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LARGE TRANSVERSE WENTUM
DIREIZT PHOTON, w° AND n
PRODUCTION WITH A CARBON TARGET

presented by

Stephen R. W. Cooper

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LARGE TRANSVERSE MOMENTUM
DIRECT PHOTON, n° AND n
PRODUCTION WITH A CARBON TARGET

BY

Stephen R. W; Cooper

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

1985

ABSTRACT
LARGE TRANSVERSE MOMENTUM

DIRECT PHOTON, u° AND n
PRODUCTION WITH A CARBON TARGET

BY

Stephen R. W. Cooper

Measurements Of direct photonnro and n inclusive production cross
sections have been made in a 200 GeV/c positive beam at FNAL. Data are
presented for incident P and n+ beams with a carbon target in the pT
range 2.05 to 5.00 GeV/c and the CM rapidity interval of -0.8 to 0.2.
A liquid argon total absorption calorimeter was utilized as a photon

detector.

The observation of a small but significant yield of direct photons

is compatible with the predictions Of Quantum Chromodynamics.

Dedicated to RObert Keith Cooper

who said I could.

ii

ACKNOWLEDGMENTS

I would like to thank the E629 collaboration for a successful
experiment. The scientific collaborators were: Joe Biel, Alan
Jonckheere, and Charles Nelson from Fermilab, Jim Povlis, Ken Heller,
Marvin Marshak, Earl Peterson, Keith Ruddick, and Michael Shupe, from
the University of Minnesota, Barry Brown, Dave Garelick, George Glass,
Michael Glaubman, S.R. Han, sahadat Hossain, and Ed Pothier, from
Northeastern University, Clark Chandlee, Selcuk Cihangir, Tom Ferbel,
Joey Huston, Joe Lebritton, Fred LObkowicz, and Paul Slattery, from the
University of Rodhester, Carl Bromberg, Ray Lewis, and Gerry Smith,
from Michigan State University. This research was supported in part by

the National Science Foundation.

I would like to thank my advisor Professor Carl Bromberg for his

sound teaching, enduring patience and wise advice.

I thank my wife Bonnie for staying with me and keeping my children

well and happy throughout the years of my study.

I thank my father Dr. Willard G. Warrington for his help and good
advice and my mother Janet Warrington for her love, inspiration and for

her help in preparing figures for this document.

iii

1TB.

Finally I thank the Father, the Son and Holy Spirit for being with

iv

TABLE OF CONTENTS

LIST OF FIGURES

LIST OF TABLES

Introduction
1.1- A Brief Parton Model Review
1.2- Quantum-Chromodynamics, a Brief Review

1.3

High Pf Phenomenology

1.4- Direct Photon Production

Experimental Apparatus
2.1- Experimental Design and Components
2.1.1- Targets, Beam and Interaction-Counters
2.1.2— Scintillation Counter Hodoscope
2.1.3- Liquid Argon Calorimeter
2.2- Event Selection (Trigger)
2.2.1- Pre-Trigger
2.2.2- Kill-Latch

2.2.3- Final-Trigger

page
viii

xi

12
12

13

19
26
27
28

29

3. Data
3.1-

3.2-

3.3-

4. Direct—Photon, «0

4.1- Single-Photon, to

4.2-

4.3- Direct-Photon and no

Characteristics

Photon

Reconstruction

Identification of Target and Beam Associated Events

3.2.1-
3.2.2-
3.2.3-
The 9T
3.3.1-
3.3.2-

3.3.3-

"o and
4 .2 .1-

4.2.2—

4 02 03"

4 .2 .4-

4 .2 05"

4.2.6-

Time Cut

Direction Cut

Hadron Cut

Trigger Performance and Parameterization
Trigger Efficiency

The Trigger Model

Front/Back Energy Partition

and n Cross Section Determination
and n Selection Criteria

n Invariant Cross Sections

Subtraction of no and n Background
Determination of the Acceptance of the
Detector

Fiducial Limits in Rapidity and Vertical
Position

Inclusive "0 and n Production
Corrections to Beam

no and n Invariant Cross Section Calculations

and Results

Invariant Cross Sections

and their Ratio

4.3.1-

4.3.2-

Single Photon Signal

Backgrounds to the (Direct-Photon)/'1ro Signal

vi

30

30

38

38

40

46

48

48

50

54

57

57

59

59

63

65

67

69

73

75

7‘3

76

4.3.3— Monte Carlo Procedures for n°, n: n' and w 78
Direct Photon Backgrounds
4.3.4- Monte Carlo for the Charged Hadron Direct 79

Photon Background

5. Final Results and Conclusions 81
5.1- fl° and n Inclusive Production Cross Sections 81
5.2- Y/fi° and Direct Photon Inclusive Production Cross 94
Section
Appendix A - LAC Fast Outputs 92
Appendix B - LAC Trigger Efficiency (pT) 98
Appendix C — E629 variables and Lorentz Kinematics 100
Appendix D - Experimental Determination of Invariant 102

Differential cross Sections

LIST OF REFERENCES 103

vii

LIST OF TABLES

Table 3.1; Energies and positions of groups in a 2
photon event.

Table 3.2; weights of the X
Argon Calorimeter.

front read-Outs of the L1quid

Table 4.1; Software reconstruction efficiencies of the
1' and '1 with respect to asymmetry and multiplicity.

Table 4.2; Fiducial limits in rapidity and vertical
position in the LAC.

Table 4 3; Inclusive "0 and n event yields for incident
p and fl .

Table 4.4; "o and p invariant cross sections for
incident p and I at 200 GeV/c with a carbon target in
the center of mass rapidity interval (-0.80 to 0.20).
Table 4.5; r/Io data and backgrounds.

. 0 3
Table 5. ; Inclu51ve Y/1t and Ed0(Y)/d p/nucleon
(cm /GeV ) .

viii

page
34

51

66

68

70

74

77

88

LIST OF FIGURES

Chapter 1 Figures
1.1- a) Photon exchange in the QED reaction, b) gluon

exchange between colored quarks and c) quark gluon
scattering via gluon exChange.

1.2- a) q+g+q+g b) q+g+q+y (QCD Compton) c) qiqrgi‘g
d) q+qu+y (Annihilation) e) q+g+q+g+y (Brem.)
f) q+Q*q+q+Y (Bram).

Chapter 2 Figures

2.1- Layout of experiment E629.

2.2- a) Lucite window frame for a hodoscope p1ane,b) end
View of a complete hodoscope scintillator plane
assembly.

2.3- Complete hodoscope plane assembly.

2.4- Exploded view of the Liquid Argon Calorimeter.

2.5- Calorimeter cover plate and cryogenic vessel.

2.6- a) Electronics for one channel of the LAC b) signal

sampling system.

Chapter 3 Figures

3.1- An energy deposition profile in the x view showing
five peaks; A, 81' 32, C1 and 02°

3.2- The X(front) , Y(front), X(back) and Y(back) views (a-d
respectively) of a l photon event with energies of
5.51, 4.76, 1.26 and 1.48 Gev respectively.

3.3- The X(front), Y(front), X(back) and Y(back) views (a-d
respectively) of a 2 photon event with group energies
of 6.66 and 2.31 GeV in X(front) and 6.73 and 1.73 cev
in Y(front). In the back views only the first photon

ix

page

14

16

18

2O

22

23

31

35

3.4-

3.5—

3.6-

3.7-

3.8-

3 .9-

is visible as a peak with group energy 2.36 Gev in
X(back) and 1.82 Gev in Y(back).

27 Effective mass of all 21 combinations with p > 2 5

GeV/c for a) 21 events b) 3y events c) 41 events and d)
> 47 events.

Time vs. energy for X(front) Strip 93.

Timdng spectra for single photon triggers with
PT > 2.0 GeV/c.

Angular orientation of the LAC.

Off Axis (AXB ¢ 0) and target associated (4XB 3 0)
photons.

Timing spectra for single 7 triggers.

3.10- a) Fraction of hadron energy deposited b) fraction

of deposited energy that is deposited in the back.

3.11- Trigger efficiency vs X(front) momentum for strips

a) 2-47 h) 48—71 C) 72-89 d) 90-111.

3.12- «0 distribution in Y(LAC).

3.13- Trigger variable value at threshold.

3.14- Back to total energy ratios for a) 0-5 Gev, b) 5-10

Gev c) 10-15 Gev d) 15-20 Gev photons.

Chapter 4 Figures

4.1- 2 Photon mass spectrum for all photon multiplicities < 8

4 04.

With P _>_ 2.5 GeV/c and asymmetry _<_ .8 in the ,0 and—h
mass ragge. Peak and sideband regions are delineated
by vertical lines.

2Y mass spectra for P 2.0-2.5 GeV/c, asymmetr .0-.3
and photon multiplic ty 2, a) no mass region g) n mass
region c) «0 background subtracted d) n background
subtracted.

21 mass spectra for PT 2.5-3.0 GeV/c,

asymmetry .6-.8 and photon multiplicity 3, a) 1° mass
region b) n mass region c) m° background subtracted d)
n background subtracted.

Asymmetry distributions for a) 1r° mass region and b) n
mass region, where the sideband distributions are shown

X

37

39

41

42

44

45

47

49

53

53

55

58

62

64

as dashed histograms. Background subtracted asymmetry
distributions and Monte Carlo predictions (curves) for
c) m° mass region and d) n mass region.

Chapter 5 Figures

5.1- no and n invariant cross sections at 200 GeV/c taken
with a carbon target in the center-Of-mass rapidity
interval (1.8 to .2) a) for incident p and b) for
incident m .

5.2- Ratio of inyariant crass sections Edo(pA+n°+x)/d3o
and Edo(m A+m°+x)/d p vs p for A = carbon and
A = hydrogen at 200 GeVéS , hydrogen data are from
Donaldson et al., 1976.

5.3- Inclusive (direct photon + background) to n° ratio at
200 GeV/c with a carbon target in the center-of-mass
rapidity interval (-.80 to .2) a) for incident p b) for
incident m , shaded bands are background estimates.

42

5.4- Fit to E 29 and R806 data t ung i Q O p an
3 10 3:8 'ng 8.3-0 .fubycevi .

xT Eda/d p = (34il4)(l-xT)
Appendix A Figures

A.l- a) Ionization in a single LAC cell b) pulse height
vs time for energies E1<E2<E3.

A.2- Signal formation in a simple LAC model.

Appendix B Figures
B.l- Trigger turn-on a) step function trigger for an event

with Gaussian smearing about P b) Gaussian spreading Of
the trigger turn-on.

xi

83

85

86

90

93

95

99

Chapter 1

Introduction

This chapter will outline the theoretical basis for the prediction

.and significance of direct photon production in strong interactions.

