of an excessive number of hot cell or W —r eu events in any one bin.

Figure 3.9 is a plot of the efficiency of the trigger for Monte Carlo photons which

have passed the offline selection cuts. The trigger efficiency is 100% for most of the

 

transverse energy range.

53

54

 

 

Efficiency

i

0.8 [—

0.6 _
0.4 -

0.2 —

 

 

o 11111111111llllllLlJllllllllllllllllllllllllllll

10 20 so 40 so so 70 so 90100
Photon Transverse Energy (GeV)

 

Figure 3.9: Trigger efficiency for Monte Carlo photons which have
passed offline selection cuts.

Chapter 4

Background Subtraction

As discussed in Chapter 1, the simplicity at the theoretical level makes direct photon
production an inviting test of QCD. There are experimental issues, however, which
make the measurement more problematic. The largest of these difficulties at high

transverse energy is the subtraction of background from the data sample.

Jet production at Tevatron energies has a cross section about three orders of
magnitude larger than direct photon production. A jet is composed of both charged
and neutral particles. The charged hadrons in a jet leave most of their energy
in the hadronic section of the calorimeter, while some neutral hadrons often have
decay modes into photons and thus can leave a sizeable fraction of energy in the
EM calorimeter. So a “typical” jet will create a shower with both hadronic and
electromagnetic components. It will also be larger in transverse size than a photon
shower (see Fig 4.1). However, the number and type of particles that a jet will

fragment into is a probabilistic process. Roughly one out of every 1000 partons will

55

56

Jet Width

 

800;

700'—

 

 

 

o ‘1 ALlLlALLlllellAALlell

0.5 ‘036 “0.7
scrim + Av’)

 

Figure 4.1: Width of jet candidates from data.

form a jet with 90% of its energy carried by one neutral hadron (see Fig 4.2). It
is these narrow electromagnetic jets that provide a substantial background to direct

photon production.

The neutral mesons in jets that can provide a background to direct photon pro-
duction are listed in Table 4.1, along with their branching ratios [28] and production
ratios [29]. Of these, only two (no and 1)) were found to contribute substantially to
the candidate sample. Mesons which decay into more than two photons are often
rejected by the isolation cut. For example, the [ff/1r0 production ratio is 0.4, but

after photon cuts this is reduced to less than 0.05.

Some previous direct photon experiments subtracted the neutral meson back-

 

57

Jet Electromagnetic Fraction

 

400

TIjfiTT‘ll

350

250'-

200—

150-

 

 

 

Figure 4.2: Electromagnetic fraction of jet can-
didates from data. Roughly 4/1000 jets have an
electromagnetic fraction higher than 90% .

Table 4.1: Neutral Meson Background.

 

 

 

 

 

 

 

 

 

 

particle mass o/a,» decay branching
ratio
no .135 1 77 .99
r) .547 .55 77 .39
n .547 .55 3'II'0 .32
K 9 .494 .40 2W0 .31
w .781 .50 «by .09
1)! .958 1 «W017 .21

 

 

 

 

 

 

 

 

 

58

 

 

 

 

 

E LMinimum Sgporotion Between Photons in 1r°/n Decoys
u 20 — ‘.
E ‘
l- ‘
.. ‘
17.5 _ g ‘,
i- 2 \
I- :: \
'2 \
15 E- ‘,
i = \
" '. \
.. -._ o
12.5 '- 1‘ \\ n
: ‘\
\
10 —
\
‘ . Cell Width at 11:0
7.5 — \
s — 7“~-~
2.5 L ...............
o ‘LJlllLAllllllllllllAAlAlLlII|14111L14J11
o 2.5 s 7.5 10 12.5 15 17.5 20

Meson Energy

Figure 4.3: Minimum separation between pho-
tons from no and 17 decays at the first layer of
the calorimeter. The horizontal line denotes the
cell size at pseudorapidity of 0.

ground by constructing an invariant mass between the decay products (photons).
This technique can be used only if the calorimeter granularity is fine enough to re-
solve the photons as separate clusters. The minimum distance between two photons
from a no or 17 decay is:

2m,,o/,,L

d... = —— .
E (4 1)

where mfo/n and E are the mass and energy of the 1r° or r], and L is the distance
from the decay point. At the first layer of the DO calorimeter L = 75 cm. This

separation is plotted vs energy for «0’s and 17’s in figure 4.3. As can be seen from

59

the plot, the segmentation of the DO calorimeter is not fine enough to resolve the
photons from a no or 17 decay in the energy range of interest. The two photons
coalesce to create one electromagnetic shower in the calorimeter. However, there are
differences between single and multi-photon showers that can be exploited. Statisti-
cal fluctuations in calorimeter shower development make event-by-event background
subtraction impossible, but the differences in shower development can be used to

estimate the amount of background in the sample on a statistical basis.

