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lllll-‘II

1293 00533 8623
LIBRARY "
Michigan State

University
4—H

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This is to certify that the

dissertation entitled

"A STUDY OF DIRECT PHOTON.
PRODUCTION AT THE CERN INTERSECTING
STORAGE RINGS"

presented by

Carlos Walter Salgado—Galeazzi

has been accepted towards fulfillment
of the requirements for

Ph.D. degree in PhYSiCS

8%‘1’4 6 £72

 

Major professor
Prof. B. G. Pope

Date August 3 1.988

MS U is an Affirmative Action/Equal Opportunity Institution 0. 12771

 

 

 

 

 

 

 

MSU

LIBRARIES
W

 

 

RETURNING MAIgRlAL§z
Place in book drop to
remove this checkout from
your record. ELEE§ will
be charged if book is
returned after the date

stamped below.

 

~-—----- » - -T—--—-—--- ----- ---[ --——---—----'

 

 

 

A STUDY OF DIRECT PHOTON PRODUCTION
AT THE CERN INTERSECTING STORAGE RINGS

by

Carlos Walter Salgado-Galeazzi

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
1988

72974

ABSTRACT

A STUDY OF DIRECT PHOTON PRODUCTION
AT THE CERN INTERSECTING STORAGE RINGS

by

Carlos Walter Salgado-Galeazzi

A measurement of direct photon production at high pT from proton-
proton collisions at the CERN ISR center of mass energy of .G - 63 GeV
is reported. Arrays of lead glass calorimeters and multiwire
proportional chambers were used as photon detectors. A single photon
signal was extracted using a newly developed direct identification
method. Backgrounds due to neutral meson decays were corrected by Monte
Carlo simulation of the detector. Data for the direct photon cross
section are presented in the transverse momentum range of H.S to 10
GeV/c and compared with QCD predictions. Constraints on the gluon
properties of the nucleon and the QCD scale parameter Afig are provided.

By using the lead glass arrays in conjunction with a drift
chamber barrel detector inside a superconducting solenoid, accompanying
charged particles were studied. The ratio of the number of positive to

negative charged particles in the opposite side hemisphere and azimuthal

distributions of accompanying particles are also presented.

ACKNOWLEDGEMENTS

I would like to thank my supervisor Prof. Bernard G. Pope for all
these years of support and continued guidance. I am truly thankful to
Prof. Pope and to Prof. James T. Linnemann for innumerable weekly
meetings that made this research possible.

I would also like to thank the R110 collaborators that. while at
CERN, introduced me to the experiment and the 188 environment.
Especially, Drs. Leslie Camilleri, Hans-Jurgen Besch,(flndstoph‘Wm1
Gagern, Timothy Cox and David Hanna. My stay in Geneva would not have
been as pleasant without Mlle. Marie-Anne Huber's friendly support and
excellent secretarial skills.

I thank Dr. Stuart Stampke for his critical review of this
research and his analysis of the n° data, and Mr. Bjorn Nilsen for his
help with the E68 runs. I am very thankful to my office and Geneva
apartment-mate Mr. Boyce Humphries for many discussions over particular
and general physics topics. Thanks to Dr. P. Aurenche for providing us
with programs to calculate the 2nd. order QCD predictions for the direct
photon cross section.

My friend Dr. Felix Marti made possible my arrival to Michigan
State University. To him and his family (Elida and Sergio) that became
part of my family during these years, I am truly thankful.

"Muchas Gracias" to my wife Nayda M. Flores for her support and
help during these last stressful years of analysis and thesis writing,

and to my son Sebastian Carlos for providing much happiness.

iii

Pflg
LIST OF TABLES... .................. . ................. Vii
LIST OF FIGURES......... ..... .... ....... .... ..... ...{Viii
Chapter I.- INTRODUCTION.

I-1. General Overview.................. ..... . ...... .. 1
I-2. The R110 Experiment.............................
I-3. Brief Introduction to High pT Physics...........
I-A. Direct Photon Production at High pT............. 11
I-S. Overview of Experimental Techniques Used to

Detect Direct Photons........................... 29

Chapter II.- ACCELERATOR AND EXPERIMENTAL APPARATUS.

11-1. The Intersecting Storage Rings (ISR)........... 35
II-2. The I1 Intersection............................ A1
II-3. Apparatus 0verview............ ..... ............ uu
II-A. The Solenoid................................... A7
II-S. The Drift Chambers............................. ”9
II-6. The Back Lead Glass Arrays..................... SS
II-7. The Front Lead Glass Arrays.................... 57
11-8. The Shower Counters............................ 59
11-9. The Strip Chambers............................. 61
11-10. The 6“

TABLE OF CONTENTS

 

 

seintillatorSOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

iv

Chapter III.- DATA TAKING.

III-1.
III-2.
III‘3.
III-u.
III‘S.

 

Control Room.................................. 69
Calibrations.................................. 7O
Trigger Logic................................. 72
On-line Programs.............................. 77

The Data...... ..... 0.0.0....OOOOOOOOOOOIOOO... 78

Chapter IV.- BASIC DATA ANALYSIS.

IV-1.
IV-2.
IV-3.
IV-A.
IV-5.
IV-6.
IV-7.
IV-8.

 

Overview of the Basic Analysis................. 82
Clustering in the Back Glass Arrays............ 8A
Track Finding Algorithm........................ 87
Energy Corrections...... .......... ............. 87
DSTing and B-Vetoing........................... 90
The B-veto Cut................................. 92
General Cuts................................... 9A
Strip Chamber Clustering Algorithm.............100

Chapter V.- SEARCH FOR A DIRECT PHOTON SIGNAL.

V-1.
v-2.
V-3.

v-9.

 

Introduction....................................111
Further Strip Chambers Cuts.....................112
Search for a Variable to Distinguish

Single from Multiphoton Showers Among the

Trigger Clusters................................121
The Main Method of Strip Chamber Analysis.......130
Simulated Neutral Meson Decays..................137
The B-veto Simulation...........................1AO
Simulated Single Photons........................1N9
Simulated Single and Multiphoton

o Distributions................................150

t
A Front/All cut......... .......... ..............158

V

V-10. Fits to the ot Distributions....................168
V-11. Corrections to the Direct Photons Observed......169

v-12. Statistical ErrOFSOIOOIOOOOOOOOOOOOOOO0.0.0.0...172

Chapter VI.- RESULTS AND CONCLUSIONS.

 

VI-1. Fraction of Single Photons.....................177
VI-2. Direct Photon to n°-meson and Direct Photon

to Neutral Meson Ratios........................191
VI-3. Direct Photon Cross Section....................192
VI-A. Systematic Errors..............................199
VI-S. Comparison with QCD Predictions and with

Other Experiments..............................20A
VI-6. Direct Photon Event Correlations...............215
VI-7. Subtraction of the Neutral Meson Background....216
VI-8. Estimation of Other Backgrounds................222
VI-9. Charged Particle Distributions...... ........ ...225
VI-10. Away Side Studies..............................228

VI-11. Summary and Conclusions........................229

APPENDIX A: Single Photon Background from Neutral

Meson Decays.............................233
APPENDIX 8: Neutral Meson Decay Kinematics............236
APPENDIX C: Shower Simulations (EGS Monte Carlo)......2u8
APPENDIX D: Neutral Meson Decay Monte Carlo...........256
APPENDIX E: The n° Trigger Data.......................261

LIST OF REFERWCEOOOOOOOOOOO0.0.0.00.00.00.0000000000265

vi

Table

Table
Table

Table
Table

Table

Table
Table
Table

Table

Table

Table

I-1:

III‘1:
III‘Z:

V"1
V-Z

VI-Z:
VI-3:
VI‘u:

A-1:

D-1:

LIST OF TABLES

Direct Photon Experiments.............

Data. Luminosities and Data Sets........ 79

Data. Condensed Tapes................... 80

Cut Efficiencies........
Values of the Parameters in the

B-veto Simulation...... ..... ............1u6

Inside and Outside Values of the
Parameters Used to Calculated the
Cross Sections, Y/all and Y/n°.. ..... ...190
......193
Results for the Outside Trigger.........193

Results for the Inside Trigger....
Final Error‘Weighted Average Results of

the Cross Sections, Y/all and v/n0......19u

Neutral Meson Decays.. ....23A

EGSA runs...............................254

Values of the Simulated Cut
Acceptances in the Neutral Meson

Decay Monte Carlo.......................259

vii

Figure
Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure
Figure

Figure
Figure

Figure
Figure
Figure

Figure
Figure

I-1
I-2.a:

I-6 :

I-7 :

I-8 :
I-9 :

II-1
II“2 :

II-3 :
II-H
II‘S :

II-6 :
II‘7 :

LIST OF FIGURES

Hadron Scattering Kinematics..........
A) Drell-Yan process. B) First Order
QCD corrections to Drell-Yan..........
Leading-order,quark-antiquark and
quark-gluon QCD subprocesses..........
QCD Leading Order Diagrams for

Direct Photon Production..............
Kinematics of Direct Photon
Production A + B + Y + X..............
Some Higher Order QCD Contributions

to Direct Photon Production. 3) Real
Emission Diagrams to the Compton and
b) the Annihilation. 0) Virtual
Corrections to Compton................
Renormalization and Factorization
Scheme Dependence of the Second

Order QCD Direct Photon Cross Section.
Kinematics of Two-body Parton
Scattering............................
Two-photon production diagrams........

The Conversion Method.................

ISR Layout............................
Vacuum Pipe Cross Sectional View

and Beam Density Profile..............
Rate vs Beam Displacement.............
I1 Intersection Layout................
Overview of the R110 Apparatus in

the Direct Photon Trigger Position....
Sextant Definition....................

System of Coordinates.................

viii

Page
7

13

13

1H

17

21

2A

26
28

Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure

Figure

Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure

Figure

Figure

Figure

Figure

Figure

II-8 :
II‘9 :

II-1O :

II-11

II-12 :
II-13 :
II-1A :
II‘15 :

III-1

IV‘1

IV-Z :

IV-3 :
IV-A :
IV-S :
IV-6 :
IV-7 :
IV-8 :

IV-9 :

IV-10:

IV-11:

IV-12:

IV-13:

Coil Cross-sectional View............. A8
Drift Chamber Sector Assembly......... 51
Drift Chamber Cross-sectional View.... 52
Back Lead Glass Array................. 56
.............. 58

Strip Chambers Cross-sectional View... 62

Front Lead Glass Array..

Strip Chamber Layout.................. 63
Position of MM Scintillators.......... 67

Flow Chart of the Trigger Logic....... 75

Flow Chart of the Analysis ............ 83
View of the Apparatus................. 91
........... 91
..... 93
Az Differences in the B Counters...... 93
...... 96
NaI Trigger Cut....................... 97

Geometry of the B Cut......
B Counter Pulse Heights..........

Vertex Positions (Diamond)......

A! vs. AZ, Differences Between Charged
Particle Hits and Trigger Position on

the Back Glass Array.................. 99
Angular Correction to the Observed
Front/All Ratio.......................101
F/ALL Distributions for Various ApT
Ranges in the Direct Photon Trigger.

All Events and Events with Front/All
Greater than 0.02.....................102
Number of Clusters per Event in the
Strip Chambers........................103
Gap Determination. Number of Clusters

vs. Separation Between Two Charged
Particle Hits in the Back Glass Array.10A
Total Pulse Heights of Strip

Chamber Clusters......................106

ix

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

IV-1A:

IV-15:
IV-16:

V—10:

Widths (or Span) of Strip
Chamber ClustePSCOOCOOOOOOOOOO0.00.00.107
Pulse Height per Strip................109

Variations Across the Chamber.........110

(Mean Pulse Height in Window)/w vs.
Window Size (w) for the n° and Direct
Photon Triggers.......................11A
Number of Strips per Cluster vs.

Window Size (w) for the n° and Direct
Photon Triggers.......................11A
Half-Width at Half-Maximum of the
Diff-(PHY-1.75-PHZ)/(PHY+1.75-PHZ)
Distribution vs. Window Size (w) for

the n° and Direct Photon Triggers.....115
Distribution of the Differences

Between Cluster and Shower Positions

for the Direct Photon Trigger Data....116
Distribution of the Differences

Between Cluster and Shower Positions

for the n° Trigger....................117
Total Pulse Height of Clusters

Inside a w- i 20 cm Window............119
Total Pulse Height of Clusters

Inside a w- t 5 cm Window.............120
Distribution of the Ratio
Diff-(PHY-1.75-PHZ)/(PHY+1.75-PHZ)....122
Fraction of Clusters in the Y and 2

Views Inside the Matching Window for

the Direct Photon Trigger Data........123
Fraction of Clusters in the Y and 2

Views Inside the Matching Window for

the n° Trigger........................12A
Standard Deviation of Clusters Inside

the Matching Window...................126

X

Figure
Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

V-12:
V-13:

V-1A:

V—15:

V‘16:

V‘17:

V-18:

V-19:

V-20:

V—21:

V—22:

V-23:

V-ZA:

V-ZS:

V-26:

V-27:

Moments Method........................127
Distance Between Photons vs. Asymmetry

in Simulated n° Decays and the

Asymmetry Distribution (ApT-A.S-10
GeV/c)................................129
ot Distributions for Direct Photon
Trigger Data at Various pT bins for the
Inside and Outside Triggers...........131
oy and oz Distributions for Direct

Photon Trigger Data...................132
Criterion of Limit Selection..........13A

Strip Chamber Analysis Flow Chart.
Y

YY mesons pT
Meson Decay Monte Carlo...............135

vs. from the Neutral
Probability of Observing a Shower in

the Strip Chamber vs. Energy..........139
Probability "tree" of the B-veto

Logic without Associated Particles....1A2
Probability "tree" of the B-veto

Logic with Associated Particles.......1AA
Gatti-Mathieson Image Charge

Distribution in A Bins of 0.1.........152
Mean of the 0t Distributions vs.

Energy for Single Photons from the

n° Trigger and Simulation.............155

Maxima of the o Distributions vs.

Energy for SingIe Photons from the

n° Trigger and Simulation.............155
Mean Pulse Height vs. Energy for

Single Photons from the n° Trigger

and Simulation........................156
Front/All vs. °t for the Direct

Photon Trigger Data...................160
Front/All distribution for A GeV EGS
Electron Initiated Shower Simulation

and A GeV Electron PS Test Data.......161

xi

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

V-28:

V-29:

V-30:

V—31:

V-32:

VI-1:

VI-2:

VI-3:

VI—A:

VI‘S:

Front/A11 Distributions for the Direct
Photon Data and EGS Simulation in the
Range ApT- A.5-5 GeV/c................162
Front/All Distributions for Simulated
Single Photons........................165
Front/All Distributions for Simulated
Multiphotons..........................166
Front/All Distributions for the Direct
Photon Data and EGS Simulation in the
Range ApT- A.5-5 GeV/c After Rebalance

of Front and Back.....................167
CY Distributions for the pT Bins of the
Inside and Outside Triggers...........175

Non-smeared °t Distributions for the
Inside Trigger Single and Multiphoton
Simulations, Direct Photon Trigger

Data and Likelihood Fit for Various

pT (C.M.) Bins........................178
Non-smeared ot Distributions for the
Outside Trigger Single and Multiphoton
Simulations, Direct Photon Trigger

Data and Likelihood Fit for Various

pT (C.M.) Bins........................180
ot Distributions for the Inside Trigger
Single and Multiphoton Simulations,
Direct Photon Trigger Data and
Likelihood Fit for Various pT (C.M.)
Bins..................................183
ot Distributions for the Outside Trigger
Single and Multiphoton Simulations,
Direct Photon Trigger Data and
Likelihood Fit for Various pT (C.M.)
Bins..................................186

Ratio of Smeared to Non-smeared Versions

xii.

Figure
Figure
Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure
Figure

VI-6:
VI-7:
VI-8:

V1-9:

VI‘10:

VI-11:

VI-12:

VI-13:

VI-1A:

VI-15:

VI’16:

V1-17:

VI-18:

VI-19:
VI-ZO:

of the Direct Photon Cross Sections as
Function of pT (C.M.).................189
Y/all Versus pT (C.M.)................19S
Yln° Versus pT (C.M.).................196
Direct Photon Invariant Cross Section

for the Inside and Outside Triggers

and their Ratio.......................198
Direct Photon Invariant Cross Section
Compared with other ISR Experiments...200
Ratios between Direct Photon Cross
Sections Measured in Other Experiments
and R110..............................205
pA.91E do

T 3'53
NAZA, WA70 and R110...................207
Gluon Structure Functions for the
Owens [DUK8A] Set I and II...209
Direct Photon Cross Section
Compared with QCD Predictions by
et a1. [AUR88]...............210

Direct Photon Cross Section

vs. xT, for Experiments

Duke and

Measured

Aurenche
Measured
Compared with QCD Predictions by
Contogouris et a1. [ARGB7J............212
pg-E figs. vs. xT, for Different QCD
Predictions and Experimental Results

for R806, R108 R110...................213
"All" (Direct Photon + Neutral Mesons)
Invariant Cross Section vs. pT (C.M.)

for Experiment R108 and R110..........21A

Representation of the ocut for the

Extraction of a Direct Photon Sample
and Correction of the Neutral Meson
BaCkgroundOO0.0.0.000...0.0.00.0000000218

Signal-to-Noise Ratios vs. for

9?

Various Values of o t""""""°"'221

CU

Values Ofevs. ocut..................221

Azimuthal Distributions of Associated

xiii

Figure VI-21:

Figure VI-22:

Figure

Figure

Figure
Figure

Figure

Figure

Figure
Figure

3-3 :
B-A .

C-1

E‘1

E-2 :

Particles for the Enriched Photon and
Neutral Meson Samples in the pT Trigger
Range A.5-6 GeV for Three Different

pT track Ranges.......................226
Azimuthal Distributions of Associated
Particles for the Direct Photon and
Neutral Meson Samples (After Background
Extraction) for pT Trigger Greater

than 6 GeV and for Three Different

pT track Ranges.......................227
Ratio of the Number of Positive to
Negative Charged Hadrons in the Away

Side vs. 2 for the Direct Photons

F!
and the Neutral Mesons Samples. Also

QCD Predictions [HAL80] are shown.....230

Neutral Meson Two-body Decay
Kinematics............................237
Geometry of the Neutral Meson Two-body
Decay.................................237
Dmin vs E for n°+ YY and n°+ YY.......2A3
Distribution of the Distance Between
Photons for 5 GeV n° and n° Decays....2A3
Dalitz Plot and Kinematics of Three

Body Neutral Meson Decays.............2A5

EGSA Detector Geometry................251

no Mass Spectrum.0.00.00.00.0000000000263
Energy Spectrum of Single Photons

from no DecaYSO00000000000000.0000....263

XiV’

CHAPTER I

INTRODUCTION

 

I-1. General Overview.

 

This dissertation describes the detection and analysis of direct
photons produced in proton-proton collisions at the CERN Intersecting
Storage Rings.

The first chapter is mainly an introduction to the topic of
direct photons, reviewing their importance in the present status of the
phenomenology of Quantum Chromodynamics (QCD). An overview of the
techniques utilized to detect direct photons and a list of experiments
are also presented.

The second chapter describes the experimental apparatus used to
collect the data included in this dissertation. A very brief description
of the accelerator is included. In the description of the detector those
parts that were particularly important for the present study are
emphasized.

Chapters III and IV explain the data taking process and the
basic analysis used. In chapter V the method of analysis used to

determine the direct photon signal is introduced in detail. A

description of how backgrounds were calculated and extracted from the
data sample is also included.

The final chapter presents results of a direct photon cross
section in the transverse momentum (pT) range of A.5 to 10 GeV/c. Event
correlations made from a direct photon sample are studied and the
results presented. All these results are compared with QCD predictions
and considered in the framework of perturbative QCD. A comparison with
other ISR experiments is presented. Other experiments in different
regions of’/§ (center of mass energy) are briefly discussed in order to

complete the present status of direct photon physics.

I-2. The R110 Experiment.

The R110 experiment was the last of a series of experiments to
look at proton-proton collisions at the CERN ISR intersection 1. From
1971 to 197A the CERN-Columbia-Rockefeller collaboration (CCR), ISR
experiment R103, used two walls of lead glass blocks coupled with planes
of wire spark chambers to address the topics of direct single electrons,
electron pairs and n°'s at high transverse momentum. This experiment was
the first to observe a large cross section for the production of 1r°'s
with large transverse momentum, thus opening a new branch of hadron
physics. This large cross section was interpreted as being due to the
hard scattering of partons (quarks and gluons) [BUS73].

A second generation experiment, R105. in collaboration with
Saclay (CCRS) included a gas Cerenkov counter, additional spark chamber

planes and a magnet. The collaboration continued to extend and improve

AI

studies of e+e‘ production, n°

inclusive and single electron
measurements, adding n°, A°, A° and K° data to its work and resulting in
many papers published between 197A and 1976 [i.e. BUS76a].

In 1977 a completely new, third generation experiment involving
CERN, Columbia, Oxford and Rockefeller (CCOR) performed ISR experiment
R-108. The apparatus now consisted of a superconducting solenoid and a
set of cylindrical drift chambers. The omiginal lead glass was
supplemented with twice as many blocks of the same cross sectional area
but 15% longer. The performance of the drift chambers was reported in
the 1978 Vienna wire chamber conference [CAM78] and papers published by
the experiment from 1978 to 1982 included studies of high mass e+e-
pairs (including the T); correlation and Jet studies; n° inclusive
spectra; direct photons; triple jets; and a novel method for analyzing
w°w° production [i.e. ANG78].

In order to increase the solid angle of the electromagnetic
calorimeter, lead-scintillator sandwich counters were added inside the
solenoid during July 1979 and the experiment was renamed R110. Columbia
did not participate in this collaboration leaving the acronym as COR. In
this mode the experiment collected a large luminosity of 63 GeV p-p data
and also observed a-a, a-p and p-p collisions. In 1981 R110 was modified
‘with no change of experimental number. Additional lead glass walls were
added in front of the originals, intended (in conjunction with
proportional chambers) to provide a good Y/n° discrimination. In
November 1982 a group from Michigan State University Joined the
experiment forming CMOR. No change was made to the detector at this time

and the physics goals remained basically the same. During the summer of

1983 a-a running became again possible and a group from Brookhaven

entered the experiment especially for the era and d-d analysis creating
for this purpose BCMOR [ANGBAa]. The detector was dismantled during the

first months of 198A after the closing of the ISR in December 1983.

I-3. Brief Introduction to High pPPrLysics.

When experiments at SLAC in the late 1960's started to probe the
structure of the nucleon by inelastically scattering electrons off
protons, it was revealed that the proton is composed of point-like
objects. Feynman called them "partons" and they were eventually
recognized to be consistent with the "quarks" of the original Gell-Mann
Zweig model. These charged lepton scattering experiments probed the
charge structure of hadronic matter. Complementary information was
obtained with neutrino beams that coupled to matter via the weak
interaction only, hence probing its weak structure. The scattering of
hadrons enables us to explore the strong interaction structure. From
hadron spectroscopy considerations a new quantum number called "color"
was added to partons. A dynamics of partons was created based on this
new property. This new field theory was called Quantum-Chromodynamics
(QCD). The discovery of "asymptotic freedom", the decrease of the
effective coupling at short distances, allowed use of perturbative
techniques in QCD to calculate measurable quantities, for example high
transverse momentum hadron scattering. On the other hand, "infrared
slavery", the increase of the effective coupling at large distances,
provided a mechanism to make plausible quark confinement. A self-

consistent gauge theory of the strong interaction was born by building

on the field technology created by QED. Today QCD is an essential
ingredient in the "Standard Model", SU(3)xSU(2)xU(1), that has motivated
a new search for the grand unification of the fundamental forces. Very
good reviews on perturbative QCD have been produced in the literature
recently [REY81, DUK85, BUR80, YND83, QU183].

The ISR was the first hadron machine to test QCD at high center
of mass energy where the perturbative QCD predictions could be compared
with the data. This dissertation deals with the study of strong
interactions between the hadron components at the high center of mass
energy of the ISR.

Among hadron reactions the production of particles that have a
large component of momentum transverse to the beam direction (131.) is a
good example of a reaction in which the basic parton scattering process
is fairly well separated from the more complex confinement mechanism
which prevents the partons from escaping as free particles and causes
them to reassemble into hadrons.

High energy hadronic interactions are characterized by the
production of a large number of particles. In most of such events, the
produced secondaries have small pT. The origin of these soft events at
high energies is understood as the two particles being excited by
passing each other and later becoming de-excited by, for example,
bremsstrahlung. This is then a collective effect and difficult to study
in the QCD perturbative framework.

A different thing happens when we consider large pT events.
These events allow us to study directly the inner structure of the

hadrons and their interactions.and compare them with perturbative QCD

predictions that will be accurate at small values of the coupling
constant (high energies).

The large transverse momentum events involve the "hard
scattering" of a parton constituent of each of the hadrons. This process
is similar to the one that allowed Rutherford, Geiger and Marsden
[RUT11] to study the structure of the atom 80 years ago.

The partons involved are scattered at large pT but because of
the QCD confinement of partons they materialized as a set of well
collimated hadrons called "Jets".

The simplest configuration of hard scattering shown in figure I-
1 implies the existence of at least four Jets. The beam and target Jets
(labelled "spectators") represent the soft interaction case. The other
two are due to hard scattering. A trigger particle with high pT signals
a possible Jet and defines it as the "trigger Jet" or "same side Jet" as
opposed to the "away" or "opposite side Jet".

In the parton model the inclusive hadronic reaction A + B + C +
X is expressed in terms of the elementary elastic parton-parton cross
section do/d; for the reaction a + b + c + d, where a,b c and d are the
parton components of hadrons A,B C and D that interact.

‘The inclusive invariant cross section for the hadronic reaction

can be written as [LEA82]:

 

do . . . . do (ab + CX)
EC 3 (AB + CX) agb I dxa I dxb F(a,xa,A) F(b,xb,B) EC 3
d P d P
C C
(I-a)

and using the relation:

spectators

 

 

 

Figure

1‘1

spectators

Hadron Scattering

D(c,zc,C)

 

 

 

 

 

 

 

34:52:32.8:
‘::‘:":':-':‘:'Z-': '
‘3:":-':':‘?.-':".-E 3
“$33: -:

‘fimfi

 

 

Kinematics.

 

tflgger
jet

away jet

 

 

E -d-°- (ab -> CX) - Z 1 -D(c.z :0) do (3b + Cd)
C 3 c,d 1r 2 C
d pC dt

written as:

l l
E -d-°- (AB + CX) - Z I dx J dx -F(a,xa;A)-F(b,xb;B)-
x

 

C 3 m b
d pC abcd a xb
. D("Jemima (ab + cd) (I-b)
1r'zc dt

The functions F(a, xa; A) and F(b, x B) are called "structure

b;
functions" and represent the probability of finding the parton a with a
fraction xa - qa/ pA of the hadron A momentum. The momentum transverse

to the beam direction is neglected (it is introduced later as a

correction). D(c,z C) is called the "fragmentation function" and

0;
represents the probability that the produced parton c produces a hadron

C with a momentum fraction 2 / qc. s, t and u are the Mandelstam

c' DC

A A A

variables (with a caret, s, t, u, when referring to the subprocess) and

m
b

prediction for the cross section we need to know the invariant cross

x:- -u/(s+t) ; x - -x:-t/(s-x:+u) [REY81]. Therefore in making a
sections for the parton sub-processes and also the structure and
fragmentation functions of all the parton constituents that can
contribute to the reaction. The sub-process cross sections are easily,
at least to the first and second order, calculated directly from the
appropriate perturbative QCD diagrams. But QCD makes no predictions for

the form of the structure and fragmentation functions; they should be

extracted directly from the data. The structure functions of quarks have
been studied in deep inelastic lepton-nucleon scattering processes (DIS)
[DUK85].

The fragmentation functions of quarks and anti-quarks have been
measured in e+e‘ machines [SAX85]. Dimensional counting rules can be
also used to estimate these functions at least in Unalimit of x-:1
(valence quarks) [BR075].

The most difficult problem is to determine these functions for
the gluon constituents. Since the quark, anti-quark and gluon structure
functions are related by the evolution equations [ALT77]. using these
equations one can calculate the gluon structure and fragmentation
functions knowing the quark and anti-quark distributions. However, since
gluons only interact via the strong force and we do not have in hand a
parton probe the only way of directly extracting the gluon structure
functions is from the more complicated hadron-hadron interactions.

We should look then for the simplest of these interactions.
Simplicity is the principal advantage of the direct photon reaction, in
which one of the strong vertices in the parton scattering diagram has
been replaced by a better known electromagnetic vertex. Another kind of
these interactions is high mass lepton pair production or the Drell-Yan
process. This last topic also has been studied by the R110 experiment
[ANG8Ab,HUM88].

However, the picture given by equation (1E1>) is not complete.
Actually we should include corrections referred to as "scaling
violations" that are already important in the energy range covered by

the ISR.

10

It was known for a long time that there is a roughly exponential
cut off in the pT distribution of secondary particles for pT < 1 GeV/c.
This phenomenon was usually interpreted in a thermodynamic approach to
hadronic matter. It was believed that this exponential cut off would
continue to hold at higher pT values. Using the parton model, BJ orken
predicted that hard parton-parton interactions should produce a tail in
the large pT distribution, which should exhibit a transition from an
exponential to an inverse power behavior. This behavior was confirmed by
the CCR data [BUS73]. This can be seen as the first confirmation of
quark structure from a hadronic machine.

The CCRS, CCR and CCOR collaborations showed [BUS76a, ANG78]
that the invariant cross section for production of neutral hadrons at

high pT, mostly n°'s, follows a general scaling of the form:

do -n m
E -—3- a pT ( 1 XT)

dP

(I-c)

where XT - 2pT//_s and m an 10 and n =- 8.A, valid for pT > 3 GeV, a
larger value of n than the value of A required by the BJorken scaling.
Various mechanisms were suggested to explain this phenomenon (i.e, CIM
[SIV76]). However, it was perturbative QCD that explained the data, from
the fact that the structure and fragmentation functions, and the strong
coupling constant are actually dependent on the momentum transfer (0’).
Beyond the simple parton model, in perturbative QCD, one must
consider the contribution of more complicated scattering diagrams

creating radiative corrections that give rise to momentum dependence of

the structure functions and the coupling constant. The evolution of the

11

structure functions has been given in a quantitative QCD approach by the
"evolution equations" [ALT77]. The strong coupling constant "runs" with
the momentum transfer and also produces scaling violations that shuauld
be taken into account [DUKSS].

Another issue is the intrinsic transverse momentum of the
T' There is much confusion about the role of kT since it

implies a transverse component of the incoming partons. Partons may

parton, called k

acquire transverse momentum by gluon emission before scattering. Thus
the high order QCD scattering diagrams produce kT' The experimental
values of <kT> found in the literature lie between O.A GeV/c and 1
GeV/c.

It is customary to introduce a "K factor" (especially in lepton

pair production) to parameterize the importance of the higher order

corrections, define as [0WE87]:

HO

K ' 1 + Born

 

(I-d)
where "HO" represents the high order prediction (or data), and "Born"
the first order or Born term of the perturbative QCD expansion

prediction.

 

I-A. Direct Photon Production at High_pm.

The investigation of simple diagrams in which one of the
vertices is purely electromagnetic has been used for some time to study
the fundamental physics of QCD. A well known example, is the Drell-Yan
mechanism of production of high mass lepton pairs from a virtual photon

produced at the parton level. In the first order, this proceeds via the

12

annihilation of a quark-antiquark pair contained in the colliding
hadrons [DRE70]. In figure I-2.a the Drell-Yan production diagrams are
shown (compare with the Direct Photon diagrams of figure I-3).

In hadronic collisions the overall inclusive yield of photons is
comparable with that observed for pions (1:. 1f). Of course the main
source of those photons is attributed to the rapdd decay of neutral
mesons as n° + YY , n° + YY and other electromagnetic decays of directly
produced hadrons. In addition, the production of direct Ux'prompt)
photons, those produced directly from the high energy collisions of
partons, is predicted by QCD [ESC75, FAR76].