1.1 A Brief Parton Model Review

Quantum-electrodynamics (QED) has been shown to describe
electromagnetic interactions to a very high degree of accuracy.1 The
success of QED has allowed the structure of hadrons to be probed in
high energy experiments in which beams of electrons or muons are
collided with hadronic targets. Results from these experiments,
performed at SLAC, Brookhaven, Fermilab and CERN, have revealed the
presence of structure within the proton. For example the high energy
scaling behavior of the inclusive reactions ep+ex and up+ux is in
agreement with the predictions for the scattering of charged point
particles. Using the results of these experiments and information
taken from particle spectroscopy the presence of fractionaly
charged,spin 1/2, point-like components or quarks (q) within the proton

and neutron has been inferred.2

2

The experimentally Observed scaling of deep inelastic charged
lepton scattering has also suggested that in the fundamental
interaction between a virtual photon and a quark, the quark behaves as
if it were a free particle at high momentum transfers (asymptotic
freedom3). In sharp contrast to this observation it has been impossible
experimentally, to remove a quark from a hadron.4 Instead, the final
state quarks in Charged lepton scattering appear to fragment into a
"jet" of hadrons collinear with the direction of the virtual photon in
the quark rest frame.§'6 This, naively, contradictory evidence of
quarks being free at small distances but unable to be separated to
large distances, was an important clue in the development of the field

theory for the strong interaction.

A further lead was Obtained from 'measurements of proton quark
probability distributions and momentum fractions derived from these
experiments. They showed that only about 50% of the momentum of the
target hadron is accounted for by quarks.7 This signaled the presence
of an electromagnetic neutral component, comprised of particles called

gluons (g), carrying the balance of the momentum of a hadron.

Additional evidence suggested that the developing parton model Of
hadrons required a new quantum number. The spin 3/2 A++-baryon with a
valence quark assignment of three identical quarks in the same state
was in conflict with spin statistics.2 Also, QED predictions based on
the parton model underestimated the lifetime of the w° by a factor of

8

five. Finally predictions of the ratio o(e+e'+hadrons)/o(e+e’+u+u')

differed from the experimental values by factors of 2-3 depending on

3
the center of mass energy.8 Each of these difficulties was removed by

the introduction of a three-valued quantum number called "color".2'8

The evidence for quarks and gluons within hadronic matter outlined
in Section 1.1, the large number of hadrons observed in experiments and
the compelling evidence for the new color quantummnumber, led to the
formulation of Quantum-Chromodynamics (QCD); a theory which describes
hadrons and their interactions in terms of colored quarks bound

together by a strong "color" force mediated by gluons.

1.2 Quantum-Chromodynamics a Brief Review

In 0CD, baryons are composed of 3 valence quarks while ‘mesons are
composed of a valence quark-antiquark pair.9 Both baryons and mesons
contain a small admixture of quark-antiquark pairs (sea quarks) in
addition to their valence quark content.10 The quarks come in various
species (flavors), at this time all hadrons have been described with
five flavors of quarks; u,d,s,c and b while at least one more flavor
(t) is postulatedll. The color force is associated with the color
Charge of the quarks,arbitrarily Chosen to be Red, Blue and Green in an
analogy with the three primary colors of light. Hadrons, which do not
exhibit color Charge, are assumed to be color-singlet combinations of
the colored quarks; the analogy with light holds here as well, as
Red+Blue+Green light appears as white (colorless) light. The color
force is mediated by 8 massless gluons which simultaneously carry color

and anti-color charge.

4

Since QCD is a field theory, many Of the teChniques of QED are
directly applicable. In QED the elastic scattering Of electrons
requires the calculation Of the effects of diagrams suCh as the one
shown in Figure 1.1a. The elastic scattering of quarks, mediated by
the exchange of gluons, requires the calculation of the effects of
diagrams suCh as the one shown in Figure 1.1b. Due to the existence of
the three gluon coupling, QCD requires the calculation of new diagrams
such as the one shown in Figure l.lc which are absent in QED. Another
distinguishing Characteristic of QCD is the dependence of the coupling
constant on momentum 'transfer. In QED the effect of vacuum
polarization loops (virtual photons that convert to virtual lepton
anti-lepton pairs) is to surround each electric Charge with a
dielectric medium which in turn is polarized by and shields the
electric Charge. The canonical unit of electric charge measured by
Millikan is observed for low 02 processes. At high Q2 the polarized
region filled with virtual lepton anti-lepton pairs surrounding eaCh
Charge is penetrated and the unshielded "bare" Charge is seen. This
screening effect in QED is parameterized by a "running coupling
constant" 0(02) as opposed to the classical constant coupling strength
1/137. Functionaly the QED "running coupling constant" diverges with
increasing Q2 but for all currently accessible energies is essentially
1/137. In QCD virtual gluons formlquark anti-quark vacuum polarization
loops that screen the color Charge in analogous fashion to that
described for QED. However, the gluon-gluon coupling results in vacuum
polarization loops formed by gluon pairs. These gluon loops provide an
anti-screening effect. The eight gluons that are possible as opposed

to 6 quark flavors result in the gluon loops making a larger

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6
contribution than the quark anti-quark vacuum polarization loops.2 The
QCD running coupling constant as a result decreases for large Q2 and
increases for small 02. The anti-screening effect accounts for why
quarks appear to behave as free particles at high 02, where as(Qz)
approaChes zero, and yet cannot be separated beyond hadronic
dimensions; at large distances the anti-screening yields an infinite
color coupling whiCh results in the "bremsstrahlung" of gluons and

quarks ultimately forming a jet of hadrons.

1.3 High PT Phenomenology

The parton ‘model incorporating pointlike constituents within
hadronic matter predicts the large angle scattering of the
constituents. This leads to the production of large transverse
momentum. secondaries in high energy collisions. Early calculations
based on QED interactions between partons predicted pT'4 dependence for
production above pT 2 Gev/¢,12 Calculations using QCD to lowest order
also predicted pT’4 production.13 Experimentally, hadron single
particle cross sections decrease exponentially with increasing
transverse momentum until 1 GeV/c. cross sections at larger transverse
momenta are ‘muCh larger than predicted by an extrapolation of the low
pp exponential, however, a pT-4 dependence is not observed.8 In the pp
range 2-6 GeV/c the production cross sections varies as
(l-xT)10pw'8'24, where the scaling variable xT is the transverse

momentum fraction pT/meax' Recent experiments have found that for

.7

PT > 6 GeV/c and xT > .25 the production data behave more like the pT'4
behavior expected for point like scattering.8 The implication is that
for PT < 6 GeV/c lowest order QCD processes are not adequate to

describe the complete large PT picture. For this reason tests of this

theory are most easily done in reactions where large momentum transfers
are assured. A number of theorists have suggested that the production
Of direct photons at sufficiently large pT would be a ideal reaction

for testing QCD.14:15116

-l.4 Direct Photon Production

Experimental tests of the fundamental quark-gluon interaction of
QCD are fraught with difficulties. For one, the final state quarks and
gluons of the process shown in Figures l.lb-c are observed only
indirectly through the hadronic jets into whiCh they fragment. The
detection and analysis of the hadronic jets that are produced by the
scattered hadron quarks and gluons proved to be difficult for early
experiments at fixed target maChines.17 Recently, experiments at CERN
utilizing the large center of ‘mass energies available in colliding
beams have been successful in producing quantitative information on
parton scattering at large transverse'momentum.18 However, it is still

experimentally impossible to distinguish between quark and gluon jets.

In order to avoid this prOblem, and to select specific fundamental

scattering processes we Chose to exploit the fact that quarks through

8
their electric Charge are able to couple directly to photons. In
principle any reaction with a quark emitting a final state gluon can
also proceed with a quark emitting a photon. Such photons would be
"prompt" in that they would arise from the point-like coupling of the
quark to the photon. In this fashion a final state photon with its
well understood QED production ‘meChanism replaces one of the final
state jets of a purely quark-gluon interaction. The lowest order
processes leading to the production of a direct photon at large
transverse momentum (where perturbative QCD expansions are valid) are
shown in Figures 1.2b and 1.2d (note that these Figures have a final

state photon replacing a final state gluon in 1.2a and 1.2c).

Through these processes we hoped to test quark-gluon dynamics. Due
to the statistical limitations of the data, we were unable to perform
many of the tests of QCD possible with this reaction. For example the
isolation and comparison of the processes in Figures 1.2c (Compton) and
1.26 (Annihilation) which have either a hard quark-gluon initial
scattering with a quark jet in the final state (Compton) or a final
state gluon jet (Annihilation) can probe the gluon structure function
of hadrons and inspect the fragmentation function of scattered gluons.
This comparison will be the subject of a new experiment to be performed

at the Tevetron.

A competing ‘meChanism to production via the Compton and
Annihilation diagrams is "Final Bremsstrahlung" whiCh is illustrated in
Figures 1.2e-f. Upon inspection this process appears to be of higher

order (asza) than the Compton and Annihilation processes (use),

 

‘93 (I)
HY /q ‘7 q

Figure 1.2; a) q+9+q+g b) q+9*q+i (QCD Compton) c) qtfi‘gfla 6) q+§*9+v
(Annihilation) e) q+g~q+g+y (Brem.) f) q+qrq+q+v (Brem.).

10
However, the fragmentation of quarks to photons is proportional to o/os

resulting in the Bremsstrahlung processes being Of order (cos),14

Early calculations made for the pT dependence of prompt photon
production predicted a pT"4 dependence at fixed xT where an assumption

of scaling in the structure functions was made.14'15

Experiments to
date have indicated a approximately pT"6 dependence (this will be
discussed in the final chapter). More recent calculations
incorporating scaling violations (color force radiative corrections), a

"running coupling constant" for the color force coupling and higher

order production ‘meChanisms have shown better agreement with

data.16'19

For pp+y+x, qQ'annihilation would necessarily have to occur from
the interaction of a sea antiquark with a valence or sea quark and
therefore is suppressed relative to the Compton process. In m+p and
m+n the annihilation of valence d quarks (dd) can occur but does not

compete with the Compton process due to the reduced Charge coupling of

d quarks to photons. Bremsstrahlung is expected to be important at

large XT values via the q+q * q+q+Y process but in the kinematic region

covered in this experiment -2 < XT < .5 Bremsstrahlung is estimated to

occur at 30% of the Compton process.20

The experiment on which this dissertation is based searched for the
presence of direct photons at large transverse momentum values between
2.0 and 5.0 GeV/c which are produced in collisions of 200 Gev/c proton

and «I beams with a variety of nuclear targets (carbon,aluminum and

ll
beryllium). Only the results obtained with a carbon target will be
presented here. Nuclear target effects observed in this experiment are

described elsewhere.21

Chapter 2

Experimental Apparatus

This Chapter describes the experimental configuration used to
'measure the production of single photons at large transverse momentum

(PT)in Fermilab experiment E629.