4.1 Longitudinal Shower Profile Method

Photons lose energy in matter by three main processes: photoelectric absorption
(7 + e -—> e’), Compton scattering (7 + e —-> 7’ + e’), and pair-production (1 —) e+e").
At photon energies above 1 GeV pair-production is by far the dominant phenomenon.
Therefore a photon will pair-produce before it deposits energy into the calorimeter.
The probability that a photon pair-produces depends on the number of radiation
lengths of material the photon traverses (a radiation length is defined as the thickness
of a given material required to reduce the mean energy of an electron beam by a
factor of e). If the probability of one photon converting to an electron-positron pair

0

is P,, then the probability that at least one photon from a 11' converts is

P,r = 2P, — P3. (4.2)

60

 

350 :- —— MC Photons
........... MC pizeros

300'—
250-

200*]

 

100—

...... ....

.......

 

 

o".I.I.I.I.I.I.I.I.I."
0 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25

EMi/E

 

Figure 4.4: Histogram of the fractional energy contained in
the first layer of the calorimeter for 10 GeV Monte Carlo
photons and 1ro’s.

Multi-photon backgrounds tend to convert and shower earlier than single photons,
as figure 4.4 demonstrates. A substantial fraction of photons leave no energy in the

first layer of the calorimeter.

This difference can be used to estimate the fraction of single photons in the data
sample. If a given cut has an efficiency of 6,, 6,, and 64.,“ for photons, background,

and data respectively, then

6datalvdata = eyNy + 511er (4.3)

61

where the N is simply the number of candidates in each sample. Equation 4.3 can

be rearranged to solve for the fraction of photons in the data sample:

N a a _ 1r
Photon Fraction, 7 = —7 = Edi—i, (4.4)
N 6., — 6,r

using N1r = Ndata — N,.

A discriminant between photons and background was devised using the energy

deposited in the first layer of the calorimeter. An 6 was defined for each sample as

_ Number of Candidates with EMl/E < 1%
6 _ Total Number of Candidates

 

(4.5)

Figure 4.5 shows the behavior of this variable vs transverse energy for the three

samples.

The fraction of candidates that are single photons can be found from equation 4.4.
Figure 4.6 shows a plot of this photon fraction vs transverse energy. Table 4.2

contains the numerical values of the data points.

The choice of the discriminant value is not arbitrary, but is based on two dif-
ferent criteria. The value must be chosen from a region of the distribution that is
modeled well by the Monte Carlo. The Monte Carlo distributions were compared
with Z ——> e+e" data, as shown in figure 4.7. The 1% value was also chosen because
it maJdmizes the difference between single and multi-photon showers, and therefore
reduces the error on the photon fraction (the error is proportional to (6., — 6,.)‘1).

If the Monte Carlo were in perfect agreement with the data the value of the photon

62

 

/E<l°%
3 is
I""l'

.0
N
at

Fraction 5:” Candidates with EU”
2.. 0
0' N

.0
d

IITUIW'UTMVIIWTUIITMT

 

0.05

I I I I I I T I

 

 

 

20 40 so so 100
Er

Figure 4.5: Fraction of candidates with EM 1 / E < 1% vs trans-
verse energy for samples of Monte Carlo photons, background,
and data.

 

63

Photon Fraction. Longitudinal Shower Profile Method

 

I

1.2

Photon Fraction

0.8

0.6

0.4

IIIWWW‘IIII'IIIIIII

I

0.2

I

 

 

 

I I I I I I I I T

l L l l 1 l L l 1 l l l 1 l l l l l l l

20 40 so so 100
Transverse Energy

 

Figure 4.6: Photon Fraction vs Transverse Energy for the Lon-
gitudinal Shower Profile Method. The solid line is a fit to the
function 1 — a x e’bXET The dashed lines are from varying the
parameters a and b by enough to change the x2 one unit.

64

Table 4.2: Photon Fraction from the EMI Method.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ET Bin Photon Statistical Systematic
(GeV) Fraction Error Error
7—8 0.04 0.05 0.03
8-10 0.06 0.04 0.03
10-16 0.03 0.05 0.03
16-18 0.16 0.06 0.04
18-22 0.11 0.06 0.04
22-34 0.15 0.08 0.04
34-38 0.40 0.04 0.05
38-50 0.48 0.03 0.05
50-70 0.60 0.06 0.05

70-100 0.93 0.13 0.05

 

 

 

 

 

 

 

 

 

fraction would not depend on the discriminant cut value. Figure 4.8 shows the de-
pendence of the photon fraction on cut value. This cut value dependence is included

in the systematic error on each photon fraction point.

The dependence of the photon fraction on the 1) /1i'0 production ratio was also
checked. The ratio was varied by 20% and found to change the photon fraction by
40% at 10 GeV. The effect of the 17/71") ratio becomes markedly smaller at higher
transverse energies, falling to less than 5% at 20 GeV and above. This effect was

included in the systematic error on each gamma point.

4.2 Central Drift Chamber Conversion Method

The difference in conversion rate between single photons and multi-photon back-

grounds can also be exploited to subtract background using the tracking detectors.

65

EM1 / E Comparison Betwgen Data and Monte Carlo

 

 

I

— Monte Carlo Z electrons

8
I T W I

0 Data Z electrons

I

I

 

 

4o—

 

                  

I . l . . '0‘
0.125 0.15 0.175 0.2 0.225 0.25
1

Eu/E‘“

 

 

0 1 l 1 l I l r I
0 0.025 0.05 0.075 0.1

 

Figure 4.7: Comparison between Monte Carlo and data electrons
from Z events.