The study of direct photon production offers an important tool
for examining QCD and all of its associated phenomenology. A large yield
cfi’direct photons, particularly at large transverse momentum (pT).
supports the presence of point-like charged obJects within the hadrons
and provides means of studying the sub-structure of hadrons. However,
there are some relatively weak sources of direct photons at low
transverse momenta other than those mentioned above. Pion inner
bremsstrahlung processes and the direct coupling of neutral vector
mesons to photons produce direct photons in the low p1. energy range. At
the pT values studied in this dissertation QCD leading order processes
should dominate.

Calculations based on the hard-scattering of partons predicted
that the ratio Y/n° production in hadronic reaction would exceed 10% at
large pT [FAR76]. This prediction was made before a direct photon yield
at large pT was first reported at the ISR in 1976 [DAR76].

Figure I-3 shows all the leading order contributions to direct

photon production in hadronic reactions at large pT, where a

13

e)

 

Figure I-2.a: A) Drell-Yan process. 8) First Order

QCD corrections to Drell-Yan.

 

Figure I-2.b: Leading-order,quark-antiquark and

quark-gluon QCD subprocesses.

1A

A) Compton

 

 

B) Annihilation

 

Figure I-3 : QCD Leading Order Diagrams for

Direct Photon Production.

15

perturbative expansion in QCD is expected to be valid. Diagram A is the
QCD analog of Compton scattering, called the Compton graph or QCD
Compton, and diagram B called the annihilation graph. These diagrams can
be compared with the pure-QCD diagrams of order 032(where as is the
strong coupling constant of QCD) of figure I-2.b. The photon emission
probability relative to the gluon yield is reduced essentially by the
ratio of as/a (a is the electromagnetic coupling constant). Thus one
would expect the yield of direct photons to be reduced by a factor of
100. However what is really relevant to us is the ratio of direct
photons to hadrons. Because hadrons are produced in Jets and the Jet
production is a factor one hundred times bigger than single hadrons of
the same pT, the photon to hadrons ratio is expected to be approximately
equal to one, at high pT [FER8A].

The importance of studying direct photon production comes from
the fact that we have a good understanding of the electromagnetic
(point-like) coupling of a photon to a quark. This process permits us to
isolate the more complex quark-gluon dynamics and the hadron structure.
In particular the diagrams of figure I-3 permit us to study the gluon
component of the hadron. From the diagrams we can see that when a photon
appears in the final state, either it is accompanied by a gluon, or the
hard scattering was initiated by a gluon. If the contribution of
diagrams A and B can be separated, direct photon production can be used
to extract information on both the gluon fragmentation function and the
gluon structure function inside hadrons.

Another advantage is that the direct photons emerge from the
collision as free particles, and consequently provide first hand

information about the hard scattering itself. In contrast gluons and

16

quarks fragment into hadrons (of reduced pT) before they can be
detected. The resulting hadrons must then be associated with their
respective partons before the extraction of the physics of the hard
scattering is possible.

This can be done but with difficulties that in turn create
biases. For example, one might attempt to identify all of the fragments
of a Jet associated with a single parton hard scattering. Doing that one
needs to select an energy or momentum requirement that will bias the
energy or momentum distributions of the particles in the Jet. Apart from
the experimental difficulties in such a task there are theoretical
difficulties in the definition of constituent Jets. Nevertheless this
technique has been used to extract information on the constituent
scattering [JACBO]. Another possibility is to select a single hadron
with large pT, hoping that its properties are related to those of its
parent partons. The selection of a particle with high pT tends to bias
the sample towards those events in which the fragmenting partons give
most of their momentum to that single hadron. For single hadron-
triggered experiments, it is difficult to identify which of the
subprocesses for the scattering of partons contribute to the measured
cross section. However a study of the charge correlations in the away
Jet can give some indication of the nature of the parton scattering.

To obtain the cross section in leading order perturbative QCD
for the production of direct photons in a hadronic collision, we must
convolute the cross section for the elementary subprocesses with the
gluon or/and quark content of the participating hadrons. Figure I-A

shows the diagram for the kinematics in the reaction A + B + Y +

17

 

 

 

 

 

away
spectators .
Jet
trigger
spectators
Figure I-A : Kinematics of Direct Photon

Production A + B + Y + X.

18

AA A

anything. The p1 are the four-vectors of the hadrons; s,t and u are the
Mandelstam variables for the subprocess.

From (I-b) the invariant cross section for the reaction can be
written in the infinite momentum frame (where all masses can be

neglected), in the following factorized form [LEA82]:

A

 

do E do
EY-Eg (A+B + Y+...)= I dxa-dxb-F(a,A;xa)F(b,B;xb) d3
DY pv
(I-e)

where the invariant cross section for the subprocess a+b + c+Y is:

 

 

EY d; “3 d9. 6(s + t + u) (I-f)
d pY dt

The x1 are the fractions of the four momentum of the incident
particles that are carried away by the partons. As for equation (I-a).
the functions F are the "structure functions" of the partons inside the
hadrons. Note that the fragmentation functions of partons do not appear
in the cross section equation.

For the QCD Compton subprocess the elementary cross section is

[FER8A]:

n a a 2 “2 “2
+ 1-
do (qg + qY) _ _ 3 eq u s ( 3)
dt 352 s . u

and for the annihilation subprocess [FER8A]:

do _ 8x a as 2 u2 + t2 (I-h)
-r(qq+gY)- —-:.—2-—e T—T'
dt 93 q u-t

19

where eq is the charge of the interacting quark. For a large pT process

A A

where production occurs at 90° in the (a,b) center of mass, 3 - ~2u -
-Zt , the cross sections for the two subprocesses are comparable.
However, their respective contributions to the direct photon yield are
clearly a function of the nature of the constituent distributions within
the hadron (structure functions).

The (8)”2 fknxn in do/dt leads naturally to an inclusive photon
cross section from equation (I-c) that scales in the parton model as
p;u. That is, if we assume that the structure functions depend only on
the x and not on the momentum transfers ( we are assuming scaling in

1

the structure functions), then for any given x -2p.I.//s and scattering

T

angle 6 in the center of mass, the cross section becomes:

 

f(x ,6) g(x , e) _
E (1" (AB+y+,,,) .____T__ ,__T____ (Ii)
Y (13 32 A

In fact, without scaling violations, the’cross sections for
production of Jets, single hadrons and direct photons at large pT should
all follow this form, but with different forms for the functions g(xT) .
reflecting different parton-level processes. As we will see, the
experimental pT dependence for photons is closer to p.126. This softer
distribution can be explained by the presence of higher order
corrections and scaling violations [BER82].

In perturbative QCD the strong running coupling constant has a

02 dependence, which, to the lowest order corrections in the gluon

propagator [DUK85], is given by:

20

12 - 1r (I-J)

(33’2-f)°ln Q2/A2fig

where 02 is the square of an appropriate momentum transfer (of order pT)

as(02) =

that characterizes the collision, f is the number of flavors that
contribute to the scattering, and Afig is a parameter that sets the scale
for 02 in the standard minimal subtraction renormalization scheme (MS).

2 (and 1n 02 >> ln[ln 02])

This expression is only valid for 02 >> A
(leading-logarithm approximation), i.e., when as<< 1.

In perturbative QCD there are two kind of singularities that
have to be considered before arriving at quantitative results. (hue kind
are the mass singularities arising from diagrams as I-5(a), which can be
factorized and separated from the subprocess scattering. The
factorization theorem can be used to absorb these singularities into the
uncalculated portions of the structure and fragmentation functions. In
addition, there are ultraviolet singularities that arise from diagrams
as I-5(c). The technique for regularizing these singularities is called
renormalization. Therefore, every quantitative perturbative QCD
calculation has at least two arbitrary scales which have to be chosen.
If fragmentation to hadrons is involved a third scale appears. The
degree of arbitrariness decreases when we consider more terms in the
perturbative expansion. It is important, therefore, for the definition
of the scales to calculate the next-to-leading order diagram
contributions.

Some of the 3000 terms of the next order QCD diagrams [DOU8A]
that contribute to direct photon production are shown in figure I-5.

Aurenche et al. [AURBA] have performed a detailed quantitative

21

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure I-5 : Some Higher Order QCD Contributions
to Direct Photon Production. a) Real
Emission Diagrams to the Compton and
b) the Annihilation. 0) Virtual

Corrections to Compton.

22

calculation of the invariant cross section at large pT beyond the
leading order.
The authors of reference [AURBA] express the inclusive photon

cross section as:

E‘“Tg (s p V)= do
d p ’ T’ dydzp
T T
1 2 2
151 T. I F(Xa,A,Ms)'dxa°F(Xb,B,Ms)°dxb°
do .. 2 M M
"fr- 1 —-—Ll(s, v) 6(1-w) “8(u2 w)'9(1’W)'K1J(Sf—g-y—wgf-TQ,V,W) }
s s s s
(I-k)
where:

. — . . 'Y
v 1 xb (pT//P§) e

. . . -y
w - (1/v xa) (pT//P§) e

and y - tanh’1(pz/E) is the rapidity of the photon. The indices 1 and J

run over the parton content of the initial hadrons. do /dv are the

1J
leading order QCD (Born) cross sections. The KIJ contain the finite

next-to-leading order corrections. The masses M3 and M are parameters

d
associated with the scale breaking of the structure and fragmentation

functions.
Therefore to perform a detailed quantitative comparison of QCD
and the direct photon data (i.e. invariant cross section). we need more

than the gluon structure function and the QCD scaling A- The finite

MS

23

order perturbative predictions are affected by ambiguities due to the
choice of the renormalization (RS) and factorization (FS) schemes. They
enter the calculations (I-h) via two parameters, u the renormalization
point (where the coupling constant as(u2) will be defined); and M, the
factorization mass. In most of the applications 112 - M2 - Q2 is taken.
Most present high-pT phenomenological calculations choose 0 - c-pT
where a - 1. Some calculations use 02- -t, Q or 2QEQ/(§+E+S). There is
no universaly accepted method to determined the QCD scales [CON86a].
This leaves us with a cross section which depends on the
arbitrary parameters u and M, E-do/d’p(s,pT.y) - F(os(u).M). Aurenche et
al. have calculated this two-dimensional function as shown in figure I-6
[BAI86]. Different choices of u and M (RS and FS) give numerically
different predictions. In first order QCD calculations these quantities
are not constrained, but they are taken "ad hoc" to agree with the data.
In the next-to-leading order it is possible to define an "optimized
second order QCD" using the "principle of minimal sensitivity" (PMS)
[STE81]. Since the physical cross section is RS and FS independent, it
is reasonable to require that a truncated perturbative calculation obeys
at least a local stability condition in the parameters 11 and M. This is
done by choosing the saddle point in figure I-6 as the optimized second
order QCD predictions. With the values of u and M fixed, a comparison
with the data is possible assuming AEE and a set of structure functions.
Duke and Owens [DUK8A] have proposed two sets of structure functions
called "soft" (lower momenta) (set I) and "hard" (higher momenta) (set
II). The two sets differ chiefly in the gluon distribution. There is a
correlation between the QCD coupling scale parameters A— and the shape

MS
of the gluon distribution [DUK8A]. A soft gluon distribution (more low

pp-ujx, fs-aSJGQV ‘
pT s mow/c '."° ~..
9.0
’ 100

v

E d’a/d’p (cmZ/Gevz) 7.5 ’
10'” .
/
9 o
12 A- .

 

 

" 20
“t
_ ,0 - M z(Gev’xcz)
‘ ‘L, I 1 l #7.,
009 005
a. (11W
pp-‘IX, {7-63 GOV, pt I ”GOV/C
0.13

. 0.11

ODS

 

«sun/1r

007

095

 

 

 

M ’(GeVz/c 2)

Figure I-6 : Renormalization and Factorization
Scheme Dependence of the Second

Order QCD Direct Photon Cross Section.

25

momentum gluons) results in a relatively smaller value of Afig, while a
harder gluon distribution (more high momentum gluons) gives a bigger
value of Afig.

Contogouris et a1. [CON81] have developed another method to
calculate the direct photon cross section to the next-to-leading order.
They used the leading-logarithm approximation, kT smearing and K factors
calculated in the soft-gluon approximation by constant nz-terms
[CON86b]. The scale is defined as uz- 02- M2. pé. There are in the
literature opinions in favor and opposed to both methods [CON86a,OWE87J.

Measuring the direct photon cross section then allows a
comparison with a quantitative QCD prediction, although it does not
allow a direct measurement of the parton distribution. There is a way of
obtaining the parton distributions almost directly. If one can measure
the double inclusive photon-away~Jet cross section the two-body
kinematics of the parton reactions are completely determined. The two
body kinematics of the reaction are shown in figure I-7. In this case
one can measure the gluon structure function. Further, the distribution
of the hadrons in the Jet will measure the fragmentation function D(z)
of the quark (in the QCD Compton scattering) and of the gluon (in the
annihilation process), provided one assumes that the valence structure
functions are known, for example from DIS.

Halzen et a1. [HAL80] have calculated the inclusive photon-Jet

cross section for the first order Compton diagram when photon and Jet

are both measured aproximately at 0 - 90°:

C O 0 ep
do 51! (insight, 11) F2 (x, u)

dndeJde 3-x233/2 (I-l)

 

26

 

(X +X )p =Ey+EJ

1 2 cm
Therefore:
x1: 1/2pcm(E 7+EJ+pLy+pL)
X2 = “mummy +12J ‘Piypif
Figure 1—7 : Kinematics of Two-body Parton

Scattering.

27

where x - 2-pT//-§, n - ln( cot 0/2) is the pseudo—rapidity and F:p(x,u)
is the valance quark structure function as extracted from deep lepton-
hadron scattering experiments.

One should first isolate Compton scattering if one wishes to use
this method. One has more opportunities of doing that by comparing
photon production with beams or targets of different anti-quark content.
This is done particularly well with 11+ and it. beams incident on fixed
targets [FERBA]. In our case, only proton-proton beams were used. We can
make use of the fact that Compton scattering has been shown to be the
dominant diagram [BEN83] in this kinematic regime. However, the
bremsstrahlung contribution has been shown [AKE83] to contribute up to
30% in the pT range of the ISR.

Another area where QCD predictions could be checked via direct
photon data is the comparison of prediction for the associated event
topology. I will reserve the discussion of this subJect for chapter VI
of this dissertation. All the topics discussed in this section have
been extensively reviewed in an article by J. F. Owens [0WE87], and the
work of the P. Aurenche, R. Baier, M. Fontannaz and D. Schiff in
[AUR87].

Finally we should mention the hadroproduction of two photons in
processes as shown in figure I-8 [OWE87J. The production of two photons
has been measured at the ISR [AKE86J and the SPS [BAD86] and also QCD
predictions have been made [AUR85, CON87]. However there are important
sources of background, such as normal direct photon production (i.e., qg
~> Yq) with a second photon originated from bremsstrahlung from the

recoiling parton. This contribution can be as large or larger than the

28

 

Two-photon production diagrams.

I-8

Figure

 

 

 

\\\\\\\\\\\1\\\\\..\\\\\\\\\\\\\\\\\\\ . .\ ..\\\\\W\.\\\|\\\\\\\

     

 

S

 

 

  

 

* *

 

 

The Conversion Method.

I-9

Figure

29

Born term subprocess. No attempt has been done to look for two photons

in the present dissertation.

I-S. Overview of Experimental Techniques Used to Detect Direct

Photons.

The principal problem in the study of direct photons is the
background produced by non-direct photon sources. The primary source of
background is the electromagnetic decay of neutral mesons such as 1r° +
YY, n° + YY ...etc. These decays can contribute to the background in two
different ways: (1) one photon from the neutral meson decay remains
undetected thus yielding an isolated photon, and (2) the photons from
the decay merge into one shower in the detector.

The two main techniques that have been used to isolate a direct
photon signal from this background are called the "direct method" and
the "conversion method". The "direct method" consists in recognizing the
photons from the neutral mesons decays through a measurement of the
meson mass or any other parameter provided by space-resolved photons. In
the "conversion method", neutral mesons and photons are separated
through the measurement of the conversion probability in a thin
converter placed in front of the calorimeter.

The characteristics of the detector are determined by the
detection method chosen (or viceversa). A direct method measurement
requires a fine transverse segmentation to isolate every single shower,
a good capability for detecting low energy photons and a large solid

angle acceptance so that all photons from the neutral meson decays are

30

fully detected in the energy range of interest. The photons from the
meson decays cover a broader range of energies than the direct photons.
It is also important to achieve linearity in the energy response of the
calorimeter, since one must be sure that the detector responds to one
photon of energy E (i.e. a direct photon) the same as it responds to
several photons of energies 2 E1- E.

A good understanding of the neutral meson decay kinematics is
important to undertake measurements of direct photons, from the
experiment design to the analysis. See Appendix B for a detailed account
of these kinematics. Two essential properties of the two-body meson
decays (i.e. 1r°+ YY) are the following. First, the energy distribution
of each of the photons has a flat distribution between zero and the
energy of the neutral meson, therefore the asymmetry of the decay,
defined as A-(E1- E2)/(E1+ E2) . runs with the same probability in the
center of mass, between -1 and 1. Second, the distance between the two
photons in the laboratory system, on the contrary, has a distribution of
probability highly peaked near the minimum distance.

If we place our detector at a certain distance L from the 1r°
decay, the minimum distance between photons is given, in the small angle

approximation, by the relation dm - 2-m1r-L/ Err . For example, in our

in

case L-21A cm, therefore at E"- 5 GeV dm - 11.5 cm, and for Efl- 9 GeV

in
dmin- 6.A cm. These values put a constraint on the transverse
segmentation of the detector and the possibility of isolating both
photons from the u° decay.

The inefficiency in detecting low momentum gammas can also

provide a substantial background of large pT photons from asymetric u°

decays. The second most important contribution to the background comes

31

from the n° decay. The n° contribution to the background is reduced
because the ratio of production is n° + YY / u° + YY - .21.

The conversion method relies on the fact that the probability of
observing a photon conversion is greater for a neutral meson (more than
one photon) than for a direct single photon. Such a detector would
consist of a thin convertor surrounded by detectors that determine if
conversion has occurred. This is sketched in figure I-9. The technique
is to measure the fraction of events that show conversions in the
convertor and compare this with the conversion probability expected from
multi and single photons. In order to make a good measurement the
absolute conversion probability must be known accurately, as must any
non-linearity in the detector.

Comparing both methods we can find advantages and disadvantages
for each of them depending on the goals, the pT regime of study and the
means to perform the measurements that we have. An advantage of the
direct method is that most of the background can be measured and
removed, so in an event by event basis a sample of direct photons can be
isolated. This is then the best way to study event correlations or event
structure properties. The advantage of the conversion method comes from
the fact that it does not require as finely segmented a detector as the
direct method and that it does not impose an intrinsic pT limit on the
measurement caused by the limit on the space resolution. Therefore this
method has advantages if what we want is to study the cross section over
a large pT range, and up to high values of pr. If the ratio of direct
photons to background is high both methods could be competetive.

The first indications of a direct photon signal were produced at

the CERN ISR using a direct method in 1976 [DAR76]. The results were

32

rather qualitative due to uncertainties in the systematics and the
background subtractions. There were also at the same time indications of
a possible direct photon signal at fixed target experiments at Fermilab
[FER8A]. The next experiment to show a signal of direct photons was R107
at the ISR, also using a direct method [AMA78].

Table I-1 shows a summary of the principal characteristics of
all the experiments recently done or planned for the near future with
the intention of looking for direct photons in hard scattering hadron
collisions.

The more recent measurements of direct photons include
experiments at the ISR, the fixed target SPS program, the fixed target
program at Fermilab and the SBpS collider at CERN. Previous ISR
experiments that measured direct photons were R806 [ANA82], R108 [AN080,
ANG81] and the AFS collaboration using an open axial field magnet
containing cylindrical drift chambers and sourrounded by an uranium-
scintillator calorimeter [AKE85]. At Fermilab the experiments E95
[BAL8OJ and E629 [MCL83] measured direct photons at the Meson area, the
former using a lead-liquid argon calorimeter of fine transverse
segmentation. More recently the SPS fixed target program with WA70 using
a lead-liquid scintillator electromagnetic calorimeter, drift and MWPC
[BON87], NA2A using Cerenkov counters, MWPC and a "photon position
detector" consisting of lead sheets and proportional tubes of triangular
cell shapes [DEM87] and NA3 using lead/scintillator strips and PWC with
strips and pad read outs [BADB6]. presented data studying direct
photons. In the SPPS collider UA1 [DIc87]. UA2 [APP86] and UA6 [BER87]
also have presented data. UA6 looks at collisions of one of the collider

beams with a H2 Jet to study high pt phenomena at V s - 2A.3 GeV.

Table I’i:

33

Direct Photon Experiments.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Experiments beam+target J? GeV 223k pT Place of M5322,“
R 806 p + p 63 12 ISR Direct
R 108 p + D 45.63 12 13!? Conversion
E 95 p 4. 3. 3:; 4 Fermilab Direct
E 629 p+C. it? + C 19_4 5 *Fermilab Direct
AFS p + p , p + ‘35 53.53 10 ISR Direct
R 110 p + p 63 10 ISR Direct
UA1 p + i5 630 80 :35?" Conversion
UA2 p + a 56;: 43 if???" Conversion
”A 6 p + p p + 'p' 24 6-7 sips Dir-ct
NA 3 p+C . I: + C 19.4 6 SP8 Direct
NA 24 p + p , 1;: + p 24 6.7 SP8 Direct
WA 70 p + p.1t:+ p 23 6-7 sps Direct
E 705 p-o-D. 1:340 24 8 Fermilab Direct
E 706 6+C. E. c .41 10 IF°'"‘"‘“’ Dir-ct

CDF p + 5 2000 40 taxi.) Direct
00 p + p 2000 7 mailer.) Conversion

 

 

 

 

 

 

3A

The R108 experiment and recently UA2 and UA1 are the only
experiments to use a conversion method to measure the direct photon
signal. Because the variety of accelerators used in all these
experiments we have, by now, measurements over a broad range of center
of mass energy (if-3). For our case only the earlier experiments at the
ISR are directly comparable with our data because they include
measurements at J”; - 63 GeV. In chapter VI of this dissertation I will
discuss the results obtained by these experiments and compare theniirith
those obtained in the present experiment.

The maJor contributions from Fermilab will come presumably from
E705 (with a scintillating barium glass electromagnetic shower detector)
[COX82] and E706, a second generation experiment (from E629) based on
liquid argon calorimetry [FER86]. These are planned to run with
improved detectors especially designed to detect direct photons. In
addition the Tevatron collider experiments CDF [BLA88] and D0 [D08A] are
planning to look for direct photons.

For a detailed account of all of these experiments I refer to
the review article by T. Ferbel and W.R. Molson [FER8A] or to the

specific references.

CHAPTER II

ACCELERATOR AND EXPERIMENTAL APPARATUS.

 

II-1. The Intersecting Storage Rings (ISR).

The Intersecting Storage Rings (ISR) was the first machine ever
to store two continuous proton beams and make them collide [HUB77]. The
ISR was composed of two almost circular rings in which protons
circulated in opposite directions. A layout of the ISR is shown in
figure II-1. Collisions occurred in 8 places, called intersections,
numbered from 1 to 8 (Ii to I8) where the two beams collided at an angle
of a - 1A.77°. The protons were accelerated in the CERN PS (Proton
Synchrotron) and inJected into the storage rings through two transfer
lines. The beam eJected from the PS was inJected into one ring at a time
and accumulated by successively stacking. Only a small acceleration was
provided in the ISR to replace energy losses and maintain the same beam
characteristics for a long period of time.

Because the ISR was a collider machine, almost all energy which
was invested in the acceleration became available in the center of mass
for reactions or particle creation. However due to the crossing angle
between the beams, the proton-proton center of mass moved with a

velocity of [JAC75]:

35

36

 

 

 

   
  

I6
Large X hadron physics and cor- ' \ l7
rciutionstRbOO) Chennon'um W with e
pbeeitieridfl,terlet(ll704)
15
Search for magnetic monopole: -’
(nun) ‘\“l8

P mutton
Study of direct photon production
(R800)
SFM [4
Study oft-vents with forward identi-
fied particlestR4 l9) II
"in 3" physics in pp interactions ‘— Highmelootmpeinflllm
(R420)
Comparison of pp and pp colli-
sions(R42|)

- I2
‘Pw" pitotelcroee-eectioeflzlm
l3 ' pil’orverdcrou-eectioefllll)

Figure 11-1 : ISR Layout.

37

Bav/c-sin(a/2)-p/E (II-a)

with respect to the laboratory frame, where p is the particle's momentum
and E is its energy. At the high energies at which the ISR run 8 was
essentially independent of the beam momentum (E - p) and was equal to
0.129. The square of the total energy in the center of mass is given by
[JAC75]:

s - A-pZ-cosz(a/2) + Am2 a A-pzocosz(a/2) (II-b)
where m is the proton mass.

The beams circulated inside vacuum pipes that had the cross
section shown in figure II-2. Also shown is a typical beam density
profile. The ISR could operate in a broad range of beam momenta and
currents. An important quantity is the counting rate or number of
collisions per unit of time which lead to a certain reaction. In a
collider the rate can be calculated from the geometry of the beams,
their density and their energy.

A usual way of giving the rate is to define the luminosity (L).
The luminosity is defined as the rate per unit of cross section. For
'beams of rectangular cross section and uniform density, it can be shown

[HUB77] that the luminosity is given by:

 

1dN 1 2 __
L 0 dt (II c)

c - e2 - h - tan (a/2)

 
 

,1

injection

 

5

20rmmlfi

38

 

801nn1

 

-]r_--_-

 

    
   

 

 

‘__________-__-_

Figure 11-2

150 mm

Vacuum Pipe Cross Sectional View

and Beam Density Profile.

39

where I1 and 12 are the beam currents in Amps, o is the process cross-
section in cm2, dN/dt the counting rate, h the beam height in cm, e the
electron charge and c the speed of light ( assumed to be the velocity of
the particles in the beam). L is normally expressed in units of
cm-Zs-1.

In practice the luminosity was measured experimentally using the
rates measured in the MM counters (described in section II-10 of this
chapter). The experimental determination used the Van der Meer method
[VAN68]. To account for the non-uniformity of the beams, h in equation

(II-b) is substituted by an effective height heff' Then, the luminosity

can be written as:

L = 10 "’TT'_" (II-d)

where I and I are measured in Amps, h in cm and the value of a for

1 2
the ISR was introduced.

eff

The value of he is obtained experimentally by making a plot of

ff
the rate as a function of the vertical beam displacement (A2). A plot of

this kind is shown in figure II-3. It has been shown [VAN68] that heff

is given by:

area under the curve -
heff ' (dN/dt)max (II 9)

 

where (dN/dt)max is the maximum counting rate. Introducing the value of
heff into equation (II-c) and knowing the beam currents the luminosity
can be calculated. The ratio of the maximum counting rate to the

luminosity is called the "monitor constant" (K):

A0

 

 

MM counts

 

 

 

O l I I I l l

O 1
AZ (mm)

 

“1'

 

Figure 11-3 : Rate vs Beam Displacement.

 

A1

(dN/dt)max

K - L (II-f)

 

As the observed rate is o-L, K is the effective cross section
seen by the monitor. It depends only on the energy of the beams and the
layout of the particular monitor. Once calculated, the monitor constant
could be used directly (for a particular ISR stack) to convert MM counts
to luminosity by L - K - (MM counts). The highest luminosity ever
observed in intersection region II in proton-proton collisions was

reached for 63 GeV running and was 6.31 x 1031 cm-zs-A.

11-2. The I1 Intersection.

 

The detector used in this experiment was located at the
intersection region 1 (I1), as shown in figure II-A. The p-p center of
mass for I1 was moving towards the outside of the rings.

As can be seen from equation (IIrb) there are other alternatives
to increase the luminosity besides increasing the beam currents. One is
to reduce the crossing angle and the other is to reduce the height of
the crossing beams, that is what the "low-8" insertion does. I1 and I8
were the only two intersections equipped with low-B insertions.

The beam height is determined by the focussing and the emittance
of the beam. The focussing is measured by the number of transverse
oscillations (O) which the particle performs per revolution around its

equilibrium orbit. These are called "betatron oscillations". The area

A2

 

 

 

.uaoamq :ofiuooncoucH PH

 

 

 

i--i .

 

" ziHH ogsmqm

 

 

 

 

 

 

 

 

i-ellufl'l'll

 

 

 

 

 

 

 

 

 

 

 

Aqu'

 

222: a

‘ [mi 1 _____.

 

 

 

 

 

 

 

 

 

 

 

l.‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:33): 00.0%.!
IS“ tWfiMWrmntii e I

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O-

 

T

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

eflnrso

"3

inside the locus of motion in the phase plane of betatron motion is a
beam characteristic and is called emittance (6). Since transfer from one
emcelerator to another does not change its value, the emittance is
determined by the PS.

It can be shown [HUB77] that the beam height h is related to e
and Q by:

n - 24’ {7—3— (II-g)

where R is the radius of the particle's orbit. The wavelength of the

betatron oscillations is varies as a function of the azimuth (s). It can

be written as:

.2-1r-R(s)
B Q

 

(II-h)

or also expressed as is a 2-1r°B(s) where 8(3) is called the "betatron

function". Therefore,

 

/*'t _
I) ~ 2°/ T ° BVI (II I.)

where BVI is the vertical B-function in the intersection. A low-B means
lower h and thus greater luminosity. Therefore, in order to increase the
luminosity it is sufficient to increase the focussing locally. This was
done by four quadrupoles lenses for each beam; two before and two after
the intersection. In the case of Ii a factor of 2.2 in luminosity was
gained over a standard interaction region. The 8 quadrupoles (LBQ1-L808)

layout that provided the extra field for low-B focussing is shown in

AA

figure II-A. All data presented in this dissertation were taken with the
low-B magnets on.
The I1 vacuum pipe consisted of a 1mm thick titanium cylinder

with conical ends (see figure II-15).

II-3. Apparatus Overview.

 

The R110 detector was designed for several specific physics
purposes. These were to study high mass e+e- pair productkniand in
general high pT processes where an electromagnetic energy deposition
trigger could be used. Over time other topics were also studied. These
included Jet structure studies, pp-pp comparisons, are, d-d and p-p
comparisons, direct photon production and high mass n° pairs. To achieve
these purposes an electromagnetic calorimeter with a large coverage was
designed to trigger on electromagnetic deposition. A charged particle
momentum measurement system was also included. The detector can be
separated into two main parts: 1) the electromagnetic calorimeter and 2)
the high magnetic field spectrometer composed of drift chambers and a
superconducting solenoid. Various scintillation counters and
proportional chambers were also included. The detector covered almost Zn
in azimuthal angle ¢ but with very different detector characteristics.
The figure II-S shows a general view of the detector. The azimuthal
angle was divided in sextants as shown in figure II-6. Sextants 1, 3, A
and 6 were covered by lead-scintillator shower counters and 2 and 5 by

the lead-glass Cerenkov arrays. The main components for the purpose of

this dissertation were the lead glass arrays in sextants 2 and 5. In the

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A6

INSIDE
h

 

Figure 11-6 : Sextant Definition.

 

Figure II-7 : System of Coordinates.

5E

96

9‘

”‘71 .
I

:1

A7

trigger used for this dissertation one of the lead glass arrays, the one
used in the trigger, was moved away from the intersection region (back
glass front face at 236 cm) to increase the angular resolution of the
apparatus. The other array was kept in its original position (back glass
front face at 1AA cm), closer to the intersection, as shown in figure
II-S. (Triggers were taken with each array alternately retracted). The
specifics of the trigger will be discussed later in the dissertation.
The system of coordinates used in the R110 experiment is (see
figure II-7): a right-handed x,y,z with: x, towards the inside of the
ISR rings; y, vertically up; 2, along the solenoid axis (towards 18).
The 0,0,0 is at the center of the solenoid. For cylindrical coordinates
(r,¢, z) 0-0 is along x, and the 9 increases anti-clockwise (from x to

y), with -n < ¢ < n.

II-A. The Solenoid.