2.1 Experimental Design and Components

Experiment E629 was conducted in the M-1 beam line of the Meson
laboratory at Fermilab from the fall of 1981 through the spring of
1982. The collaboration for the experiment included physicists from
Fermilab, MiChigan State University, University of Minnesota,

Northeastern University and University of ROChester.

The experiment used a beam line Cerenkov counter provided by
Fermilab, a Beam-Hodoscope constructed by MSU, a Scintillator Counter
‘Wall (80" X 40") provided by MSU, nine PWC planes constructed by
University of ROChester,a Liquid Argon Calorimeter jointly constructed

by University of Minnesota and University of RoChester, and a PDP-ll

12

13
computer provided by Fermilab. The details of these components and
their relationship to the experimental data are described in the

following sections.

2.1.1 Targets, Beam and Interaction-Counters

Figure 2.1 shows the overall arrangement for E629. A Cerenkov
counter upstream of the apparatus (not shown) was used to tag the beam
(85% p,15% m+) as either a p or m+. A unique scintillation counter
hodoscope, detailed 'more fully in the next section, was placed in the
beam line to generate a "Beam" signal. Two carbon blocks eaCh of
approximately 0.025 interaction lengths separated by 25 cm‘were used as
targets. A target cave constructed of concrete shielding blocks
surrounded the targets. Two scintillation counter pairs downstream of
the target, eaCh separated by l" gaps centered on the beam line, were
used to define an interaction in the target. One or more charged
particles detected in one or more of these four counters in coincidence
*with a beam particle generated an "Interaction" signal. various veto
and halo scintillation counters suppressed triggers from the halo
around the beam. A wall of eight 20" X 20" scintillation counters
arranged in two rows of four that shadowed the electromagnetic shower
detector ‘was used to suppress triggers from particles produced by
interactions upstream of the target. A signal from any one or more of
the eight counters in the veto-wall generated a "Veto-wall" signal.

Similarly, a signal from either of the two Halo-Counters produced a

"Halo" signal.

14

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2.1.2 Scintillation Counter Hodoscope

The experiment was designed to utilize an intense beam of 107
charged particles per second in order to access large pT values where a
direct photon signal could be separated from the background. For this
beam a scintillation counter hodoscope22 was designed and constructed
at Michigan State University to provide (1) a ‘monitor of the beam
profile and beam intensity; (2) latChed information on the beam
position and multiplicity in eaCh triggered event; and (3) fast signals
to veto the presence of two or more beam particles within a single rf
bucket ( 1 ns bursts, separated by 19 ns). The counters feature two
staggered rows of scintillator elements,set in a precision mounting
frame, whiCh allows 100% coverage of the beam ‘while limiting the

overlap of adjacent elements to approximately 5% of the covered area.

In order to position the scintillator elements accurately to
10.01 mm. precision slots were machined in a lucite window frame as
shown in Figure 2.2a. Two frames, when bolted face to face, formed two
rows of staggered elements as indicated in Figure 2.2b. The spacing of
the slots was set suCh that adjacent elements would overlap by 0.02 mun
Eight 1 mm elements span the central portion of the hodoscope flanked
on either side by one 2 mm and one 5 mm element. The slots are
machined 2 mm in depth (the beam direction) to accept scintillators of

this thickness.

16

 

 

 

b) ”H"— lmm

_1_ [10000 :21
2mmT EUDUUD

i

BEAM

Figure 2.2; a) Lucite window frame for a hodosc0pe plane, b) end view
of a complete hodoscope scintillator plane assembly.

17

The scintillators were wrapped with two layers of 0.008 mm
aluminized mylar and sealed with a contact cement at one end and along
the edge facing out from the slots. Approximately 3'mm of scintillator
extended beyond the support frame allowing the light guides to be glued
on. The light guides, Of rectangular cross section, were tapered to
approximately match the scintillator size on one end and the active
area of the 1/2" diameter phototube on the other end. Before wrapping
with aluminum foil and black tape, the light guides were heated and
bent to shape in a jig in order to space the phototubes and bases as
shown in Figure 2.3. Space limitations required that the six elements
in one row be viewed from one side while the remaining six elements be

viewed from the other side.

The scintillator support frame, phototubes, and bases were mounted
on a 1/4" aluminum plate with a 6" square cut-out for the beam and
halo. A light-tight box, through which the light guides penetrated,

was also mounted on the aluminum plate.

Three hodoscope planes were built; two were placed just before the

target (Bx'By) while a third (BV*), was placed lO‘m downstream of the

target and used as a tag for a noninteracting beam track.

Measurements of the probability for greater than 1 element to be
active at low beam intensities were consistent with the expected yield
(5%) based upon the spatial overlap of neighboring elements. The

increase in this probability at the nominal beam intensity

18

BASES

  
    

PHOTOTUBES

LIGHT

 

 

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Figure 2.3; Complete hodoscope plane assenbly.

19
(approximately 1 x107/s) agreed with that predicted from the beam
structure. The efficiency of a plane was measured to be >98%
indicating that few, if any, spaces were left between elements. At 10
MHz there was no indication of phototube gain sagging. During a
particularly bad excursion in the beam intensity, 2.1 X 107 counts

(twice the normal) were recorded during a single 1.0 s spill.

The signals from the 12 counters in eaCh plane were discriminated
and linearly summed to produce a final signal proportional to the
number of hits in eaCh plane. This signal was then discriminated at
two different thresholds to differentiate between single and multiple
hit events on eaCh plane. The low threshold discriminator provided two

signals, Bx>0 and B >0 indicating a hit in the x and y planes of the

Y
hodoscope respectively. The higher threshold discriminators produced

two signals. Bx>l and B >1 for the presence of multiple hits in the x

Y
or y planes.

2.1.3 Liquid Argon Calorimeter

The detector (LAC) was located 8‘m from the target, and centered at an
angle of 100 mr relative to the beam; at large pT, this corresponds to
production at 90° in the center of mass for this experiment. The
theory of operation and the design details of similar detectors, have

been described previously.23

Figure 2.4 shows an exploded view of the detector. It consisted of

61 lead sheets (2 ‘mm thickness) and 62 copper-clad G-lO sheets

20

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21
separated by G-lO spacers along the edges, and by small G-10 pins in
the active area. The entire sandwiCh was held together and attaChed to
its support structure by stainless steel rods. ‘When immersed in liquid
argon, the detector was 25 radiation-lengths and 1.2 pion

interaction-lengths thick.

The copper-clad G-10 sheets were divided into strips 1.27 cm in
pitCh, with 0.5mm interstrip gaps. The strips extended along the X-
and Y-directions on alternate sheets. The strips with same X and Y
positions along the axis of the detector were connected to a single
amplifier Channel. However, the Ydmeasuring sheets were divided
electrically into left and right sections, and the LAC read-out was
further subdivided into front and back halves (eaCh containing

approximately 12 radiation lengths of material).

The detector-cradle assembly was suspended from a flat
stainless-steel cover plate for the cylindrical cryostat (see
Figure 2.5). This vacuum-insulated vessel was supported in a tall

steel structure (tower).

Cryogenic temperatures were maintained in the vessel by sensing the
liquid argon vapor pressure and controlling the flow of liquid nitrogen

through internal cooling coils.

Figure 2.6a shows the block diagram of the front-end electronics
for the detector.24 The ganged strips from the detector were connected

to individual amplifiers through multiconductor flat cables.

22

     
 
   

   

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Figure 2.5; Calorimeter cover plate and cryogenic vessel.

23

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24
A Charge-sensitive and capacitively feedback amplifier was used.
The amplifier output passed through a 400 ns lumped delay element to
the sample-and-hold section. The CMOS switChes SW1 and SW2 could be
opened at the times appropriate for measuring the rise in the output
for the event of interest as shown in Figure 2.1.6b, After both
switches have Opened, the output of the difference amplifier is

proportional to the integrated charge for the event of interest.

In addition to the sample and hold section outputs, outputs for
triggering purposes were provided by another difference amplifier
driven by the front end. Baseline restoration was accomplished by
delay-line differentiation using a 200 ns tap in the lumped delay
element. The fast trigger outputs could be appropriately weighted,
summed and discriminated to form an overall calorimeter trigger
decision. The fast trigger outputs for all front x-strips were
connected to low-threshold discriminators whose outputs went to time
digitizers. The timing information later proved to be critical for the
seperation of single photons from the background. A more complete

description of the read-out electronics may be found elsewhere.24

A "G10bal-PT" signal was formed with specialized electronics that
added all of the x-strip energies from the fast trigger outputs. EaCh
x-strip's fast trigger output was initially attenuated by a factor

proportional to sin e for that strip, where e is the laboratory angle;

112

i'e'l Global-pT = 2 Bi sinei. The trigger threshold was later
i=1

adjusted by modifying the attenuation factors in order to equalize the

data accumulation rate across the detector. This resulted in an

25
effective threshold in PT which varied from approximately 2.3 GeV/c at
large angles, to approximately 3.0 GeV/c at small angles. This
variation will be described in ‘more detail in Section 3.3.1. The
trigger reaChed nearly full efficiency approximately 0.5 GeV/c above

the nominal threshold value.

In addition to Global-pT, a "Local-pT" signal was formed whenever

at least 0.6 Gev/c was present in three neighboring x-strips. This
served to suppress cOherent noise and those multiphoton events in whiCh

there were no n° or n mesons produced with pf above 1.2 Gev/c.

Operationally the GlObal-Pe discrimunator threshold was set at 150
mv. This trigger setting was used for the majority of the E629 run
time. Near the end of the run a dual threshold Global-pT was
installed. In the dual mode the 150 mv threshold signal was always
enabled and the result latChed. For 1 out of 3 events a 110 mV
threshold signal was also enabled. In Section 3.3.1 a comparison is
made between 110 mV threshold data where the 150 mV signal was, or was
not, present in order to obtain the efficiency as a function of pT for

events requiring the 150 my signal.

Not shown in Figure 2.1 was the proximity of power supplies (for
beam line magnets) to the LAC. The Silicon Controlled Rectifiers
(SCR‘s) in these power supplies induced electromagnetic pickup in the
LAC. This noise produced levels above threshold in the Global-pT
signal with a duration on the order of l-10 us, and induced a strong

background to the LAC pp trigger. The SCR noise was Characterized by a

26
bipolar oscillating signal. The negative part of the oscillation
provided a signature for the presence of SCR noise. A signal gate was
installed that would open whenever a Global-pr pulse below -50 mV
Occured. The gate was continuously updated when additional negative
pulses were encountered. Section 2.2.3 will describe how this gate was

used to reduce SCR background signals to acceptable levels.