66

EMi Comma Fraction with Different Cut Value;

 

g #-

31.2—

0 1-

2

L1. .

g 1~ 01/27:. >
~ - i
g 01%

a b

0.3—— 112%

 

0.6 -
0.4 .—

0.2 -

 

 

 

"' 1 1 1 l 1 1 m l 1 1 1 l 1 1 1 l 1 1 1 l
0 20 40 60 80 100
Transverse Energy

 

Figure 4.8: Photon fraction for different values of the EMI / E
discriminant. The lines are fits to the three sets of data points.

67

The Central Drift Chamber (CDC) was used in this analysis to tag conversions.
Roughly 10% of photons convert in the material in front of the CDC (the exact
conversion probability depends on 17). DC has no central magnetic field, so electron-
positron tracks from 7 —-> e+e‘ do not curl in opposite directions and tend to lie on
top of one another. Conversion tracks are identified as single tracks with twice the

minimum ionizing energy.

This analysis uses a sample of candidates which fulfill the selection cuts detailed
in Chapter 3 with the exception of the track veto cut. The sample therefore contains
the same photons and background candidates from the previous analysis, plus a
sizeable portion of electrons and photon conversions. The electrons typically leave
ionization in the CDC which is consistent with 1 minimum ionizing particle (mip),
and photon conversions leave 2 mip ionization (see figure 4.9). One mip was defined
as CDC dE/dx between 0 and 1.4, and two mips was defined as between 1.4 and 3.0.
Tracks were also required to match with the centroid of the calorimeter shower with

a significance of less than 5. Track significance is defined as:

 

 

..,...=¢(g;\;r+(§_;r (4.6)

where R is the radial distance from the vertex to the center of the shower, Ad and
A2 are the differences in azimuthal angle and beam direction between the track
position and the shower center, and Reid and 62 are the position resolutions of the
calorimeter. Candidates which had a track but did not pass the significance cut were

dropped from the sample, rather than reclassified as 0 mip.

68

000 mig Qigtributign From Elgctrgmggngtig nggters

p

III—WVI‘IITTIrTI’

IVVIITTIIIITITYVI

 

1-
11 AAJAIA

      

h._-~

 

 

llll‘llLLLllLLllLl‘Alll I ll

 

05115225335445:
mips

Figure 4.9: CDC dE/dx distribution.

69

4.2.1 Matrix Formulation

The three final states of 0, 1, and 2 mip candidates are a mixture of the three initial
states of photons, neutral mesons, and electrons. The transition from initial particle

to final candidate can be modeled with a matrix formulation [31]:

{0mip\ ( 3X3 \KN,\

1mip - transformation Ne . (4.7)

 

 

 

 

 

 

(2mip ) \ matrix ) (N, j

The transformation matrix describes the conversion and tracking process, deter-
mined from Monte Carlo and data. It can be further broken down into four separate

matrices:

 

 

 

 

 

 

 

 

( tracking l { charged \ ( conversions & mip \ ( neutral \
efficiency overlaps transformation overlaps - (4-8)
( matrix J ( matrix ) ( matrix ) ( matrix )

The matrices do not commute and therefore the order is not arbitrary.

Neutral Overlap Matrix

There is a small chance that the underlying event can contribute a soft (low trans-
verse energy) particle which will fall in the same tracking road as the particle from

the hard scattering. The neutral overlap matrix accounts for these particles which

70

are uncharged.

(neutrall (l—Vl 0 0”
overlaps = 0 1 0 (4.9)

 

 

 

 

( matrix ) ( Vl 0 1 )
The probability of a neutral overlap, V1 , was studied from data and found to be very
small (< 1%). The effect of this matrix is to move some of the single photons (N,)

to double photons (N,). The number of electrons remains unchanged.

Conversion and MIP Transformation Matrix

The next matrix applied handles the probability that a photon will convert into a
6+6“ pair, along with accounting for the finite resolution of the dE/dx measurement.

The matrix can represented as:

 

 

 

 

( conversions & mip \ f 1 — P 0 (1 _ p)2 I
transformation = LIP Y 2L2P(1 — P) . (4.10)
( matrix ) ( SIP X 25'2P(1 - P) )

The probability that a photon will convert is P. L1 represents the probability for
photons that the converted electron-positron pair will be separated enough for the
track to be classified as one mip and L2 is the corresponding probability for photons
from neutral mesons. 5'1 and S; are the probabilities for photons and background
that the track will be identified as 2 mip. Note that it is not necessary for L1 + 51
(and L; + 32) to equal one, since there is a small probability that the track will be

identified as greater than 2 mip. X and Y represent the probability that a single

Table 4.3: CDC Conversion Method Parameters.

71

 

 

II

[25 GeV 1 40 GeV I so Gevfl

 

 

 

 

 

 

 

 

X 0.021 0.022 0.023
Y 0.935 0.931 0.925
L1 0.011 0.009 0.002
L2 0.049 0.031 0.025
51 0.931 0.940 0.943
52 0.745 0.852 0.967

 

 

 

 

 

 

electron track will be identified as a 2 or 1 mip track, respectively.