 

The magnet was a superconducting solenoid with a field of 1.A
Tesla [MOR77a. MOR77b]. The advantage of using a superconducting magnet
was that a high field could be produced while having a small amount of
material between the intersection region and the lead glass arrays
outside the magnet. The coil itself was 170 cm long with an external
radius of 89 cm and an internal radius of 70 cm. The magnetic flux path
was completed by soft iron pole pieces capping the ends of the solenoid
cylinder. Stray field not confined to the return yoke interfered with
the external detectors, thus preventing operation of the magnet at any

higher field. The uniformity of the field was checked to be within 1.5%

A8

 

 

COIL

 

 

 

to A! A
as 40 urea: or seam iNSULATDR

l W

23 He 188 I

 

6. . . VETRONITE

20 Al

23. 4O LAYERS OF SUPER INSULATOR

 

 

I"

3; * AI J

PARTICLE
FROM
INTERSECTION
REGION

Figure 11-8 : Coil Cross-sectional View.

to t
laye

SITE

EVQPé

Sis:

A9

over the warm bore (138 cm in diameter), with the worst non-uniformity
being near the holes in the iron end pieces through which the beam pipes
passed.

Particles reaching the B counters and the lead glass arrays had
to traverse the coil and its aluminum dewar. The coil winding was five
layers of a conductor that consisted of niobium~titanium superconducting
strands embedded in a copper wire matrix and given mechanical strength
by a steel core; strips of pure aluminum surrounding this matrix
provided a current path and thermal sink in the event of the magnet
going normal. The layers were partially wrapped in an insulator to hold
them apart while allowing free circulation of the helium. The total
average thickness of material in the solenoid coil was: 7.5 cm of Al,
1.25 cm of fiberglass, 0.12 cm of steel, 0.075 cm of Cu, and 0.025 cm of
Nb-Ti. This structure corresponds to a thickness of 1.0 radiation
lengths (see figure II-8).

While the magnet itself was quite reliable, the refrigeration
system was considerably less dependable; significant amounts of running

time were lost due to compressor problems.

II-5. The Drift Chambers

 

The drift chambers provided momentum analysis of charged
particles over the full azimuth by measuring their radius of curvature
in the magnetic field of the solenoid. Because of the high magnetic
field produced by the superconducting solenoid only a small lever arm

was needed to measure the momenta of charged particles up to a few GeV.

g—O

Ce:
the
rig

€02";

50

The chambers were cylindrical, but constructed in sectors
previously assembled in the laboratory (see figure II-9) [CAM78]. There
were at least four sectors in any azimuthal direction and five in some
places. Three complete cylinders, DCM1-DCM3 were in place and six of
the ten sectors (DCMA,DCM5) of a chamber, (which prior to the addition
of the shower counters were used as a fourth complete cylinder) , were
inserted in available spaces between DCM2 and DCM3. In front of the lead
glass acceptance they remained outside DCM3 (as indicated in figure II-
5).

Each sector had two drift chamber gaps of an adJustable field
design. A diagram is shown in figure 11-10. There was an offset between
the drift cell in the two gaps to help in the resolution of the left-
right ambiguity. Every gap had a cathode plane on both its surfaces
consisting of printed circuit copper strips. The 20 um gold plated
tungsten sense wires, with a tension of A0 g, alternated with field-
shaping wires of 100 um copper beryllium stung at a tension of 100 g.
The gap width was 0.6 cm. The sense wires were held at 0.3 cm from the
cathode planes by means of glass beads placed every 50 cm along the wire
and maintained at a voltage of 1.7 kV.

The time recorded on a sense wire measures the azimuthal
coordinate of a particle hit. For the measurement of the Z coordinate
(along the wires) delay lines were glued opposite to each sense wire.
The times of the induced pulses (caused by electromagnetic shower
multiplication on the sense wires) in these were read out at each end.
The delay lines were chosen to have a high impedance (550 0) and low
resistence/impedance ensuring good voltage/noise reJection and low

dispersion. Close tolerance specifications during manufacture led to

51

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Figure II-IO : Drift Chamber Cross-sectional View.

53

line to line variation in velocity (2.3 ns/ cm nominal) being less than
3 1 and the internal reflections less than 1 1.

The basic cylindrical shape of the chambers was formed of
moulded Rohacell (This is a polymethacrylimide foam manufactured by Rohm
Gmbh.). These main forms were mounted in precision diecast aluminum end
pieces. Since Rohacell is hygroscopic an outer layer of vetronite (fiber
glass) was added to exclude moisture. In the case of DCMI-DCM3 the end
pieces were semi-cylinders and contained several sectors. Each group of
sectors mounted in their end piece could be alignmened as a unit.

In order to compensate for the Lorentz force on the drift
electrons caused by the solenoid field, the voltages supplied to the
individual cathode strips were adJusted to result in a field pattern
with both a tangential drift angular component Ed, and a compensating
radial component Ec as shown in figure 11-10. The voltage on the cathode
strips could be individually adJusted to account for the magnetic field
effect. The choice of Ec and Ed is dependent on the gas used in the
chambers. A monatomic gas would yield a drift velocity proportional to
the drift field, which would complicate the operation of the chamber
since a good position resolution requires a precise knowledge of the
time-distance relationship. This relation is less critically dependent
on the exact details of the electric field pattern in the chamber if one
chooses a polyatomic gas, in which excitation of low-lying energy levels
causes a saturation in drift velocities: once above some critical
electric field value a velocity plateau is reached. The gas selected
was a 50-50 1 by volume mixture of Argon and Ethane, which resulted in

an Ed of 1.0 kV/cm and an Ec of 1.2 kV/cm. The drift velocity was

5A

approximately 0.5x107cm/s. For these chambers this corresponds to a
maximum drift time of 0.5 us.

The drift chambers were powered by DanFysik Supplies. Current
monitoring devices were set to turn off the high voltage if the currents
drawn by the chambers became too large. The voltages to individual drift
chamber cathode strips could be controlled using plug-in cards from the
counting room.

Placing the chambers in a test beam (at the CERN PS) allowed the
extraction of some chamber parameters such as the delay line velocities
[NIC82]. However, the presence of the magnetic field, the interacting
beams and the need of a precise chamber position (alignment) meant that
the other parameters had to be measured in place.

Alignment and the correct parametrization of the time-distance
relation are crucial for obtaining a good momentum resolution. The
alignment was carried out between running periods. Data were taken with
the magnet on using the "Y" counters (see section II-10.f) triggering in
cosmic rays. Tracks were fitted using a simple time-distance
relationship and the exact position of the chamber half-cylinders was
adJusted in the off-line analysis to minimized these residuals. This was
an iterative process.

The time-distance relationship has to be obtained for the actual
data taking conditions. The time-distance relation was parametrized by a
quadratic in time multiplied by a small angular dependence. These
factors were different for each gap. The best position resolution was
obtained with a r.m.s. of A00 pm. This was converted to momentum
resolution with a Monte Carlo which generated points of well defined

tracks and observed position resolutions. The overall momentum

of
'I'

I?

‘e

an

55

resolution obtained was Ap/p- 0.07-p (p in GeV). varying with the number
of points and event multiplicity between values of 0.03p to 0.15p

[NIC82] .

11-6. The Back Lead Glass Arrays.

The lead glass arrays were the same as used in the R108
experiment [BEA7A,ANG78J. The operation of a lead glass detector is
based on the principle of total energy absorption. Photons or electrons
incident on the lead glass initiate a shower of secondary electrons and
photons. The refractive index of this SF5 lead glass (for composition
see Appendix C) was such (1.67) that the electrons in the shower radiate
Cerenkov light until they have a kinetic energy of less than 127 keV.
This light was collected by phototubes at the end of the glass blocks.
Provided that the lead glass array is made so thick that it contains all
the shower, the light collected will be proportional to the energy
deposited.

The back glass array of 17 radiation length-deep blocks (figure
IIE“II) ensured that the maJority of the shower was contained within the
array. An array consisted of 168 SF5 lead glass blocks arranged in a 12
(vertical) by 1A (horizontal) matrix, the overall dimensions of which
were 180 cm by 210 cm. Each block was 15cm square, including its
wrapping which was aluminized vinyl and soft iron foil with an outer
mylar layer to ensure electrical isolation [BEA7A]. The blocks were
mostly AOcm long (17 radiation lengths) but the outermost blocks were

only 35cm and were arranged as seen in figure 11-11. An RCA-8055 5"

56

+1.5 cm

 

 

 

 

 

J

 

 

 

 

 

 

 

 

 

 

 

 

/ Iron

 

 

224 cm

Figure II-II : Back Lead Glass Array.

W+

‘ /

 

57

photo-multiplier tube was glued to the back face of each block using RE-
10 optical glue. Every block had a small light source on its front face
to facilitate calibration (This will be explained later).

The high voltage supplies to the lead glass arrays were
Heinzinger HN 3200-0A05. The output of these were fed into Oxford made
stepping boxes which supplied 20 outputs in increments of 20 or A0
volts. Matrix boards and Zener diodes pegs then allowed the individual
photomultipliers to be supplied'to within 5V of the optimum value.

The tubes were surrounded by a u-metal magnetic shield and the
whole array was further shielded from the solenoid fringe field by an
iron cage consisting of a 6 mm thick plate of 2A7 cm by 22A cm front
face, and 1.5 cm thick, 88 cm deep sides. The arrays werelmounted on a
train which permitted them to be withdrawn when the ISR was being filled
with protons. This feature was necessary to prevent radiation damage to
the glass (yellowing). They also provided mobility to allow the

retraction of an array as discussed above.

11-7. The Front Lead Glass Arrays.

 

Original to the R110 experiment was an extra lead glass Cerenkov
counter array in front of the old (back) array sandwiching the MWPC
(Strip Chambers). This new array consists of 3A blocks, of the same
material the back glass arrays were made of, arranged as shown in figure
11-12. The overall dimensions of the array were 102 cm by 1A1.6 cm (Y by
Z). Each block was 10 cm square. The vertical blocks were 50.2 cm long

and the horizontal 35.2 cm long. The total array was then approximately'

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59

A.2 radiatitni.lengths in depth. The phototubes collecting the Cerenkov
light were at the sides (as shown in figure II-12), therefore the
collected light travelled perpendicular to the direction at which the
particles struck the glass. This made the light collection in the front
glass less efficient. Due to the complicated geometry of these arrays
they were used mainly for energy and not position measurements.

In order to improve angular resolution the strip chambers and
glass arrays were placed about two meters from the intersection. It was
undesirable to allow the shower to spread before measurements in the
strip chambers were made. The addition of this new array provided an
active converter close to the strip chambers. By requiring non-
conversion in the solenoid coil (using the B counters) the showers
measured in the strip chambers were restricted to those that have been

produced in the front glass array.

II-8. The Shower Counters.

 

The shower counters consisted of 32 azimuthal segments, grouped
into A sets of eight, two modules above and two below the intersection
region. Each set of eight (SCM1-A) was an independent instrument encased
in its steel box. The shower counter layout is seen in figure II-5.

Because of the return yoke of the magnet, a substantial fraction
of the solid angle could not be easily instrumented for electromagnetic
detection outside the magnet: the shower counters overcame this
difficulty by being inside the solenoid. The construction chosen was a

wedge-shaped sandwich of lead and scintillator the principle of which

ft]

(3
..4
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60

was to integrate the electromagnetic shower curve by sampling it at
several points in its development. The counters consisted of 16 layers
each of 0.5 cm thick lead followed by O.A cm thick scintillator. The
first four layers of scintillator were read out separately and called C
counters. The remaining 12 layers constituted the D counters. A shaped
supporting iron plate was necessary before the first layer of lead; this
was 0.6 cm thick for the upper modules and 0.3 cm for the lower.

The segments were individually wrapped in aluminum foil and it
was necessary to put two layers of 100 pm thick mylar between segments
during construction (for lifting). The light from the scintillator was
collected at both ends of each segment. Thus each module of eight
segments was monitored by 32 phototubes, four per segment: two on each
end of a segment; one reading the first 3.6 radiation lengths, the other
the last 10.7 radiation lengths. The 105 cm long shower counters were
located inside the solenoid, but the phototubes were outside: 85 cm
long light guides going through holes drilled in the pole pieces were
employed. These butted onto the internal light guides via a dry Joint,
close contact being insured by mechanical pressure.

For calibration purposes an optical fiber capable of delivering
a flash of light to each of scintillators was attached to each end of
each segment. These left the solenoid and were glued into a "flasher
box" containing a krytron light source. An additional fiber left this
box and entered a reference counter phototube. There was one flasher box

and one reference tube per shower counter module.

['4‘

(J

’F’.

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61

11-9. The Strip Chambers.

 

The most important part of the detector for this dissertation
was the strip chambers. They were designed for the purpose of isolating
single photon showers produced in the front glass.

The chambers were multi-wire proportional chambers (MWPC)
[DIM78] with 200 cm (horizontal) by 180 cm (vertical) active area
sandwiched between the two glass arrays (see figure 11-13). For photons
converting in the front glass, these chambers allowed considerably
better spatial resolution than that afforded by the back glass array
alone.

The 1000 anode wires per chamber were 20 um gold plated tungsten
strung vertically in a pitch of 2 mm and held in three places along
their length by support wires. They were maintained at A.5 kV. The
support wires, which ran horizontally, were electrically isolated from
the anodes. There were cathode planes each side of the anodes at a
distance of 1.0 cm. They consisted of 0.8 cm wide 35 pm thick etched
COpper strips on a 75 um Kapton board at a spacing of 1.0 cm (resulting
in a 2 mm gap between strips). The 160 strips on the plane nearest the
intersection region ran horizontally, while the 192 strips on the other
plane ran vertically. Both sets of cathode strips were read out, so that
Y and Z coordinates were available. However, this gave proJected signals
of the showers along Y or 2 rather than a fully two dimensional view.

Figure II-13 shows a view of the chamber cross-section. The
walls of the chambers were constructed of 0.9 cm thick styrofoam to
which the cathodes boards were glued with abundant Epoxy (to give

support). All this was inside a 230 pm thick polythene gas envelope.

62

 

 

Copper on Kapton (strips)

toil

   

\\\\\\\\\\\\\\\\\\\\\\
IIIIIIIIIIII/IIIIIIII

m
V.
M

Styrofoam

Mylar

Strip Chambers Cross-sectional View.

Figure II-13

Box-Secuon
Frame

I 40 mm

920mm

 

 

-_ --.V.--

MWPC

   

63

Rlsheet
9.1 mm ‘

 

 

---d

Iron

 

 
 

Back Gloss

 

Strip Chamber layout.

Figure II-1A

6A

Furthermore» the whole chamber (including the first pre-amplifiers) was
placed inside a Faraday cage of aluminized mylar. Outside the gas bag,
but still inside the Faraday cage, towards the back glass, was a 0.91 mm
aluminum plate as a strong back for the chamber assembly. The resulting
total thickness was about 0.02 radiation lengths. In figure II-1Aza
diagram of the total array is shown. The gas used was a mixture by
volume of 70% Argon and 30% Ethane with a 0.1% addition of Freon to help
prevent sparking problems.

The strip chambers were powered by DanFysik supplies. The 70A
signals from strips in the strip chambers were fed immediately into
preamplifiers with an appropriate input impedance. These drove buffer
amplifiers, mounted near the chambers, via co-axial cable. The buffers
supplied push-pull outputs to 120 m of twisted pairs cable which went to
the counting room. ADCs‘ designed and built at Columbia University then
digitised the pulse height from all strips [DIM78]. A hardware processor
supplied CAMAC with pedestal-subtracted digitized amplitudes for all the
ADCs with a non-zero content. In this way the amount of redundant

information written to tape was minimized.

11-10. The Scintillators.

a.- The A counters. The A scintillators formed a complete barrel

 

hodoscope of 32 counters 87.5 cm long around the intersection region at
a radius of 26.5 cm (figure II-5) between D01 and D02. They were 0.6 cm
thick and were physically demountable in two half-cylinders which had

0.1 cm thick aluminum covers on each surface. The total thickness of the

65

A counters was 0.036 radiation lengths. The counters were read out by
Mullard XP2230 high gain phototubes at both ends after a curved length
of light guide consisting of 1.88 cm diameter Perspex between 186 cm and
226 cm long. Because of the long light guides and thickness of the
scintillators the resolution of the A counters was limited by photo-
electron statistics; only a few per minimum ionizing particle being
expected.

The A counters were very close to the intersection region
therefore the light guide damage yellowing by radiation was severe; at
one time during the course of the R110 experiment it was found necessary
to heat treat the guides to recover transmission properties. Timing was
the primary function of the A counters. The phototubes selected had a
1.6 ns rise time. They could also give information regarding the number
of charged particles produced in an event or "multiplicity". Their times
were recorded in the same system as the drift chamber read out and were
used as the zero time of the event. Thus the resolution of the drift

chambers depended in part on the time resolution of the A counters.

b.- The B counters. These counters formed a partial cylinder of
18A cm long and 1.0 cm thick scintillator slabs at a radius of 90 cm
Just outside the coil dewar. covering all the solid angle not covered by
the return yoke (figure II-S). There were 2A in all: each was 11 cm wide
and covered an azimuth angle of approximately 7°. The light guides were
short, and 56 AVP phototubes had sufficient gain as to be used. High
voltage for the B counters was supplied by means of two 32-channel
LeCroy HV 20323 which were adjustable to t 1 Volt. They also were used

to supply high voltage to other scintillators (ST and MM, see below).

66

The B counters have been used in various ways in our experiment.
For the present dissertation, the most important was to indicate when.a
photon had converted to charged particles and started a shower in the
coil. It was also possible to extract longitudinal position information
on the basis of time differences between the pulses from either end of

the counter, or from the relative pulse heights.

c.- The L counters. The L counters were maintained and operated
by the ISR division. A copy of the signals was supplied to the R110
counting room and used for background monitoring.

The L counters were 10 m upstream in pairs separated by 3 m and
uneasuring 25.5 cm by 21 cm, with 1 cm thick scintillator. A coincidence
was formed between the pair of scintillators in pairs and a background
count was recorded for each hit. They were useful to verify beam losses,
since as the beams spread the background rate measured by these counters
increased. The ISR operator acted to remove particles at the periphery

of the beams when the L count rate became too large.

d.- The MM counters. These were the main luminosityrmHUtor
counters. There were eight scintillator slabs measuring A3 cm by 20.5 cm
mounted in pairs on four of the corners of the magnet. Due to the
presence of the low-B quadrupoles, our intersection was more crowded
than most intersection regions. Rather than placing the luminosity
monitors near the beam pipe, where they would intercept more events,
they were placed one on each side of the intersection, see figure II-15.

From the interaction region and looking inwards these appeared top-right

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and bottom-left, looking outwards they were top-left and bottom-right;
thus an interaction producing back to back particles would have hit two
sets of MM counters, one top set and one bottom set; a coincidence of
four scintillators in this combination was defined to be the real event.
As explained before, the rate of such coincidences was used to measure

the luminosity in our intersection.

e.- The ST counters. A 190 cm long vertical scintillator 7.5 cm

 

wide and 1.0 cm thick was positioned behind each glass array. They could
be moved by remote control behind each colurm of blocks in the glass
array. Triggering on energy deposition in the ST's ("straight through")
gave data containing a substantial proportion of muons or hadrons that
did not interact in the lead glass. These deposited a characteristic
amount of aerenkov light in the lead glass blocks, which could then be
used as a calibration check and stability monitor. The ST counters were
read out at both ends and a trigger was defined as a coincidence between

pulses from each end.

f.- The Y counters. 105 cm long, 15 cm wide, 1.0 cm thick, the Y
counters were mounted on top of the return yoke and below it. There
were 12 in total, each read out at both ends. They were used for
triggering on cosmic rays to help in drift chamber alignment. These

counters were provided with high voltage by Fluke "15 8 power supplies.

CHAPTER III

Data Taking and Calibrations

 

 

III-1. Control Room.

Most of the electronics and a Hewlett-Packard (HP) 2000 mini-
computer were situated in a room Just outside the experimental area.
From there experimenters were able to monitor and control the collection
of data. Single-person shifts lasting eight .to thirteen hours covered
the data-taking which, due to the high reliability of the ISR often
covered several days of continuous running.

The trigger thresholds were set by hand on the electronics and
rates were monitored during data taking. The HP 2000 mini-computer
allowed the experimenters to have on-line access to the data collected.
Event dumps and special histograms made it possible to monitor the data
quality.

The lead glass arrays were moved by remote control to the
desired position and fully retracted when the ISR beams were stacked.
The position and movements were viewed through a closed-circuit TV
monitor. Information from the ISR beams were constantly monitored and

direct communication was maintained with the ISR control room. This made

69

70

possible interaction with the beam handling in order to reduce the beam-
associated backgrounds.

The writing of the data to tape was controlled by the HP 2000.
The speed of tape writing depended on the trigger selected and the
instantaneous luminosity of the ISR. A typical 1600 bpi tape for the
triggers under discussion was filled with raw events in about N5

minutes.

III-2. Calibrations.

 

Calibration refers here to the process of determining the energy
scale of the calorimeter. I will only describe in detail the calibration
of the lead glass arrays used in this dissertation.

We can distinguish two kinds of calibrations done during the
experiment. First is the initial calibration, where the calorimeter is
exposed to an energy standard to determine the energy-to-signal
relation. The initial calibration of each individual block of the arrays
was done with an electron beam at the CERN PS before our MSU group
Joined the collaboration and is described elsewhere [NIC82]. The second
is maintanance calibration, an on-site calibration done during the
running of the experiment to track changes in the parameters determined
in the initial calibration. There are many time-dependent effects in the
energy-to-signal relation. An important factor in this experiment has
been the radiation damage of the glass and material of transmision
(wires and light guides). Other sources can include geometrical or

structural changes, aging of the electronic read-out, etc.

71

I will describe here only the on-site calibration of the glass
arrays. The back lead glass arrays were monitored using light sources
produced by sodium iodide (NaI) crystals doped with Am’“. The Amz‘”
decay produces 5 MeV 0: particles and these produce scintillation light
pulses in the NaI which are constant and well defined in nature since
the range of the 0 particles is much less than the size of the crystals.
Typical rates were 100-150 scintillations per minute. A source container
was in a small aluminum can with a glass window glued onto the front
face of the lead glass block. The lead glass calibration could vary with
time due to glass yellowing by radiation damage, or changes in the
phototube gains, etc. The NaI pulse heights were measured at the end of
every ISR stack (ISR running period, 3 to 12 days). The glass blocks
were calibrated by the known energy equivalence of the NaI
scintillations (originally measured at the same time in the electron
beam PS calibration).

There were two problems associated with this procedure. First,
NaI is hygroscopic so the crystal must be well sealed. If moisture were
to enter the crystal, the light characteristics would be irreversibly
changed. At first 40% of the sources were found to have this problem due
to manufacturing errors. A second batch of sources, after many talks
with the manufacturers, was found to behave better.

To correct for this problem a second method of calibration was
also used for the glass. This used a special trigger called "straight
throughs". The ST counters situated behind the array triggered on
particles (charged hadrons) going through the glass blocks. The spectrum

formed by the Eerenkov light of these particles had a broad peak which

72

was found to have an energy equivalence of about N50 MeV. These runs
were performed every two or three stacks and monitored NaI changes.

The front glass arrays were also calibrated using Am“‘ sources
in NaI. They were monitored by a flasher system similar to the one used
for the shower counters [NIC82]. The flasher system was used before
every ISR stack. The method of monitoring the glass blocks with respect
to the reference NaI was to generate a flash of light from a Krytron
tube, a fixed fraction of which went to each block and to a separate
"reference counter" phototube. The light from the Krytrons was fed to
the block beside the phototube end. The Krytron tubes were mounted in
small boxes ("flash boxes") from where the optical fibers carried the
light to the blocks. Measuring the NaI to flasher ratio in the reference
counter and the flasher to signal ratio in the blocks allowed one to
transport the reference to each block.

The calibration of the NaI to flasher ratio in the reference
counters and the flasher to a u GeV electron beam ratio was performed at
the PS and is described elsewhere [NIC82]. For the front glass a
correction was applied to the phototube voltages in order to account for

changes in the glass calibration.

III-3. Trigger Logic.

 

In collider machines at high energies the rate of interactions
is enormous, therefore it is necessary to select which events will be

recorded. The requirements for the data to be recorded are defined by

73

the "trigger logic". In this experiment all the main triggers involved
electromagnetic energy deposition in the calorimeters.

The R110 experiment ran normally with four or five simultaneous
triggers. More than one trigger could be satisfied at the same time.
Since the trigger used to collect the data presented in this
dissertation required a different lead glass arrays position than the
other triggers, no other trigger involving back glass energy deposition
could run at the same time. However, triggers requiring energy
deposition only in the shower counters were taken simultaneously.

Our experiment had two levels of triggering decision. A fast
hardware (electronic) trigger made decisions using analog pulses from
the phototubes and controlled whether the event was digitized. Then a
software trigger using digitized data in a HP2000 mini-computer placed
more stringent requirements on the events. This latter will be referred
to as "on-line" filtering. The trigger used in this dissertation was
called "glass singles with half-back geometry". It was designed to
require at least one energy cluster in the back glass array with an
energy greater than a certain threshold.

The "glass singles" trigger looked for electromagnetic energy
deposited in the glass arrays, adding the energies in the front and back
glass arrays. The lead glass block voltages were adJusted so that a
given pulse height from any tube was equivalent to the same energy. Thus
the sum of pulses was in principle equal to the total energy deposited.

The trigger took advantage of the segmentation of the arrays to
attempt to trigger on single particles. The two photons from the decay
of a neutral pion of 5 GeV/c transverse momentum (in the ISR center of

mass) will fall within a 3 x 3 matrix of the glass 951 of the time for

fi

fr

718

the inside array and 98% of the time for the outside array. The
difference is due to the opposite sign of the Lorentz transformation in
the two sides. Requiring that the pulse height in a 3 x 3 matrix
exceeded a threshold would act as a good single particle detector.

There are, however, one hundred and twenty 3 x 3 submatrioes in
each array and this would require an enormous number of discriminators.
To avoid this, a set of blocks in four adjacent rows and the set of
blocks in four adjacent columns defined what was called "roads" and
"cols". Each array was divided into six "roads" and five "cols", offset
from each other by two rows or columns respectively. Every possible 3 x
3 submatrix in a array lies entirely within exactly one overlap region
of a "road" and a "col". The trigger required that one "road" and one
"col" satisfy individual discriminator levels in coincidence with a
higher discriminator level being satisfied by the sum of the side.

Figure III-1 shows a flow chart of the "Glass singles" trigger
logic arrangement. The phototube signals were fed to a splitter-mixer
system where part of the signal (about 1%) was diverted from the ABC's
to the trigger logic electronics.

The splitter-mixer system provided four kinds of output (in
figure III-1). The first output defined the NaI trigger. Each signal
from an entire column of blocks was added and discriminated. A
multiplexer under CAMAC control then selected one column at a time
during the block calibration run to record NaI events.

The second and third outputs permitted one to look for energy
deposition in the 3 x 3 matrix "cluster". The second output sums all the

blocks in a column, then the column sums in sets of three in all

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76

possible combinations of neighboring columns (0013). The third kind of
output does the same for rows of blocks (roads).

A coincidence between a "road" and a "col" then defined a 3 x 3
array (cluster). The energy in this 3 x 3 array was added to the energy
found in the front glass array. If the total energy was greater than the
energy threshold taken, the event was recorded.

As previously stated, each lead glass array was set to produce
the same pulse height for the same incident energy. Therefore the
linear sum of the pulse heights in any set of blocks would be
proportional to the energy deposited. Since the arrays are
approximately at 90° to the beam line the energy deposited is
approximately equal to the transverse momentum. Thus an energy
threshold (pulse height cut) will generate a trigger for events
satisfying a minimum transverse momentum. This was made with the fourth
output. The threshold, cluster busy signal and an A counter signal were
then put in coincidence to define the glass singles. At normal ISR
luminosities reached in intersection I1 (~ 51:10:"1 cm‘zsq), the rate of
taking data resulted in about u events/sec.

Other triggers used in our experiment are described elsewhere
[AN082, HUM88, NICBZ, YEL81]. They included ETOT, the total energy
deposited in all electromagnetic calorimeters (Jet studies); PAIRS, that
required two clusters, each above a given threshold, with the sum of
these being greater than a second threshold (electron pairs studies).
Some requirements in spatial position of the clusters could also be
demanded.

Another trigger used to gather data for the analysis presented

in this dissertation was the n° trigger. The hardware trigger consisted

77

of "glass singles" events where either side could trigger. In addition
the B counters were used in veto and a requirement of a signal in the A

counters was also required. The logic representation of the trigger was:

(A21)~{GI(3.0)°(Bu-BSoB6-B7-88-Bg)+GO(3.5)°(B16-B17-B18- os1g~320-321)}

GI and 00 represent "glass singles" hardware logic, with the energy
threshold used shown in parentheses. The B counter number used in the
veto appear as subscripts (see figure IV-3 for 8 counter number
definitions).

Another configuration used for the n° data gathering was a
"double glass trigger" that took two cluster triggers having a summed

energy greater than a given threshold. More details of these n° triggers

are given in Appendix E.

III-fl. On-line Programs.

 

Various checks on the detector could be requested via the HP
2000 mini-computer. There were programs to check minimum ionizing peaks
in the A and B counters, glass and shower counter calibration, ADC's and
TDC's pedestals and the drift chamber and strip chamber read-out. The
programs to control the front glass and the shower counter calibration
through the flasher system and the "straight through" program also were
run through the HP-2000.

An on-line filtering program sharpened the trigger by executing

a CAMAC read on the glass ADCs, going now to two dimensional 3 x 3

78

clusters, not projections. The program searched for the highest energy 3
x 3 submatrix centered on a block with energy greater than 1400 MeV and
required an energy threshold on each. This on-line filter was measured
to be 100% efficient (in terms of events eventually processed) and
decreased the trigger rate by a factor of four from the rate satisfying
only the hardware trigger.

The events which satisfied the trigger were then read in full by
the computer and written to a magnetic tape. Each magnetic tape, called
a raw tape, held about 8000 events. The information in the A003 for the
lead glass and the scintillators, and the pattern units and scalers was
read first as a fixed length buffer. The scalers counted the number of
counts received from the luminosity monitors since the previous event
was read, the pattern units contained information about the kind of
trigger the event has satisfied.

This information was followed by the information from the TDCs
for the scintillators and drift chambers. During the reading process the
on-line computer compiled histograms on most of the information read.
These histograms were viewed regularly on a terminal to monitor the data

acquisition process.

III-5. The Data.

The data for this dissertation was collected mostly during 1983,

the last year of ISR running. we took a total integrated luminosity of

37

8.54x10 cm-Z. A total of 928 raw data tapes were written resulting in

about 8x106 total events registered, with about 80% satisfying the glass

79

 

 

 

 

 

 

 

 

 

 

 

 

 

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80

Table III-2: Data. Con Tapes.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

lntegreted
CON Lumlne number i of ISR
any
TAPE SET TRIGGER ”1.2 of events rune
MIXED . 37
1 DEC'83 1.27X10 39,990 145
4.5 GEV INS
37
2 acres 4.5 GEV INS 1 .92X10 63,883 145
ocrsa 37
3 4.5 GEV INS 0.20X10 10.033 27
Sp. B filter
. 4.5(5) GeV 37
4 001‘ 33 outside 1.29x10 79,109 165
37
5 SPRING'83 4.5 GEV ms 1.33x10 43.000 173
37
6 SPRING-'83 3.5 GEV INS 0.26x10 19,086 37
37
7 SPRING'83 4.56EVOUT 0.64x10 53,234 73
4.5 GEV INS 37
8 BEF'82 0.13x10 24,153 34
dedicated
4.5 GEVOUT 37
9 BEF'82 0.21x10 24,722 30
dedicated
MIXED 37
1 0 BEF'82 0.53x10 47,139 43
3.5/4.5 ins/out
MIXED 37
1 1 BEF'82 0.26x10 47,347 40
3.5/4.5 ins/out

 

 

 

 

     

8.54x10 452,246

81

singles trigger. The corresponding total number of events written on the
condensed (CON) tapes, after various cuts described in the next chapter,
was “52,2u6.

Most of these direct photon runs were done in three periods of
approximately one month each, one in Spring, another in the Fall and the
last in December of 1983. Some runs from early 1982 are also included in
this dissertation.