Due to restricted beam time at Fermilab in 1981., there was not
sufficient time during the execution of E629 to calibrate the
calorimeter using an electron beam. Instead the relative amplifier
gains were measured by injecting pulses of fixed charge into the
amplifiers. These results along with normalization to the 1r° mass
provided the energy calibration for the experiment.25 Photon
reconstruction was accomplished by use Of a program used in a previous
experiment and modified for the E629 configuration. The reconstruction

algorithm will be described in Section 3.1.

A more detailed description of the construction and performance of

the LAC is available in a recent publication.26

2.2 Event Selection (Trigger)

As stated in Section 2.1, E629 was designed for a beam rate Of
approximately 107 Hz. The targets with a total of 0.05 interaction

lengths yielded interactions at a rate of 106 Hz. The time required

 

27
for data acquisition limited E629 to a maximum of approximately 50
events to be recorded on magnetic tape per one second beam spill. The
high event rate and relatively low data acquisition rate combined with
the low rate expected for the production of high pT photon event527

required the formation of a highly selective trigger.

2.2.1 Pre-Trigger

The Global-pT and Local-pT signals in the LAC described in Section
2.1.3 had a rise time of approximately 200 ns. The PWC signals had a
rise time of approximately 20 ns and a duration of 60 ns. Delaying the
PWC signals long enough to include LAC information in a latCh decision
(> 100 ns) was impractical, this resulted in the need for a early or

"Pre-Trigger" for the PWC latch decision.

A Pre-Trigger was formed when both the Bx>0 and By>0 hodoscope

signals were in coincidence with the Interaction signal and a

"Computer-Ready" signal which indicated the computer was free to record

data. A coincidence with both the Bx>l and B )1 signals or the Halo

Y
signal would veto the formation of a Pre-Trigger. The logic is

summarized as follows:

Pre-Trigger = (Bx>0) ° (By>0) ° (Computer-Ready) ° (Bx>l'By>l) '

 

(Interaction signal)'(HalO sIgnal).

28
When a Pre-Trigger was formed, a latch was set that prevented the
formation of subsequent Pre-Triggers until cleared. The resulting dead
time between the Pre-Trigger formation and the interrogation of the LAC
was continuously monitored by counting beam in scalers whiCh were gated

Off when the Pre-Trigger latch was set.

The long response time of the LAC, approximately 400 ns as
described in Section 2.1.3, implies that contamination of a given event
by preceding and succeeding events is possible. In order to protect
the trigger from pile-up, any one of three states to be described would
set a "Kill" latch whiCh would block the formation of a Final-Trigger

until cleared.

Two of the "kills" used an Interacting-Beam signal (IB) formed by

the coincidence between the Bx>0 and B >0 Hodoscope signals and the

Y
Interaction signal. An IB signal occurring up to 100 ns prior to the
event being processed would generate an "Early-Kill". A "Late-Kill"
was formed if a 18 signal occured up to 75 ns after the event being
processed. The "Veto-wall/Halo-Kill" occured when a veto-wall or Halo
signal occured up to 100 ns before or approximately 50 ns after the
event being processed. These pile-up protections had a dramatic effect

on the large PT trigger rate. Prior to their introduction the trigger

rate (triggers/beam particle) was linearly proportional to the beam

29
intensity. Following their introduction the trigger rate was

independent of the beam intensity.

2.2.3 Final-Trigger

The Pre-Trigger signal indicated that a single beam particle had
interacted. in the target and that the computer was ready to accept
data. If the Kill latch was not set the event was isolated in time.
The Global-pT and Local-pT signals then provided information on the

probable Presence 0f high PT photons. The Final-Trigger was formed by

requiring a coincidence between the Pre-Trigger, Global-pT and Local-pT
signals with the SCR and Kill signals acting in veto. The logic can be

summarized of follows:

Final-Trigger = (pre-Trigger)'(Global-pT)'

 

(Local-9T) ° (ER) ' (Kill) .
An event satisfying the Final-Trigger initiated the sample and hold,
digitizing and read-out procedures of the LAC under computer control.
'When an event failed to satisfy the Final-Trigger requirement an
appropriately delayed Pre-Trigger signal cleared all latches to be

ready for the next event.

Chapter 3

Data Characteristics

This chapter will detail the procedures used to reconstruct photon
positions and energies, to remove spurious sources of photons from the

raw data and to parameterize the acceptance of the detector.

3.1 Photon Reconstruction

The LAC construction, as described in Section 2.1.3, provided x and
y views of the energy deposition profiles of electromagnetic showers.
The longitudinal division of photon energy into front and back energies

was also described.

In the first stage of photon reconstruction the X(front) and
y(front) views are independently analyzed for possible electromagnetic
showers. Figure 3.1 displays a typical view containing three "groups"
of energy (A,B and C), where a group is defined as one or more
consecutive read-out strips with energy depositions above threshold

(threshold=.10 GeV). EaCh group is then analyzed for peaks; any strip

30

31

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32
in a group with a higher energy than its adjacent strips is defined as
a peak. In the figure groups B and C have two peaks each and group A
has one peak. In subsequent analysis B1 and 82 were interpreted as the
x-view of showers from two separate photons with a combined effective

mass of .136 Ge‘V/c2 indicating a possible no (see Chapter 4).

The interleaving of x and y signal planes in the LAC as described
in Section 2.1.3 results in a near equivalence between the x and y
views of a electromagnetic shower in the front and in the back segments

of the detector.

In order to illustrate the character of the data analysis a
breakdown of the steps involved in the reconstruction of two events
will be given. The four views of an unCharacteristically simple event
are shown in Figure 3.2. A single group with only one peak is seen in
eaCh View. The energies of the front groups are 5.51:0.33 GeV and
4.76:0.31 GeV located at strips 22 and 44 in the x and y views
respectively. The energies in the back views are 1.26:0.16 Gev and
1.48:0.17 GeV and are located at strips 21 and 44 in the x and y views
respectively. After a summation and correction for shower shapes of
the energies in eaCh view this event was interpreted as an isolated
photon with an energy of 12.5i0.49 GeV, located at strip numbers x=22
and y=44 With PT=2.49i0.22 GeV/c. Subsequent use of a shower shape
parameterization allows the spatial position to be determined within
a=£hnm for any given view.28 Note also that the energy in the back is
centered at nearly the same x and y positions as the front energies

indicating a nearly normal incidence for the photon. The dotted line

33

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34
in the y plots delineates the electrical division of the y-strips into

left and right sections as described in Section 2.1.3. This results in

Y'StIiP k: where 1fkf64, having the same y position as y-strip k+64.

In events with more than one photon incident on the detector,
position ambiguities are resolved by direct energy matChing. An event
in whiCh two photons were reconstructed is shown in Figure 3.3. The
energies and positions for the groups in eaCh view are given in Table

3.1.

Table 3.1; Energies and positions of groups in a 2 photon event.

x Group xfl 19:2 x_b_
E (GeV) 6.66:0.36 2.3110.21 2.36:0.22
x-strip# 52 58 52
y Group yfl “yfg [yb
E (GeV) 6.73:0.36 1.73:0.18 1.82:0.19
y—strip# 23 79 23

Each group contains a single peak which can be unambiguously paired by
energy matching. In the front section groups xfl and yfl are nearly
equal in energy as are groups xf2 and yf2. Similarly, in the back, xb
and yb are nearly equivalent in energy. By assuming near normal
incidence for photons, xb and yb can be associated with xfl and yfl
respectively. Summing the x,y, and back energies of the associated
groups the two clearly indicated photons are reconstructed with
energies of 17.7110.59 and 4.6210.30 Gev located at strip coordinates
(52,23) and (58,79) respectively. Note that only the large energy

photon is associated with energy in the back views of the event; it is

35

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36
indicated, therefore, that the lower energy photon did not deposit a
significant fraction of its energy in the rear section. The effective
mass of the two photons is .141 GeV/c2 indicating a possible 1° and the

PT Of the two photons together is 3.44 GeV/c.

The two events just examined were chosen because of their
straightforward interpretation. In cases where the electromagnetic
showers overlap in one or more views or the energies Of photons are
nearly equal, resolution of the ambiguities in view matching requires
specialized coding. Shower shape parameterizations were used to
partition the energy in multiple peak groups between the overlaping
showers.28 Reconstruction of special cases with complications beyond
those just ‘mentioned are also present. However,as they apply only to
limited class of events, they are not individually treated here.29 A
l Gev 'minimum energy requirement resulted in a average reconstructed
photon multiplicity of 4.4. The effectiveness of the reconstruction is
demonstrated by the 21 mass spectra shown in Figure 3.4 with a pf cut
of 2.5 GeV/c. Every 21 combination is included and clear m° and m
signals are in all but the highest multiplicities where only the n° is
evident.

° and n

A Monte Carlo study was used to determine the y, m
reconstruction efficiencies. The results of this study are used later
in Section 4.3.1 to correct for contamination in the direct photon

signal.

37

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3.2 Identification of target and beam associated events

The experimental trigger was designed to select interactions in the
target yielding a large PT electromagnetic energy deposition in the
LAC. Triggers due to energy depositions from beam halo, hadronic
interactions in the LAC and pile-up from previous and subsequent
interactions were removed from the data by applying cuts on the time,
direction and the energy deposition Characteristics of each event.

These cuts are described fully in the following sections.

3.2.1 Time Cut

As described in Section 2.1.3 the x—strip read-outs in the first
12.5 radiation lengths of the LAC were provided with low threshold
discriminators; eaCh discriminator output was used as the start signal
for a time—to-digital converter (TDC). An appropriately delayed
interaction signal provided the common stop signal for all channels
(See Section 2.1.1). The signal on an individual LAC strip had a
typical rise time of approximately 200 ns as described in Section
2.1.3. A true target associated signal in any given LAC strip should
have a fixed TDC result (pronpt time) due to the time-of-flight, the
intrinsic delay due to cabling, and the delays in the other associated
electronics. However, due to the fact that signals with a fixed rise
time cross a given threshold at times which are a function of the
ultimate signal height, the actual TDC result for in-time events varied

from the prompt time. This time-slewing is exhibited in Figure 3.5

Time (nsec.)

39

 

320-

240"

200 -

o
_...-.--------------—----------.-‘.—-.--‘----—-1

160-

120 #-

 

280.1

 

 

 

I J J
1 2 3 4 5
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Figure 3.5; Time vs.

energy for X(front) Strip 93.

 

40
where a scatter plot of strip time vs energy is shown for x-strip 93;
in order to insure a high proportion of in—time events the timing
analysis was restricted to entries taken only from photons that formed
a 1°. The prompt or minimum response time is indicated by the dashed
line in the plot. The solid curve shown on the plot is of the form
(energy)"1 times a scale factor plus an offset (see Appendix A). A
scale factor and offset were deternuned for each x-strip. Corrected
strip times were then taken as the difference between the original time
and a time calculated on the basis of the relationship just described.

Prompt events in this regime have a corrected or prompt time of Zero.