The values of these six parameters were measured from a. well understood tracking
simulation. The background was composed of «0’s, 17’s, and Kf’s in a 1:0.55:0.4
production ratio and was found to be fairly insensitive to changes in this ratio.
These parameters do depend on transverse energy, as expected (see table 4.3). Decay

products become more collimated at higher energies, leading to tighter tracks.

Charged Particle Overlap Matrix

Charged particles leave tracks without converting, so the Charged Particle Overlap

Matrix is applied after the Conversion Matrix. The matrix is defined as:

charged 1 — V3 0 0
overlaps = Vg 1 — Vg 0 (4-11)
matrix 0 V; 1 — V3

The two probabilities, V2 and I/3, arise from the two difierent effects that charged

particle tracks can create. V3 (7.5 :I: 0.5%) is the probability that a charged overlap

72

will fall inside the tracking road, while V) (1 :I: 0.2%) is the probability that the track
will pass the significance cut. Thus while 7.5 % of unconverted photons are lost from

the 0 mip sample, only 1 % are recovered in the 1 mip sample [30].

'hacking Matrix

The tracking matrix encompasses the efficiency of the CDC along with the software

track finding algorithm:

tracking 1 1 — T 1 — T
efficiency = 0 T 0 . (4.12)
matrix 0 0 T

The tracking efficiency, T, is measured from Z —1 €+e_ events to be 0.87 :t 0.04 in

the CDC.

Photon Fraction Calculation

The photon fraction can be calculated from equation 4.7 by solving for N,, Ne,
and N," with the number of candidates in the 0, 1, and 2 mip samples as inputs.
The complicated matrix manipulation was solved using the MAPLE mathematical

package. The number of photons in each of the three samples (0, 1, and 2 mip) can

73

Table 4.4: Photon Fraction from the CDC Conversion Method.

 

 

 

 

 

 

 

ET Bin Photon Statistical Systematic
(GeV) Fraction Error Error
22-28 -0.03 0.18 0.23
28-35 0.18 0.10 0.19
35-45 0.35 0.06 0.16
45-70 0.35 0.09 0.16
70-90 0.51 0.20 0.13

 

 

 

 

 

 

 

 

 

then be found by multiplying the vector

0 (4.13)

by the transformation matrix. The fraction of photons in the 0 mip sample for

different transverse energy bins is shown in table 4.4.

A comparison of the two methods of background subtraction is shown in fig-
ure 4.10. The uncertainties inherent in the CDC method are larger, due both to
errors in the parameters involved and to the small number of candidates in the con-
version sample (only 10% of photons convert). Because of the larger errors the CDC
method is not used for background subtracting the cross—section, but is shown here

for comparison only.

74

Photon Fraction from EM1 and CDC methods

 

c .
.3 1.2 —

o b-

E

g 1 L O EM1 Method

E C o CDC Method "
O. 0.8 h

++
M“ (P

 

 

I
.o
N
TITY

 

 

 

# l l l l I I l 1 1 l l A J l L A l l

20 40 so so 100
Transverse Energy

 

Figure 4.10: Comparison of the photon fraction from the
two methods.

Chapter 5

Isolated Direct Photon Cross

Section

5.1 The Differential Cross Section Formula

The differential cross section for p13 —> 7 + X can be written as:

J20" _ N7
dedn — £agApTAn’

 

(5.1)

where N is the total number of candidates, 7 is the photon fraction as defined in
equation 4.4, [I is the luminosity, a is the geometric acceptance, 5., is the efficiency,
and APT, A1] are the bin size in [)1 and 1; respectively. A discussion of these factors
and their associated errors follows below. It should be noted that the cross section
measured here is for isolated direct photon production, i.e. it is not inclusive. Back-

ground levels at the Tevatron make the measurement of an unisolated cross section

75

76

Table 5.1: Number of Candidates after cut for each trigger.

 

 

 

Cut Low Trigger Medium Trigger High Trigger
# ‘70 # ‘70 # %
17"“ 45866 100 22029 100 98713 100

 

1] 37818 82.5 18342 83.3 84787 85.9
Track Veto 25033 54.6 10429 47.3 41123 41.7
EM Fraction 20154 43.9 8713 39.6 33528 34.0
Isolation 18936 41.3 6660 30.2 21771 22.1
H Matrix 10924 23.8 4455 20.2 16608 16.8
Missing ET 10903 23.8 4385 19.9 15384 15.6
Z Vertex 10282 22.4 4099 18.6 14367 14.6

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

difficult. This makes comparisons with other experiments which have different isola-
tion requirements difficult. It is important to compare with a theoretical prediction

that models the isolation cut correctly.

5.1.1 The Number of Candidates, N

The candidate selection criteria were detailed in chapter 3. The data for the three
triggers are shown in figure 5.1, with the number of candidates after each offline cut
being shown in table 5.1. It is possible for an event to have more than ‘one good
photon candidate and therefore be added into the cross section more than once. The

error on N is simply the Poisson statistical error, VN.

77

Ray Number of Candidates from the 3 Triaaers

T

1

103

TTTITIYI

 

 

10

I YTTI

 

 

 

IlIlllllllLllllllllllllllLLllllllllllllllllllJL
0 1O 20 30 4O 50 60 7O 80 90 100

Transverse Energy

 

Figure 5.1: Raw number of candidates vs transverse en-
ergy. The three large peaks are from the three different
trigger thresholds. The small peak a low ET is from low

energy, non-triggered photon candidates.