.A special.tf’ trigger run was performed during Spring '83 where
37 cm-2

an integrated luminosity of 1.91x10 was taken. The December'83

run was a combined direct photon/n" trigger trigger that collected a

luminosity of 1.271(1037cm-2

‘The characteristics of the different data sets, run periods and

luminosities accumulated are shown in Tables III-1 and III-2.

CHAPTER IV

BASIC DATA ANALYSIS

 

 

IV-I. Overview of the Basic Analysis.

The method.of analysis can be divided into two main stages. In
the first, performed mainly at CERN, we went from the raw data tapes tc>
the data summary tapes (DSTs) and then to so-called condensed (CON)
tapes. The second stage is the search for direct photons.

First I will describe all of the analysis up to the analysis of
the strip chambers information. This is the basic analysis with the
purpose of producing a clean sample of strip chamber showers (mainly
produced by neutral mesons or direct photons). The search for direct
photons was done by analysing the strip chamber data and will be
described in the next chapter.

This chapter describes the analysis from the raw tapes to CON
tapes and general cuts made afterwards. This includes re-clustering in
the back glass array, tracking, vertex finding and energy corrections.
The analysis of the CON tape includes cuts on the number of clusters in
the back glass, the fraction of energy deposited in the front glass and
the tracks pointed to the trigger cluster. Figure IV-1 shows a flow

chart of the analysis.

82

 

 

ITRIGGERI

 

l -

 

tracking,vertex
and clustering (DST)

I

it clusters in BG

 

 

NaI Triggers
vertex in diamond
FG fiducial (13 cm)

charged part. pointing
to trigger cluster

fraction of energy in F0

1

I STRIP CHAMBER ANALYSIS I
1

 

 

 

 

 

BACKGROUND
SIMULATION

 

 

6 - - I ,

DIRECT PHOTON DIRECT PHOTON
CROSS SECTION SAMPLE

 

 

 

 

 

 

Figure IV-I : Flow Chart of the Analysis.

814

For the making of a DST tape the B counters were put in veto.
This important cut will be explained in detail in section 5 of this
chapter. The strip chamber clustering algorithm is introduced at the end

of the chapter.

IV-2. Clustering in the Back Glass Arrays.

 

The standard R110 clustering algorithm to search for clusters in
the back glass was used at the CON tape analysis level. First a search
for all blocks with energy greater than a seed energy ESEED - 0.3 GeV
was done. These blocks were taken as seeds for clusters. Neighbors with
energies above a cut-off, EMIN - 0.02 GeV, were added to the seed block
and a cluster was formed.

These clusters were then checked to ensure that their shapes
were inconsistent with side splash (beam protons interacting in the
shielding) or cosmic rays. With this purpose a maximum number of rows,
columns and total number of blocks in a cluster was defined, ROWMAX - ll,
COLMAX - II and NBLMAX - 9, respectively. A minimum energy of a block
which can cause a cluster size to be considered too large was fixed on
EMCUT - 0.1 GeV. The clusters were also rejected if their energies were
above a maximum energy (BLKMAX - 50 GeV), discriminating against
possible NaI triggers, if the block with the maximum energy in the
cluster was in the edge of the array, or if all of their energy was
contained in one block.

At the DST level a different set of values was used for these

parameters to relax the restrictions and keep more data for further

85

studies. They were: NBLMAX - 20, ROXMAX - 5, COLMAX - 5, ESEED - 0.15

GeV, EMIN - 0.02 GeV and EMCUT - 0.15 GeV.

The calculation of the cluster positions was done in two steps.

In the first step the center of gravity of the cluster at the front face

of the back glass was calculated as:

 

 

n n
21-1 y1°Ei Z1-1 ZI'EI
- ; Z - (IV-a)
.03 n cg n
21-131 21-151

Where n is the number of blocks in the cluster,(y1,zi) the coordinates

01" their geometrical centers and E their energies.

i

The above calculation approximates an integral over shower shape
by putting all the energy in a block as concentrated at the geometrical
<2eluter, which is obviously correct only when the block size is much
1 arger than the shower. The second step corrects for the fact that the
Center of gravity of the energy deposition (cluster) is not at the front
f‘ace of the glass and that the energy is not concentrated in the block
Qenter.

The method [ANGBZ] is based on the study of the longitudinal and
tr‘ansversal development of a shower. Studying the longitudinal
development of the shower inside the glass it was found that the maximum
occurred around 111.3 cm deep in the glass. The center of gravity was
aSsumed to be at 15 cm from the front face of the back glass in the

q irection of the shower.

An exponential shower profile [AKO77] of the form:

86

E(?)- lilaenlizl/b was taken, where the shower was assumed to have a
radial symmetry, i: is the radial distance from the center peak, E0 is
the maximum energy at the center and b is a parameter to be adjusted
experimentally.

A routine was developed to take the first order position
calculations and correct them using a shift in distance due to the
exponential assumption. It can be shown [ANG82] that the corrections are
given by:

AY - bosinh‘1[(Yo/l)°sinh(l/b)]

AZ - b-sinh-1[(Zo/l)-sinh(l/b)] (IV-b)
where l is the half length of the front face of a block, 1- 7.5 cm; and
Y0 and 20 are the positions of the first order center of gravity
cg-¥block’z°-zcg-zblock

The parameter b was empirically determined in a test performed at the

).

relative to the geometric block center (Yo-Y

CERN PS resulting as:

b - (1.0+0.H/E)-(l.0+3.0-0) cm (IV-c)
where 0 is the angle of incidence in the XY plane or XZ projection
(according to the direction in which the shift is calculated) and E is
the cluster energy as measured in the back glass in GeV.

This correction has been shown to improve the position
resolution of the back glass. Although is not totally free from errors
since it does not include shower fluctuations, the fact that the
exponential profile is only a first approximation (a two component
exponential profile is more adequate) and the asymmetries caused by

angular differences of incident particles.

87

IV-3. Track Finding Algorithm.

 

The track finding was a complex and slow process using an
average of 2 seconds of computing time per event on the CDC 7600. It has
been already fully explained elsewhere [YEL81, NIC82]. Tracks were found
starting from points in the outside drift chambers and working inwards.
Once preliminary tracks were found, they were fitted to circles in the
xy projection, and straight lines in the radius-z projection. This was
possible due to the uniformity of the magnetic field over the volume
considered. The preliminary track list was then reduced by not allowing
more than one track to share a point, except in the innermost drift
chamber. A track was required to have at least five points.

When all tracks had been found and fitted, the track parameters
were written to DST's, together with all the space points used on the
tracks. The corresponding momentum was determined from the radius of
curvature of the circle that was the best fit to the points. The Ascoli
method [P0879] was used to fit the circle. When the alignment constants
were changed, the tracks were refitted from the space points but without

going to the track finding again.

IV-H. Energy Corrections.

It was found during PS tests [NICBZ] that the response from the
phototubes of the lead glass counters decreased when the incident beam
was not normal to the block faces. This is because the pulse height from

the phototubes is a measurement of the Cerenkov light actually

88

collected, not necessarily proportional to the energy deposited. The
optical properties of the glass, geometry and properties of the
conection between phototube and glass influence the amount of light
collected by the photocathode.

Defining Eraw as the energy measured by the glass arrays by
adding the individual blocks of the clusters, then, the angular
dependence of the measured energy studied in the PS calibration has the

empirical form:

E - (1.0 4' 0.22-6)-E

BG (IV-d)

raw(BG)
where O is the incidence angle of the particle with respect to the
normal to the face of the back glass array in radians. The angular
acceptance in this trigger resulted in a 9 range of 0 to 0.28 radians.
Therefore, the energy corrections were never greater than 6 1.

Due to the asymmetric geometry of the front glass, the front
glass energy measurements were less accurate. The clustering in the
front glass was done in two separate passes. First the blocks in the
array were associated with back glass clusters. In case of overlap
between front clusters the energy in shared blocks was allocated in
proportion to the total (front + back) energy of the two clusters.

The second pass considered blocks not assigned to clusters in
the first pass. Among these, blocks with energies above FGESEED- 0.05
GeV were potential cluster seeds. Each seed formed a cluster with its
immediate neighbors. As each cluster was formed its blocks are removed

from consideration as seeds. Only the first pass clusters were relevant

89

for the energy of the triggering shower; but the second pass clusters
could be used, for example, in a cleaning out.

Test data taken at the CERN PS [NIC82] used a small array of
blocks in a front-back geometrical arrangement. Angle and position
corrections were extracted for the raw energies measured by the

phototubes. The expression for the correction was:

EFG‘ [1/(1+C1-0)]-[(1+A)/(eXp(AL/a,)+A°exp(AL/cz)] (IV-e)
where O is the angle of incidence to the face of the block in radians
and AL the distance between the incident particle hit on the glass face
and the position of the beam during calibration. The empirical constants

are: A - 0.126, A

short ‘ 0:063: 01' 15‘30 cm, 02' 21.1! cm and C,- .lI65.

long
The short and long subindeces refer to the block sizes.

To obtain the energy of the shower we should add the energy
losses of the shower going through the detector. Figure Ill-2 shows an
apparatus diagram where is possible to see for a typical direct photon
trigger shower the parts of the apparatus crossed. The main energy
losses were due to the crossing of the magnetic coil and the iron walls
in between arrays. Since the events analysed in our case went through a
B-veto cut that assure non-conversion in the coil, there were
practically no losses in the coil. The most important loss was in the
iron cage of the back glass array.

The iron losses were estimated by running a EGS (Electron-Gamma
shower simulation Monte Carlo) simulation of the detector. The details

are explained in Appendix C. This simulation estimates a 5 5 loss in

the iron for all energies. This value is consistent with the energy

90

scale factcm*found to minimize the rms width of the n° mass peak in the
11° data. A small angular dependence of the correction was also found,
but in the angular acceptance of the trigger, this additional correction
was always less than 1%, and felt to be negligible.

Thus, the total energy in the glass arrays including

corrections, is:

E:glass . E80 + EFG (IV-f)

°(1.05)

Eshower ' E:glass iron losses (IV-g)

IV-S. DSTigg_and B-vetoing.

 

Each DST contained about 8000 events. They already included
different cuts to improve the data selection. The introduction of new
calibration and alignment constants produced a new energy re-evaluation
and some events were now rejected when the energy threshold was applied.
The introduction of a event veto using the B counters was of the most
importance.

The "B-veto cut" was very important for the analysis and
therefore will be discussed at several points throughout this
dissertation. The main purpose of this cut was to eliminate triggers
produced by conversions in the solenoid coil.

If the conversion (photon or multiphoton) occurred in the coil

the resulting shower will deposit the equivalent of at least one minimum

 

 

 

 

 

 

 

 

 

WEE;

W.

 

m
w

of the Apparatus.

View

Figure IV‘Z :

Glass

 

 

B counters

 

  

Geometry of the B Cut.

Figure IV-3 :

92

ionizing particle signal in the B counters. This cut was implemented
when writing the DSTs from raw tapes.

In order to speed up the analysis, CON (condensed) tapes from
DST's were written which contained the relevant information in the
fewest possible words. This information excluded the track points but
included the track parameters and a vertex position. The maximun number

of events in a CON tape was about 80,000.

IV-6. The B-veto cut.

 

We rejected events that started showering in the magnet coil by
demanding no shower signal in the B counters, since such showers would
have spread more before reaching the strip chambers than showers
starting in the front glass. Then, the front glass was the prime
converter for the strip chamber shower sample.

The B-veto cut was performed in the following steps. First the
back glass cluster position (trigger cluster position) was projected
towards the event vertex and the B counter traversed was found, as shown
in figure III-3. The pulse height signals of this B counter were
examined. If the pulse height from at least one phototube (left or
right) was greater than 50 counts, the signal was described as a shower.
A typical B counter pulse height spectrum is shown in figure IV-ll. A
minimum ionizing particle signal in the B counter corresponds to 80
counts [ANG81].

If the pulse height in at least one counter end was then greater

than 50 counts, we checked the 2 position of the shower as given by the

93

 

number of events

..

e ..e
0.4 4 ' ”e. .. .
O . .. ...
e 'e'.e.
0.2 - .0

 

 

o. I l l J
0 200 400 SW 800 1000

pulse height (counts>

 

Figure IV—H : B Counter Pulse Heights.

.10

 

1.75 -
l.5 _

1.25 - . o

0.75 F 0

number of events
I
I

.05 _ . O

0.25 —

 

 

-40 -2o 0 20 40
AZ

Figure IV-S : Az Differences in the B Counters.

9M

counter. A typical AZ distribution is shown in figure IV-S, where AZ is
28- ztrigger, ZB is the shower position as determined by the B counter

(see section 11-10) and Ztrigger the projected back glass shower
position in Z. If AZ was less than i 20 cm, we concluded that the shower
registered by the B counter was associated with the trigger cluster.
Therefore, the shower started in the magnetic coil and the event was
rejected.

When the projected shower position was near the edge of a B
counter (within a 25% of the length to the border), the adjacent counter
was analyzed in the same way but adding the pulse height of respective
adjacent ends, since the shower could be shared between both counters.

The pulse height cut of 50 is below the minimum ionizing
particle peak of 80 counts, so we expect a good efficiency in vetoing
showers that originated in the magnetic coil. Charged particles from the

trigger cluster may also cause the vetoing of the event, the overall

efficiency of this cut is discussed in section V-6.

IV-7. General Cuts.

After track finding in the drift chambers, a common vertex was
determined in order to find out if the event was consistenthith a real
beam-beam interaction. The vertex finding process was iterative. For the
first iteration the vertex was considered to have yo- 0. The first
iteration vertex was then found by the average of the track
interceptions with the y - 0 plane. Then the tracks were approximated by

straight lines tangent to the point of nearest approach to this final

95

vertex. For the second iteration a second vertex was found for these
straight lines. Tracks whose x2 for pointing to the vertex were too high
(more than 30 away) were rejected. Iteration continued until no more
tracks were rejected.

The event vertex was required to be inside a volume defined by
the beam intersection region. Figure IV-6 shows a two dimensional
histogram of X-Z ("diamond") and a histogram in Y of the vertex
positions found in the direct photon data. The requirements for the
vertex were: |xo| S 5, -6 5 yo 5 20 and |zo| S 50, where x,, yo, 2, are
the coordinates of the vertex in cm. Events with vertices outside this
region were rejected. Such events may be produced by a beam-vacuum pipe,
or beam-residual gas, or cosmic ray interaction.

Another cut made at this stage was to reject triggers caused by
charged particles interacting in the NaI sources intended for
calibrating the lead glass. The lead glass pulse heights summed over the
whole array were analysed using two different ADC gates, a long 600 ns
gate: (X), and a short 200 ns gate: (Y). Since the rise time of the
electromagnetic interactions (Cerenkov light) was shorter than the pulse
of the NaI scintillation, comparing the energy reading with both gates
it was possible to veto the NaI initiated triggers.

Figure IV-7 shows x vs. Y for the data collected. The events
under the diagonal are NaI trigger candidates ( X>Y ). A cut was
implemented requiring Y z (1.15-X - “5) for X 2 300.

The front glass array phototubes stood in front of the back
glass acceptance (see figure 11-12). To reject events where part of
their energy could be produced by showering in the phototubes a fiducial

geometrical cut was proposed. A Monte Carlo study of neutral meson

96

 

 

 

l
20

l
-20

 

 

20

cm

15 _

10 -

-10 L

-20

cm

 

 

 

”L!-

l

-25

5. 25 10.
ch

Z5

-75

 

 

450 F

«XIL

350 -

300 -

250 -

200 -

1001—

501—
0

-10.

Vertex Positions (Diamond).

Figure IV-6 :

pulse height (short,

t1O

1.4

1.2

0.4

0.2

97

 

 

 

 

 

 

0.2 0.4 0.6 0.8 1 . 1 .2 1.4

pulse height (wide)

Figure IV-7 : NaI Trigger Cut.

e10

 

98

decays in the detector showed that for a trigger shower to have both
photons of the decay inside the front glass array 90% of the time, the
fiducial would have to be placed at 13 cm inside the front glass
geometrical boundary.

The B veto out was, of course, not 100% efficient (see section
V-6). There were tracks pointing to the trigger zone (back glass
cluster) still after the B veto cut was applied. Figure IV-8 shows the
distribution of charged particles hits as extrapolated from the drift
chamber measurements in a Y-Z view of the front face of the back glass
array. Events with at least one charged track pointing to a region of 1
25 cm in Y and Z of the back glass trigger position were vetoed. The
efficiency of this cut to discriminate between trigger associated
charged particles and charged hadron backgrounds will be discussed in
section VI-8.

The fraction of the energy of the shower deposited in the front
glass is of great importance. As was stated in chapter I, a
longitudinally segmented calorimeter could separate, using the
conversion method, direct photons from the neutral meson background. The
parameter used to measure the fraction of the shower energy deposited in

the front glass was defined as: Front/All (F/ALL) -

eneggy in the front glass
event total energy

 

, with all the corrections to the energy
discussed in section IV-6 applied. The front glass calibration constants
derived from the PS test data were obtained with a beam at normal angle
of incidence. A correction for extra front glass energy deposited at
finite angles had to be performed. The PS test data has shown that the
corrected form of F/ALL is given by:

F/ALL - (F/Ce) / E (IV-h)

shower

 

99

AZcm so

 

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. - - ‘: 1’: .
- 0 0 20 40 60 80

AV cm

 

-eo -so -40

Figure IV-8 : A! vs. AZ, Differences Between Charged

Particle hits and Trigger Position on
the Back Glass Array.

100

where the angular dependence, fitting the PS data at different angle of
incidence, is given by:

2
Ce- 81+ Balcose + Ba/cos O ; with B,= -2.9u6, 82- 5.77 and 83- -1.818.

Figure IV-9 shows C vs (0030). Figure IV-10 shows F/ALL distributions

0
for the direct photon data at different pT ranges. There was an
important cut applied to the data using F/ALL. The cutenulits

efficiency will be discussed in section V-9.

IV-8. Strip Chamber Clustering Algorithm.

 

The strip chamber information is given by pulse height and strip
position, 1 1x3 160 in Y and 1 to 192 in Z. We use the notation (i,ph1)

where i is the strip number and ph is the associated pedestal

i
subtracted pulse height.

The strip chamber clustering algorithm looks for strips with
pulse height greater than a given minimum value (in this case IPHCUT -
20,equal to the pedestal), to be used as a "cluster seed". All
contiguous strips with pulse height greater than 20 counts were added to
the "cluster". Figure IV-11 shows typical cluster frequency distribution
for the Y and Z projections.

For a uniform illumination of the chambers by charged particles
and a large mean separation between tracks, we expect that the
distribution of the distances (d) between the clusters will have the

d/k, where k is a constant (by analogy with Poisson statistics).

form: e-
This would give a a straight line on a semi-logarithmic plot. Figure IV-

12 shows a semi-logarithmic distribution of the distance between two

101

 

1.75 '-

1.25 '-

C.

0.75 '—

0.5 '-

0.25 -

 

l | l l L l I

 

 

Figure IV-9

1015202530354045
ANGLEd

Angular Correction to the Observed

Front/All Ratio.

§§§§§

O

o§§§§§§§§

 

 

 

 

 

 

 

 

 

0 0.4 0.8
F/ALL
L.
r
$6.5 GOV
W L
0. 0.4 0.5
F/Nl

 

 

 

 

 

 

 

 

an
an
an
an
«m
an
an
we
on A4 as
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mo
'0 essew
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Figure IV-lO:

 

102

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

010
1.2
‘ __ 1000 I-
_ soo »
°'° 5-5.s GeV 5.5—3 cw
0.6 ~ 50° N
400 »
zoo MK
0 L l J.
o. 0.4 0.8
F/ALL F/ALL
600 '- 7m ..
500 L 600 P
400 i’ 500 l'
, 6547aw «n . 7—acw
300 j-
. 300 ~
200 ~
200 r-
‘°° I 100 L
W _1_ W I
o
o o. 0.4 0.3 o. 0.4 0.3
F/ALL F/ALL

 

 

5-5.5 GeV

 

 

 

 

 

 

  

 

 

 

 

 

as
F/ALL

so

so

‘° esacw 74smv

.w

z:

w

0 l l 1 EU”. 1 1 134114.

0. d4 as a d4 33

F/NL F/fiLL

F/ALL Distributions for Various ApT
Ranges in the Direct Photon Trigger.
All Events and Events with Front/All
Greater than 0.02.

103

 

 

 

 

 

 

 

 

 

 

 

° 2 4 6 ' 8 10 12 14

 

 

O

3 number of clusters (Y)

 

 

 

 

 

 

 

 

 

2 h I ALE—.—
I I l 1 I

0 2 4 e a 10 12 14

number of clusters (Z)

 

 

 

 

 

Figure IV-11: Number of Clusters per event in the

Strip Chambers.

10“

 

1O

IIIIII

I

I
.-

number of events
N

I I I IIIII

{

10

 

 

10 I I I I l I I I
0 4 8 12 16 20 24 28 32

distance between clusters Y view

 

10

 

IIIII

I
0-

number of events
N

I I I IIIII

/

10

 

 

1 O l I I I I I I I
0 4 8 12 1 6 20 24 28 32

distance between clusters Z view

 

Figure IV-12: Gap Determination. Number of clusters
vs. Separation Between Two Charged

Particle Hits on the Back Glass Array.

105

clusters in the chamber. We verified that each track is associated with
a cluster. Thus, the enhancement from the straight line at small values
of the distance indicates that we had artificially created extra
clusters and we should merge clusters with distances less than this
inflection point. In other words, clusters should be merged across a
"gap". This gap is defined as the minimum number of strips with pulse
height less than 20 counts needed to define a break between adjacent
strip chamber clusters. The plot in figure IV-12 suggests a value of ll
strips for the gap. A second method used to determine the gap was to
study the balance between the Y and 2 planes signals (pulse height) as a
function of the gap. These studies suggested a similar value for the
gap.

Thus, we saw that the minimum distance between edges of two
distinguishable clusters was greater than 11 strips (ll cm). This was a
fundamental limit in our ability to separate multiphoton from single
photon showers.

Several parameters describing the clusters were calculated from
the pulse height information. The position was defined as the pulse
height weighted average location of the strips of the cluster.

2 1' phi (IV-i)

2 ph1

<i> is a real number. The width or span is essentially the number of

position - <i> -

strips belonging to the cluster (including any gaps). If L1 is the first

strip number of the cluster and L the last, the width is defined as:

2

width or span - W - L2 - L1 + 1 (IVrj)

106

010

 

(Pl-IT) I- 1 784.

 

—

o I I I I I I l
0. 0.4 0.8 1.2 1.6 2. 2.4 2.8 .10 3

3 cluster totol pulse height toounts> (Y)

 

 

 

 

<PHT> - 889.

 

 

 

O l l l l ‘ l I l
0. 0.2 0.4 0.5 0.3 1. 1.2 1.4 .103

cluster totol pulse height mounts: (Z)

 

Figure IV-13: Total Pulse Heights of Strip

Chamber Clusters.

107

 

3" <w>-6.6

 

 

 

 

0 I I I I I
4 8 12 1 6 20 24 28

410 :5 widths tom> (Y)

 

12'-

10L <W>-4.5

 

 

 

 

 

I _.I I
4 8 1 2 1 8 20 24 28

widths (cm) (2)

 

Figure IV-1N: Widths (or Span) of Strip

Chamber Clusters.

108

the widths are expressed in cm. The R.M.S (0) is the standard deviation
of the pulse height distribution of the cluster calculated from a

continuous histogram, given by:

 

RMst 02 . <12) - <i>2 + 1/12 (IV-k)
where
Z phi- i2
2 I
<1 > 2 phi

Histograms of total cluster pulse height and width for the
inside and for the Y and Z planes are shown in figures IV-13 and 1M.

Each pulse height ,phi, measures the integrated signal along the
i strip. We did not have a two dimensional description of the shower in
the (y-z) plane, only a projection of the shower ionization along that
axis.

Figure IV-lS shows data histograms of ph1 for the y and 2
planes. There is a ph1 cut of 20 counts at the hardware level. For both
planes an exponential fall-off is seen. The mean pulse height for the y
plane (389) is similar to the pulse height for the 2 plane (311).

The variation of strip chamber parameters across the chamber was
also studied. The results are shown in figure IV-16. The values of
<PHy/E) vs. Z, (PHz/E> vs. Y, <Wy/E) vs. Y and <Wz/E> vs. 2 are plotted.
E is the shower energy, PH the total cluster pulse height and W the
cluster span. There is a small increase in pulse height as one gets away
from the center of the chamber. This relative variation can be as high

as 25% at the edges for the Z view, but smaller than 8% for Y view.

However, there is no variation in W (span).

.10

109

 

 

 

 

l l I l

 

200 400 600 800 1000
pulse height mounts, per strip (Y)

 

 

 

 

l l I l

 

200 400 soo 800 1000
pulse height counts: per strip (Z)

Figure IV-iS: Pulse Height per Strip.

Y PHM/E

110

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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I— ¢ ¢ I— 2. '—
E! + 5! ¢
32 3 1' t
' _ ¢
>_ N 15 ¢ § §
1. -
11-
05 —
0 1 1 1 1 1 o 1 1 1 1 1
40-40-20 0 20 40 60 '—60-40—20 0 20 40
Y II 2....

Figure IV-16: Variations across the chamber.

CHAPTER V

SEARCH FOR A DIRECT PHOTON SIGNAL

 

V—1. Introduction.

 

The chief purpose of the multiwire proportional chambers in the
R110 detector was to identify multiphoton showers among the back glass
single cluster triggers.

In principle, each cluster in the strip chamber could be equated
with a single photon shower. Under this hypothesis, counting the number
of clusters in the strip chamber region in front of the back glass
trigger cluster one could measure directly the number of photons
contributing to the back cluster. In practice, this was not the case.

As will be discussed throughout this chapter, due to the
intrinsic fluctuations of the showers, the important contribution of
low-energy large-angle delta rays and the asymnetric properties of the
chamber read out, the task was much harder than expected.

To overcome these difficulties a special method of analysis was
developed. The method essentially compares a strip chamber shower
property of the data with Monte Carlo simulations of the same property

for single photon and multiphoton produced showers. The distribution

112

from the data is fitted with the single and multiphoton distributions to
obtain their relative contributions to the data sample.

This chapter explains how the property for comparison was
chosen. The description of the single- and multiphoton- initiated shower
Monte Carlos and chamber simulation is included together with the method
of fitting the single and multiphoton distributions to the data. The
background and acceptance corrections are also discussed, and the

chapter ends with the description of the statistical error calculations.

V-2. Further Strip Chamber Cuts.

 

Two main cuts were applied to select from all strip chamber
clusters those associated with the shower: a matching chamber window and
a total pulse height cut for the cluster inside this window.

The "matching window" is defined as the strip chamber region
around the projected back glass cluster position where one finds
activity associated with the shower. The determination of the matching
window is important because it has direct influence on the efficiency
and purity of the strip chamber information. A "matching window" of size
w in cm, is a window covering :1: w cm about the center position and is
thus 2w cm wide on each view. The same size was used in both Y and Z
projections.

Two independent determinations of the window were made, one for
the 11° trigger and one for the direct photon trigger data. Most of the
single back glass clusters of the 11° trigger sample (after a mass out)

are produced by a single photon (see Appendix E). However, for the

113

direct photon trigger most of the single back glass clusters are
produced by 11° + YY decays merged in the back glass. Therefore we
expect activity in a wider region for the direct photon trigger than for
the n° trigger.

In the chamber, the shower signal is superimposed on a
background produced, for example, by other particles of the same event.
Because of the jet structure of the events, we expected this background
to be concentrated around the trigger cluster, although the background
level had been reduced by cuts already applied to the data. Superimposed
on the background we expect a region of greater activity from the
trigger shower. The edges of this region would be characterized by a
strong variation of cluster parameters as a function of the window size.
This variation depends on the transverse shape of the shower and on
background properties. Several parameters have been studied as a
function of the window size. Figures V-1, V—2 and V-3 show parameter
variations with w (window's size) for the n° trigger data.

An inflection point in these distributions would give a natural
place to set the window values. However, the inflection points of the
curves are not very well defined. Analysing all of these curves we have
chosen w - 15 cm as the minimum size of the window that can be taken
without losing shower information for the n° trigger data. The same
parameters for the direct photon trigger are also shown in figures V-1,
V-2 and V-3. We have chosen a window of w-20 cm in this case.

Figures 11-“ and V-S show the distance between projected back
glass position and the cluster position in the Y-Z planes for direct
photon trigger data and for 11" trigger data. For the direct photon data

there is a "two shoulder" structure as expected from having a second

11H

 

 

 

 

 

 

 

 

103
i—
_ o 0mmchH0nn1TmcGaa
' o n" TRIGGER
3: T o
E
I O
G. 102 _— ' O
— O O
E : C I .
— o
10 l l l l l
o 10 20 30 40 50 so
window size (W in cm)
Figure V~1 (Mean Pulse Height in Window)/w vs.
Window Size (w) for the n° and Direct
Photon Triggers.
102 —-
: 0 oman'PmmbN1RmGaz
: o n'nmmxn
m u.
.9- _
L
...a
m -
L O
.8 10 r 3 o O O
E :
3 _
c _
1 1 1 1 1 1
o 10 20 30 40 50 60
window size w in cm
Figure V-2 : Number of Strips per Cluster vs.

Window Size (w) for the n° and Direct
Photon Triggers.

115

 

 

 

 

10
p—
p
- o DFECTPHOKRITNGGB?
'- 0 17° TRIGGER
E _
.c
z
.c
I
— o
I
O O O O O O C
O O
O
1 l l l l l
10 20 30 4O 50 60
window size <w in cm
Figure V-3 : Half-Width at Half-Maximum of the

diff=(PHY-1.75-PHZ)/(PHY+1.S7-PHZ)
Distribution vs. Window Size (w) for
the n° and Direct Photon Triggers.

116

d
t

 

number of clusters

 

 

 

0. l I 1 1 1
-4o -20 0 20 40

3 distance «cm:

 

 

Z‘WBN

L5 -

number of clusters
p
I

‘1

T

05

 

 

O. I I l l 1
-40 -20 O 20 4O

distance (cm)

 

Figure V-N : Distribution of the Differences
Between Cluster and Shower Positions

for the Direct Photon Trigger Data.

117

 

200

175 - Y VIEW
150 '-
125 -

10.. r

75-

 

number of clusters

 

 

 

O l P l l l
-40 -20 O 20 4O

distance (cm)
200

 

175 -—
150 —
125 L

100 l-

 

number of clusters

8
l

 

 

 

O l l l l l
-40 -20 O 20 4O

distance <cm)

 

Figure V-S : Distribution of the Differences

Between Cluster and Shower Positions

for the n° Trigger.

118

resolved photon from meson decay. Because we want both photons to be
inside the window for our study, we need w - 20 cm as the minimum
possible window. This agrees with our previous result of 20 cm as a
reasonable value.

A smaller window could be used for the n° trigger where no
second photon is present. Because we want the same window size flm~
comparison, we used a window of w . 20 cm for both analyses.

Another cut for cluster selection was done on the total pulse
height of the clusters. Figures 11-6 and 11-? show total pulse height
distributions for all clusters with positions inside a w - 20 cm and a w
- 5 cm matching window, for the direct photon trigger and the rfl
trigger.

An.interesting pattern emerges for the 5 cm window clusters,
which are clusters whose positions match very well with back glass
showers. There are many low pulse height clusters, which we associate
with noise in the strip chamber. After a minimum, the distribution
begins to rise at higher pulse heights, which one could reasonably
expect of a shower. It is reasonable, then, to associate this 5 cm
window with the chamber activity of a single photon shower. We want to
cut out the noise without losing any shower signal, especially from low
energy photons of asymmetric meson decays. We chose the minimum possible
value of the pulse height that still rejected most of the noise. A value
of "00 counts in Y and 200 counts in Z was adopted. By studying charged
particles hitting the chambers, the pulse height associated with the
minimum ionizing particle deposition has been measured to be about 120

counts for the Y plane and 75 for the Z plane.