Energy weighted averages of the corrected strip times were used to
determine a time for each shower. The time spectrum of photons from
single photon triggers is shown in Figure 3.6. The structure in the
tail of the in—time peak reflects the l9ns rf bucket structure of the
FNAL accelerator(see Section 3.2.2). In subsequent analysis a time cut

of 125ns was applied to the highest energy photon in eaCh event.

3.2.2 Direction Cut

The front and back segmentation of the detector provided a method
of differentiating between events originating in the target from those
originating elsewhere. The method is demonstrated with Figure 3.7. A
photon from the target, traveling along the dashed line, deposits most

of its energy in the front half of the detector at position XF' and the

41

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Gev c.

42

T
AXB=——'=5C—(x,.-xo)

DLAC

BEAM TAfijGET

J:

\
\

HALO

\PREDICTED
RAY

 

FRONT
(l3 rod lengths)

BACK
(l3 rad lengths)

Figure 3.7; Angular orientation of the LAC.

43
remainder in the back half directly behind XF. For a photon traveling
parallel to the beam direction and striking XF the back energy is

displaced from the expected position AXB° The AxB distribution for

photons that originate in the target is centered at zero. Figure 3.8
is a scatter PlOt 0f AXE versus XF for events in which only one photon
was found in the detector. Two distinct bands are present: one,
corresponding to sources from the target, centered at AXB=0
(independent of XF), and another tilted relative to AxF=o. The tilted
band is that expected for the dependence of AXB on XF for photons or
hadrons traveling parallel to the beam direction. (The two horizontal
gaps are due to dead amplifiers in several of the back x-strips.)
Taking the rms width of the central peak, and estimating the effective
lever arm between the front and back of the LAC, we find an angular
resolution for determining the directions of incident photons of

'130 mr (rms).

The combined effect of both the direction and the time cuts is
shown in Figure 3.9 where those events passing the direction out are
indicated by the shaded portion of the plot. In the pf ranges 2-3 and
3-4 GeV/c, the vast majority of the photons in the central in-time peak
also satisfy the direction cut. In the pf range greater than 4 cev/c
the application of the direction cut in conjunction with the time cut,
which are both effective at removing halo backgrounds, leaves a clean
sample (shaded events at t=0) of single photons originating from, and
in coincidence with a beam interaction in the target. The veto wall
protection described in Section 2.2.2 is clearly evident in Figure 3.9c

as is the the 19 ns rf bucket structure of the FNAL accelerator.

 

44
A X3‘Cm)

A XB VS. XF

-2

 

 

 

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and target associated

We ,t 0)

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Figure 3.8;

photons.

45

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' ' j ‘p >4seV/c
Veto woll T
lOO"—' protection I 3
50

 

 

-4o 0 40 so :20
PHOTON TIME (ns)

Figure 3.9; Timing spectra for single 7 triggers.

46

3.2.3 Hadron Cut

The difference in response of the LAC to hadron-induced showers and
to electromagnetic showers provided a basis for eliminating hadron
induced triggers. As noted in Section 2.1.3 the LAC had a thickness of
25 radiation lengths, but only 1.2 interaction lengths. The fraction
of pions which deposit more than a given percentage of their total
energy in the LAC is shown in Figure 3.10a.30 Less than 20% of all
hadrons will deposit greater than 50% of their energy in the LAC. This
»results in a strong suppression of large PT hadronic triggers due to
the steeply falling cross sections with increasing pT_ The fractions of
pions and electrons (equivalent to photons) which deposit less than a
given percentage of their total energy in the back half of the LAC is
shown in Figure 3.10b (the 30% of the pions which deposit less than 10%
of their total energy in the LAC have been excluded). The cut on
EBACK/ELAC of 0.5 which was applied to the largest energy shower in
each event eliminated 55% of pion-induced showers (mislabeled as
electromagnetic), with a negligible effect on photons. ‘When considered
in combination with the consequences of Figure 3.10a, it is clear that
the LAC provides excellent discrindnation against hadron background to
high-energy photons. The small residual hadronic background is

discussed in Section 4.3.4.

47

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mo cowuomuu An cobwmommp >mumcm coLcmc uo comuospm Am “CH.m musvwm

 

 

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48

3-3 The Fe Trigger Performance and Parameterization

As described in Section 2.1.3 a large pp signal in the LAC was
required for a trigger. In this section the efficiency of the trigger

is measured and then parameterized in a model based on the LAC design.

3.3.1 Trigger Efficiency

The dual trigger described in Section 2.1.3 was used to measure the

trigger efficiency as a function of pb, The electronic trigger

thresholds were set at 110 mV and 150 mV, where 150 mN’was used for the
majority of data in the experiment. In the dual trigger mode the
status of the 150 mN trigger was latched for each 110 mv trigger
- accepted. A data sample was used in which the criteria described in
Sections 3.2.1-3 were applied to the highest energy photon in each

event.

The trigger efficiency was analyzed for events with energy
depositions localized to one of four x-regions; approximately equal
numbers of events were localized in each region. The efficiency of the
150 mN trigger in each region is shown in Figure 3.11 where the
fraction of events taken with the 110 mV threshold which would also
have satisfied the 150 mV threshold is plotted with respect to

pTx = : Ei Sinai, where pTx IS the x component of momentum in the front

49

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2.. maxim pow 63560.: Scoutx m> \Gcmwoflmm ummmmfi. “:8 953m

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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5:031:15};

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50
half of the detector. The slow trigger "turn-on" in each of the four
regions can be attributed to pTx "smearing" due to detector resolution,
electronic noise and to variations from sine weighting within each
region (see Appendix A). Assuming a gaussian noise source in addition

to a sharp trigger threshold in pTX the trigger turn—on can be

parameterized as (see Appendix B):

Efficiency(pbx) = .5[l. - erf(pTx-threshold,0)].

Fitting the above function to the data in Figures 3.11 yields 2.04,
2.13, 2.22 and 2.62 i 0.05 GGV/C for the pTx thresholds in the four

regions respectively with o's of .393, .286, .346 and .483.

3.3.2 The Trigger Model

The pTx trigger for the experiment was implemented by forming a
weighted sum of the fast signal output of the x read-out strips as

described in Section 2.1.3.

Naminally. a Prrx signal could be formed with weights wi = sinei
where, 6i is the laboratory polar angle of the ith Strip- However,
capacitive effects necessitated a departure from sine weighting (see
Appendix A). Image charge appears on all strips for each
electromagnetic shower detected. The total amount of image charge is
proportional to the ratio of detector capacitance to ballast
capacitance. This ratio was kept as low as cost would allow

(approximately 1/3) to minimize the image charge effects. The

electronic strip weights wi are given in Table 3.2 were chosen to

51

000.0 000.0 HOH.0 m0~.0 NHaImOH
m0~.0 50H.0 mo~.0 0a~.0 NHH.0 v-.0 QOHIMOH
0HH.0 mHH.0 0ma.0 HNH.0 vm~.0 0NH.0 NOHIhm
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musmwmz mwuum omcmm
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comu< 003000 mnu mo masonpmmu x on» 00 musmwmz m~.m waste

52
compensate for the expected capacitive effects and roughly correspond
to sinei. A simple model of the effects of the trigger electronics is
given by
T = AEEiNi-a] ,
where E1 is the energy deposited in the front half of the detector in
strip(i), a is an image charge coefficient and A is a scale factor (see

Appendix A).

In events where energy depositions are confined to a localized
region of the detector the strip weights wi are slowly varying and
result in a approximately constant pTx threshold throughout the region.
The triggeramodel parameters, a,A in addition to a gaussian noise
parameter a were selected to best reproduce the thresholds in p

TX

described in the previous section.

A vertical (y) dependence to the trigger threshold was not
anticipated. However, it was observed that the up yield, as shown in
Figure 3.12, was not symnetric above and below the beam line. After
careful study, the only reasonable source of this effect was a vertical

asymmetry in the trigger.

The detector was divided into four vertical regions of equal width.
Thresholds were determined for the four regions by the method described
in the previous section; the trigger variable T was used instead of
pTx‘ These thresholds in T are shown as a function of y (LAC) in
Figure 3.13. A small but linear decrease in the threshold with

AZEi(wi—0)

53

 

20C)"

1'75.—
1.50.—
12‘?-
1.00"-
75-
50—

25-

 

l

J

l

 

l l

 

-uo

-30

20

30 no
X(IJHZ) 511 can

Figure 3.12; n° distribution in Y(LAC).

 

2.1*-

 

2.23:7‘\\\\\\7

l

 

l l

l

l

l l

 

“b0

-30

i-ZO

'IC) 0

1()

20

 

3o .uo
Y(IJAC) ix) can

Figure 3.13; Trigger variable value at threshold.

 

54
increasing y (LAC) is Observed. A linear fit to this data was

incorporated into the parameterization as follows:

T = A§Ei<wi-a)/<ayi+b)
1

The parameters A and a were then slightly adjusted to maintain the pTX
dependence shown in Figures 3.11. The final values for the
triggersmodel parameters were:

A=l.0, a=0.067, a=-1.35xlo-3, b=l.0, o=.3 and trigger threshold=2.05

(see Appendix B).

One explanation of this effect requires that small changes occur in
the fast signal pulse shape depending upon the vertical position of the
shower. The integrated pulse shows no such effect as the energy
calibration (and thus the n° mass) is found to be invariant with
vertical position of photon showers. Referring again to Figure 3.11,
Monte Carlo generated events, when required to pass the triggeramodel,
reproduce the threshold behavior across the detector as shown by the

cbrves which overlay the data.

3.3.3 Front/Back Energy Partition

The trigger used only the energy depositions in the first 12.5
radiation lengths of the detector. In order to simulate the trigger
for Monte Carlo generated photons, a model for the energy split between
back and front was required. The E(back)/E(total) distributions in

four energy ranges are shown in Figures 3.14. The most probable value

Of E(back)/E(total) grows linearly with increasing photon energy,

55

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56
however the tails in these distributions could not easily be

parameterized. Therefore, the E(back)/E(total) ratio for each

generated photon was selected randomly from these distributions in the

Monte Carlo program.

Chapter 4

Direct-Photon, no and n Cross Section Determination

This chapter presents the steps in the analysis leading to a

I I I o I I I
determination of the direct-photon, n and n invariant cross sect1ons.

4.1 Single-Photon, no and n Selection Criteria

In addition to the time, direction and hadron cuts described in
Sections 3.2.1-3.2.3, a minimum energy of l Gev was required for each
photon identified in the reconstruction program. This eliminated
backgrounds due to fluctuations in the tails of electromagnetic showers
and electronic noise. To eliminate photons with energy losses near the
edges of the detector all reconstructed photons were required to be at

least 5 cm from each edge.