78

Table 5.2: Photon Fraction Fit Parameters

 

 

 

 

 

 

H l — a x ebeET H
a 1.14 :1: 0.05
b 0.0177 :1: 0.0021
x2 0.90

 

 

 

 

 

 

 

5.1.2 The Photon Fraction, 7

It is necessary to scale N, the total number of candidates, to account for background
contamination in the sample. The details of the background subtraction method
were given in Chapter 4. The fraction of photons in the sample was determined for

several bins of transverse energy and were fit to a function of the form

1 — a x e'bXET. (5.2)

Table 5.2 contains the details of this fit. The functional form was chosen because
it fit the data best and had the necessary physical constraints (the photon fraction
cannot go above 1). The specific errors on the photon fraction for each pT bin
were described in Chapter 4, with the statistical and systematic errors summed in
quadrature to give the final error on each point. The final error on 7 from the fit
was determined by varying the parameters of the fit enough to change the x2 by one
unit. This is the dominant error on the cross section for most of the kinematic range

addressed in this thesis (see figure 5.2).

Fractional Error

79

Error on the Photon Fraction

 

0.8

0.7

0.6

0.5

 

0.4

0.3

0.2

0.1

TUITIIIIIIIIIIlITITITIIIIUIjleTITIUIIIllll

 

 

0IlLlLiJJLJllJllllllll1111114141]!lllllllllllll

1o 20 so 40 so so 70 so so
Transverse Energy

 

Figure 5.2: Error on the Photon Fraction vs Transverse Energy.

80

5.1.3 The Luminosity, L

The luminosity was measured using the Level 0 scintillator counters, described in
Chapter 1. The instantaneous luminosity is related to the Level 0 counting rate by:

R
£=.__£’2

, 5.3
m ( )

where am is the cross section subtended by the counters. It can be expressed as a

product of the Level 0 efficiency and the total inelastic cross section, madame.

This equation is only strictly true when the luminosity is low. Higher luminosity
can cause more than one interaction per bunch crossing. Since multiple interactions
only get counted once, the counting rate becomes smaller than the interaction rate.
A correction for this can be calculated based on Poisson statistics. The average

number of interactions per crossing, fl, is given by:
1'; = £70“), (5.4)

where 1' is the time between bunch crossings (T = 3.5 psec). The correction factor

for multiple interactions then becomes:

£ _ fi, _ ‘- 111(1 - cmeasTULO)

Linea: 1 —‘ e_fi £meas7'a'L0

 

 

 

(5.5)

The inelastic cross section, used for determining am, is derived from the weighted

average of the published values from the CDF [33, 34, 35] and E710 [36] experi-

81

Table 5.3: Luminosity of the Photon Triggers

L oslty nb’
Gam Low 13.1

Gam Medium 169.0
am 14670

 

ments. Since there is an 8% discrepancy between the two measurements, the error
on madame is scaled by x, where x2 is a measure of the consistency between the two

measurements (3.43). The value used for 010 is 46.7 :i: 2.5 mb.

The integrated luminosity for the run Ia photon triggers is given in table 5.3. The

lone source of error on the luminosity is from the error on em, which is 5.4% [32].

5.1.4 The Geometric Acceptance, a

The geometric acceptance accounts for candidates which hit uninstrumented regions
of the detector. As detailed in Chapter 3, two fiducial cuts were applied to avoid
regions of the calorimeter where the energy measurement was not well understood.
The first of these required that the 2 position of the interaction vertex is less than
50cm from the nominal vertex. The acceptance of this cut is 93.8%. The second
fiducial cut removed candidates with shower centroids that were within 1.125° of a
()5 crack region. The acceptance of this cut is 80%. The total geometric acceptance

is therefore 75%, with a negligible error (less than 1%).

82

5.1.5 The Photon Efficiency, 6.,

The efficiency for photons was measured with a sample of single particle Monte
Carlo photons with data from minimum bias events added. The trigger and offline
efficiencies are shown in figures 3.9 and 3.7 respectively. The statistical error on the
efficiency is small (~ 1%), but there is a systematic error on the reliability of the
Monte Carlo. The efficiencies were checked in the kinematic region of the electrons
from Z decays (20 < p; < 50) and found to agree with the Monte Carlo to within

4%. An error of 4% was therefore assigned to the photon efficiency.

5.1.6 The Bin Size, APT and A17

The cross section is normalized by dividing by the size of the 127 and n bins. The
size of the M bin was set at 3 GeV. The eta range (I 17 I< 0.9) was chosen to ensure
that the photons were within the active region of the Central Calorimeter. There is

no error on either bin size.

There is an error on the pp scale, however. The error from the W mass measure-
ment was found to be less than 1% . Since the direct photon cross section falls as

roughly p715, this translates into an error on the cross section of 5%.

5.2 Cross Section vs Transverse Energy

The isolated direct photon cross section is plotted vs the transverse energy in fig-

ure 5.3 and the numerical values of the points are listed in table 5.4. The three

83

triggers are used in regions where they have flat efficiency and reasonable statistics.
Each trigger is normalized by its respective luminosity. The cross section falls steeply

with transverse energy in typical QCD fashion.