119

 

 

 

 

 

 

 

 

 

10m:
Y
emu-
(I)
L
0
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3
23 axl—
“—
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.8
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0 1 2 3 4 510 3
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0)
L
m
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U)
2
o
\0—
o
L
0
.o
E
3
C
ol 1 1 1 1 1 1 ‘
0. 0.4 0.3 1.2 1.5 2. 2.4.“, 3
pulse height tcounts»
Figure V-6 : Total Pulse Height of Clusters

Inside a w- 1 20 cm Window.

120

o.»

.zoocuz so m H 13 m mofimcH

mLmumaao uo acmfio: mmaam HmuOH " 51> mgzmfim

 

 

 

 

 

mmwhmDJU I
Cu 0...; FIG—w: UMJE N WKMFMDJQ OuIUhi ...Imxuz umdal >
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121

Another chamber property extracted from the information in
figure V-7 is that the mean pulse height of the clusters in the Y view
(311110) is about twice the value for the Z view (18011). Figure v-8 shows
the distribution of the ratio (PHY-a-PHZ)/(PHY+a-PHZ) for all clusters
in a matching window of w- :t 20 cm. A value of a =- 1.75 was chosen for
plotting. As the mean of the distribution shown is greater than zero, a
larger value of a is needed to balance the Y and Z pulse heights. The
particular value of a depends of the cuts used to select the chamber
information. a values ranged between 1.7 and 2.1 , but 2.0 was the value

used for the analysis reported here.

V-3. Search for a Variable to Distingyish Single from

Multiphoton Showers Among the Trigger Clusters.

The search for a variable to distinguish among single and
multiphoton initiated showers is, of course, the core of the analysis.

If we equate one shower to one strip chamber cluster, the job of
separating single- from multi-photon triggers is reduced to counting the
number of clusters within the chamber matching window. Figure V-9 shows,
in a matrix form, the fraction of clusters in the Y and Z matching
windows for different pT ranges in the direct photon trigger data. In
the matrices there are many off-diagonal counts (especially important
are the (1-2) and (2-1) components), making for a considerable ambiguity
in the number of showers associated with the event.

After analysing figure V-9 it can be asked whether the original

hypothesis of equating showers and clusters is correct. Looking at the

122

 

240-

200 -

 

160 -

120 *-

 

80—

40-

J1
r1 1 1 1 1 1 1 1””—

O
-l. -O.75 -0.5 -0.25 O. 0.25 0.5 0.75 1.

 

 

 

(PHY-l.750PHZ);’(PHY+1.75-9H2)

Figure V-8 : Distribution of the Ratio
diff-(PHY-l.750PHZ)/(PHY+1.75-PHZ).

3

.9.

3 3
°;2
-y
°>
-N‘
B

E O
3

z

{‘3

2

3 3
°3=2
-y
-N
3

E 0
3

z

123

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

pT - 4.5-5.5 GeV. pT - 5.5-6.5 GeV.
2
.- .029 .030 .004 g - .052 .032 .-
.007 .219 .117 .013 “’5 014 J90 .137 .018
‘5 _.
.013 .329 .127 .019 ._: .024 -320 .098 .021
O
.043 .010 .003 .. E .074 .007 .003 ..
E
0 1 2 3 0 1 2 3
Number of Clusters Number of Cluster:
vaw vaw
F’T . 6.5-7.5 GeV. PT - 7.5-8.5 GeV.
2
-- .043 .022 .. § .. .. .. ..
2
O
" .161 .034 .013 a -- .069 .059 .069
3 ‘
.013 . 03 .03 .. >
3 2 3'“ .. .137 .103 .034
.274 .043 .. . g .517 .. .. ..
2
0 1 2 3 0 1 2 3
Number of Cluster: Number 01 Clusters
YWHBN Y1naN
Figure V-9 Fraction of Clusters in the Y and Z

Views Inside the Matching Window for
the Direct Photon Trigger Data.

12H

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

pT I 0H5'25 GOV.
E
O
:3 3 - .019 .005 .-
2
0
5 2 '- .057 .014 .005

'5;
EN1 .031 .507 .029 ~-
g 0 .182 .090 .009 ..
2

0 1 2 3

Number 01 Clusters

YVIEW
pT . 2.5-4.5 GeV.

3
O
‘5 3 -- -- -- --
_=.
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5 2 -- .127 .033 .018
°51 .036 .391 .073 ..
..N
3
E 0 .018 .. -. ..
3
Z

0 1 2 3

Number of Clusters

Y VIEW

Fraction of Clusters in the Y and Z
Views Inside the Matching Window for

Figure V-10:

the n° Trigger.

125

single photon sample from the 11° trigger data we obtained the matrix
shown in figure V-10. It clearly shows that multiple clusters are
associated with a single photon shower. This is caused in part by shower
fluctuations (as was later demonstrated by the EGS simulation, Appendix
C). The inverse phenomenon is also expected to occur as two nearby
clusters can merge, producing a single cluster. For example, in meson
decay the photons can coalesce into a single chamber cluster. This is
made worse by the fact that we are only looking at the Y and Z
projections of the shower. Clearly, the geometry and properties of the
strip chamber make the direct method of counting the number of clusters
an impractical method of separating single and multiphoton triggers.

We then studied the shape of the clusters and the shape of the
chamber pulse height distributions in the matching windows on an event
by event basis. The shape of a distribution can be studied by analyzing
its moments. Figure V-11 shows the second moments (standard deviations)
for the individual clusters inside the matching window. There is no
obvious structure, for example in the form of a two component
distributirni, to allow us to separate single from multiphoton showers.
The third (skewness) and four (kurtosis) moments were also studied, and
showed similar behavior.

An effort was made to adapt the "moments method" [JOH75] to our
case. The motivation for the "moments method" is shown in figure 11-12.
It tries to obtain the distance between two distributions by knowing
their standard deviations and areas. The total standard deviation is

given by:

126

:10

 

1.2-

0.8 *-

O.6 -

number of clusters

0.4 -

0.2 ‘1

 

 

 

 

.10 3 or <cm)

 

2.4

1.6 '-

1.2-1

0.8 -'

number of clusters

0.4 _b

 

 

 

 

0‘, cm»

Figure V-11: Standard Deviation of Clusters Inside

the Matching Window.

127

 

 

 

Figure V-12: Moments Method.

128

ogeA§+ O§OA§+ ueAleA2e(o§+ o§+ DZ)

' (A,+ A2)2 (V-a)

 

Fifi)

where 01 and 02 are the standard deviation of each distribution, A, and
A2 their respective areas (energies) and D the distance between centers.

Assuming equal area and equal standard deviation of the two
distributions (clusters), the distance between means (cluster centroids)

is given by:

D - 2 . / a; - a; (V-b)

where 0T is the joint standard deviation of both distributions and 03 is
the standard deviation of each of the distributions. Full application of
the method requires two dimensional knowledge of the shower and
knowledge of the standard deviation of a single shower.

In our case, we defined a variable applying the formula for each

view:
2 2 2 2
dY- 2 - / oYt °Ys dz- 2 - / OZt - 0ZS (V-c)
‘ 2

and combined them as d - / d; + d . This formula gives the correct

Z

separation (d) in the case of symmetrical decays of the neutral mesons.
However, the asymmetry distribution of w°'s, even after acceptance
effects, is almost flat between -1 and 1, figure V-13. (Asymmetry -

(E - E2) /'( E1 + E2), where E and E

1 1 2
in the decay). After investigating the use of this variable it was

are the energies of each photon

decided that the assumptions do not match the data closely enough, and
the uncertainties introduced by the assumptions are too important for a

good use to be made of this method.

129

 

DISTANCE (cm)

 

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0.5 1.
ASYMMETRY

 

60

50>-

EVENTS

20-

‘10-,

 

I l l l l l l

 

 

 

 

 

 

 

 

 

 

Figure V-13:

-0.5 0

. 0.5 1.
ASYMMEI' RY

Distance Between Photons vs. Asymmetry
in Simulated n° Decays (ApT=N.5-10
GeV/c) and the Asymmetry Distribution.

130

Another proposed method was to utilize the ratio of the energy
deposited in the front glass array (front) to the total energy deposited
(all) as a statistical method of separation. The method compares the
front/all distributions obtained from the direct photon trigger data
(figure IV-9) with single photon and multiphoton distributions from
Monte Carlo simulations.

In addition to the difficulty of the simulation (discussed in
section V-9) the separation power of this variable is very poor since
the single and multiphoton distributions overlap over a wide range,

making the separation either inefficient or ineffective.

v-u. The Main Method of Strip Chamber Analysis.

 

The variable finally chosen was the result of a simplification
introduced in the moments method. The variable 0t (total RMS) is defined

as:

0 - 02 + 02 (V-d)

This variable directly combines the Y and Z plane standard
deviations (0y and oz) without the introduction of any extra
assumptions. Figure v-1u shows the 0t distributions for the direct
photon data trigger at different p1. ranges. The Y and 2 standard

deviations are calculated with all the strip chamber information found

in a 40 cm matching window (w - t 20 cm).

131

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132

 

0.6 1-

number of events

0.4 *-

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1.4 '-

O.6 '-

number of events

 

0.2

 

 

 

 

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Figure V—15: 0y and 02 Distributions for Direct
Photon Trigger Data.

133

Compared with other distributions discussed above, a remarkably
good two component distribution was found. It is interesting to notice
that this two component distribution is not shown in the projections oy
and 02 of figure V-15. Since the separation between two decay photons
from a neutral meson need not be aligned along either projection; only
when both are added do they produce a realistic picture.

Clusters were used to fix the lower and upper limits of the
strip range in which 0y and 02 were calculated. Only clusters with
positions inside the matching window and pulse height greater than llOO
counts in Y and 200 in Z were considered. Figure V-16 illustrates the
criterion for limit selection. The left edge of the left-most cluster
inside the window was taken as the left edge, and the right edge of the
right-most cluster inside the matching window as the right edge of the
"information window".

A flow chart of the strip chamber analysis is shown in figure V-

17. The method consists in fitting the 0 distributions of the direct

t
photon trigger data to simulated single photon and multiphoton (neutral
meson decays) distributions.

The single and multiphoton 0t distributions are based on EGS
shower simulations and Monte Carlo detector simulations. The EGS
(Electron-Gamma Shower) simulation is described in Appendix C. It
propagated through the detector single photon initiated showers in a
range of energies between 0.5 to 10 GeV. For each event generated, the
energy deposited in each chamber strip was obtained. Further simulation

of the strip chamber response translated this energy deposition to pulse

height counts. This "chamber response algorithm" that transformed the

1311

Projected
Shower Position

"“ a 11

 

 

 

 

 

 

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l
I
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I
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| I
| I
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I I
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L1 '- 2

Figure V-16: Criterion of Limit Selection.

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136

energy deposited in each strip to pulse height counts will be discussed
in section V-8. A sample of single photon showers from the n° data
trigger (described in Appendix E) was utilized to normalize the EGS
output.

A sample of direct photons hitting the chambers was generated
via Monte Carlo (MC) in the energy range of ”.5 to 10 GeV. Strip chamber
pulse height information was attached to these strip chamber hits
("positions"). We then produced a simulated direct photon sample in the
appropriate energy range. The details of this MC will be explained in
section 6.

Another Monte Carlo, described in the next section, generated
neutral mesons and traced their decay photons into the detector. The
trigger and all other cuts were also simulated by this MC. The photon
positions at the strip chambers were calculated. As with the single
photon simulation, photons with appropiate energies were then taken from
the EGS generated strip chamber information ("EGS bank") and inserted at
these positions. A sample of neutral meson decays in the appropriate
energy range was thus generated. Again, the "chamber response algorithm"
was then convoluted with these energy depositions to simulate the pulse
height response to these multiphoton decays.

The simulated 0t distributions for single and multiphotons were
then fit to the data. As described in section 8, a likelihood fit with
one free parameter gave the fraction or single and multiphoton produced
showers in the data sample. The fraction of single photon produced
showers was corrected for background and detector acceptance in order to
obtain the fraction of direct photons produced. These corrections were

evaluated using the single photon and neutral meson decay Monte Carlos

137

rmnfldoned above. An important background to single direct
photons,corrected with this MC information, came from the asyumetric
decays of neutral mesons in which one of the photons missed the detector

acceptance or was too weak to produce a signal in the strip chamber.

V-S. Simulated Neutral Meson Decays.

 

One of the most important parts in the analysis was to formulate
a Monte Carlo simulation of the detector in such a way that by
introducing the various physics processes that we expected to observe,
we could calculate the acceptances, evaluate the main single photon
backgrounds, and create a pure neutral meson decay sample from which to
calculate the multiphoton ot distributions.

The main background processes in direct photon production are
those involving production of neutral mesons. The neutral mesons
included in the Monte Carlo are described in Appendix A. A detailed
description of the Monte Carlo is included in Appendix D. The MC
includes the geometrical acceptance of the apparatus. the trigger
requirements and all of the cuts (requirements applied to the data
during the analysis). It also takes into account resolution effects.

The MC was used in several ways. One was to calculate the
acceptance for the neutral mesons, Am. defined as:
total number of neutral mesons observed

Am - total number of neutral mesons generated (V-e)

138

Since we generated neutral mesons in a specific interval in y (rapidity)
and o (azimuthal angle), the Am calculated refers specifically to this
solid angle (Ay - 10.8 , A¢ - 10.6 rad).

Another important quantity derived from the MC is the number of
neutral mesons that manifest themselves as single photons in the
detector (especially in the strip chamber). because only one of the
decay photons is detected. The number of strip chamber single photons

produced by the decay of neutral mesons is given by the ratio:

Y _ single photonsgproduced by neutral mesons

YY mesons multiphotons produced by neutral mesons (V-f)

In the pT range of our experiment these single photons are produced
mainly from asynmetric meson decays and multiphotons are mostly double-
for

photons, predominantly n° decays. Figure v-18 shows vs.

7%- m pT
the neutral mesons studied.

The MC also provides a sample of pure multiphoton decays as seen
by the strip chamber. Using this sample the at distributions of
multiphotons used in the fits were created.

Another output of this MC is the number of events that do not '
produce a signal in the strip chamber. These events produce showers
which are totally contained in the front glass and/or do not produce an
appreciable signal in the chamber. Combining the results of this MC with
the EGS simulation we can calculate the probability that this can
happen, shown in figure V-19 as function of pT.

This probability was in fact observed to be much higher in the
data than predicted by the Monte Carlo. There are other possible

explanations for these events. They can be produced from beam-pipe or

139

 

 

 

 

 

 

 

 

Q4
0 msoe1wnoa!
0.35 ‘- o OUTSIDE TRIGGER
0.3 L
0.25 -
_g
S: ‘ -
\ 0.2 '- . .
?~ 0 .
0.15 — o '
° ° 0 o o
0.1 - o
i
nos--
0 1 1 1 1 1
' 4 5 6 7 a 9 10
p, GeV/c
. Y
F1 ure V-18: -—- .
8 YY mesons vs pT from the Neutral
Meson Decay Monte Carlo.
I._
I.
E; O
E 0.1:.
2 ¢
‘5 : +
2: - + o o o
9 _
.—
g b
u.
1 1 1 1
oO 1 2 3 4 5
p, GeV/c
Figure V-19: Probability of Observing a Shower in

the Strip Chamber vs. Energy.

1’40

beam-gas interactions (side splashes,etc.) or by hadron interactions in
the lead glass. The total number of these events contaminating the data
was reduced by requiring more than 114 Z of the total observed energy to

be in the front glass, as will be discussed in section V-9.

V-6. The B-veto simulation.

 

The B counters were used to veto all single photon triggers
converting in the coil. As explained before (section IV-6), the B-veto
was not implemented at the trigger level but was used early in the
analysis (while writing Data Summary Tapes, DST's) to include only
events that did not convert in the magnetic coil. As shown in table V-1,
the B-veto is, quantitatively, the most important cut applied to our
data. It is important, therefore, that we understand its effects and
make the appropriate corrections to the observed signal.

The out has two parts. First we check for the pulse height in
both ends of the B counter hit by the triggering particle. If each of
the pulse heights is less than 50 counts, we conclude that the trigger-
particle did not convert in the coil. Second, if either pulse height is
greater than 50 we check its position. If the B counter position of the
trigger-particle (as measured by time differences in the B counters) is
inside a t 20 cm window around the projected position of the trigger,
the event is vetoed; otherwise the event is accepted.

The probability of a photon crossing through one radiation
length of material (coil, at normal incidence) without conversion is

given by v(E) - .H53 + .031/ [E'- [YELBZ]. For the average energy of

1N1

 

 

 

 

 

 

 

 

 

Table V-1 : Cut Efficiencies.
analysis Cuts acceptance (7.)
ApT - 4.5 - ID Gall/c
Ins out
Clustering in the
Back Glass 94 9"
Vertex position 95 95
‘ NaI triggers 99 99
fl Multi-clusters 95 90
Front Glass geometrical
acceptance 67 67
7 B-veto 38 41
l
l Front/All cut 85 82
Signal in Strip Chamber 99 99

 

 

1N2

 

Figure V-ZO: Probability "tree" of the B-veto
Logic without Associated Particles.

1A3

approximately <E> - 5 GeV in our sample, the non-conversion probability
is then <v> - .1167; and the probability of conversion is given by (1 -
<v>) - .533. For n photons the probability of non-conversion is Anc-
v(E)n, and the probability of conversion Ac - (1 - v(E)n).

To check for angular effects in the B-veto, a slightly
simplified model, using exp(-7/9) and exp(‘7/9cos(6)) for the normal and
oblique conversion probabilities, was done. The angle of incidence 6
distribution was taken from the neutral meson Monte Carlo. The result
was a change in the B veto acceptance from 0.3u1 to 0.336.

For the B-veto we have to consider two efficiencies: on, the
probability of detecting the pulse height associated with the conversion
and n, , the probability of the position measured by the B counter being
outside the window. Since our pulse height cut is less than one m.i.p
(83 counts) we will assume a, - 1. Figure 11-20 shows the probability
"tree" of a trigger-particle through the veto logic; the probability of
passing the veto is given then by

A0 - z PASS - Anc + A°- n,- a, + Ac-(i - a,)-n, (V-g)
and, with the assumption that a, - 1

nc + A0.n3 (V’h)

Ao - A

The presence of particles associated with the trigger particle

complicates the situation described in figure V-20. Each of the

"branches" of figure V-20 opens now to a group of "2nd order" diagrams
represented in figure V-21.

Let us define the following quantities, f : fraction of triggers

with associated particles in the region covered by the B cut; a; : the

probability of a track depositing enough pulse height in the B counter

to pass the cut; (1,: probability of a track plus a shower (conversion)

11m

    

correction

 

COFFECUOI’I

 

 

 

correction

 

 

-— First Order

 

Second Order [ .. omitting but 3 terms}.

Figure V-Zt: Probability "tree" of the B-veto
Logic with Associated Particles.

1N5

depositing enough pulse height in the B counter to pass the out; n,: the
probability for a B counter position of a track being outside the A2
twindow and n2: the probability for a B counter position of a track Elfli
a shower (conversion) being outside the Az window.

Figure V-21 shows the probability "tree" for all the
possibilities encountered by a trigger-particle going through the B-veto
logic. If formula (V-g) is viewed as a sum of all the terms represented
by the first order diagrams, then figure V-21 shows that each gets a

correction term:

nd

 

 

first order 2 order correction
A - Ano - A“°-f-a,-(1 - m)
+ Ac°as'n3 - Ac'f'a,°az'n,°(1 - n2)
- O + Ac-f-o3-a2-n2-(1 - n3) (V-i)

The probability of passing the B veto, the B-veto acceptance, is

now (with o,- 1):

A 3 Anc+ Ac'n3‘ f'Anc'Ql‘(1’n1)+ f°Ac’(1-n3)'az'nz- f°Ac°n3°az'(1-nz)
(V’J)

and after some algebra we obtain the expression:

A - Anc-[lrf-a,-(1-n,)3 + Ac-[n.+f-cz-(nz-n,)] (V—k)
We have to calculate it sets of these parameters. For the direct
photon and meson events and for the inside and outside detectors. We

average over any energy dependence. The values are given in table V—2.

1116

Table V-2 : Values of the Parameters in the

B—veto simulation.

Inside Inside outside outside
photons mesons photons mesons

.21 .13

 

 

 

 

 

 

 

.56 I .34
.54 | .23
.27

 

 

 

 

f : traction of triggers with associated particles

(1 ‘ : probability of a track to pass the 8 pulse height cut

a 2 : probability of a track plus a shower to pass the B pulse
height cut

(13 : probability of a shower to pass the B pulse height cut

TI 1 : probability for a B counter position of a track being
outside the 2 window

T] : probability for a 8 counter position of a track plus a
shower being outside the 2 window

Tl : probability for a 8 counter position of a shower being
outside the 2 window

1'47

We have a CON tape in which the B-veto was not applied. We used
these data (which contains both inside and outside triggers) to measurer
the fraction f for 1r°'s, by counting the number of associated particles
within 1 u degrees in azimuthal angle from the trigger position (a
region comparable with the B counter geometrical acceptance).

To measure the f value for direct photon triggers we assumed
that direct photons have no associated particles other than the
spectators (i.e. we ignored the bremsstrahlung process). The value of’f
for the direct photon trigger is then the spectator level that was
measured at an azimuthal angle of 90 degrees from the trigger position,
well away from either the recoil Jet or the trigger.

The value of 01, the efficiency of the B counter for tracks
[ANGBZ] is a, - 0.87. Since we assumed a,- i , therefore 02' 1. The
value of n, was measured directly from the non-B veto CON tape
considering only triggers with no associated particles at t 1 degrees in
the azimuthal angle (o) of the trigger position. in for 1r°'s was
calculated from a Az histogram from the non-B veto data where only
triggers with no conversions in the coil (B counter pulse heights less
than 50 counts) were considered. The :12 value for 1r°'s was obtained
directly from the A2 histogram of all the non-B veto data.

For the direct photon value of m, a Monte Carlo was written to
calculate the A2 histogram. This MC produced tracks from a flat
distribution in y (rapidity). One particle per trigger was considered,
and the value of oz - [track - trigger] was calculated.

The n2 value for direct photons was calculated using the same MC
mentioned before but the B counter position was obtained as the averagee

between track and trigger , therefore a value of oz - {(track + trigger)

1118

/2 - trigger} was calculated. This averaging is appropriate for cases
where the position is calculated using time differences of two ends
[LIN82].

To test this formalism we compared calculated values of the B -
veto acceptance with that measured for the non-B veto data (a mix of

direct photons and mesons). From table 11-1 the measured are, A s- 0.38

in

and Aout' 0.111. We had to assume a fraction of photons in the sample.
Based on previous results of experiments R108 [ANG80] and 8806 [ANA82]
we took Y/all - 0.1. Also needed is the fraction of single photons
resulting from asymmetric meson decays. These numbers came from the
meson decay MC: Y/rr°- 0.081 for the inside and 'Y/1r° - 0.0117 for the
outside. These values gave the following sample composition: inside,
a-831 1r°'s; b-71 Y from 1r° and c-iOS direct photons: outside: a-861
1r°'s; b-llz Y from 1r° and c-lOi direct photons, then: A - a-A".+ b-A",Y+

coAY. Applying equation (V-k) with all the values of table V-2 we

obtained for the inside AY- 0.569; Afloy- 0.506: Aflo- 0.339; A - 0.3711
while the measured value was 0.38. For the outside AY- 0.606: An°Y'
0.527; An°' 0.392; A - O.u18 while the value measured was 0.H1.

If associated particles were ignored (f - 0), the values

obtained are AY- 0.568, Afioy- 0.568, Aflo- 0.366 and A- 0.110 for the

inside, and AY- 0.611, A - 0.611, Aflo- 0.1129 and A - 0.145 for the

1r°Y
outside. We take the agreement between calculated and measured values as
evidence that a B-veto consisting of a pulse height cut and a Z-position
cut is well understood.

Comparing Anc with the sets of values, with, and without

associated particles, we concluded that the most important correction to

the non-conversion acceptance comes from the inclusion of the position

1119

resolution of the B counters. However the effect of the associated
particles is also noticeable, especially in the n° component.

In the analysis, formula (V-k) was introduced directly in the
Monte Carlo simulation of the total acceptance (where various neutral
meson decays are considered) to account for multiphoton triggers with

more than two photons.

11-7. Simulated Single Photons.

 

As previously stated there was a single photon Monte Carlo that.
produced the same kind of output as the Neutral Meson decay MC described
in section 11-5. The geometrical acceptance, trigger and requirements
(cuts) were the same as utilized for the neutral meson MC, as explained
in Appendix D.

The kinematics are, of course, different and more simple. We
start by producing photons using the Aurenche et a1. [AURBIi] pT
distribution for y - 0 prediction using Duke & Owens set I structure
functions [DUK8N]. We take a uniform rest-frame angular distributitni in
¢ (azimuthal angle) and a flat distribution in rapidity. We produce
photons in the rapidity interval of Ay - :i: 0.8 and in M - :1: 0.6 red;
the same used in the neutral meson MC.

The acceptance for direct photons, A is calculated by applying

Y.
all the geometrical and analysis requirements, Just as in the case of
the neutral mesons. A sample of pure single photons as seen in the

chambers is produced with the correct pT distribution within each of the

pT bins utilized in the at fits. It is assumed that the single photon

150

background from the neutral mesons has nearly the same pT distribution
as the real photons. Therefore we take these at distributions to be the
distribution of all the single photons in the chamber (direct photons

plus single photon background).

V-8. Simulated Single and Multiphoton o, Distributions.

To obtain the simulated 0t distributions for single and
multiphoton decays we combine the EGS simulated strip chamber shower
information with photon positions generated by the Monte Carlos
described in previous sections.

The EGS output provided the energy deposition by strip in the
chamber. The simple scaling of the energy to pulse height using the n°

trigger data for normalization is not enough. The a distributions

t
produced in this way are clearly in disagreement with the data.

Of course, what is missing is the response of the chamber to the
signal. This is difficult to simulate. Strip chamber properties have
been studied by the Charpak group at CERN [CHA70, BRE77]. These studies
concentrated on position resolution using MWPCs. Various sources of
errors are presented, some related to the algorithm to calculate
positions [CHA78], others to the chamber geometry [GAT79] and charge
collection, or to systematic errors of external source such as
electronic cross talk [P1082].

A good model of the way the signal is read-out by the cathode

strips is available [SAU77]. However, each chamber possesses its

individual signal—response relation. Essentially, the ions and electrons

151

caused by the ionization of the chamber gas start moving with different
speeds due to the electric field in the chamber towards their respective
opposite sign poles. When the electrons are very near to the anode
wires, the high field present there gives to the electrons enough energy
to start an "avalanche". The electrons of the avalanche are rapidly
captured by the anode. The positive ions, however, form a very slow
moving cloud moving towards the cathode. This positively charged cloud,
on the time scale of the electronic read-out, can be approximated to be
at the wire position. The induced image of this charge in the cathode
strips is what is detected.

The electrostatic problem of the distribution of induced charge
has been resolved analytically [ERS82,MAT8ll,VAN86,GAT79]. The charge
distribution is given by the Gatti-Mathieson [MAT8‘1] formula:

1 - tanh’(K,A)
1 + tanh’(K2A)

where A - x/H, x is the coordinate along the cathode plane, H is the

r(1)- K,

 

(V-l)

distance between wires and strip cathodes, K2 - 1r/2-(l - Van/-Rr). The
parameter K,, that depends on H, the wire spacing and the wire radii,
was taken from [MAT811], K, - 0.05 for our chamber geometry. K1 is a
normalization constant such that J I'(A)dl - 1. Figure V-22 shows the
Gatti-Mathieson distribution for our chamber parameters. We used the G-M
distribution to spread each wire energy deposition among adjacent
strips.

Other properties also have to be taken into account. The gain
fluctuations between strips [CHA78] account for some smearing of the
signal. To simulate it, we used a Gaussian distribution with a R.M.S.

given by APB/PH - a We also introduced a Gaussian noise, with mean at

G.

0.8 —

0.4 i-

0.2 *-

 

 

152

 

 

Figure V-22:

 

Gatti-Mathieson Image Charge
Distribution in A bins of 0.1.

153

the calculated value of the pulse height and a standard deviation of 0N
counts, to account for random noise in the strip read-out electronics.

Where a and a

G are parameters to be determined (values given in next

N
page).

Further improvements of the simulation require information on
the specific characteristics of the chamber such as geometry (wire
spacing, wire-strip spacing,etc.) [GAT79] as well as electronic read-out
and connections between components [PIU82]. Unfortunately we were not
able to increase further the accuracy of our simulation. First the
simulation was done long after the detector was dismantled and precise
written information was not available. Second, we lacked an accurate
model of how to proceed. The chambers showed an asymetry between the Y
and Z views. This was related, presumably, to read-out characteristics;
Y strips run perpendicular to the anode wires, while Z strips run
parallel to them. The electrical coupling characteristics of the Z
strips was thus different. The positive charge of the ions created in
the avalanche could induce a positive charge in the adjacent anode
wires. The Z strips running parallel to this wires would see a lower
charged anode and then could get more positive. This would affect the
shape of the signal in the Z view. This phenomenon is likely to be of
less importance in the Y view since the wires are perpendicular, thus
integrating the signal over various wires. This effect has not been
simulated.

To summarize, the "chamber response algorithm" is composed of:
an energy to pulse height scaling of the form Pl-i - oPH-E , the Gatti-
Mathieson charge distribution formula, strip by strip gain fluctuations

and random noise. The values of “PH’ “0 and a" were adjusted through the

1511

normalization using the n° trigger data. As explained in Appendix E,
these data provided a sample of single photons in the energy range
between 0.5 to 11 GeV. The 2 GeV bin was used as normalization point. As
was proven later (see section VI-l) the most important feature is to

make the ot distribution maxima to agree. Thus the values were chosen

such that MC 0 maxima, mean 0

t oand mean pulse height agree with n°

1'.

data. Figures V-23, V-2H and V-25 show the values of mean °t , °t

distribution maxima and mean pulse heights for single photons from n°
trigger and simulations as function of the energy. The values chosen
were: aN- 17. “0 P112

For the single photon sample we took events generated with the

- 0.2 and a Y. 1111000, a - 22000.

PH
single photon MC and simulated chamber energy deposition of each event
choosing from the EGS shower bank (the set of energies between 0.5 and
10 GeV generated by EGS) a shower with the appropriate energy. We need
to interpolate since the energies of the generated events have a
continuous distribution within the bin, but the EGS runs were made for
discrete energies. The EGS runs used for the single photon simulations
are at ll ,5 ,6 ,7 ,8 and 10 GeV. For example, if we want to create a
strip chamber shower at 11.73 GeV we have to interpolate the properties
from the 11 and 5 GeV EGS banks. The algorithm uses linear interpolation
for the pulse height and the standard deviation of all the clusters in
the window with pulse height above the out (1100 counts in Y and 200
counts in 2). Given an event with energy E, if E, is the closest energy
from the EGS bank and ii:2 the second closest (such that E,S E 5 3,), we

take an event from the E, bank and scale each strip pulse height by:

 

155

 

 

 

 

 

10
O n'TriggerlNS
I n'Trigger OUT
0 Simulation INS
8" D mmmmbnmn
E 6 ‘
9
1- B U a D a O
., l
. 4. 1
° 1
o
E
2 .—
1 1 1 1 1
oO 2 4 6 B 10
E... GeV
Figure V-23: Mean of the ot Distributions vs.
Energy for Single Photons from the
n° Trigger and Simulation.
8
I n'Trigger INS
7 - I n‘TriggerOUT
0 Simulation INS
6 _ 13 SimulationOUl’

momma (cm)
a
I

 

 

 

. a B 03 o

O

3- . 3

18 a
O I

2~|

11-

o 1 1 i1 1 1

o 2 4 a a 10
EL. GeV

Figure V—ZH: Maxima of the 0t Distributions vs.

Energy for Single Photons from the
n° Trigger and Simulation.

 

156

 

 

 

 

 

 

:10 3
14 O n'TrioserY
I n'TriggerZ
O SimulationY
12" D fimmmbnz °
If to — o
.9 °
2 8 - °
3 o
a. 6 - o a
C D
8 4 + D D
E V a
1 . D
2 1“ 8 I .
B
o 1 1 1 1 1
O 2 4 8 8 10
E;. GeV’
Figure V-25: Mean Pulse Height vs. Energy for

Single Photons from the n° Trigger

and Simulation.