The two photon effective mass spectra for all photon multiplicities

0f 8 or less With PT Z_2.5 GeV/c is shown in Figure 4.1. Six regions
0 . .
within the mass spectrum were selected; the W and n mass regions with

25 and 50 Mev width respectively, and the “O and n sidebands with 80

57

58

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59
and 100 MeV widths respectively. The boundaries of the six regions are

marked by vertical lines on the plot.

A photon pairing with an effective mass within either peak region
was designated as as a no or n meson decay. A photon not included in
any no and n pairing was designated as a single photon. A photon
pairing with an effective mass falling within a sideband region was

designated as a sideband no or n.

4.2 no and n Invariant Cross Sections

The no and n invariant cross section determination consisted of
weighting the data for detector acceptance, subtracting background and

normalizing to the target and beam parameters.

4.2.1 Subtraction of no and n Background

In events with only two observed photons,the background to the no

and n production is composed of photons from two separate meson decays
where the second photon from each decay misses the detector or is below
the minimum energy criteria. In events with more than two observed
photons, a combinatorial component in the background due to ambiguities

in photon pairing is also present.

60

Two photon effective mass spectra for various ranges in pT for
two-photon events were shown previously in Figure 3.4a and for three
photon events in Figure 3.4b. The sidebands in the two photon event
spectra are less populated in comparison to the peak than is the case
in the three photon event spectra where the expected combinatorial
ambiguities in photon pairing are present. An estimate of the
background can be made in each case by extrapolating the sideband

population under the peak.

To minimize effects from observed differences in the mass spectra
profiles With respect to Changes in PT, photon multiplicity and meson
decay asymmetry (see Appendix C for the definition of decay asymmetry),
the effective mass data were separated in these variables. Mass plots

were generated for combinations of photon multiplicity, selected ranges

in PT and asymmetry.

As an example of the quality of the background fitting procedure,
the 1° and n plots for a photon multiplicity of two, a PT range of
2.0-2.5 GeV/c and a asymmetry range of 0.0-0.3 are shown in Figure 4.2.
The ‘mass spectra in the mass and sideband regions are fit to a
polynomial background plus a gaussian mass peak. After subtracting the
polynomial background from the mass spectra, the gaussian peaks shown
in Figures 4.2c-d are obtained. Comparable mass plots for a photon
multiplicity 0f three, a PT range of 2.5-3.0 GeV/c, and a asynmetry
range of .6-.8 are shown in Figure 4.3. Similar fits were made to all

the generated mass plots.

61

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63
The background estimates were made by normalizing the sideband data
to the ‘background under the peaks. The normalization factors were
obtained for the various combinations of photon multiplicity, pT and
asymmetry by determining the integrals of the background fits in the
‘meson mass regions and then dividing the integrals by the sum of the

data in the sideband regions.

4.2.2 Determination of the Acceptance of the Detector

An analysis of the decay asymmetry distributions confirms the
effectiveness of the background subtraction procedure. The asyrmnetry
distributions for the data in the n° and n mass regions are shown in
Figures 4.4a—b with the asymmetry distributions for the background as
determined from the weighted sideband data shown as dashed profiles
overlying the plots. The data after background subtraction are shown
in Figures 4.4c-d. The background subtracted distributions fall with
increasing asymnetry where the opening angles of the meson decays are
larger. The n distributions show a poorer acceptance than the w°'s due
to the greater mass of the n and correspondingly greater decay angles.
In the determination of cross sections a upper limit of .8 in asymmetry
was applied to the data to avoid the poor geometric acceptance and

strong backgrounds at high asymmetry.

A Monte Carlo procedure was used to determine the geometric and

O

trigger acceptances. For each a or n (peak and sideband) in the data

64

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moms : at can common mums on 30 now Amm>usov mcomuowpmum oaumu
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65
a set of two-photon decays was generated with the same 3emomentum. The
decay photons were then tested for geometric acceptance within the
fiducial region. Both generated photons in each decay were also
required to be above 1 Gev in energy. The trigger parameterization
described in Section 3.3.2 along with the back to total energy
partitioning procedure described in Section 3.3.3 were then jointly
applied to each decay meeting the above criteria to obtain the trigger
efficiency. Particular care was taken to include the effects of any
additional energy (photons and hadrons) which accompanied the meson
decay. Decays were generated until ten were accepted or a maximum of
100 decays was reached. The ratio of accepted to generated decays
defined the geometric acceptance while the trigger efficiency was
defined as the average of the trigger efficiencies for the accepted

decays.

In a Monte Carlo study discussed elsewhere31 the reconstruction
efficiencies for u° and n were determined for various ranges of
asymmetry at photon multiplicities of 2 to 8 and are given in Table

4.1.

4.2.3 Fiducial Limits in Rapidity and vertical Position

The P5 trigger threshold as described in Section 3.3.1 decreased

smoothly from the beam side to the away side of the detector. Near the

edges of the detector the geometric efficiency for accepting both

66

 

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67
photons from a no or n was lower than for the center of the detector.
Additionally, for fixed pT the energy is higher at high rapidity than
at low rapidity, resulting in smaller opening angles and better

geometric acceptance on the beam side of the detector (See Appendix C).

Fiducial limits in vertical position and rapidity were selected to
exclude regions of the detector where the combined trigger and
geometric efficiency was less than 10%. Table 4.2 gives the rapidity

and vertical position limits of ranges in pT for the no and n.

4.2.4 Inclusive no and n Production

Each event in the no, n or n°(n) sidebands that fell within the
rapidity and position limits given in Table 4.2 was weighted by the
inverse of the trigger (ct), geometric (:9) and reconstruction (er)
efficiencies described in the previous section. Additionally, the
azimuthal range (AO) of the detector as determined from the vertical
position limits in Table 4.2, and applied as a correction for azimuthal
acceptance. The combined correction for detector acceptance is
summarized as follows:

Correction = 1/(et) (cg) (er) (MI/21!)
This factor was multiplied by a background weight, as described in
Section 4.2.1, normalizing the sidebands to a background estimate. The
inclusive production for each range of 9T and rapidity was then

obtained by subtracting the corrected n°(n) sideband data from the

68

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69
corrected «0 and n data. The inclusive production of n0 and n for

incident n+ and p are given in Table 4.3.

4.2.5 Corrections to Beam

As described in Section 2.2.1 the fraction of each beam spill
during which the experiment was unable to accept events (dead time) was
‘monitored. The total beam was ‘monitored as well. By applying
corrections for dead time and some smaller corrections to be described,
the total number of beam particles which struck the targets while the

experiment was able to accept events was determined.

In passing through a target a beam is attenuated by absorption.
The total number of beam particles N(z) seen at a distance 2 within the
target is N. the initial number of beam particles multiplied by the
factor exp(-z/l) where x=49.9 cm is the absorption length (in this case
for carbon). The carbon targets presented a total of 2.54 cm depth of
target to the beam. By integrating N(z) over the target depth and
dividing the result by the total target depth a average N(z) is
determined. For the two carbon targets together a attenuation factor
of .975 is applied to the total number of beam particles to get the

effective average number of beam particles seen in the targets.

The incident beam consisted of protons, positive pions (about 13%),

K+ and from previous beam studies u+ (approximately 1%). At the start

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71
of the experiment the helium pressure in the beam Cerenkov counter
. . . . . . + .
mentioned in Section 2.1.1 was adjusted to max1mize the w detection

efficiency.

From inspection of the pressure curve it was determined that 2% of
the particles tagged as n+ were protons. The overall efficiency of the
detector was found to be 80%. The total number of incident particles
tagged as w+ or proton were then accordingly adjusted for contamination
and counter inefficiency. Correction was also made for the 1% u+
contamination. The 3% K+ component in the beam was identified by the
Cherenkov as n+ and due to the expected dominance of the u quark in

direct photon production (see Section 1.4) no correction for K+

contamination to the w+ signal was made.

The 50 MHz radio-frequency of the Fermilab accelerator resulted in
a 19 ns bucket structure as observed in Figure 3.9. The 107 particle
per second beam spill intensity resulted in an average beam bucket
occupancy of 0.2. By assuming a Poisson distribution for the bucket
occupancy the probability for a empty bucket was 81.87%, for a singly
occupied bucket 16.37% and for a doubly occupied bucket 1.64%. Higher
occupancies have probabilities on the order of 0.01% or less. As
described in Sections 2.2.1 and 2.2.3 the trigger vetoed events with
multiple particle hits in both planes of the beam hodoscope. From
geometric considerations the probability for a two particle event to
overlap in one or both planes of the beam hodoscope and thereby remain
unvetoed was determined to be 21.7%. As a result 21.7% of the

.0164/.1637 fraction of events with two particles passed the trigger

72
and contributed to the total beam particle count of the experiment.
The correction is then the product of the above (2.1%). Additionally,
it was determined in off-line analysis that due to discriminator
problems .5% of all triggered events had two particle hits in both
planes of the beam hodoscope. Rescaling for the extra particles from
the two particle events that triggered results in a 2.1% plus .5%
correction which is applied as a scale factor of 1.026 to the total

number of beam particles.

Data was taken without targets to measure backgrounds from
interactions in non-target material in the target area. The results
for “o and n were consistent with the target data but lacked sufficient
statistics to adequately determine a PT dependent background
subtraction. Instead the total particle count was scaled up by a
factor of 1.03 which gives the same effect as a background subtraction

with the same pT dependence as that of the target data.

The combined effect of these corrections was to increase the total
beam particle count by a 3% for incident proton beam and decrease the

particle count for incident fl+ beam by 5%.

73

4.2.6 to and n Invariant Cross Section Calculations and Results

. . O . .
In preliminary results of the n and n cross sections it was

determined that within statistical uncertainty there was no dependence
in rapidity range observed. Therefore, in order to maximize the data
the full range of rapidity for each FT range listed in Table 4.2 was
used in the final calculations. By using the corrections described in
the preceding section to get the total beam particle count and applying
a formula for the cross section described in Appendix D to the data in
6 Table 4.3 the results for the n° and n invariant cross sections for
both incident n+ and p are obtained and given in Table 4.4. The listed
errors are statistical. However, a systematic error due mainly to the
calibration of the energy scale to the no mass is also present. This
calibration resulted in a 1.8% shift in the n mass from its accented
value. A shift in the energy scale of the experiment of this magnitude
would result in an uncertainty in the cross sections of up to 16%.
Therefore a i 16% systematic error should be assigned to each cross

section reported here.

For use in single photon background studies a function of the form
exp (ainT) was fit to the no and n invariant cross sections determined
from the incident proton data. values of¢:=-57.9t0.06 and 3=—3.97i0.03

1

(GeV/c)- were obtained for the 'no data with <1=-59.2t0.33 and

=-3.71:o.12 (c;eV/o)"1 obtained for the n data.

 

74

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75

4.3 Direct-Photon and no Invariant Cross Sections and their Ratio

The invariant cross section was determined for direct-photons by

. . . . . o . .
first finding the direct-photon to «0 ratio. The W invariant cross
sections listed in Table 4.4 were then used to recover the

direct-photon invariant cross section.