5.2.1 Comparison with Theory

The theory curve plotted in figure 5.3 is from a Monte Carlo program from J. F.
Owens [37]. It is based on a next-tocleading-logarithm calculation [38], using the
CTEQ2M parton distribution functions [39]. The Monte Carlo has an isolation cut
applied at the parton level to match the data. It is also smeared by 15%/ JE to
match the detector resolution, but this effect is minimal and nowhere changes the

theory by more than 3%.

A better visual comparison of data and theory is provided by the plot of the point-
by-point difference between data and theory (normalized by the theory) in figure 5.4.
The theoretical prediction shows excellent agreement with the data in both shape
and normalization. The default theory is a next—to-leading order prediction using the
CTEQZM parton distribution set and p2 = 12%, scale. A leading order prediction is
also shown for comparison. Changes in the scale will effect only the normalization of
the theory; figure 5.5 shows the variation of the theoretical prediction when the scale
is halved or doubled. Figure 5.6 shows how reasonable choices of parton distribution
sets can effect the theory. The CTEQ2MF set contains fewer low a: gluons than
CTEQ2M, while CTEQZMS contains more. The differences in the theory are small

compared to the systematic errors on the data.

84

Table 5.4: Cross Section Points

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ET bin E—T da/de (11] Stat Err Sys Err
(GeV) (GEV) (Pb) (‘70) ('75)
12-15 13.4 2.13 X 103 4.2 41.1
15-18 16.4 9.77 X 102 7.3 28.6
18-21 19.4 5.63 X 102 10.9 23.8
21-24 22.4 2.63 X 102 4.6 22.3
24-27 25.4 1.43 X 102 6.8 21.0
27-30 28.3 1.06 X 102 8.5 20.2
30-33 31.6 6.76 X 101 11.3 20.2
33-36 34.3 3.18 X 101 17.1 19.6
36-39 37.4 2.97 X 101 2.0 19.0
39—42 40.4 2.30 X 101 2.4 19.0
42-45 43.5 1.67 X 101 2.9 19.0
45-48 46.4 1.35 X 101 3.3 18.4
48-51 49.4 9.57 X 100 4.0 18.4
51-54 52.5 7.29 X 100 4.7 17.9
54-57 55.5 5.93 X 100 5.4 17.9
57-60 58.5 4.45 X 100 6.3 17.9
60-63 61.4 3.85 X 100 6.9 17.5
63-66 64.4 2.93 X 100 8.1 17.5
66-69 67.4 2.82 X 100 8.4 17.5
69-72 70.4 2.17 X 100 9.8 17.5
72-75 73.5 1.52 X 100 11.9 17.0
75-78 76.4 1.30 X 100 13.0 17.0
78-81 79.5 9.28 X 10'1 15.6 17.0
81-84 82.4 9.51 X 10‘1 15.6 17.0
84-87 85.7 1.02 X 100 15.2 16.6
87-90 88.5 7.57 X 10'1 18.0 16.6
90-93 91.6 6.25 X 10_1 20.0 16.6
93-96 94.6 3.33 X 10‘T 27.7 16.6
96-99 97.6 3.39 X 10"1 25.8 16.6

 

 

 

 

 

 

 

<d’a/dP1d‘n > (pb/(GeV/c))

10

10

85

 

 

   
 
 
   

 

C Di] Preliminary

__ -o.9 < n < 0.9

E O Level 2 Trigger P, > 6 GeV/c

: C] Level 2 Trigger P, > 14 GeV/c

~ A Level 2 Trigger P, > 30 GeV/c

:- lnner errors - statistical

E Outer errors - systematic

E

I

5“ Solid Curve

: QCD-based Prediction (Owens. et ol)

I CTEO 2M parton distribution

'- NLL. " - P.

: l l l l l l l l l l l l l l I l l l l l l
20 40 60 80 1 00

Transverse Momentum, P, (GeV/c)

Figure 5.3: Photon Cross Section vs Transverse Momentum.

 

86

d

 

Ignter errors - statésticatl. 13¢ Preliminary
r rr r - em
u e e o s sys 0 IC CTEQZM “2:731,

----------- Leading Order, CTEQZL, u.’=P,z

p
m
Frlrtl

.0
a

(Data - Theory) / Theory
9 o
N 01

 

Ifirlrrtlrrllr

l
I
|

l

l
l
+
+

 

 

 

 

 

I111]
+
-o-

T

n—o"
......
""""""""""
o.-
oooooo

 

I
O
01
ITTIIITTTFTII

 

 

 

20 40 so so 100
Transverse Momentum

Figure 5.4: Comparison of Photon Cross Section with QCD prediction. The shaded
error at the bottom represents the normalization error on the data due to lumi-
nosity uncertainty.

87

d

 

Ignter errors - statésticotl, Dg Preliminary
r rr r — m
u e e o s sys e 0 IC CTEQZM “2:731:

----------- Next-to-Leading Order. crson. M’=o.5p.2
- — -- Next-to-Leading Order, CTEQZM. if=2p,2

.0 9
-# on
I l I I l I l l I I I I l I l I I I

(Data - Theory) / Theory
5: o
N 0’

 

 

 

 

 

 

 

 

'/////////////N¢W7WliMM/WMH/fl/N/N/H/L

IIIIIfiTITIIIIITIIII

 

 

_1 1 #1 I I l l 1 J l 1 l l l I l l l I 1

20 40 so so 100
Transverse Momentum

 

Figure 5.5: Comparison of data and theoretical predictions with different p scales.