157

(PHTin>E
<PHT> , where <PHT> is the mean

3, E!

 

PHT1(E) - seeming), with a -

pulse height of the cluster in 13,, and <PHT1n>E is the linear-

interpolated mean pulse height at energy E, as:

(PHT n> - <PHT> + [<PHT)

1 E E; " (””3943 ‘ lid/(E.- E.). The width of

E:
the clusters is also scaled. Every strip is scaled by a factor a, while

keeping the centroid of the cluster fixed. Thus, if x is the strip

1
position and (x) the centroid position, [x1(E) - <x>(E)] - o-[x1(E,) -

0(3) + <01n>E- <o>E
<x>(E,)], with a - o ‘, where <01n>E is the

+ [<O>E‘-

 

interpolated mean standard deviation as: <0 > - (o)

in E E11

(0)}; ]~(E - E,)/(E,- E,). A rebinning of the pulse height information
2 .

into 1 cm strips is performed after the width scaling.

After the interpolation we apply the "chamber response
algorithm" to the energy distributions to obtain the pulse height
information. Once we have created an event sample of pure single photon
events we use the standard algorithm to calculate the 0t distributions
in the pT range of “.5 to 10 GeV.

For the multiphoton case we proceed in a similar way. Now for
each of the events generated in the neutral decay MC we have two or more
strip chamber positions at which we should insert the appropriate
chamber signal from the EGS bank. Due to the kinematical properties of
the decay (discussed in Appendix B), the photons cover a large range of
energies. For this reason we ran EGS simulations for incident photons as
low as 0.5 GeV. Below 0.5 GeV the probabilities that this photon passes

through the front glass and produces a signal in the chamber are very

low (see figure V-19).

158

The same interpolation of chamber properties from the EGS bank
as described above was used. Then the "chamber response algorithm" was
applied to the joint information of the photons. The multiphoton sample
obtained was analysed using the standard algorithm to obtain the o

t
distributions.

 

V-9. A Front/All out.

A study of the counting matrices of figure V-9, the Front/All

histograms of figure IV-9, and the 0 data distributions of figure 11-15

1:

showed an excess of data events with no strip chamber clusters, low

Front/All, and lower a values than those expected from the simulation.

t
We studied a sample of these events and concluded that they correpond to
several sources distinct from direct photons or neutral meson decays.
These included side splashes (beam-gas or beam-pipe interactions).
"glass misfireds" (large energies in a single cell with no neighbors)
and a small hadron background (to be discussed in section 111-9). These
classes of backgrounds will tend to give low °t
The ratio Front/All was defined in section IV-7. The ratio

and low Front/All.

measures the fraction of energy deposited in the front glass array, or
how deeply in the glass array the shower had started.

A requirement of a minimum Front/All could ,then, clean the
sample of these spurious events. Figure V-26 shows a scatter plot of

Front/All vs. 0 . The region of low Front/All ( < 0.111) has excess

1’.

concentration of low 0 events with few events at high 0 . Requiring

1: t ,

159

Front/All greater than 0.111 improved the agreement between made MC °t
simulations and data.

This cut must be taken into account in the acceptance correction
for the observed signal. The correction affects the single and
multiphoton samples differently. Therefore we need to know both
Front/All distributions.

Front/All distributions for single photons were obtained
directly from the EGS simulation (Appendix C). The multiphoton Front/All
distributions were obtained using the EGS output in combination with the
meson decay simulation. For each photon we obtained from EGS Front/All -

(F/A)1. An event with n photons, of energy E will have Front/All given

1
by:

n

218 °(F/A)1

 

Front/All - (V-m)

Nah“

1E1

To find if the simulation was correct, two checks were done.
First, a special electron initiated EGS run at 1 GeV was made to compare
with a 1 GeV PS test run done with a front-glass back-glass
configuration [NIC82]. The test and simulation distributions are shown
in figure 11-27. Evidently, the simulated values are lower than the PS
measurements.

A second check was performed using the direct photon trigger
data. For a given pT bin, a simulation of the data was taken as a
combination of 0Y1 single photons and (1- CY), of multiphotons. Figure

‘V-28 shows the data Front/All distributions for the data and the

 

FRONT/ALL

160

 

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l ..‘ "f
O . : ' o ‘ .- . e.
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a 10 12 14

Figure V-26: Front/All vs. °t for the Direct
Photon Trigger Data.

161

 

 

 

 

 

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0. 0.2 0.4 0.5 O 8 1.

F/Ali

 

Figure V-27: . Front/All distribution for H GeV EGS
Electron Initiated Shower Simulation

and A GeV Electron PS Test Data.

 

162

 

010- 3
100
I SIMULATION
8° F - omm
w —

 

 

 

 

 

Figure V-28: Front/All Distributions for the Direct
Photon Data and EGS Simulation in the
Range ApT- A.5-5 GeV/c.

 

163

simulation in the ApT= A.5-5 GeV/c bin. Here also the simulated values
are lower than the data.

The simulation does not agree with the data. There are two ways
to explain the disagreement: either the simulation is wrong or the
evaluation of the data Front/All is wrong.

This last possibility is related to how the front plus back
glass arrays were calibrated at the PS [HUM83] using a 11 GeV electron
beam. The calibration constants were determined such that Front + Back -
4 GeV and setting the ratio Front/(Front + Back) such that minimized the
energy resolution. There are problems with the method, because an:
fluctuations that cause the resolution smearing are induced not only by
the shower fluctuations but also by dissimilar light collection.

The simulation presents two main problems; first one has to be
sure in: take the full shower simulation down to the Cerenkov threshold,
and second, the light collection was not modelled.

It is not obvious how to add light collection effects within
reasonable simulation times, and how this will affect the results. There
are more low-energy shower electrons in the back glass than in the front
glass array. Low energy electrons have their light emitted farther
forward than high energy electrons. Due to the geometry of the arrays,
this will make the lower energy electrons have better collection
probability in the back than in the front since they are, in average,
podnting forward. This effect then will tend to lower the Front/All
ratio. On the other hand, low energy electrons are produced at larger
angles, therefore half of the time this will help some low energy

electrons in the front glass but the other half they will point away

 

16“

from the photomultiplier tube. All these effects would tend to lower
Front/All in the simulation.

For the direct photon trigger data we may consider also the
effect of associated particles and the clustering in the front glass
(complicated due to the poor spatial granularity) which will tend to
increase the Front/All ratio of the data.

Due to these considerations we decided to adjust the Front/All
distributions phenomenologically. We changed the Front-to-Back balancing
of the Monte Carlo energy depositions such that the A GeV electron
Front/All simulation and PS data agree. This requires:

Front/Allnew- Front/Allold/(.78 + .23-Front/Allo ) . For each pT bin,

ld
random numbers from the Front/All histogram for photons (and mesons)
were generated to recalculate new Front/All using the previous relation.
New histograms were then produced and from them the acceptances were
calculated. The Front/All distribution for photons are shown in figure
V-29 and for mesons in figure V-30.

A new comparison of the simulation with the data, shown in
figure V-31, shows a good agreement between distributions. At low
Front/A11 the excess showed by the data is in agreement with the
expected background. Note that energy scale nonlinearities are implied
in this MC Front/All transformation. Changing the front-to-back energy

balancing at one energy produces an energy shift in the calibration (see

section VI-fl).

.ncouoca camesm
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167

 

010- 3
100
I SIMULATION
80 1—
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60 1—

 

 

 

  

; l

O. 0.2 0.4 F/ALL 0.6 0.8 1.

 

Figure V-31: Front/All Distributions for the Direct
Photon Data and EGS Simulation in the
Range ApT' A.5-5 GeV/c After Rebalance
of Front and Back.

6:3
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168

V-10. Fits to the o, Distributions.

A maximum likelihood fit [EAD82] to the data histogram was
performed to find CY ( fraction of single photons in the data sample)
such that:

fd - CY- fY+ (1 - CY) - fn° (V-n)

where, fd is the normalized 0t distribution for the direct photon data

trigger, fY and f“, are the normalized °t distributions for photon and

multiphotons.

The likelihood function for binned data [EAD82] is defined as:

 

“1
1 N (fdi) (v—o)
h- n n ,
1-1 1

where the sum is over the bins of the histogram and n1 is the number of
events in the i-th bin.
The most probable value of CY is obtained by making the most

probable f distribution as a combination of fY and fflo. The value CY

d
maximizes the likelihood function:
3L
or minimizes {- Ln(L)}: a ln(L) (V-p)
———-- 0 --——-——- - 0
3CY 8CY

‘The CERN library subroutine MINUIT [JAM87] was used to find the

minimum of {- Ln(L)} for each of the pT bins.

169

V-11. Corrections to the Direct Photons Observed.

 

Once CY (fraction of single photons) is obtained, we make
acceptance and background corrections in order to extract the number of
direct photons produced by nature.

The meson decay Monte Carlo provided the acceptance for meson
decays, Am, and the background of single photons from meson decays in

the single'photon sample. This can be described by Y / YY Imeson : the

ratio of single to multiphoton produced events by neutral meson decays
in our detector.

For each pT bin the number of single photons observed is given

by:

Y - CY- N

obs (V-q)

D

where ND is the total number of events in the pT range considered, ApT.

To obtain the number of direct photons observed we need to subtract the
background of single photons due to neutral meson decay:

YD - yobs- Ybackground (V-r)

From the MC we obtained Y / Yylmeson' If NYY is the number of

multi-photons in ApT, the number of background single photons is:

Y
Yback- YY mesons NYY

but
NYY ' (1 ‘ CY). ND
therefore
7 ..
YD ' CY. ND '77— mesons (1 CY) ND (V S)

obs

WM“

“.1 ww-

.
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In.
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170

To find the total number of direct photons producedimemust

correct by the apparatus acceptance. Therefore:

1
Y =-—-— - Y
Dp AY D

1

Y
Y - -——- N { CY

DD AY D ‘77— mesons“1 - CY)} (V-t)

where Y is the number of direct photons produced by nature in this ApT

DD

range over the rapidity Ay and the azimuthal angle A41 range considered
in the Monte Carlo calculation of Ay.

It is conventional to express the result of the direct photon
measurements as the ratio of direct photons to 1r°~mesons produced. To
obtain this ratio we first calculate the number of neutral mesons

produced,

(mesons) = (1 - CY). N (Vru)

D

Since some neutral mesons are observed as single photons, the total

number of neutral mesons is really:

(mesons)obs - (mesons) + (V-v)

Ybackground

Using (V-u) and (V-v) we obtain:

)0N + Y

D YY mesons (V-X)

 

(mesons)obs' (1 - C - (1 - CY): N

Y D

Dividing by the acceptance, Am, given by the meson decay MC we

obtain the number of neutral mesons produced:

171

 

1 Y
(mesons)p A ND (1 CY) 1 1 + YY mesons}

m

(Vry)

the subscript p refers to the number produced in the Monte Carlo range
of A41 , Ay and ApT. The ratio of produced direct photons to neutral

mesons is then:

 

 

 

 

{.___._l_____L }
YD Am 1 - CY YY mesons
(mesons) p. . Y (V-z)
A l 1 + }
Y . YY mesons

 

To obtain the ratio of direct photons to n°~mesons we form:

 

 

 

 

 

 

 

YD YD ,

(mesons) p a n° + other neutral mesons p
YD/ n°
_P

l + other neutral mesons

n° p
therefore
Y Y ‘
D _ ( 1 + other neutral mesons ) . D (V-A)

n5 p o° p (mesons) p

 

where the ratio of other neutral mesons to 1r°-mesons produced can be
calculated knowing the production cross sections and branching ratios of
all the neutral meson decays considered.

In Appendix A the neutral meson decays that contribute to our
background are discussed. They were included in the neutralimeson decay

Monte Carlo. In Appendix A we found that:

172

 

 

 

 

( 1 + other negtral mesons ) _ 1.627
P
therefore:
{———C" —" 1
YD Am 1 - CY - 'YY mesons
__1__. . 1,527 . . - (VrB)
n p A Y
Y { 1 + -——— 1
YY mesons

 

 

V-12. Statistical Errors.

This section describes the calculation of the statistical errors
associated with the number of direct photons and the quantities derived
from it.

The error in a bin 1 of the data 0 sample distributions is,

t
using a multinomial model for the distribution fD [EA082]:

(V-C)

where n1 is the number of events in the 0t bin, ND is the total number
of events in the pT range considered and £01. ni/ND'

Since the errors of the o distributions for the single and

t
multiphoton samples depend on both the neutral meson decay simulation
and the EGS shower simulation, they are not easy to calculate directlyu
For the multiphoton sample, part of the statistical error came from the

statistics of the neutral meson decay Monte Carlo, the number of mesons

generated. This gives a lower limit to the real statistical error. The

173

true error also involves the number of events generated by the EGS Monte
Carlo, which is smaller. However, the number of independent combinations
of EGS photon showers available to the decay Monte Carlo is large

compared with N so this correction is small. The error in fm is

EGS’ i

approximated by:

 

 

(V-D)

where nmi is the number of events in the ot bin (generated by the meson

decay MC), NIn the total number of events generated in the pT range and

f is the normalized number in the OT bin, fm

m i i

For the single photon sample we considered both NEGS'the total

' nmi/ "m7

number of showers from the two energies used to interpolate for the pi.
bin, and NY’ the number of events generated by the single photon Monte

Carlo in the pT range. The number of independent entries in the ot

distribution is limited by N not the number of single photons

EGS’

generated by the Monte Carlo N The statistical error of fY is:

Y? i

// “v1 // in
°v' x’r—TN— ' / T’ "’“E’
1 / EGS Y / EGS

where nY1 is the number of events in the ot bin and in - n71/ N7.
Since we were not able to run the Monte Carlo long enough to
make the MC statistical error negligible with respect to the data

.statistical.error, the standard maximum likehood error formulas did not

apply.

1711

The error associated with the fit was found by a Monte Carlo
simulation of the variations expected for each of the distributions.
This MC repeatedly generated fd, fY and fIn from Poisson distributions
with appropriate number of entries and the observed values as the means,
and performed a fit for each set of fluctuated distributions. A
distribution of CY resulting from these fits was formed for each pT bin
as shown in figure V-32. The error, ACY’ for each pT bin was calculated
by two methods. the first method took the rms of the distribution of the
values of CY. The second method took different right and left side CY
errors such that 68% of the distribution fell within their limits. The
error ACY quoted for each pT bin was taken as the largest of the three
values, rms, |CY+- CYI, |Cy_- CYI. The ACY values are shown in table VI-
1. The statistical errors were dominated by the Monte Carlo statistics
for the lower pT bins (pT < 6.5 GeV/c) and by the data statistics for
the higher pT bins (pT > 6.5 GeV/c).

Applying propagation of errors to calculate the error in the

number of direct photons of formula (V-t) we obtain:

 

 

1 /7
/ Y 2 2 Y 2
A YDp - To // {CY W (1 CY)} ND ‘1' ND {1 ‘1' YY m} ACY
(V-F)

The error in the ratio of direct photons to neutral mesons or 1r°-meson

is from formulas (V—z) and (V-B):

Am , ACY

Y 0
YY m} (1 " CY)2

A{._Y__ }-

m p A7'{ 1 +

 

 

(V‘G)

 

175

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176

Y Y
11° D}- 1.627'A{-m—-p}

 

A {

(V-H)

CHAPTER VI

RESULTS AND CONCLUSIONS

VI-l. Fraction of Single Photons.

Figures VI-l and ill-2 show the inside and outside trigger °t

d istributions for the single and multiphoton simulations, the data and

the maximum likelihood fit for each of the pT bins. As explained

previously, the simulation of the strip chamber response was only
approximate, ignoring electronic cross-talk, shower particle propagation

beyond simulation cut-offs, etc. We add a resolution in °t , Act, as a

phenomenological description of these effects. For each Monte Carlo

event we calculated the ot value from a Gaussian distribution with mean

0t (the value calculated by the response algorithm) and rms = Mt' The
a .

Value of A0 wwas parametrized as: Mt' A°(°t+ B), where the values of A

1'.

and B were chosen to best fit the data. The values were 8 = 0.6 for all

energies and A- 0.1 for E abs 5 GeV , A - 0.07 for 5 GeV S E abs 7 GeV

1 1

dependence on a can be viewed as

1'.

a - 0
nd A 0.05 for Elab > 7 GeV The Act

an uncertainty associated with the distance between photons in

multiphoton decays. The other term can be associated with the

177

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178

 

 

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Figure VI-l

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Distributions for the

Inside Trigger Single and Multiphoton

Simulations, Direct Photon Trigger
Data and Likelihood Fit for Various
pT (C.M.) Bins.

179

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure VI-l: Continuation.

 

o u
0.12

179

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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t
Outside Trigger Single and Multiphoton

Simulations, Direct Photon Trigger
Data and Likelihood Fit for Various
pT (C.M.) Bins.

010
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181

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure VI-2: Continuation.

182

uncertainties in the single photon o distributions. Thus, the error in

t
the model is expected to decrease for increasing lab energies, as indeed
it does.

Figures VI-3 and VI-h show the o distributions for simulations,

t.
data and likelihood fit after introducing this smearing. It can be seen
that there is a considerable improvement in the fits, especially for the
width of the distributions. The maxima remain practically in the same
position. Figure VI-S shows the ratios between smeared and non-smeared
versions of the cross section. As can be seen, they do not differ by
more than 15%. This shows that the likelihood fits are driven by the

positions of the maxima of the o distributions and not their widths.

t
The smeared set of distributions fit the data clearly better but do not-

change the final answer significantly. We took the smeared set of CY

values as our best results.

Table VI-1 shows the values of acceptance, luminosity, CY and

other parameters used to calculate our results. The inside and outside

triggers are given independently. As can be seen from the CY fit

distributions of figure V-31 and errors of table VI-1, the values

obtained from the last two outside pT bins are very unstable and have
large uncertainties. This is due to the fact that at these lab energies,

1r°'s are really merged, as can be seen from the 0t distributions of

figure VI-ll. The final results (for Y/n", Y/all, direct photon and meson
cross sections) were obtained by an error-weighted average between the

inside and outside triggers. If ¢insi “bins is the value of o (a given

183

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185

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Figure VI-S: Ratio of Smeared to Non-smeared Versions

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war—Jag ¥_ 4

Function of pT (C.M.).

190

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result) for the inside trigger and ¢outi M’out for the outside trigger,

the final result was obtained by [BEV69]:

¢ o(1/A¢ )2 + ¢ ~(1/A¢ )2
¢ _ ins ins out out (VI-a)
2 2
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and the error:

.../ 1

(1/A¢1ns)2+ (1/A¢out)2 (VI-b)

 

 

where only statistical errors were considered. The discussion of

systematic errors will be reserved for section VI-H .

VI-2. Direct Photon to n°-meson and Direct Photon to Neutral

Meson ratios.

 

It has been common in the literature to give the ratio of
produced direct photon to 1r°~meson as the experimental result of direct
photon measurements. This is generally the case among the experiments
using a direct technique to differentiate w° triggers from direct photon
triggers on an event by event basis. Giving a ratio of the two
quantities measured with the same detector minimizes the systematic
errors.

Ratios of direct photons to "all" also have been given in the
literature. In this case the term " all " can be misleading, since it
has to be clearly specified what was included in the "all" definition.
We define "all neutral mesons" by the list of decays included in

Appendix A, and "all" as "all neutral mesons" plus "direct photons".

192

Table V-2 and Table V-3 show the Y/n° and Y/all resulted from the inside
and outside triggers. Table v-u shows the error-weighted averages.

The CCOR collaboration (experiment R108) [ANGBO] has given
values of direct photon to all found using the conversion method. In
figure VI-6 our values of direct photons to neutral mesons plus direct
photons ("all") are shown. The R108 results are also shown.

The ratios of direct photons to 1r°-mesons produced are better
defined. Figure VI-7 shows our values of the direct photon to w°-mesons
ratios. The values for the ISR experiment R806 [ANA82] are also shown.
However. they depend on both how well the direct photon signal is
measured and how well the n°- meson signal to noise ratio has been
evaluated. We believe that this double measurement made the inter-
experiment comparison more difficult. The easiest and least biased
comparison is to compare directly the direct photon signal, as is done

in section VI-S.

VI-3. Direct photon cross section.

 

The invariant direct photon cross section as a function of pT, ¢

(azimuthal angle) and y (rapidity) can be written as:

 

do do _
E F5 ppoT-d¢°dy (VI 0)

For a given phase space volume ApTA¢Ay, the average in this volume can

be calculated as:

 

do do
<E-y——> - < > -
d D APTA¢AY PTdPT'A¢'AY

 

193

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table VI-2: Results for the Inside Trigger.
inside Trigger - Results
bins (Bell/c) .
p T 4.5-s 5-5.5 5.5-6 6-6.S 6.5-7 7-6 6-10
Direct Photon 2.21 i 034 1.31: 0.05 6.301: 2.96 3.91: 0.72 1.691 0.66 6.53: 3.11 1.66: 1.22
Cross Section x 10'3‘ x 10‘34 x 10'35 x 10'35 x 10'35 x 10‘36 x 10'36
Neutral M8800 3.62: 0.11 1.681’ 0.15 7.24: 0.67 3.141: 0.21 1.511 0.20 4-991 0.88 9.391 3.50
Cross Section ‘ 10-33 x 10‘33 x 10'“ x 10-34 x 10'3‘ x 10‘35 x 10'36
'flll' 3.641: 0.11 1.61.4: 0.16 7.67: 0.92 3.53: 0.22 1.701 0.21 5.64: 0.93 1.13: 0.37
Cross Section , 10'33 x 10‘33 x 10'3‘ x 10'34 x 10‘3‘ x 10‘35 x 10‘35
0.061 0.076 0.067 0.125 0.125 0.171 0.200
7 / "‘9‘”: t 0.010 t 0.031 t 0.042 1 0.024 t 0.046 t 0.069 t 0.150
7 / all 3-057 0.072 0.060 0.111 0.111 0.145 0,157
- 0.009 1' 0.026 t 0.039 t 0.021 t 0.042 1: 0.056 1 0.122 I
o 0.099 0.127 0.141 0.203 0.204 0.276 0.325
7 / it t 0.015 1 0.050 t 0.069 t 0.040 t 0.077 t 0.113 t 0.244
All Cross Sections in cm 2c 369V2
Table VI-3: Results for the Outside Trigger.
Outside Trigger - Results
bins Sell/c
0 I ( ) 4.5-s 5-5.5 5.5-5 6-6.5 6.5-7 7-8 84 0
Direct Photon 2.72: 1.23 1.64: 0.79 7.10: 4.22 4.021: 1.37 2.261: 1.40 3.09: 5.53 6.65:122
CFO” Section :1 10'3‘ x 10°34 11 10'35 x 10’35 x 10'35 x 10'36 x 10'5"7
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Cross Section x .033 ,‘ 10-33 x 10‘3‘ x .0-34 x 10-34 1: 10°35 :1 10'3“
'flll' 3.92: 032 1.64: 021 6.651: 1.06 2.941' 0.35 1.371 0.35 6-0431-37 1-063 0-30
Cross Section , 10-33 x 10-33 x 10'3‘ x 10'3‘ x 10'34 x 10‘35 x 10‘35
0.074 0.112 0.116 0.156 0.196 0.054 0.069
7 / ”930'“ i 0.034 t 0.056 1' 0.071 t 0.057 t 0.133 t 0.097 t 0.128
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0 0.121 0.162 0.166 0.257 0.319 0.066 0.145
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d p d p ApTA¢Ay APT 01 Av APT 00 AV“ pT de T

 

1 1 J J J do
I o o < > dp d¢dy (VI-'9)
ApT Ao Ay pT ApT ApT A¢ Ay de T
where we have dropped the average symbol on 511%; for notational

convenience. Now

Y
do , 22 .
JApTJA¢JAy— de dPTd¢dY L . therefore.

Y <—-1 >

do Dp pT

'd’p ' L-ApTAoAy (VI—f)

 

E

where (—:—)—-> is the average of —:)— in the bin ApT wide; Y from

'
T T DP

equation (V-t), is the number of direct photons produced in the volume

ApTAoAy. L is the accumulated luminosity of the sample. L was 5.9701037

37 cm“2 for the outside and AoAy - 1.92

cm—2 for the inside and 2.57-10
is the (o-y) sub-space volume used in the Monte Carlo for acceptance
calculations.

Tables VI-2 and ill-3 show the values of the cross section for

the seven pT bins considered in the inside and outside configurations.

Figure VI-8 shows the R110 cross section for the inside and outside

198

 

 

 

A R110 INS 0 R110 out
10'” A if!
0 R108
o R”
- 0
A10-” 5' o
5% E o
..0 - 1
NE 10"“ f
9 1+
Q1045 f .91
'20 a
\ r 0
b ‘1
B 10’“ .
O
1+ 1
1 1 f
'3‘ I 1 L I 1 1

 

 

 

 

3.5 -

2.5 - T

1.5 -

, l
11

 

 

INS/ OUT SMEARED
N
l
__..__

 

 

 

 

 

 

 

 

Figure VI-B: Direct Photon Invariant Cross Section
for the Inside and Outside Triggers

and their Ratio.

199

samples and their ratios. Figure VI-9 shows the values of the cross
section calculated from the error-weighted average of the inside and

outside values. Table 111-“ gives the final results for the seven pT

bins.
The values of the cross section were plotted at values p1. £MJCh
0
that:
do 1 d0 _
<E d’p >pT APT JAPTE d’p de (VI g)
0

pr was determined iteratively starting with the bin centers.
0

Only two iterations were necessary. The final values are shown in table
VI-1 .
The statistical errors of the measured direct photon cross

section were calculated using:

 

A(<E $35») = (E d3; >°(AYDp/YDp) (VI-h)

where AYDp is given by formula (V-F).

 

VI-u. Systematic errors.

There were five main sources of systematic error in the
evaluation of the direct photon cross section: luminosity measurement,
energy calibration of the detector, selection of strip chamber

information (strip chamber cuts and windows), modeling of the detector

10

10

10

200

 

 

 

 

I 0 R110
" A AFS
é?’ ,0 R108
E .
m 0 R806
— o
E— o
t of?
*- 1i
E- LP
-_- in.
: o
A
i.

E— O
E + +
" 1
..r 1 1

1 1 1 1 1
2 4 6 8 10 12

PT (GeV/c)

Figure VI-9: Direct Photon Invariant Cross Section

Compared with other ISR Experiments.

201

and physics processes (strip chamber response algorithm and EGS) and
acceptance calculation.

The error associated with the luminosity measurement was about
AL/L - 10% and thus A(cross section)/(cross section)- 10%.

The overall energy scale uncertainty due to the uncertainty in
the beam momentum during the PS calibration of the NaI(Am) sources, and
the uncertainty in their deterioration with time was estimated to be
less than 5% in the energy scale. There are additional effects due to
the relative calibration of the front plus back arrays, discussed below
with the Front/All cut acceptance.

In the evaluation of Ot’ there were several parameters used to

select strip chamber information. We studied how the uncertainty in the
determination of these parameters propagates to the value of the cross
section. The most important influence on the cross section is through

the shape of the 0 distributions. The most sensitive parameter was the

1:
cut on total pulse height of the cluster, used to determined the limits
of the information window (section V-2). We set the pulse height cut as
low as we could, while still rejecting noise. The out could potentially
bias our sample. Low energy photons from asymmetric decays may have

t more like a single

their clusters fail to pass this cut, giving a 0
photon than a multiphoton. Therefore, the impact of the cut value in the

0t distribution shape is substantial. We found that a 5% increase in the

out (which was the largest we felt was credible) produced a 10% increase
in the cross section. We associated a 10% uncertainty to the cross

section due to our uncertainty in all the strip chamber cut values.

202

The study of systematic errors associated with the EGS
simulation is difficult, since it would take large amounts of time to
run with all the cut-off and geometry possibilities. We chose to run
several cut-offs (0.5.1 and 3 MeV). In the course of our simulations, we
used several different detector geometries. Studying the variation
produced in the shape of the strip chamber energy deposition by the

different parameters, propagating these variations to the °t

distribution, and fitting to get the cross sections, we have concluded
that a systematic error of about 5% in the cross section can be
attributed to uncertainties in the EGS simulation.

The systematic errors in the acceptance calculations come from
the cut simulations introduced in the Monte Carlos. We studied the most
important cuts: the B veto, the Front/All cut and the trigger simulation
in the case of mesons. In section V-6 we discussed the B-veto simulation
and how it compares with the data values. From the comparison between
data and simulated acceptances we estimate an uncertainty in the cross
section of about 2.5% from the B-veto acceptance.

For multiphoton decays, the trigger was simulated by defining a
merging window in the back glass array. Photons hitting the back glass
at distances less than 30 cm produced one cluster in the Monte Carlo
simulation (”see Appendix D). We changed the merging distance to 35 cm.
The shift changed the total meson acceptance by 1.7 1. The only effect

in the direct photon cross section is through the value of Y/YYlm. The
effect on the direct photon cross section of the Y/YYIm change is

negligible.

203

As explained in section V-9, the Front/All cut rejected spurious

events that populated the low end tail of the 0 distributions. The

t
problem was that the direct EGS simulated Front/All distributions do not
agree with the data. There are reasons to believe that both data and
simulation are erroneous. Light collection is not modelled in the Monte
Carlo and the Front-Back calibration of the array was done ignoring the:
energy variation in the light collection ratio between the front and
back.

'We opted, then, to phenomenologically adjust the Monte Carlo to
the data. Comparing the calculated Front/All acceptance and the observed

data acceptance in the first pT bin, where the extra background events

are less important, we associated a 2 S systematic error for the
acceptance Front/All simulation.

Associated with the Front/All simulation problems, there is a
balancing front-back uncertainty in the energy calibration. We evaluated
this uncertainty by two methods. First, we calculated the data energy
shift for making PS data and simulated Front/All agree. The energy shift

resulted in: Enew- Eold- (1.08-.2H-Front/All). The ratio

E-%%B(p1. )/E-%%b(p1. ) indicates the cross section shift caused by
0 n

1d ew

the energy change. Energy shifts from 1% in the first pT bin to 3.3 I in
the last pT bin were calculated. The corresponding cross section changes
ranged from 9% in the first bin to 25% in the last pT bin. This method

overestimates the values of cross section shifts since does not account

for possible backgrounds present in the direct photon sample. The second

2011

method calculates, event by event, the recalibrated data cross section.
since the Front/All of data and simulation will now agree, the Front/All
ac ceptance is calculated directly from the EGS Front/All distributions.
Th e shifts in the cross sections using this method ranged from -2% in

t; h e first bin to 12% in the last pT bin. This method accounts for

backgrounds in the direct photon sample. However, they are not all
ac counted for in the acceptance correction (other hadrons and extra

backgrounds with low at). We believe that the values of the systematic

er rors associated with the front-back balancing uncertainty lie between
th ese results.

If we add in quadrature all of the systematic errors discussed
ab ove, then the total systematic error in the direct photon cross

3 ection should range from 18% at the lowest pT bin to 30% at the

1'1 i ghest .

VI-S. Comparison with QCD Predictions and with Other

Experiments.

Other experiments have measured pp + YX reactions at the ISR.

Figure VI-9 compares our direct photon invariant cross section with

other ISR measurements at /-§‘- 63 GeV, the CCOR (R108) collaboration
l:ANGBO], the AFS collaboration [TREBS] and experiment R806 [ANA82].
Iiatios among experimental cross sections are showed in figure VI-10.
They represent the cross section ratios of AFS, R108 and R806 values to

our 8110 measurements, calculated from a functional form fit discussed

205

 

 

 

 

 

 

 

 

 

 

 

 

 

26 _
0 us
2‘ h I Rum
2 _ .3 mum
9 ‘1 ‘
z; 1... 1 1
\. ‘ 1
d 1 1
o 1 1
E
E
o 06»-
. +
...— 1
0 L l I l l l
2 4 6 6 10 12 14 16

Figure VI-iO: Ratios between Direct Photon Cross
Sections Measured in Other Experiments
and R110.