4.3.1 Single Photon Signal

Each photon designated as a single photon in the procedure
described in Section 4.2.1 was corrected for trigger and azimuthal
acceptance, and for losses due to single photons randomly pairing with
another photon to form a no or n effective mass. The ranges in pT,
rapidity and vertical position for nos given in Table 4.2 were also
used in the selection of the single photon sample. For each single
photon the residual energy contribution to the trigger was determined
for all other photons in the x-front view of the detector. Then in a
procedure analogous to that outlined in Section 4.2.2 the back to total
energy partitioning procedure of Section 3.3.3 was applied to the
single photon energy a total of 10 times. For each generated back to
total partition a trigger efficiency was determined. The average of
the 10 efficiencies was then taken as the trigger efficiency (at) of
the single photon event. In order to compensate for single photons

eliminated from under the “o and ripeaks, a normalized number of single

76
photons from the no and n sidebands were added to the singles spectrum.
The azimuthal range (A4) of the detector for the fiducial limits at the
position and pT of each single photon was determined. Each single
photon was then weighted by l/(et) (Av/2n). Additionally, a downward
correction for contamination due to software reconstruction
inefficiencies of the no and n was applied. This correction varied
from 2.1% at 2.0-2.3 GeV/c pf to 1.4% at pf > 3.5 Ge‘V/c.31 The
resulting weighted single photon distribution was then divided by the
inclusive no production to produce a combined inclusive single photon
"y" to no ratio. This data is presented in Table 4.5 under the
heading, data ("y"/n°). The sources of background to the direct-photon

ratio in the above data will be presented in the following sections.

4.3.2 Backgrounds to the (Direct—Photon)/1ro Signal

Photons from unreconstructed «O, n, n', w decays and from charged
hadrons which simulated photon showers by interacting early in the
detector contribute a major part of the data "y"/u°. To recover the

direct-photon contribution these backgrounds must be eliminated.

These contributions to the background were modeled by use of Monte
Carlo techniques which relied on the no and n cross section results of
Section 4.2.6, estimates of the n‘ and w yields and evaluation of the

hadron contamination.

77

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78

4.3.3 Monte Carlo for 1°, 1, n' and w Direct Photon Backgrounds

The contributions of 1° decays to the direct photon background were
determined by generating decays with a uniform distribution in
PT,rapidity and azimuth throughout the region of space occupied by the
detector. The photons in each 1° decay‘were required to land at least
5 cm from each edge of the detector. Both photons in each decay were
also required to have an energy greater than 1 Gev. In decays where
one photon failed the above requirements the accepted photon was
designated as a background single photon. Each generated 1° and any
resulting background single photon from the 1° decay was tested for
acceptance within the fiducial limits in PT,rapidity and vertical
position given in Table 4.2. For each generated 1° a weight
proportional to the fitted value of the 1° inclusive cross section
(presented in Section 4.2.6) at the pT of the generated 1° was
calculated (ZWPTexp(a+BpT)). This weight was applied to each accepted
1° and any accepted background single from the 1° decay. The resulting
"inclusive" background single distribution was then divided by the

weighted 1° distribution to produce the background to the direct-photon

to 1° ratio given in Table 4.5 under the heading 1°("y"/1°).

In an analogous procedure an equal number of n decays were
generated using the n cross section given in Section 4.2.6. However,
in this case the "inclusive" background single photon distribution was
divided by the weighted 1° distribution described above. The resulting

"y"/1° ratio was then weighted by the .39 branching ratio for the

79
electromagnetic decay of the n and given in Table 4.5 under the heading

n ("Y"/“°)o

Estimates on the production ratios of n'/1° and m/1° were used
(0.9010.25 and 0.44:0.08 respectively) to generate n' and w+1°+y decays
in the manner described for the 1° and n above.32 These decays were
analyzed in the same way as the 1° and n decays to provide the upper
lhnits on the "y"/1° background given in Table 4.5 under the n‘("y"/1°)

and w°("y"/1°) headings.

4.3.4 Monte Carlo for the Charged Hadron Direct Photon Background

Approximately equal production of 1°, 1+ and 1‘ has been

observed.33 Based on these results the 1° cross sections given in
Table 4.4 can be used as an approximation to the 1+ and 1‘ cross

sections.

The LAC presented a 1.2 absorption length to pions (see Section
2.1.3). This implies that 70% of all charged pions that entered the
LAC interacted and deposited energy. As noted in Section 3.2.3 any
candidate photon which deposited more than half of its energy in the
back half of the detector was rejected as being a probable hadron.
However, there was no rejection of hadrons which interacted in the
front of the detector and deposited more than 50% of their energy

there. To estimate the contamination to the direct photon signal due

80

to this source a model was derived from E272 data in which charged
pions hitting the LAC were independently' measured with a magnetic
spectrometer. The usage of the LAC in E272 is described elsewhere.26

Analysis of this data determined that the distribution in the fraction
E(total)/Efi where E(total) is the energy deposited in the LAC by a
charged pion of energy E1 was independent of the pion energy. This
distribution was fit to a low order polynomial in the region where the
fraction exceeded 0.5. Similarly, the distributions of
E(back)/E(total) where both are deposited energies, were fit to a low
order polynomial in several ranges of E(tota1)/E1 in the region
E(back)/E(total) greater than 0.5. The distributions of
E(back)/E(tota1) showed that between 49% and 67% of interacting hadrons
(depending on the total energy fraction) deposited more than half of
their energy in the front of the LAC Which would allow them to pass the
hadron rejection described in Section 3.2.3. with the
parameterizations of the various distributions it was then possible to
use the 1° cross sections given in Table 4.4 to generate a inclusive
distribution of 1+ and 1' and predict howwmany charged pions would
appear as photons within the fiducial limits described in the previous
SGCtiODS- The resulting PT spectrum was compared to the inclusive pT
spectrum for 1°s used in Section 4.3.3 to provide the estimate of
"y"/1° due to charged pions. A upper limit on charged hadron
contamination was obtained by rescaling the charged pion contamination
by the sum of the production ratios of K+\‘, /p and n/h'to 1+ or 1’.
This results in a factor of 2.0 due to the 2 species of charged pion,
0.S3+0.l7 from Kaons and 1.11+0.03 from Protons and Neutrons.34 The

upper limit on charged hadron contamination is then 3.84 times the

81
estimate for charged pion contamination and is given under the charged

hadron ("y"/1°) heading in Table 4.5.

Chapter 5

Final Results and Conclusions

In this Chapter the w°, n and Direct Photon inclusive production
cross sections for p and 1+ beams interacting in carbon targets will be

presented. Comparisons with world data will be discussed.

5.1 1° and n Inclusive Production Cross Sections

The 1° and n cross sections listed in Table 4.4 for incident p and
1+ are presented in in Figures 5.1. Within experimental errors, the 1°
and n cross sections have the same pT dependence. The ratio of n to 1°
production averaged over all the data on carbon is n/1° =0.49i0.03,
whiCh is consistent with recent measurements at large pT on hydrogen35
and on beryllium36 at 200 GeV/c. The production ratio of 1° to n for
p—C at 2.89 GeV/c is 0.538i0.052. Measurements of K+/1+ at 200 GeV/c
report ratios of 0.42:0.02 for p—p , 0.487t.OlO with pew, 0.489i0.009
with p—Ti and 0.46210.029 with p-Be all at 3.08 GeV/c pT,33 All but

the p—p data compare within experimental error indicating an

approximately equal production of K+ and n at large pT.

82

83

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84

One of the earliest indications that large-pT production could be
related to hard scattering of constituents was provided by Donaldson
et al.,37 in their observation of an increased yield of 1°s at large pT
in 1+p relative to pp collisions. This increase was attributed to the
higher probability of finding a large-x valence quark in the structure
function of a pion. The results shown in Figure 5.2 indicate a sinfilar
effect in interactions on a nuclear target (carbon). This suggests
that any rescattering which occurs in the nuclear targets does not
obscure the differences observed in meson production from the hard

interactions of pions and protons on single nucleons.

5.2 y/1° and Direct Photon Inclusive Production Cross Section

The ratio of single photons to the inclusive 1° yield listed in

Table 4.5 under the "data (y/1°) " heading is shown for proton and 1+

beams in Figures 5.3a and 5.3b respectively.

The data have been integrated over c.m. rapidities between -0.75
and +0.2. Also shown are the background contributions to the ratio
expected from the undetected 1° and n decays, m° and n' decays, and
hadron contamination listed in Table 4.5. Typically, the 1° and n

decays constitute, respectively, 56% and 19% of this background. Below

a PT of 2.5 GeV/c the data are consistent with contributions expected

from the background. F0; P§>3.0 GeV/c the data are consistently above

the level expected from the background. The inclusive cross sections

85

 

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86

 

a)

 

 

 

 

2.0 3.0 4.0 5.0 6.0
pT (GeV)/c

 

b)

 

 

Y/w°

 

 

 

 

 

 

 

 

 

2.0 3.0 4.0 5.0 6.0
pT (Cell) I:

Figure 5.3; Inclusive (direct photon + background) to 1° ratio at 200
GeV/c with a carbon target in the center—of-mass rapidity interval
(-.80 to .2) a) for incident p b) for incident 1*, shaded bands are
background estimates.

87
for direct-photon production computed from the inclusive y/1° and 1°
inclusive cross sections after subtraction of the y/1° background are
given in Table 5.1. It is important to emphasize that these are
inclusive measurements; no restrictions have been placed on the
associated event structure. In fact, most of the single-photon and 1°
triggers above a PT of 2.5 GeV/c consist of isolated showers with
little if any additional electromagnetic activity within the acceptance

region of the photon detector.

In the following paragraph comparisons will be made to other

measurements . 38

These results are in reasonable agreement with a previous

measurement of the y/1° ratio at Fermilab (Baltrusaitis et al.3°) of

Y/I° =0.05-0-09 in PBe*YX: for 9T)3 GeV/c. However, at smaller values
of transverse momentum (PT<2.5 GeV/c) the data presented here show an
upper limit for y/1° of 0.02; this result is well below that of the
previous measurement. The results presented here are more consistent
with those obtained at the CERN intersecting storage rings (ISR), where
‘measurements of direct photons39 and of lowamass virtual photons (e e’

)40

pairs indicate several-percent upper linuts for the y/1° ratio in

the pT range of 2-3 GeV/c, and a subsequent rapid rise of that ratio

With increasing PT. The measurements of Amaldi et al.39

in the PT range
of 3-4 GeV/c at l§251 Gev are consistent with the value of y/1°=0.03
that is found here for l§el9.4 Gev. The value of 0.03 is just below
but within systematic error of the measurements of Diakonou et al.39 in
the same pT range but at at /§231 Gev. Theoretical estimates for y/1°

are about a factor of 2 below the results presented here.41

88

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89
It is useful to note that the results for the y/1° ratio are
similar in both the proton and 1+ data. In view of the predicted
dominance of the u-quark (see Section 1.4) Compton process for photons
in this range of p , only small differences in the ratio would have

T

been expected.