88

d

 

Ignter errors - statisticotl. Dg Preliminary
er errors - s em n
" 3’ ° ° CTEQZM az=P12

----------- Next-to-Leading Order, CTEQZMF, /.(.’=p,2
- - -- Next—to-Leading Order. CTEQZMS, u’=p,’

- _ - 12+; 1

.0
a:

.0
.5

(Data -— Theory) / Theory
9 o
N a:

 

   
 

Tllllllrfiflfiilllf

 

 

 

 

 

l
o
a)
nIIIrfir'Irlllrllirr

 

 

 

20 40 so so 100
Transverse Momentum

Figure 5.6: Comparison of data and theoretical predictions with different parton
distribution sets.

89

A previously published measurement [40, 41] of direct photon production in the
same kinematic region by the CDF collaboration showed a steeper dependence with
transverse energy than QCD theory. In particular, an excess of 40% above the
prediction was measured for photons with transverse energy less than 20 GeV. Mod-
ifications to the parton distribution functions are unable to account for this differ-
ence [40]. It has been suggested that the source of this discrepancy is the difficulty in
modeling the isolation cut and the photon fragmentation function in the theoretical
prediction [42, 43]. Another possible explanation is a smearing of the direct photon
p7 spectrum caused by “intrinsic by”, initial parton momentum in the transverse

beam direction [44] .

The measurement presented in this thesis does not show a disagreement with
theoretical prediction at low p1. It should be noted that the isolation cut used here
is different from that in reference [40, 41]. The CDF measurement required that
the photon be isolated in a larger cone of r = 0.7, while r = 0.4 is used in this
analysis. If improper theoretical treatment of the isolation cut is the source of the
discrepancy between CDF and prediction, one would not necessarily expect to see

the same excess here.

 

 

Cl
EV

Prev?
mess
eflor
side
plot

radi

As
Phc

red

Chapter 6

3».

Characteristics of Direct Photon

r“—

Events

Previous sections of this thesis have been concerned with the identification and
measurement of only the photon in direct photon events. This chapter makes an
effort at identifying the other objects in a direct photon event. Figure 6.1 shows a
side view of a photon candidate event in the Da detector and figure 6.2 shows'a lego
plot of the same event. As is expected of direct photon events, there is a jet 3.14

radians in d) away from the photon.

6.1 The Golden Photon Sample

As was shown in Chapter 4, there is a substantial amount of background in direct
photon events. For a study of direct photon event characteristics it is desirable to

reduce this background to the smallest possible level without biasing the event. This

90

\ ..~; [5.7.]

 

Fig
low

Cal

 

 

91

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CAL+TKS R-Z VIEW 11-DEC-l992 17:31 Run 52557 Event 6264]20-SEP-1992 15:23
Max E: 48.7 Ge‘v’
CACP E SUM: 479.9 CCV
MW in 2': 32.0 (cm) ' 0.<E< 1.
El l.<E< 2.
/ / / \ | <E< 3.
. 4.
]r\
P— 1 <—P
_/ ]

 

 

 

Figure 6.1: Side view of a direct photon candidate event. The photon is in the
lower half of the Central Calorimeter and the jet can be seen in the right Endcap
Calorimeter with tracks in the Forward Drift Chambers.

92

 

LEGO CAL carp 11-DEC-l992 17:15]Run 52557 Event 6264]20-SEP-1992 15:23

 

CALEGO EMSN == 0, GeV
CACP E SUM- “: 479.9 GeV

 

ENERGY CAEP ETA-PHI

 

 

 

Figure 6.2: Lego plot of the direct photon event. The height of each element
corresponds to the amount of energy deposited in that calorimeter tower.

93

was done by creating a “golden” photon sample. This sample passes all the standard
selection cuts, plus an additional restriction on the amount of energy allowed in the
first layer of the calorimeter. Figure 4.4 shows that this is a powerful cut for rejecting
the hadronic jet background. This cut was not applied in the standard data sample
because the low efficiency would cause large statistical errors on the cross section. A
m > 40 GeV cut was also applied to the golden sample; the photon fraction becomes

too small for the lower p7 region.

The photon fraction of the golden sample can be calculated by the formula:

 

6
7': 7 7 (6.1)

6data

where e, and Edam are the fractions of photons and data to pass the EM1 cut and
7 is the photon fraction of the original sample. The golden sample was found to

contain 75 % signal.

6.2 Jet Identification and Efficiency

Jets were identified with a fixed cone algorithm. A cone was defined in 1] — 45 space

with a radius of R = «A1,? + Ar}? = 0.7. The steps of the cone algorithm are as

follows [45]:

o Preclusters are formed from a list of towers (A17 x Ad) = 0.1 X 0.1) ordered in
ET. Contiguous towers with ET > 1 GeV are merged in a cone of R = 0.3,

starting with the highest ET tower.

0P1

 

01

 

age

to

94

0 Preliminary jets are formed around the preclusters by summing all towers
within a radius of R = 0.7, using the center of the precluster as the center

of the jet.