206

below. Our results agree better with R806 for values between 6 < pT < 9
GeV/c, but for lower pT values our cross section is lower, near the AFS

measurements. The R108 values are lower but for high pT (p > 10 GeV)

T
their values are consistent with the trend of our results.

As in others inclusive hadron reactions [ANG78], the direct
photon cross section can be parametrized as:

do “n _
E—- Apr (1 x

m
d3p )

T (VI-1)

where xT- 2pT/J s .

A three parameter fit to our data values gives

30

A- 7.6610.38x10- , n- 6.06iO.36 and ma 5.761131 with a x’/D.0.F. -

0.78 (D.O.F.- 11). As this experiment covers only a short range in xT

(0.15 S x 5 0.286) and has only one 1’ 3 value, we used data from other

T
experiments that have studied pp + TX at different V s and pT ranges to
obtain a better range for the fitting. The experiment NA211 [DEM87] at

the SPS fixed target program has given data at 1’ s - 211 GeV in a xT

range 0.27 S x S 0.5, and experiment WA70 [BON87] also at the SPS have

T

data at 1’ - 23 GeV in the range .357 S x S .1196. Fitting again (VI-i)

T

to the three sets of measurements we obtained A- 2.03:0.96x10-30, n-

9.91:0.23 and m- 9.0310.39. with xz/D.0.F. - 0.95 (D.O.F.- 111). In

figure VI-11 the scaling plot p¥°91E 3%;— vs x is shown including NAZli,

T

5.1—

207

 

 

 

 

" 0 R110
— o NA24
" A WA70
10’30 —-
r +¢
L +
0.10-31 :- + +
n _
d c 1
\ 1.
C) L
.. ~ 11
.PJ — A
a. o 4
V’ -
of ‘° 32 =-
{I
h:-
10-33 -_—
10-34 1 1 L, 1 1
O. 0.1 0.2 0.3 0.4 0.5 0.6

Figure VI-ii: p¥'91-E $3 vs. xT, for Experiments

NAZH, WA70 and R110.

 

208

WA70 and R110 values (only statistical errors are shown).

As explained in the first chapter there are QCD perturbative
predictions for the direct photon invariant cross section. Using the
Bielefeld-LAPP-Orsay (BLO) group [AUR88] calculations we can compare QCD
predictions with different set of structure functions to the data. This
group used the two sets of structure function parametrizations of Duke
and Owens [DUK811]. These sets are the result of a leading logarithm
analysis of DIS, Drell-Yan pair production and production of heavy
resonances. Set I corresponds to a soft gluon distribution and a value

0 f Afig- 200 MeV, whereas the set II corresponds to a harder gluon and a

larger value of “LB - 1100 MeV. Both gluon distributions are represented

:L :1 figure VI-12. The sets differ chiefly in the gluon structure

functions, parametrized as [DUKBli]:

X°G(x,Qz) - 1.5611-(1 + 9x)-(1- x)‘5 Set I (soft), A - 200 MeV/c
o .

X°G(X,Q’) - 0.879-(1 + 9x)o(1- x)“ Set II (hard), A - 1100 MeV/c
o .

at 02 - fl (GeV/c)2
0

Figure VI-13 shows our data and the optimized ("PMS") prediction
to the second order for the set I, set II and Born terms. The dashed
Qurve represents the second order optimized prediction when no
bremsstrahlung terms are considered. A good agreement is found when set

I is used. Set II predicts larger rates than we observe.

209

 

   
 
   

 

 

 

|.8[ 1 r r 1 f r 1 I r

1.6rr\\ I ~
‘ V”

14'1- — 1.556411911111416 ~

L2'- 4 -

.. .-~ ---- O.879(|°9x)(|-x)

”0° 1 Or- "
.: 0 8L o§=4ioowm2 ‘
o .

0.6 - “

0.4 - ‘
\\\/"

0.2 11— s\\\ —1

o 0 ~. “L 4

1 1 1 1 1 .
0.0 Ci 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
11

Figure VI-12: Gluon Structure Functions for the
Duke and Owens [DUKBHJ Set I and II.

 

(cm’cBGeV’z)

Edd/d3p

10

—b
O

10

10

10-33

I
U
U!

—36

210

 

 

 

 

 

 

: -—~-- D-O set II
_ D-O set I
—--" D—O set I (no brem.)

__ —— ----- Born
:
1..
1—
:2
r—
L.

i 1 1 1 1
2 4 6 8 10 12

PT (GeV/c)

Figure VI-13:'

Measured Direct Photon Cross Section
Compared with QCD Predictions by
Aurenche et a1. [A0888].

dire

GeV.

51de

and t

 

211

The group of Contogouris et al. [ARGBN] has also calculated a

direct photon cross section for proton-proton interactions at ./’§"- 63

(3491!. Using a leading-logarithm approximation, kT smearing and K factors

calculated in the soft-gluon approximation [ARGBH], they arrive at very
s 1milar results. Figure VI-ili shows Contogouris et al. [AR087J QCD
predictions for DO set I, DO set II and our experimental results for the
d irect photon cross section.

Our data points favor, in both cases, Duke and Owens set I

structure functions with a value of Afig S 200 Mev.

A different parametrization has been used by the BLO group
I: BAIB8]. They used the gluon distribution in the universal convention

E K 0078]:
x-G(x, o:— 2 0ev2) ~ (1 — x)n (VI-j)

and the QCD scaling prediction for the direct photon cross section of

d0

13 -6 [BER82]. Figure VI-15 shows pgoEI 71-5-3 vs xT for different QCD

T
predictions based in different values of n, and our experimental results
( also R108 and R806 results are shown). Our best estimate of n from this
comparison is 11 ~ 5 to 6.

As a by-product of our measurements, a meson invariant cross
Section was extracted. Figure VI-16 shows the "all" - meson + direct

photon cross section as function of pr. These values were compared with

measurements made with the back array only by an predecessor of our
experiment (experiment R108) [ANG78]. The values agree within a 151

('1 ifference .

 

(cmZCSGeV'Z)

Edo/d’p

212

 

 

 

 

 

: -— - D 0 set II 2 2
4” —-—-- D 0 set I Q = PT
10 E— D 0 set I (no brem.)
E -——n—- D 0 set I (Q2 = 4PT2)
10-32 :_
E §\
._ \>§\
10.33 E- \
5 \\
:3 \
_ \ .
-34 \ .
10 g- \ .
E ‘\ .
C \ °.
; \,'
10’35 5— \\ -.
E ‘\
: \\\.,
- \ '
\ \
10.36 E— \\<:
: \
: \\\.,
.— \\’\..
-37 .
10 E- \ \
E \\
-38 L 1 1 I I
‘0 2 4 6 6 10 12 14
PT (GeV/c)

Figure VI-ifl:

Measured Direct Photon Cross Section
Compared with QCD Predictions by
Contogouris et al. [ARG87].

10‘31cm20ev

p11: d3o/d3p

 

 

 

 

 

213

 

 

 

 

 

P
1

20"-

10'-

0 '1 . L l l l
0.1 0.2 0.3 0.4
x 1

Figure VI-15: 6 8°

pT-E 31—5 vs. xT, for Different QCD
Predictions and Experimental Results
for R806, R108 8110.

211-1

 

 

 

 

 

10 F
3 o
h 0 R110
-32 O
10 E.- 0 R108
3 6
" O
-33
A10 :-
1) 1
0) : 0
9 — .
0 -34
N 10 E- O
E 5 o
o — 0
v : 0
10.35 E- %0
no. :
'- O
13 I
E — °
0
'0 ‘0-36
L1J
10-37 E:—
-38 1 1 1 1 1
1° 2 4 6 8 10 12
PT (GeV/c)

Figure VI-16: "All" (Direct Photon + Neutral Mesons)
Invariant Cross Section vs. pT (C.M.)
for Experiment R108 and R110.

215

VI-6. Direct photon event correlations.

The relevant characteristic of a direct photon event is that it
is produced directly from a parton interaction of the constituents of
the beam particles. The structure of the direct photon event is not as
quantitatively calculable as the cross section. However there is
qualitative understanding as to how these events should look within the
framework of Quantum-Chromodynamics (QCD) [HAL80].

To isolate a relatively pure sample of direct photons is very
c1 ifficult. The selection of direct photons tends to bias the structure
of events in an unknown way and small backgrounds are able to
contaminate the results noticably in certain regions of phase space.

A direct method of observation is the most appropriate to
produce the best possible direct photon sample, since it will remove

most of the background, especially in the pT range where Y/all ratios

are much smaller than one. In our case we do not have a complete
Separation between the single and multiphotons samples but we do have a
model to determine their ratio in any data sample.

Our method of extracting a direct photon sample is again based

on the o distributions. We determine a o

t value (ocut) such that all

t

t less than °cut form the

the events in the data sample with values of a
Sample of "direct photons". The signal is determined by the single
photon component and the noise (neutral meson background) by the

ulultiphoton component. We can determine the best value of Ocut to

Obtain a reasonable signal-to-noise ratio and a reasonable number of

216

was chosen, the Monte Carlo 0

events. After a value of ocut t

distributions can be used to calculate the signal-to-noise ratio and to

estimate the background from multiphotons still present in the sample.

VI-7. Subtraction of the neutral meson background.

We are trying to measure a certain property. «9, of the direct

photons. Using the ocut value, we divide each sample in two. We denote
w ith the subscript 1, events with °t S o ut (direct photon candidates)

C

and 2 with 0t > acut (neutral meson candidates). However each sample is

a mix of direct photons and neutral mesons. We can assume that the
property 4; is given by a combination of the property for pure direct

photons, my, and for pure neutral mesons, om. Thus we assume that the
property (9 is not correlated with Ot’ and therefore is independent of

the cut. (1’ only depends on the proportion of pure direct photons and

pure neutral mesons. Therefore we can write:

4’1 ' “HWY + (1" wi)'¢mi

¢2 ' m2°¢Y + (1‘ wz)'¢mz (VI‘k)

Where m, is the probability of the event being a direct photon for the

Sample 1, and m2 for the sample 2. Since we assume the total sample is

217

composed only of direct photons and neutral mesons, the probability for

being a meson is (1- ml), for i-1,2.

Each of these probabilities can be written in the form:

m - P P 1, where PY is the probability of being a single photon and

1 111' YD 1

PYD is the probability of this single photon being a direct photon.
i

We now define the notation illustrated in figure VI-17. Let f be

a normalized 0t distribution and F be its integral over a restricted

region, thus, f fm and f represent the normalized o distributions

Y’ D t
for single photons, multiphotons and simulated data respectively. For
any value of at:
fD- CY-fY+ (1- CY)°fm (VI-l)

where CY is the fraction of single photons in the data sample extracted

by the likelihood fit explained in section V-10.

Therefore, integrating (VI-1) over region 1 and letting,

in- Jifx(°t)d°t; region 1 is O to Gout

region 2 is o to 0, and x- D, Y or m,

out
we obtain
FDi- CY°FY1+ (1- CY)-Fmi (VI-m)
The probability PY1 of being a single photon is then:
C -F
Y Yi _
PYi- -E;———- 121,2 (VI n)

 

218

AP.-4.5-5 GEV/C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0J4 L I 2
0'” P 5g A SINGLE—PHOTONS
0.1 _ \ H1
008-— + +4
0061- l l
004- ‘4
L 4 4‘
0.02 ‘ F“ F‘z “““‘
O. 1 1 1 1 “ILL4 mi:
0 4t 6 s 10 12 14
cu a,<cnv
0J4 — I 2
0.12 — I MULTI-PHOTONS
on —
one» ++++++
0.06 - fm ¢ ++
QO4-— * ‘
032— .t"" "I-
o “I 1 EM 1 1 1 1 'I1l-
0 2 4t 6 a 10 12 14
cu o,<cnv
042
I 2
OJ r
008)— a max
006- h 駧+++§é “HT
0.04 - Ltha‘é Q
F X
0021- ' fi> ”3 o
g 1 Ana:
0. '0 1 L 1 1 1 ‘M-J
0 2 4' 6 a 10 12 14
cu c.1cnv
Figure VI-17: Representation of the ocut for the

Extraction of a Direct Photon Sample
and Correction of the Neutral Meson

Background.

 

219

 

and the fraction of direct photons in the single photon sample, PYDi; is
given by:
Y
C - -——- -(1- C )
Y YY m Y

where we assume that this fraction remains constant for different 0 .

t,
Therefore:
FYi Y
m1 - Pvi'vai“‘F;: - [cY - 77"m'(" CY)] (VI-p)
gives the probabilities, from the simulated values of FY1 and Fmi where

F is given by F

01 ' CY.FYi+(1- CY)'Fm

Di 1'

Solving the system of two equations in (VI-k) we obtain:

¢Y ' 1 ) ° [(¢l-¢2) ‘ (w2¢1 ’ w1¢2)] (VI’Q)

(ml-mg

and

1

m "T;:;::y ' (w1¢2 ‘ w2¢1) (VI‘P)

¢

The errors can be calculated by propagation as:

(A¢Y)z . (3¢Y/3w1)2°(Aw1)2 + (3¢Y/3¢1)2°(A¢1)2 + (amY/3w2)2'(sz)2
+ (a¢Y/a¢,)2-(A¢,)2
(A1m12 - <a¢mxaw,)2-(Aw,)= + <a¢mxa¢,)=.<a¢,)2 + (3¢m/3w2)2°(sz)2

+ (Bow/3¢z)2°(A¢z)2 (VI-s)

 

220

Note that,

¢i'¢2

(0)1 - (02)

 

A¢ . ¢m- ¢Y - (VI-t)

If the starting distribution values do not show already an appreciable
difference between samples 1 and 2, or if the efficiency of the cut for

separating direct photons from mesons is low (10, a 012) , this method of

extracting the background is not applicable. We must start with
sufficient signal-to-noise to obtain meaningful results.

The determination of Ocut was done by studying the ratio signal-

to-noise as function of the cut (0c ). The ratio signal-to-noise is

ut
defined as the fraction of direct photons divided by the fraction of

neutral mesons in the direct photon sample defined by 0 In terms of

cut'

m the ratio can be written as:
l

(A)

signal-to-noise =-—T;:- (VI-u)
1

Figure VI-18 shows the signal-to-noise ratio as function of pT for

various values of the cut 0 For each pT, there is a maximum for a

cut'
100% efficient out where the signal-to-noise is given by the fraction of

direct photons in the sample. The minimum corresponds to 0 - 0 (no

cut

out). The ratio increases with pT as the data gets richer h1cnrect

photons. The highest signal-to-noise ratios were found using 0c - fl cm.

ut
The average signal-to-noise ratio for the total sample was 1.01, but the

ratio reaches 2 for pT values greater than 7 GeV/c.

F"

221

 

 

 

 

 

 

 

 

 

 

 

 

7
o 2<nacu1
0 6r- U4CMCUT max.
;:
‘< A 6<nACUT
m: 5 -
uJ
Z!
o 4—
Z.
1 a-
.J
‘7?
<2 2‘
U)
1—
0‘ 1o
pTGeV/c
Figure VI-18: Signal-to-Noise ratios vs. pT for
various values of ocut‘

2

1a b
o 1.61-
E 1
CD

L4 —

. C
O
. O
12 —
1 1 1 1 1 1 1 1

0 1 2 3 4 5 s 7 a
a,CLfl' ccnv

Figure VI-19: Values of e vs. ocut‘

222

 

Another variable was studied to determined the best possible

value of 0 The idea was to find 0 such that it maximizes the

cut? cut

difference between direct photons and mesons in the variable under
study. The variable chosen was the azimuthal distribution of associated
particles as defined in section VI-9. We defined the varible e, as the
sum of the differences between samples 1 and 2 for the first five bins
of the azimuthal distribution, |¢| S 36°, where a noticable difference
of the variable between samples 1 (photons) and 2 (mesons) is expected.
Using (VI-u), we define:
as $11" (1’21

9 - z (VI-v)
1-1 (w,- w,)-/710¢m1)2+(A¢Yi)=

 

as the error weighted difference. (semi) and (A¢Yi) are given by (VI-s).

Figure VI-19 shows the variable 0 for different values of the cut. Again

 

the most favorable situation occurs for ocut = 11 cm. Therefore, a value

of o - fl cm was chosen.
cut

 

VI-8. Estimation of other backgrounds.

While discussing the Front/All out we have already mentioned
that there are backgrounds other than neutral meson decays. We study
here the class of background produced by hadrons that can most influence

the associated particle distributions.

1‘]-

1011
e:
trig

35 e1

11551

B

223

Charged mesons, mostly n+ and n“, if they are superimposed on a
low energy neutral decay, can produce a spurious high energy
"electromagnetic" cluster in the calorimeter. We have a cut to remove
tn~iggers with charged particles pointing to the trigger cluster region,
as explained in section IV-7. In figure IV-8 we showed the distribution
of charged particle hits on the back glass face. There is a small
concentration of charged particles in the trigger region. As the drift
chambers are not perfectly efficient, we have to consider the
possibility of events passing this cut.

The B-veto cut should also rule out most of this class of events
since we cut on a B pulse height lower than the minimum ionizing
particle value. However, as seen in figure IV-8, this cut is inefficient
(especially in position determination). There is some charged hadron
contamination in the events.

Another charged particle which will contribute is the anti-
proton, 5, especially since it can annihilate in the glass giving E > p.

For the same reason the anti-neutron, H, is a good background candidate.
In addition, because it is neutral, it is not tracked by the drift

chambers. Other neutral hadrons produced in proton-proton collisions at

0

rates big enough to contribute to the background are neutrons (n) and KL
mesons.

A Monte Carlo was written to determine the acceptances for the

detection of n+, n , n, K°

L’ B and n. This simple Monte Carlo only

considered the most important analysis requirements: B-veto, Front/All

cut and charged particle cut. The trigger was simulated by an energy out

 

 

2211

after energy smearing. The hadron response of the calorimeter was
extracted from previous PS tests [BEA711] and the drift chamber track
efficiency was taken to be 90 % [NIC82].

The ratios of production for the hadrons with respect to neutral

mesons were extracted from the literature and assumed to have the same

+ ..
ph.dependence as the neutral mesons. (0 +1 )/(neutral mesons) - 2.0

[AKE8H], (rHK£)/(neutral mesons)- 0.55 [DRI82] and p/mesons ~ n/mesons

. p/mesons = 0.12 [AKE8H]. The resulting Mente Carlo acceptances were:

 

 

4.5-5 GeV/c 7-8 GeV/c
A(11++1r-)/Am 0.0211 0.037
A(n+K;)/Am 0.028 0.061
Afi/Am 0.050 0.123
Ar/A 0.031 0.108
p m

 

 

 

The Mbnte Carlo simulation showed that most of these backgrounds produce
‘very low Front/All ratios, with 96% below the Front/A11 cut of 0.1N. We
estimate the total hadron contamination to be less than S 1 of the

observed neutral meson background for the low pT bins, rising to 12$ for
the high pT bins. These backgrounds will be concentrated at low

Front/All and low at values. In the worst scenario, we could consider

all these background events present in the direct photon sample defined

by at < A cm.

 

 

225

VI-9. Charged particle distributions.

Hadrons on the same side as the direct photon, i.e., having an

azimuthal angle 0 relative to the trigger particle within i 90°,
originate mainly from bremsstrahlung processes. On the other hand, the

Compton and annihilation terms are characterized by isolated high-pT

photons. Figures 111-20 shows azimuthal distributions of associated
charged particles. The value of tin/NM is plotted versus 41, where 0 is
the azimuthal angle relative to the Y or meson trigger. N is the total

number of events in the ApT trigger interval considered and An the

number of charged particles. The first bin (0°-6°) has been omitted
since it corresponds to the region vetoed by the B counters cut. Events

were selected with 11.5 s pT trigger< 6.0 GeV/c for three different

requirements in the pT of the tracks plotted: 0.2 S pT track< 0.6,

0.6 S pT track< 1.0 and pT z 1.0 GeV/c. Requirements were imposed on the

tracking algorithm to reject poorly measured tracks (on the x’, number
of space points and extrapolated distance to the event vertex).

The large peak at 0 ~ 11 is from the recoiling Jet, while the

smaller peak at <11 :- 0° in the meson case is due to hadrons of the
Jet associated with the trigger. Clear two Jet structure is shown. The
same side for both enriched photon and meson samples looks much alike,
contrary to QCD predictions and other measurements [AKEBZ]. The signal-
to-noise ratio is approximately one (as discussed in section VI-7)
assuming only the neutral meson background. There are then reasons to

believe that the separation we obtain is not good enough to observe

 

226

 

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the effect predicted. However, for high pT triggers, and after the

subtraction of the neutral meson background by the method explained in
section VI-7, the direct photon sample started to show the trend
expected by QCD calculations. Figures VI-21 shows the azimuthal

distributions for events with pT trigger > 6 GeV/c with the neutral

meson background extracted and the same track requirements as in figure
VI-19. The direct photon sample shows a lack of charged associated
particles on the same side of the trigger if compared with neutral meson
sample. Unfortunately, we have insufficient statistics to make a more

detailed study in this pT range.

VI-10. Away Side Studies.

The away side associated particles, those having an azimuthal

angle 0 relative to the photon (or meson) that is larger than :1: 90°,
will present different characteristics for meson and direct photons. In
the case of the Compton process the recoiling Jet will be caused by the
fragmentation of a quark, whereas for the annihilation process it will
be a gluon.

In proton-proton collisions the ratio of u quarks to d quarks on
the away side will be approximately:

Nu-(Zuc)2 (‘/,)a

‘3' ”Ta?

0 Nd-(zda)2 ' 8 (VI-X)

 

 

229

This ratio 8-to-1 at the quark level will give a large ratio of
positive to negative hadrons in the away side. This is, however, not
totally correct since u quarks can give rise to negative hadrons and d
quarks to positive hadrons. One might hope to approach this ratio with
leading hadrons, which might remember the charge of the parent parton.

Figure VI-22 shows the ratio of positive-to-negative associated
hadrons in a 115° semicone centered at 180° of the trigger direction for
both direct photon and meson background corrected samples. The ratios

for the direct photon and neutral meson samples are shown versus zF,

where zF is defined as:

+ +
D ' P
z I track 2 trigger
l ptrigger

 

(VI-y)

In the same plot the QCD predictions for direct photons and

neutral mesons are shown [HALBO]. For high values of z where the

F!
predicted differences are greater, the measured uncertainties are higher

due to the rarity of fragmentation at high 21,, making it difficult to

reach a definite conclusion.

VI-11. Summary and Conclusions.

Data were taken at / s - 63 GeV from p-p collisions at the CERN
ISR, triggering on electromagnetic shower deposition in a lead glass
array calorimeter. A MWPC was used to discriminate between single- and

multi-photon triggers. Unfortunately, the characteristics of the MWPC

230

+/— RATIO

 

2.3 _ o NEUTRAL MESONS

o1maan'mflnons X

 

 

 

0.4 -

 

 

 

21"

Figure VI-22: Ratio of the Number of Positive to
Negative Charged Hadrons in the Away
Side vs. zF, for the Direct Photons
and the Neutral Mesons Samples. Also
QCD Predictions [HAL80] are shown.

231

were such that a direct count of single photon showers proved difficult.
A method was devised to discriminate between single and multiphoton
triggers based on the transverse shower shape study of the trigger
shower. The data were compared with simulated single and multiphoton
characteristics. In this way the fraction of single photons present in
the data sample was obtained. The simulation of the MWPC response
introduced one the most important cause of systematic uncertainties.

A Monte Carlo simulation of the single photon background was
used to correct the total fraction of single photons and obtain the
inclusive direct photon cross section. The measured direct photon cross
section agrees well with other ISR experiments, especially with
experiment R806 [ANA82]. The R108 measurements are somewhat lower than

ours, but the high pT R108 values follow the trend for high pT values.

We compared our photon cross section results with QCD perturbative
predictions of Aurenche et al. [AUR88] and Contogouris et al. [ARGB7].
Our best agreement comes using Duke & Owens [DUK8’4] set I of structure
functions and when bremsstrahlung is neglected (Due to our cleaning cuts
our cross section will be strongly biased towards non-bremsstrahlung
events).

We can put some constraints on the gluon structure function of

the nucleon and the value of the strong coupling constant Afig. Due

especially to our systematic errors we cannot rule out Duke 8: Owens set
II definitively. It can be said, though, that given a gluon structure

function of the form:

x-G(x,Q§) « (1 - x)" (VI-z)

232

we strongly favor a value of n between 5 and 6 (slightly softer than

Duke and Owens set I value) and a value of Afig S 200 MeV.

We also studied the associated particles of the direct photon
events. There are signs that the QCD predicted direct photon event
structure is present in the data. The azimuthal angle distribution of
associated particles, when comparing direct photons and meson triggers,
showed an excess of associated particles in the trigger hemisphere for

the neutral meson triggers with pT greater than 6 GeV/c.1hm1to the

method used to obtain the sample, this study did not show significant

differences for low pT triggers. The differences are more manifest at
rugn pT where the sample is richer in direct photons. The away Jet

charge ratio shows a statistically weak trend towards the QCD
predictions.

We conclude that the agreement between our data and UNBQCD
predictions, including second order calculations, were very good. Taking
our data in conJunction with all other measurements we can be confident
in using the QCD predictions to extrapolate direct photon properties for
future experiments in different energy regimes. There are already
various "third generation" experiments taking data that will test

further the prediction of more precise QCD calculations [FER86].

APPENDICES

APPENDIX A

Single Photon Background from Neutral Meson Decays

Many of the single photon triggers in our data are caused by
neutral meson decays to two or more photons where only one of the
photons succeeded in passing the requirements imposed by the geometrical
acceptance or the analysis cuts. Therefore, the single photon sample
extracted from our data is a mixture of direct photons and single
photons produced by neutral meson decays.

Neutral mesons decay very quickly to a combination of photons
and mesons of lower masses. The least massive neutral meson, the 11°

meson, decays to two photons with a branching ratio of almost 99% and

with a lifetime of only 0.87x10-16 seconds. It is by far the most

important cause of background in the pT range of this study. Neutral

Meson Branching Ratios were taken from the particle data tables [PDT86].
Production Ratios were taken from the literature [BUS76a,ALP75.KOU8O and

DIA80] and were assumed to be all independent of pr. After candidate

meson decays were selected they were allowed to decay through the
detector simulation Monte Carlo described in Appendix D to find out if,

in the conditions of our measurements, they produced a significant yield

233

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235

of single photon triggers. The contributions were calculated as a

function of pT of the triggering photon.

Table A-1 shows the neutral mesons chosen as contributions to
the background. The production rates are given in relation to the 11°

production. The last column gives the fraction of each neutral meson

production to the sum of all the six mesons considered. The K: decays to

two 11° with a rather long lifetime of 0.89x10”1O seconds; however for
the purpose of our analysis we have assumed that all the decays occur
instantaneously after being created in the proton-proton reaction, at
the vertex of the event.

To calculate the ratio of w°-mesons to all mesons we assume that
"all" includes all neutral mesons of table A-1, so that, adding column 7
of the table:

"all mesons" / n°-mesons-

1. + .209 + .165 + .12“ + .ONS + .08“ - 1.627

or:

n°~mesons/ all mesons - 0.615

This is the ratio of production introduced in section 10 of chapter V.

APPENDIX B

Neutral Meson Decay Kinematics

Two-body Decay_,

Let us consider the two-body decay M + A + B. Figure B-1
defines the kinematics of the decay in the neutral meson center of mass

and in the laboratory frames. If the neutral meson has zero spin (as 1°,
n° and K2) the angular distributions of the decay particles in the

center of mass frame are uniform in solid angle.
Let us take as an example the decay 1° + YY, the most important

background decay. The Lorentz transformations between the center of

mass (CM) frame (11° rest frame) and laboratory (LAB) frame of the four
momenta of the photons, as defined in figure B-1, are given by (ignoring

the Z coordinate which is unaffected by the boost):

 

 

 

 

1 O 0 (m/2)-sin 6 EY1 - sin 0,
0 E/m - p/m - (m/2)-cos 6 - EY1 - cos ¢1 for photon 1
o p/m E/m (m/2) | By,

 

 

236

 

:.
*E‘it‘e

237

 

 

 

 

 

Figure B—1 : Neutral Meson Two-body Decay

Kinematics.

 

 

 

 

Figure B-2 : Geometry of the Neutral Meson Two-body

 

Decay .

 

238

and

1 O O -(m/2)-sin e EY2 . sin 02

O E/m - p/m 0 -(m/2)-cos 6 = EY2 - cos 02 for photon 2
O p/m E/m (m/2) EY2

 

 

 

 

 

 

where m is the mass of the neutral meson, p and E the momentum and
energy in the LAB system; EY1 and BY2 are the energies of the photons in
the LAB frame and 0, and 02 the angles of the photon momenta respect to
the meson momentum in the LAB frame. 6 is the angle of the photon with
respect to the boost in the CM frame.

That produced the equations:

(m/2)-sin e - EYl-sin 0, (B-a)
(E/2)-cos e + p/2 . EY,°cos 0, (B-b)
(p/2)-cos B + E/2 = EY‘ (B-c)
-(m/2)-sin B = EYz-sin 02 (B-d)
-(E/2)-cos e - p/2 - Eyzocos 02 (B-e)

“(p/2)-cos 6 + E/2 a E (Brf)

Y2

Since mz- Ez- p2

+
' (EY1+ EY2)2 - (5Y1+ pY2)2

but:

there

01‘

where

PGIat

239

yl Y2+ 2EY1EYz’ p;l‘ p;2- 2|pY1lle2|°COS(¢)

but:
E§1- p§1 and E32 = 0;:
therefore:
112 - ZEY‘EY2(1 - 008(0))
or
m2 - Ll-Eyl-EYZ-sin2 (0/2) (B-g)

where 41 - 0, + 412 , the angle between both photons in the LAB frame.

Relation (B-g) can also be written as:

m2 = (E2 - pz-cos2 6)-sin2 (0/2) (B-h)

The asymmetry of the decay is defined as

 

By (B‘c) and (B-f), A - (p/E)-cos e , and for the extreme
relativistic case p - E, therefore A - cos 6.

In the case of zero spin particles (such as 1°'s and n's), cos 0
is equally probable (flat distribution) between -1 and 1, and therefore

the asymmetry distribution is also flat.

2110

Consider a neutral meson decay from a point V:(xo,yo,z°) at a

distance L from the plane P, with the direction of E (meson momentum)
forming an angle a with the plane. Figure B-2 describes the geometry and
the notation for the decay. We will calculate the general fxnnn for the
distance (D) between the two photon hits at the plane.

We can write:

 

 

 

 

_ LZ-sin ¢13 ‘ _ a L,-sin 0,
d2 sin (90 + a) d‘ D d2 sin (90 - 0)
therefore
1
D = d1 + (12 = cos a - ( Lz-sin p, + LI-sin 0, )
or using (B—a) and (B-d):
_ n1 . sin 6 . L2 L1 _
D 2 cos a ( EY2 + EY1 ) (B i)

From this relation we find that the minimum distance between
photons (DD/Be-O) occurs for 0 - 0° and e - 90°. But, for decays with

both photons hitting the plane, not all the values of 0 are allowed.
From (B-h) we see that Ez-pZ-cosze has to be 2 0, therefore values of
B < B are forbidden, where 6 is such that cos 6 - -g— . Thus the

L L L

only minimum is at 6 - 90°.

The distance between photons perpendicular to the direction of

the meson E is :

2N1

DT - 11 + 12 - L-( tan ¢1 - tan 0,)

using (B-a)/(B-b) and (B-d)/(B-e):

 

tan ¢,=(m-sin e)/(p-E-cos 0) ; tan 62a (m-sin e)/(p + E-cos 0)
therefore:

D - Lom-sin 6 ( 1 +2. 1 )

T p + E-cos 6 p - E-cos e

 

(B‘J)

. 2’L.m°81n 8 . p2 _ Ea. 0082 e

 

 

 

but D . - D
cos a T
therefore:
2oL-m-sin B p _
D cos a ( pf’~ EZ-cosf’6 ) (B k)

Considering small angles (L is large compared with D, 01 - 0°)

and the extreme relativistic case p a B, then :

2-m-L
D ' E-sin e (B 1)

and the minimum at 0 - 90° is :

D . —— (B-m)

242

Figure B-3 shows Dmin vs. E for the 11° + YY and 11° + YY decays

in the energy range study for this dissertation.