The scaling behavior of inclusive photon production with energy was
investigated by comparing this data with the measurements from the ISR
that have the most reliable absolute normalization.42 A fit to the
form C(l-xT)MpT-N, where C is a normalization factor, yielded values of

29

M=10.li0.7, N=6.2:O.2, and c=(3.4:1.4)x1o’ cmz/Gevz. Effects from

uncertainty in the relative normalization of the two experiments have
been included in the errors.
6.2

The cross section data multiplied by 9T

fitted function in Figure 5.4. Plotted this way the data at the two

are compared to the

energies do seem to display a purely xT dependence. The fitted value
of N=6.2 is significantly lower than the corresponding value of N=8
found for 1° production, but larger than the value N=4 expected in
naive parton models and close to the value of N=5.3 found for jet

production at the ISR and SPS.17

In conclusion a clear signal for direct-photon production in both
pC and 1+C collisions for pT>3.O GeV/c has been Observed. The y/no
ratio at fixed p? appears to be nearly energy independent between
75219.4 Gev and 15563 Gev. Finally, the inclusive photon yield has a

pT dependence that is close to the form observed for production of

90

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91
constituent jets at the ISR, as would be expected on the basis of the

kind of diagrams shown in Figures l.2b and 1.2d.43

APPEND ICES

92

Appendix A

LAC Fast Outputs

a) Timing

High energy photons dissipate energy in the LAC through the
formation of electron positron pairs whiCh lose energy by ionization of
the material in the calorimeter. The number of ion pairs formed in
electromagnetic showers is therefore proportional to the energy of the

photon.

‘When ionization occurs in a LAC cell (see Figure A.la) the observed
current is given by

i(t) = Ne(l-t/td)Vd/d

where N is the number of ion pairs, v6 is the drift velocity, e is
electron Charge and td is the time required for a Charge to cross a
cell of width d.23 In the experiment Charge sensitive amplifiers were
use to process LAC signals. The amplifiers produced a voltage V

proportional to Charge where

2
vimp a Ne(t/td - t /2td) .

It is important to note that this voltage is directly proportional to N
the number of ion pairs whiCh, as noted above, is directly proportional
to the energy (E) of the photon. The voltage for the fast outputs of

the LAC, which are used for timing, rise linearly for short times

(t _<. td/Z) as

vamp a Net/t:d a Et/td.

93

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure A.l: a) Ionization in a single LAC cell b)
time for energies El<EZ<33-

pulse height vs

94
Low threshold discrimunators on the fast outputs provided the stop
signals for TDC's (Time to Digital Converters) initiated by the
pre—trigger described in Section 2.6.1. The time for a signal to come
above a given threshold (see Figure A.lb) is proportional to Vth where
Vth is the discrimunator threshold voltage and inversely proportional
to energy. Operationaly the LAC thresholds varied from channel to
Channel and delay times due to differing signal cable lengths and
amplifier responses resulted in a two parameter model for the timing of

each strip,

ti = ai +bl/E

where ai is the offset, bi accounts for differences in TDC

discriminator thresholds and E is the energy deposited in the strip.

b) Capacitive Effects in the LAC

The experimental trigger which utilized the sum of the amplifier
fast outputs was subject to capacitive distortions. The source of
these distortions will be evaluated using a simplified model of the LAC
shown in Figure A.2. Two LAC signals, 31 and 52 are amplified and
summed. The low mobility of positive ions relative to that of
electrons results in a net positive charge remaining at LAC strip 1
after all the electrons have been collected. This positive Charge
induces an image in the negative high voltage plate (lead conversion
sheets in the physical LAC) which results in a signal of opposite sign
in strip 2. The presence of a ballast capacitance (Cb) prevents the
real signal due to ionization in strip 1 from being cancelled by the

induced signal in strip 2. Image charge effects are kept within

95

 

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r:

Cb

J
|

 

 

 

i
“@9431
see»
a
6‘9»
i

 

 

 

51+52

 

Figure A.2; Signal formation in a simple LAC model.

96
'manageable limits by munimuzing the ratio of detector to ballast
capacitance. This ratio was approximately 1/3 for the LAC used in this

experiment.

C) pTx Trigger Model

To compensate for the image charge effect just described a modified
weighting of the individual strip energies where the strips are the
anodes of the LAC cells was used to aChieve a pTX trigger. Referring
again to Figure A.2 the same voltage drop appears across both the
ballast capacitance (Cb) and the effective capacitance (Cd) of the
‘detector. As a result in this simple 'model of a LAC the Charge
(Qi=Qbi+Qdi) collected from the ionization at any given strip (i) will
ultimately come from the ballast (Cb) and detector (Cd) capacitance in
the ratio Y = Qd/Qb = Cd/Cb 3 1/3. Any Charge Qdi drawn from the
capacitance of the detector at one strip will appear as a image charge
'Qd. collected from the other strips in the detector. As noted earlier
the1 energy deposited in a given strip (E1) is directly proportional to
the amount of ionization appearing at the strip. This ionization is

collected as

Qstrip = Qi-YQ/(l+r)n

where Q = §Qi and n is the total number of strips in the summation.
1

The direct proportionality relationship between ionization and

deposited energy results in

E = Ei-E/4n

strip

where (y/(1+y)=1/4) and E = 231,
i

97
The trigger was formed by giving each x-strip a weight wi and
summdng over all strips to produce
T = 523E]: (wi-G/4) o
For our detector a weighting of
recovers a transverse momentum trigger

T = PTX = fsin°i.

The correction to sine weighting that was actually used varied from
0.081 on the away side of the detector to 0.057 on the beam side of the
detector which resulted in an approximately constant yield of events
across the detector (see Section 3.3.1). With this weighting WV4=0.051
whiCh compares with the value of 0.067 derived from the data as

described in Section 3.3.2.

98

Appendix B

LAC Trigger Efficiency (PT)

The simplest model for PT trigger turn-on is illustrated by

Figure B.la. At 9T values below the threshold (4) the trigger is

completely off and for values at or above A the trigger is 100%
efficient. However, to account for variations of measured pT from
actual PT due to the resolution of the detector and electronic noise a
more complicated ‘model for the trigger turn-on is required. One
possible procedure is to assume that the measured pT varies from the
actual PT according to a Gaussian distribution (represented by the bell
shaped curve in the figure). In this model the probability of a given

event 0f PT=P being above threshold is

prObability = IS-AG(pT)de' where
1

_ _ 2 2
G(pT) —d7z?.exp[ (pT-X) /Zo 1.
The effective trigger efficiency (turn-on) as a function of pT is then

efficiency(pT) = ,5[1,.etf(pT_x),o]

where erfmT-l) = (Z/MISTX eXPl-(pT-k)2/202]de. The effect of this
trigger resolution "smearing" is shown in Figure B.lb where the trigger
turn-on is shown for Gaussian "smeared" pT (curve with point of
inflection at A). The trigger turn-on for the "sharp" threshold (step
function) is shown for comparison. For 0+0 the "smeared" trigger
converges to the step function. At the nominal threshold of A the

efficiency for the smeared trigger is 50%.

99

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100

Appendix C

E629 Variables and Lorentz Kinematics
a) Meson yy Decay

For the decay of meson + yy a straightforward application of the
Lorentz transformation and some algebra yields a useful relationship
between the lab (measured) energies of the decay photons E1 and 32' and
the angle 6* between the meson center of mass (CM) decay axis and lab

momentum axis

LLWW = (Ez-El)/(E2+E1) = 3cos°*.

Due to the cose* term, a meson with an isotropic decay will have a flat

asymmetry distribution in the CM.

b) Lab Opening Angle

Comparison of the scaler products of the meson 4-momentum in the CM
and the sum of the 4-momenta of the decay photons in the LAB yields the
following relationship

cose = 1-2/[1+P2(1-cosze*)]
E?

where P is the meson momentum and e is the angle between the 3-momenta
of the decay photons in the lab frame. For fixed P and m, a minimum is
obtained for a when e*=i1/2 radians, while a maximum of 6:1 radians is
obtained when e*=t1 radians. Also, for fixed P and e' a increase in

the meson mass m will result in a increase in the minimum a.

101

c) Rapidity

The standard Lorentz invariant differential volume element in
momentum 3-space is d3P/E.
However, when the Lorentz invariant variable of interest is pT,
Ed30/d3P = f(P1,P2,P3) is awkward. A more useful parameterization can

be formed with the variables pT and rapidity (y) where

y = .5 ln[(E+PL)/(E-PL)]
with PL being the component of momentum parallel to the rapidity

(Lorentz boost) axis. Application of the Jacobian

dedy= det[a(pT.y>/8(P.6)]dpde

yields
d3p/E=2wp dp dy
TT'
This results in the parameterization
dO/ZIQpoTdy = f(pT,y)

where Pb is Lorentz invariant and y(Lor. trans.)* y—.51n[(l-B)/(1+8)].
With this parameterization f(pT,y) has the same distribution in Pa and
the same shaped distribution in y under all Lorentz transformations

parallel to the rapidity axis.

102

Appendix D

Experimental Determination of Invariant Differential Cross Sections

The Lorentz invariant differential cross section is given by

air 6°

d p Zflpwdedy

where y is rapidity.

If a total of No particles strikes a target of density 0 nucleons

I per cmz, a total production of

N = NOZ'NPTAP by da
2prdedy
will be observed within the ranges of 4y and pTiApT/Z in rapidity and
pT. Experimentaly the differential cross section becomes for N observed
events about a given pT within a given rapidity range

do = N .
21' ppoTdy 2" No a pTA pTA y

 

LIST OF REFERENCES

1)

2)

3)

4)

5)

6)
7)

8)

9)
10)
11)

12)

13)

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103

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105

assuming equivalent production for protons and neutrons and a
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These are essentially the results of the experiment of Diakonou et
al., Ref. 37, multiplied by a factor of approximately 1.4 to
correct the 'measurements to inclusive yields. Also see
V. Burkert's study of the scaling properties of direct-photon
production, in Proceedings of the Eighteenth Rencontre de Moriond,
Les Arcs, France, 1983, edited by J. Tran Thanh‘Van (to be
published); and J. Huston, in Proceedings of the Colloquium on
Multiparticle Dynamics, Lake Tahoe, 1983, edited by J. Gunion (to
be published).

W3 Molzon, in Proceedings of the Eighteenth Rencontre de Moriond,
Les Arcs, France, 1983, edited by J. Tran Thanh van (to be
published).