0 A new ET weighted centroid of each jet is computed and used as the center for

summing towers for a new jet.

0 The previous step is repeated until the jet centroid is stable. This usually takes

3 to 4 iterations.

s Jets with ET < 8 GeV are dropped.

0 It is possible that some jet cones overlap. If the ET in the overlap region is
greater than 50% of the ET of the smaller jet, the jets are merged by summing
the energy in both cones and recalculating the centroid and ET. If the overlap
is less than 50%, the jets are split by adding the towers in the overlap region
to the jet with the closest center and recalculating the centroid and E1 of each

jet.

The jet finding efficiency was studied using the GEANT detector simulation pack-
age. The efficiency for jets with ET > 16 GeV was found to be 95%, and this rises

to 99% for jets with ET > 20 GeV [46].

 

 

 

6.3

The
Phol
Stall

sam

A

 

Vers
the

Pho

95

 

r I V 1

200*-

l I

100-

 

 

 

 

 

 

 

 

)-
p
p l l

o l l A l A L 1 l 1 L l l I I

O 1 2

I l A I I l l

4 5
Number of Jets

 

“D—

Figure 6.3: Number of jets in direct photon events
from the golden photon sample.

6.3 Jet production in Direct Photon Events

The first order direct photon processes have a final state jet which balances the
photon ET (see figure 1.2). Higher order diagrams can lead to more jets in the final
state. Figure 6.3 shows the number of jets present in events from the golden photon

sample.

QCD interactions do not involve neutrinos and should have little missing trans-
verse energy in the event. In photon plus one jet events this ET balancing will cause
the jet to be opposite the photon in 4:. Figure 6.4 is a plot of the difference between

photon and jet ()5 for photon plus one jet events. It is peaked heavily at 1r, as would

 

 

bee

mor
hea]
Whe
of t

fina

ure
rar

Ph.

 

96

Golden Photon Samgle. N” - 1

"l

 

 

p
20-

 

 

 

Figure 6.4: Photon 45 - jet 4) for golden photon sample
events with one jet.

be expected from the above argument.

The ()5 symmetry between photons and jets should be broken for events with
more than one jet. The Acfi between the photon and the leading jets is not as
heavily peaked, as can be seen in figure 6.5. However, this figure also shows that
when the jets are summed vectorially the resulting jet does retain the 5¢ distribution
of the photon plus one jet events. This is because the secondary jets are typically

final state radiation from the primary outgoing parton.

The pseudorapidity distribution for photon and jet candidates is shown in fig-
ure 6.6. While the photon is restricted to the I r] I< 0.9 region, the jet is allowed to
range out to I 1] [< 4.0. The jet is not expected to balance the photon in 17. The

photon-jet system is typically Lorentz boosted with respect to the lab frame, due to

 

 

 

the l

97

Golden Photon Sample. N” > 1

 

'77 Y'YY

Summed Jet

 

Leading Jet

 

d
N
U

 

75’-

 

25-

 

 

 

 

Figure 6.5: Photon d) - summed jet ()3 for golden photon
sample events with more than one jet.

the different momenta of the initial partons.

98

Golden Phgtgn figmglg

 

 

tn
“ F
8
>100 -
u
so - — Photon
* ---------- Summed Jet
w .-
w -
2° 7' Linea:
o 1“i“j:‘i’L l l L l l I l.:':\l"'l'
—4 -J -2 2 s 4

 

 

 

 

 

Figure 6.6: Photon and jet 1] distributions for
golden photon sample events.

 

 

C]

 

Tlus
prod

agre

ceHe
P0P

and

Stat
310

(lar

coflj

Chapter 7

Conclusions

This dissertation provides the details of the first measurement of the direct photon
production cross section at the D0 detector. The measurement has been shown to

agree quantitatively with QCD predictions over a large range of transverse momenta.

The DC detector, with it’s emphasis on good calorimetry, has provided an ex-
cellent means to make this measurement. The triggering system allowed for full
population of the p1 region for a cross section that falls by 5 orders of magnitude,

and for high rejection of hadronic jets.

While background subtraction on an event-by-event basis was not possible, a
statistical method was shown to be successful. This method relied on a detailed
Monte Carlo simulation which was shown to model the data correctly. The Monte
Carlo was cross-checked extensively with data from the D0 test beam, as well as

collider W and Z events.

The largest errors on the cross section resulted from systematics in the method of

99

bac

bat

an

CV6

 

100

background subtraction, particularly at low transverse momenta. The neutral meson
background causes a small signal-to-noise ratio in the low pT region, which leads to
an inflation of the systematic errors. Future attempts to push the measurement to

even lower p1 will have to address this issue.

Other future photon analysis on run Ia data involve the center of mass scatter-
ing angle distributions [47] and the invariant mass of the photon-jet system [48].
Studies of photons in the forward direction are also being undertaken [49], taking
advantage of Da’s excellent forward calorimetry. A large additional amount of data
(~ 100 pb‘l) is currently being accumulated during Da’s second collider run. Anal-
ysis of this data will greatly reduce the cross section errors and provide for more

detailed study of the direct photon event characteristics [50].

 

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"[11111]]"[11111]“