To find the analytic form for the distribution of D for given
values ofrn,l.and B, we calculate the probability, Prob(d<D), of d
being less than D.

dP dP

In the CM system m = a;

= 1/2, calling x - cos 6,

0 < x < 1,for the forward photons.

2-m-L

From (B-l), D (X) = E./ 1 _ x2

 

(B-n)

(relativistic 1°,i.e. E > 1 GeV).

Therefore:

 

 

Prob(d < 0) - I D d? - 00 - J g dp - dx ~00 . I X(D)—95—- dx

Dmin dD min dx dD xmin dx

Prob(d < 0) + J x<D> dx

min

 

from (B-n), x(D) - /’1 - (E-D/ 2-m-L)2
then:

r
Prob (d < 0) - J X(D)

 

dx - x(D) - /' 1 - (E-D/ 2-m-L)2
min

01"

 

Prob(d < 0) - «”1 — (0

min/ D )2 (B-o)

This is the distribution of D shown in figure B-H.

2H3

 

 

 

 

 

 

 

   

 

 

 

 

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100 —°
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9 o
q) 80 " O
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20 .0. “to 0000
.C. .1
..0...
OOCOOOOOIQO...........4
o 1 1 1 1 1 1 1
2 3 5 6 7 8 9 10
Energy GeV
Figure B-3 Dmin vs E for 1°+ YY and n°+ YY.
1. 1-
” :1. E = 5 GeV
II
I
03 - :,
1|
11
at” : 1
g, 0.6 r' / I '-1
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0 l
E 02 T 1
.0.-
O. I PL I I
O 10 20 30 4O 50
distance between photons <cm>
F1Sure B-N Distribution of the Distance Between

Photons for 5 GeV 1° and n° Decays.

 

 

2AA

Another important quantity is the energy distribution of each
photon in the LAB system, given by P(E): the probability of the photon

having the energy E.

dP(E) dP 1 dB __in_____
dE . _35_ dB , d0 dcos e-d¢ which is a constant as can be
d0

P
shown by differentiating equation (B-c). %Si is a constant for zero

dP(E)

dB is constant between zero

spin neutral mesons, therefore, f(E) -

and the max1mum energy of EY - Emeson'

Most of the two-body decays considered in this dissertation were
spinless mesons. However, the decay 01° + 1° Y , involves the spin one
w° meson. The distribution of the decay particles in the CM of m° frame

is given by (1 + cos2 6).

Three-body Kinematics.

 

The Dalitz plot [HAG6AJ is the most appropriate way to represent
three-body decays as 11° -> 1°11°11° and 11' + n°11°11°. The Dalitz plot is
shown in figure B-5.

We assumed that these decays were Just controlled by the
available phase space. Therefore the only constraints in the decay were

given by the conservation of energy and momentum:

e,+e2+e,-Q-M-(m,+m2+m,)

2U5

   
  
 

nonrelatiuistic
Inn“

ultrnrelutiuistic
Inn“

 

Figure B-S : Dalitz Plot and Kinematics of Three

Body Neutral Meson Decays.

2N6

p1 + 92 + pa 3 0 (B’P)

where 51 are the kinetic energies and 51 the momenta of the particles.

The last equation implies that the three decaying particles lie
in a plane. The decay is determined by 5 parameters, chosen to be two
kinetic energies and the Euler angles of one of the momenta in the
parent frame.

Because of their vectorial nature, the momenta have to obey the

 

relation:
2 2 2
P1 - p2 ' ps 5 1
Zopaepz

which gives the boundary curve of the allowed region of the Dalitz
plane.
In the polar coordinates of the Dalitz representation the

kinetic energies are given by:

e, --%%—- ( 1 + p- cos ¢,) 0, - 0 - (21/3) (B-q)
a, -—‘3’—- < 1 + 11- cos 4),) <1. = 11 — (211/3) (B-r)
e, --%%—- ( 1 + 0- cos p) (B-s)

The decay in the Dalitz plane is totally determined by the two

coordinates O S p S 1 and 0 S e S 21 .

Then:
pf - 2-m-el + e}
pf I 2°IH°€2 + a; (B—t)

13% ' 2°m°ea + 63

2N?

and in the plane of the decay (see Figure B-N) the momenta of the three
particles are then:
( p1. 0. 0 )1 (pg. 02(1 - 008212). 0); (p.008 1.. -pasin¢.. 0)

where:

2 .. 2 _. 2 ... _ ,
003 ‘Pa _ p2 2.311224%): F1 003 ¢2 _ PL Pspz 003 P3

(B-u)

Given the Euler angles a, B, and Y of E, the decay is totally

defined.

Appendix C

Shower Simulations (EGS Monte Carlo)

 

As part of the data analysis we needed to know the
characteristics of single photons in the energy range from 0.5 to 10 GeV
in our detector. We had a sample of well identified photons from n°
decays (Appendix E) in the range from 0.5 to A GeV.

To simulate the electromagnetic cascades (showers) produced by a
single photon in our detector, we used the standard code developed by
Nelson et al. [NEL85] at SLAC called EGS (Electron-Gamma Shower). Using
its IV version (EGSA).

The EGSA code is explained in the SLAC report 265. It is a
"general purpose package for the Monte Carlo simulation of the coupled
transport of electrons and photons in an arbitrary geometry for
particles with energies above a few keV up to several TeV". I will
explain here only the special characteristics of our EGSA running, our
geometry and materials; refering to the SLAC report for the description
of the EGS simulation itself.

‘We were particularly interested in transverse shower shapes as

observed in the strip chambers. The chambers were sensitive to very low

2N8

2H9

energy 6 rays. Therefore, our simulation gave great attention to the
production and transport of charged particles of low energy.

EGSA allowed energy cut-offs as low as 10 KeV correcting some
errors in the former EGS3 code low energy interactions, and introducing
Rayleigh scattering. EGSA also allowed us to include Landau fluctuations
in the active region of the strip chamber, as well as the ability to
change the low energy electron transport algorithm (see PRESTA below).

Landau fluctuations were added simply by replacing the energy
fluctuations macro with a call to a subroutine, for energy deposition in
the active region of the strip chamber. In this subroutine the energy
deposited was fluctuated according to a Landau distribution. Even for
electrons with kinetic energy as low as 30 KeV the thickness of the
strip chambers still made the Landau distribution the correct one. If
the resulting fluctuated energy was greater than the charged particle
cut-off of 30 KeV, a new attempt to fluctuate the energy was made, since
then, EGSA would simulate new depositions.

Since it was the shower shapes that interested us, the path of
charged particles was of great importance. With these low cut-off
energies, EGSA did not do a good Job of transporting charged particles.
To improve it we added the Parameter Reduced Electron-Step Transport
Algorithm (PRESTA) [BIE87]. This replaced the Fermi-Eyges multiple
scattering theory which EGSA used (and which worked well at energy out-
offs above 140 MeV), with the Moliere scattering theory which allowed the
use of large step sizes. Using PRESTA, there was no longer a noticeable
dependence on the electron step-size. PRESTA also included a lateral
correlation algorithm to account for large steps (in EGSA the step-size

is restricted such that these corrections are negligible). Finally, a

 

250

new boundary crossing algorithm was emplyed. This requires a particle to
cross a boundary if its actual path did so even if the starting and
ending points of the step were on the same side of the boundary.

The detector geometry was simulated from outside of the B
counters through the end of the back glass, since only photons that had
not showered before the front glass array were of interest. All
materials were considered to be of finite extent in X and infinite
extent in Y and Z.

The regions considered in the simulation are indicated in figure
C-J . All regions are formed of isotropic and homogeneous materials. In
the simulation of the strip chamber we decided not to include the Kapton
or Mylar, since they only contributed 0.2 $ of the total strip chamber
radiation length, which we believe is of the order of the uncertainty of
the thickness of the Epoxy layer. In addition we did not include the
anode wires, support wires or spacers in the active region of the strip
chamber nor did we use Styrofoam. Instead we replaced that material with
.Argon gas, since the open cell of the Styrofoam made that region mostly'
Argon. The 70-30 Argon-Ethane mixture was simulated by pure Argon.

The materials are defined as follows:

Air: 78% of Nitrogen gas and 21% of Oxygen gas by volume
at 1 atm and density of 1.2940”3 g/cc
Iron: Elemental Iron standard density, 7.86 g/cc, [CRC7A]

Lead Glass: Relative amount of atoms by weight of 51.1 Pb,
25.97 0, 18.2 Si, 3.23 K, and 1.33 Na at a density
of H.08 g/cc

Argon: Elemental gas [CRC7A] at 1 atm density of

251

M

Detector Geometry

 

 

 

 

 

 

Cu (QMS ) o
Eco-11 (0. 2 1
+ 110111 91.00 01119 chlmlm back gm:
load glass 1
Y 110.01 1
Incident 2
9”“ 1nd class
—D —> M (40.0)
(2.)
I11
(75’ ll!
(9 n (3.2)

 

 

 

 

 

 

 

 

 

sl dmenslons In until-1101010.

Argon gas

8 ‘5
°’ 5
8 e
9 3
< <

->

Coppo: .
35 pm "
Copper
35 pm

Figure C-1 : EGSA Detector Geometry.

252

1.78-10'.3 g/cc.

Epoxy: A compound of C39-H52-011 and a density of
1.11 g/cc.
1Copper: Elemental Copper, standard density, 8.93 g/cc, [CRC7N].

Aluminum: Elemental Aluminum, standard density, 2.70 g/cc, [CRC711].

The incident photon started in the front face of the iron, in
front of the front glass, in the positive direction of X at an angle
with the normal to the surface randomly chosen according to a fit of a

d i stribution of incident angles measured from the single gammas of the

11° trigger data. The fit gives: (20-arccos [1- 2-randomnumberJ/3). The
angle 41 is chosen randomly between 0 and 211. The initial Y and Z
coordinate was randomly chosen in the range -O.5 to 0.5 cm to avoid any
systematic bin edge effects in the histograms (the histograms were
binned in one cm. bins).

Particles were transported through the 19 regions defined in
£1 Sure C-1. Any shower particle exiting the rear of the back glass had
all of its energy deposited in the air behind it. The importance of
considering the materials after the strip chamber for the shower shapes
in the chamber was shown to be relevant due to an important albedo
efis‘sact. Especially, low energy photons produced in the back glass or
the iron between glasses and emitted backwards could initiate showers
8‘31 ll detectable in the strip chamber.

Particles were transported until the particle total energy fell

below a cut-off. For photons that cut-off was set at 500 keV and for

 

i.)

253

Qharged particles it was 5111 keV (30 keV of kinetic energy). These cut-

011.3 are rather arbitrary and were fixed after some trials with

(1
it‘ferent values, choosing the one than best fit the 11° trigger data

MO ton 0t distributions at 2 GeV.

Any particle produced with an energy below the cut-off was
ap proximated by a local energy loss at the beginning of the step. In the
act, ive region of the strip chamber, however, this energy was distributed

uniformly in millimeter increments along the straight line path of the
particle.

For the lead glass regions, where the energy deposited is
measured by the Cerenkov light produced, only charged particles up to

the Eerenkov cut-off value (index of refraction = 1.67) of 127 keV
( kinetic energy) were considered in calculating the amount of energy
measured by the lead glass.

A photon's shower can be fully contained in the front glass or
it may not begin showering before passing through the strip chamber.
The se effects are important in determining if low energy photons of
neu tral meson decays will be detected in the strip chamber and back
81a «53. Special EGS runs were done at energies as low as 0.25 GeV with a
photon total energy cut-off of 30 keV (allowing photons leaving the
front glass to create charged particles in the strip chamber). This
prob ability for photons to produce no signal in the strip chamber was
mea sured as a function of incident photon energy. Table C-1 gives the
mumtber of events for each of the incident energies.

The normalization of energy deposited in the Argon gas to strip

chamber pulse height was done at 2 GeV. In order to minimize any

2511

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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58

255

differences between the EGS simulated events and the sample of single

photons from resolved n°'s, the 2 GeV EGS events were run with incident
energies distributed in the same way as in the single photon sample. In
runs at other energies, all incident photons had the same energy.

The most important information extracted from the EGS simulation
entered directly in the analysis in the form of the transverse shape of
the energy deposited for the shower traversing the strip chamber.
Histograms were made to look at the transverse profile of three
quantities, the number of particles (separated into charged particles,
all particles and particles moving in the positive and negative X
direction), the distance traveled in crossing the strip chamber and the
energy deposited in the strip chamber. These last energy weighted
position diagrams, taken in bins of 1 cm were used as a model for the
response of the chambers. In addition the energies measured in the front
and back glass were used to calculate the ratio front/(front+back), and
the energy deposited in the iron plates between glass arrays was used to
correct the energy measured in the glass. All this information was store

for each individual event.
No effort was made to simulate the Eerenkov light propagation

and collection in the fierenkov counters so the agreement between data
and simulation in the ratio Front/All must be seen as approximate (see

section V-9).

Appendix D

Neutral Meson Decay Monte Carlo

 

A multi-purpose simulation for the decay of neutral mesons
through the detector was written to assist in the data analysis. Three
main outputs were extracted from this simulation. After trigger and cut
simulations were applied, positions at which photons struck the strip
chambers and their measured energy were calculated. With this
information and the pulse height distributions from EGS, it was possible

to calculate 0t for each multi-photon event. Secondly, the number of

single photons produced by neutral meson decay was extracted as flue

ratio of single to multi-photons in each pT bin. Finally, the total

acceptance of the detector for neutral mesons was extracted by comparing
input and output in the simulation.

All the neutral mesons mentioned in Appendix A wereznui
independently and, later, their results were combined. To combine the
results the rates and initial conditions had to be considered for each
case to calculate the total number of events to run. Then the events

accepted were simply added linearly.

256

257

For each event a single neutral meson was generated in the
center of mass of the ISR. The angle ¢ was chosen randomly in the
interval Ao - t 0.6 rad and the rapidity y was also chosen randomly in
the range Ay - :1: 0.8. The transverse momentum was chosen randomly but

according to the total neutral meson cross section published by the

experiment R108 [ANG78]. The absolute rate was scaled from the 11° rate
(Appendix A) by the branching ratio and cross section. The vertex of the
event was taken from a flat probability distribution within a diamond
form in the plane X-Z (long axis: 85 cm, short axis: 11 cm) and Y was
taken . 0. This defined the parent four momentum in the CM-ISR frame.
All decay photons were first defined in the rest frame of their
parents. Then, transformed to obtain the photon four momenta in the
laboratory frame. The kinematics of the decays were discussed in

appendix B. For example, in the case of the decay Kg -> 1r°1r° + YYYY ,

each of the photons four—momenta satisfies the following matrix

relation:

3 B 0R .8 0R OB Q MOQ
W 11'

K K ISR. with M - Bfl°R"-B 0R -B

CM-p LAB- LAB K K ISR

where B are Lorentz boosts, R are li--dimensional rotations and Q d

LAB 3“

QCM-p are the u-momenta of the photons in the LAB and parent CM

respectively. The four-momentum of the photon in the laboratory is found
by inverting the matrix M,

-1
Q ' M °QCM-p

The positions of photons at the back glass and strip chambers

were calculated from their LAB four-momenta. The first cut requires that

at least one photon position lies inside the geometric acceptance of the
back glass.

A simple clustering algorithm was applied to all the photons in
the back glass. Photons were said to belong to the same cluster if their
distances in Y and Z were less than 30 cm, the value extracted by
considering 1r° and n° merging in the n° trigger data. The only unit of
analysis became now the cluster, formed by single or multi-photons. The
“momenta of the clusters were calculated adding the "momenta of all
contributing photons. Clusters with energies below 0.15 GeV were
rejected. Then the energy deposited was smeared using the resolution

relation measured at the PS [ANG82]:

Esmeared' {1+ 0.05-R1}-{E+ Rz-(o.oouoE+ o.u3-/ E H. where R1 and R2 are

two random numbers between 0 and 1. As a consequence, positions of
multiphoton clusters were also smeared since they were derived from the
energy measurements.

The trigger simulation accepted the event if at least one
smeared cluster energy was more than 3.11 GeV for the inside or 11.5 GeV
for the outside.

The same series of cuts applied in the data analysis were then
applied, in the same order, as discussed below. Table D-1 shows the list
of cuts and their respective acceptances. Since we did not simulate
associated particles, cuts relating to these particles were not applied.

When more than one cluster was found in the back glass the
position of the second cluster was required to be outside a square of t
20 cm around the triggering cluster. If still there were two clusters,

the most energetic one only was considered. Only clusters with their

 

259

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260

front glass positions inside a fiducial region 13 cm from the border of
the front glass were accepted. A simulation of the B veto cut was then
applied (as discussed in section V-6).

The next cut simulations used input from the EGS runs. A random
number was compared with the probability (computed in EGS) that a photon
shower of this energy produced nothing observable in the Strip Chamber.
The Front/All cut of .1“ applied to the data was applied to the
Front/All calculated for each event (see section V-9).

The algorithm for clustering pulse height information in the
strip chambers was applied, included some pulse height cuts that could
reject events (called "00 events" : no-Y, no-Z clusters).

Events passing all these cuts were then taken as observed. These

events were used to calculateeem (neutral meson acceptance). Y/YYlm

(ratio of single to multiphotons produced by neutral meson decays) and

were used to fill the 0t plots.

Appendix E

The n° Trigger Data

The only source of well-identified single photon candidates in
the detectors were decays of n° + YY and n° + YY . For a good
identification a mass determination is indispensible. Therefore the
photons have to be separated in the back glass in order to get both
energy measurements.

We had two separate periods of n° trigger running, both with the
same geometry as the normal direct photon trigger; in Spring 1983 and in
December 1983. From the Spring '83 run we had an integrated luminosity

of L - 9.9x1036 cm.2 for the outside and L - 9.2x1036 cm"2 for the

inside trigger. Two condensed tapes (CON) were produced: one only with
inside events and another with only outside events. The number of events
was 26536 inside and l#5636 outside. Only one third of these events had
vertices and most events had only one good cluster.

The main features of the Spring'83 analysis are the following:
the hardware trigger consisted of "glass singles" events where either
Side could trigger. B counters in veto were used.

The symbolic expression for the trigger is:

261

262
(AZ1)-{GI(3.O GeV)°(Bu-Bs-B6-B7-BB-89P’GOB.5 GeV)-(816-817-818-819-820

4321)}

I and GO to

where A refers to the A counters, B to the B counters and G
the back glass arrays (inside and outside).

The DST filter accepted events with one or more good clusters.
The good cluster selection included: energy of cluster 2 0.12 GeV ;
events inside the front glass acceptance: total front glass energy
greater or equal to 0.02 GeV, and a B veto passed. Events with two or
more good clusters were accepted without further energy cuts. One-
cluster events were accepted only if their energy were greater or equal
to 3 GeV inside or 3.5 GeV outside. No additional filtering was done in
the CON tape stage.

The December'83 data was taken with the inside retracted
geometry at the same time as the normal direct photon trigger was being
taken. No outside n° data was taken at this time. A double glass trigger
hardware configuration was utilized that required two cluster triggers
having a summed energy 2 3.5 GeV. The DST filtering of these n° data
required two clusters passing a B veto test with energies summing to 3
GeV . Direct photon triggers passing these requirements were also kept.
No front glass energy cut was made for the Dec '83 n° data and no
additional cuts were applied in making the CON tape. This CON tape
contains 730R events.

The mass spectra were calculated from samples of events with two

good back glass clusters. These events passed a vertex test and a NaI-

trigger test similar to the ones used in the direct photon analysis. In

number of events

number of events

263

 

160
140 -
120 -
100 -

80-

s. - +++

6
I

20-+

0L0: l

O. 0.2

 

+++++++

H
++++++ +++
++““¢+“¢.‘

 

moss GeV/c2

Figure E-1 : n° Mass Spectrum.

70

 

50*-

10-

 

1 l'g.g5.gg.5....5....

 

 

Figure E-2 :

3 4 5 6 7 8

Em GeV

Energy Spectrum of Single Photons

from n° Decays.

2614

addition events with a number of back glass clusters less than two were
rejected. Events with front glass cluster "only" and with excessive
"unclustered" energy were also rejected. From events with exactly two
clusters a mass was calculated. The mass spectrum is shown in figure E-
1.

The best n° candidates were extracted from the mass band .H8 5 m

S .62 GeV/c2. An energy out in the second energy cluster of the event
(0.5 GeV for the inside, and 0.75 GeV for the outside) was also
required.

Every n° event gave, then, two single photons. The single photon
energy spectrum is shown in figure E-2. The glass and strip chamber
information of these photons were stored in two "banks" (one from the
outside and one from the inside) and each photon was indexed by its

energy.

LIST OF REFERENCES

[AKE82]

[AKE83]

[AKEBuJ

[AKE85]

[AKE86]

[AK077]

[ALP75]

[ALT77]

[AMA78]

[ANA82]

[ANG78]

[ANGBO]

[ANG81]

[AN682]

LIST OF REFERENCES

 

Akesson, T. et al.; Phys. Lett. 1188(1982)178.
Akesson, T. et al.; Phys. Lett. 123B(1983)367.
Akesson, T. et al.; Nucl. Phys. 8246(1984)u08.
Akesson, T. et al.; Phys. Lett. 158B(1985)282.
Akesson, T. et al.; Z. Phys. C32(1986)491.
Akopdjanov, G.A. et al.; N.I.M. 1u0(1977)uu1.
Alper, B. et al.: Nucl. Phys. B87(1975)19.
Altarelli, G. and Parisi G.; Nucl. Phys. B126(1977)298.
Amaldi, E. et al.; Phys. Lett. 77B(1978)2u0.
Anassontzis, E. et al.; 2. Phys. C13(1982)277.
Angelis, A.L.S. et al.; Phys. Lett. B79(1978)505.
Angelis, A.L.S. et al.; Phys. Lett. 9uB(1980)106.
Angelis, A.L.S. et al.; Phys. Lett. 98B(1981)115.

Angelis, A.L.S.; Oxford University, D. Phil. Thesis,
1982.

265

[ANGBNa]

[Anosub]

[APP86]

[ARGBuJ

[AR087]

[Auaau]

[AUR85]

[AUR86]

[AUR87J

[AUR88]

[BADB6]

[BAIB6]

[BALBO]

[BEA7N]

[BEN83]

[BER82]

[BER87]

266

Angelis, A.L.S. et al.; Phys. Lett. 141B(198N)1NO.

Angelis, A.L.S. et al.; Phys. Lett. 1u731(198u)u72.

Appel, J.A. et al.; Phys. Lett. 176B(1986)239.

Argyres, E. N. et al.; Phys. Rev. D29(1984)2527.

Argyres, E. N. et al.; Phys. Rev. D35(1987)158H.

Aurenche, P. et al.; Phy. Lett. 1HOB(1984)87.

Aurenche, P. et al.; 2. Phys. C29(1985)N23.

Aurenche, P. et al.; Phys. Lett. 169B(1986)Nfl1.

Aurenche, P. et al.: Nucl. Phys. 8286(1987)509.

Aurenche, P. et al.; Nucl. Phys. 8297(1988)661.

Badier, J. et al.; Z. Phys. C31(1986)3u1.

Baier, R.: in The Quark Structure of Matter, pp.113, ed.
JacobrWinter, World Scientific Publishing, Co., (1986).

 

Baltrusaitis, R.M. et al.; Phys. Rev. Lett. flu(1980)122.
Beale, J.S., et al.; N.I.M., 117 (197”)501.

Benary, O. et al.; Z. Phys. C16(1983)211.

Berger, E. L.; Phys. Rev. D26(1982)105.

Bernasconi, A., et al.: Preliminary Results on

Inclusive Cross Section in pp collision at J3-2u.3 GeV

[BIE87]

[BLA88]

[BON87]

[BRE77]

[BRO75]

[suaeo]

[Bus73]

[BUS76a]

[BUS76b]

[CAM78]

[CHA7o]

[CHA78]

267
from UA6 Experiment, Presented by M.-T. Tran, Proceeding
of the Institute of the Europhysical Conference on High-
Energy Physics. Uppsala, (1987).
Bielajew, A.F. and Rogers, D.W.O.; N.I.M. B18(1987)165.
Blair, R.; CDF Direct Photon Analysis. Talk given at the
7th Topical Workshop on Proton~Antiproton Collider
Physics, Fermilab (1988).
Bonesini, M. et al.; Production of High Transverse
Momentum Prompt Photons and Neutral Pions.in Proton-
Proton Interactions at 280 GeV/c, preprint CERN-EP/87-
185.
Breskin, A. et al.; N.I.M. 1H3(1977)29.
Brodsky, S.J. and Farrar G.R.; Phy. Rev. D11(1975)1309.
Buras,A.; Asymptotic Freedom in Deep Inelastic Processes
in the Leading Order and Beyond. Rev.of Mod.Phys.
52(1980)199.
Busser, F.W. et al.; Phys. Lett. BN6(1973)N71.
Busser, F.W. et al.; Nucl. Phys. B106(1976)1.
Busser, F.W. et al.; Nucl. Phys. B113(1976)189.
Camilleri, L. et al.; A System of Cylinderical Drift
Chambers in a Superconducting Solenoid. N.I.M. 156
(1978)275.

Charpak, G. et al.; N.I.M. 80(1970)13.

Charpak, G. et al.; N.I.M. 1fl8(1978)fl71.

[CON81]

[CON86a]

[CON86b]

[CON87]

[COX82]

[CRc7u]

[DAR76]

[DEM87]

[DIA80]

[01087]

[DIM78]

[Doueu]

[DRE70]

268
Contogouris, A.P.S. et al.; Nucl. Phys. B179 (1981) H61.

Contogouris, A.P.S.: Optimal, Complicated and Unnatural

Scales in Large -P Physics. McGill University Report,

T
(1986).

Contogouris, A.P.S. and Tanaka, H.; Phys. Rev. D33
(1986) 1265.

Contogouris, A.P.S. et al.; Phys. Rev. D35(1987)1590.
Cox, B. et al.: Fermilab Report. 82/75-76-Exp.

CRC Handbook of Chemistry and Physics, R.C Weast ed.

55th edition, CRC Press (197“).

 

Darriulat, P. et al.; Nucl. Phy. B110(1976)365.

DeMarzo, C. et al.; Phys. Rev. D36(1987)8.

Diakonou, M. et al.; Phys. Lett. 89B(1980)H32.
DiCiaccio, A. et al.; Jets,Direct-photons, W & Z
production vs QCD in UA1. Proceedings of the Int.
Europhysical Conference on High-Energy Physics, Uppsala,
(1987).

Dimcovski, 2. et al.; Use of a Cathode Read-out
Multiwire Proportional Chamber for’Separation of
Electromagnetic and Hadronic Showers,

N.I.M. 156(1978)123.

Douiri, A.; Annecy Report LAPP-TH-1OO (198M).

Drell, S.D. and Yan, T-M.; Phy. Rev. Lett. 25(1970)316.

[DRIBZ]

[Duxau]

[DUK85]

[008u]

[EAD82]

[ERS82]

[E8075]

[FAR76]

[Fanau]

[FER86]

[GAT79J

[HAG6u]

[HAL80]

[HUB77]

269
Drijard, D. et al.: Z. Phys. C12(1982)217.
Duke, D.W. and Owens, J.F.; Phys. Rev. D30(198H)N9.

Duke, D.W. and Roberts, R.G.; Determinations of the QCD
Strong Coupling as and the scale AQCD’ Physics Reports,

120(1985)275.

DO Design Report, The DO Experiment at the Fermilab
Antiproton-Proton Collider (198a).

Eadie, W.T. et al.: Statistical Methods in Experimental
d

 

Physics, North-Holland, 2" reprint (1982).
Erskine, G.A.; N.I.M. 198(1982)325.

Escobar, C.O.: Nucl. Phys. B98(1975)173.

Farrar, G.R. and Frautschi S.C.; Phys. Rev. Letts. 36
(1976)1o:7.

Ferbel, T. and Molson, W.R.; Direct Photon Production in
High-Energy Collisions, Rev. of Mod. Phys. 56(198fl)181.

Ferbel, T.; Acta Phys. Polonica, B17(1986)435.
Gatti, E. et al.: N.I.M. 163(1979)83.

Hagedorn, R.; Relativistic Kinematics, W.A. Benjamin,
InCQ, 196".

Halzen, F. et al.: Phys. Rev. D22(1980)1617.

Hubner, K.; ISR Performance for Pedestrians, CERN 77-15
(1977).

[HUM83]

[HUM88]

[JAC75]

[JAC80]

[JAM87]

[JOH75]

[KOUBO]

[LEA82]

[LIN82]

[MAT8u]

[MCL83]

[MOR77a]

[MOR77b]

270
Humphries, 8.; R110 internal memo # 105 (1983).

Humphries, 8.; Michigan State University, Ph.D Thesis,

in progress.

Jackson, J.D.; Classical Electrodynamics, 2nd edition,
John Wiley & Sons, (1975).

 

Jacob, M.; Jet Phenomena. Techniques and Concepts of

 

High-Energy Physics, ed. T. Ferbel, Plenum Press,
(1980).

James, F. and Ross, M.; CERN Computer Center Program
Library (GENLIB), long write-up D506, revised (1987).

Johnson, R.A.: University of California, Berkeley,
Ph.D. Thesis (1975).

Kourkoumelis, C. et al.; CERN preprint EP/80-160.

Leader, E. and Predazzi, E.; An Introduction to Gauge

 

Theories and the 'New Physics'. Cambridge University

 

Press, (1982).

Linnemann, J.T.; R110 internal memo # 89 (1982).

Mathieson, E. et al.; N.I.M. 227(198H)277.

McLaughlin, M. et al.; Phys. Rev. Lett. 51(1983)971.

Morpurgo, M.; N.I.M. 17(1977)89.

Morpurgo, M. and Pozzo, 0.; N.I.M. 17(1977)87.

[NEL85]

[NIC82]

[OWE87]
[PDT86]
[PIU82]
[POR79]

[QUI83]

[REY81]

[RUT11]

[SA877]

[SAX85]

[SIV76]

[STE81]

271

Nelson, W.R., Hirayama, H. and Rogers, W.O.; The EGSA
Code System, SLAC-Project-265, (1985).

Nickerson, R.B.; Oxford University, D.1%u1. Thesis,
(1982).

Owens, J.F.; Rev. Mod. Physics 59(1987)H65.

Particle Data Group; Phys. Lett. 1708(1986).

Piuz, F. el al.; N.I.M. 196(1982)US1.

Pordes, S. H.; CCOR internal memo #387 (1979).

 

Quigg,C.; Gauge Theories of Strong; Weak and
Electromagnetic Interactions. Benjamin-Cummings, (1983).

 

Reya,E.; Perturbative Quantum Chromodynamics. Physics
Reports 69(1981)195.

Rutherford, E.; Phil. Mag. 21(1911)669.
Sauli, F.; Principles of Operation of Multiwire

Proportional and Drift Chambers. CERN Report 77-09
(1977): also in Experimental Techniques in High Energy_

 

Physics, ed. T. Ferbel, Addison‘Wesley Publishing Co.,
(1987).

Saxon, D.H.; Jet Fragmentation. Proceedings of the
International Europhysics Conference on High-Energy
Physics, Bari, (1985).

Sivers, D.S.J. et al.; Phys. Rep. 23C(1976)1.

Stevenson, P.M.; Phys. Rev. D23(1981)2916.

[TRE85]

[VAN86]

[VAN68]

[YEL81]

[YND83]

272
Treille, D.; Hard Scattering of Hadrons and Photons.
Proceedings of the International Europhysics Conference
on High-Energy Physics, Bari, (1985).
Van der Graaf, H. et al.; N.I.M. A252(1986)311.
Van der Meer, 3.; Calibration of the Effective Beam
Height in the ISR, CERN Divisional Report, ISR-PO/68-31,
(1968).

Yelton, J.M.; Oxford University, D. Phil. Thesis,(1981).

Yndurain,F.J.; Quantum Chromodynamics., Springer-Verlag,
(1983).