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A COMPARISON OF NEUTRAL TO CHARGED CURRENT,
NEUTRINO-NUCLEON INTERACTIONS IN A WIDE BAND

NEUTRINO BEAM AT FERMILAB

By

John Allen Slate

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

Q

ABSTRACT
A COMPARISON OF NEUTRAL TO CHARGED CURRENT,

NEUTRINO-NUCLEON INTERACTIONS IN A WIDE BAND
NEUTRINO BEAM AT FERMILAB

By

John Allen Slate

Results of measuring Neutral and Charged Current, neutrino-nucleon
interactions, using a Wide Band neutrino beam at Fermilab are presented.
The Neutral Current structure functions are measured (relative to the
Charged Current structure functions) to determine if sufficient evidence
exists for neutrally charged constituents within the nucleon, which are
unobserved in Charged Current interactions. The struchnwefunctnni
comparison does not utilize the usual 83 orken scaling variables, but
rather, the quantity £02, calculated from measurement of Unarecoil
hadronic system. Data indicate no difference between the Neutral and
Charged Current structure functions. Based upon a corrected data sample
of 2850 Neutral and 8832 Charged Current events, we measure an
integrated ratio; Ru = 0.323 :t 0.007 (stat.) i 0.025 (sys.), which is
consistent with a value of sin’Ow - 0.217 1 0.032 (stat.)

i 0.021 (sys.).

to the Lord God,
who makes all things
possible.

ii

ACKNOWLEDGMENTS

First and foremost, I wish to thank my thesis advisor, Maris
Abolins, for his guidance, advice, instruction and encouragement for the
duration of this vmnfl<. I have learned much about being a good
experimentalist through his example and teaching, and will carry his
influence throughout the rest of my endeavors.

Two individuals, Raymond Brook and Jorge Morfin, have taken special
interest imitny work. They encouraged me to investigate physics topics
not entirely related to this work and provided me with literature, ideas
and many interesting discussions. My thanks to them both.

I thank the members of the 859“ collaboration. Each of you has had
a direct, positive influence upon me and upon my understanding of
Physics. I especially want to thank my fellow graduate students: Andy
Cohen, Mike Tartagflia, Juan Bofill, Tom Mattison, Gong Ping Yeh, Terry
Endridge, Aseet Mukhenjee, and Rich Magahiz. We shared common
interests, insights, knowledge and income levels. Thanks go to Ron
Olsen, Super-Technician, a man who knows everything and can fix
anything, and to the summer students, Sue, Carrie, Anna, and Joe, who
will always be honorary "59A'ers".

I wish to thank the Fermilab Neutrino Department Staff for their
expertise and assistance, the Neutrino Beam Line Technicians, who
answered our frantic calls anytime day or night,enuithe Accelerator

Staff, who kept the protons flying in their predetermined paths.

iii

Thanks are in order for Pam, Cheryl and Linda of the Fermilab
Housing Office, and to Phyllis, Sherry and Joy of the Fermilab Users'
Office, for providing a human side to Fermilab. Special thanks to
Phyllhsfble, for her role as surrogate mother to me and many other
lonely graduate students.

To the MSU High Energy Group, its faculty, staff and students, I
offer my thanks for providing a fun atmosphere for learning and work.
Special thanks to Steve Cooper, Lisa Dillingham, and Ron Richards for
friendship above and beyond the call of duty.

I thank my father, Alfred, whose interest in Astronomy sparked and
sustained my own interests in science, my mother, Clara, for selfless
love and encouragement, and my brother, Jim, a man of excellence in his
own right, for enhancing my understanding of the world of fine art.

I thank my two "extended" families at Blanchard Road Alliance
Church, in Wheaton and at East Lansing Trinity Church here in East
Lansing.

Special thanks to Mark Johnson and Dave Rinard, for life-long
friendship.

I thank the National Science Foundation for its support of my
education.

To all my family, friends and educators: Yes, I know my name is on

the title page, but you have all had a share in it.

iv

TABLE OF CONTENTS

List of Tables . . . . . . . . . . . . . . . . . . . . . . . .page

List of Figures. . . .

Chapter 1.
1.1.
1.2.
1.3.
1.“.

1.5.
Chapter 2.

2.1.

2.3.

Introduction . . . . . . . . . . . . . . . . . . . .
Weak Interactions . . . . . . . . . . . . . . . . .
Kinematics. . . . . . . . . . . . . . . . .

Neutrino Beams and Detectors. . . . . .

Review of Experiments . . . . . . . . .

1.”.1. Gargamelle. . . . . . . . . . .

1.”.2. HPWF/HPWFRO . . . . . . . . . . . . . . . . .
1.“.3. CITF/CITFR/CFRR/CCFRR . . . . . . . . . . . .
1.A.A. CRS-BNL/CR-BNL. . . . . . . . . . . . . . . .
1.“.5. CDHS. . . . . . . . .

1.“.6. CHARM . . . . . . . . . . . . . . .

The E59N-FMMN Experiment.

Neutrino-Nucleon Interactions. . . . . . . . . .

The Parton Model. . . . . . . . . . . . . . . . . . . .
2.1.1. Assumptions . . . . . . . . . . . . . . . . . .
2.1.2. Lepton-Parton and Lepton-Nucleon Scattering .
Charged Current Neutrino-Nucleon Scattering .

2.2.1. Structure Functions . . . . . . . . . .

2.2.2. The Parton Model, Quarks, and Structure
Functions . . . . . . . . . . . . . . . .

The Standard Model. . . . . . . . . . . . . . . . . .

ix

1O
11
13
13
13
15
17

17

21

26

2.“.
Chapter 3.

3.1.

3.2.

3.3.

3.“.

3.5.

3.6.
3.7.
Chapter “.
“.1.
“.2.
“.3.

Chapter 5.

2.3.1. The Weinberg-Salam Model for Leptons. . . .page
2.3.2. Weinberg-Salam Extension to Hadrons . . .
Neutral Current Neutrino-Nucleon Scattering .

The E59“ Detector. . . . . . . . . . . . . . . . . . .
General Overview. . . . . . . . . . .

The Flash Chambers. . . . . . .

3.2.1. Construction. . . . . . . . . . . . . . .
3.2.2. Performance .

The Gas Cart.

3.3.1. Gas Flow. . . . . . . . . . . . . . . . .
3.3.2. Gas Purification.

3.3.3. Gas Monitoring. . . . . . . . . .

The High Voltage System. . . . . . . . . . . . . . .
3.“.1. Overview. . . . . . . . . . . . . . . . . . . .
3.“.2. The High Voltage Regulator. .

3.“.3. High Voltage Pulse Monitoring System. . . .
Proportional Tube Planes. . . . . . . . . . . . . . . .
3.5.1. Construction. . . . . . . . . . . . . . .
3.5.2. Trigger Electronics . . . . . . . . . . . . . .
3.5.3. Trigger Logic . . . . .

Toroids . . . . . . . . . . . . . . . . . . . . .
Online Computer . . . . . . . . . . . . . . . .

Surveying and Alignment. . . . . . . . . . . . .
Overview. . . . . . . . . . . . . . . . . . . . . . .
Surveying . . . . . . . . . . . . . . . . . . .
Alignment .

Calibration. . . . . . . . . . . . .

vi

26

31
33
33
36
36
“1
“8
“8
“9

51

52
55
58
61
61
61
63
6“
65
66
66
66

68

73

5.2.
5.3.
5.“.
Chapter 6.
6.1.
6.2.

6.3.

6.“.
6.5.
Chapter 7.
7.1.
7.2.
7.3.

7.“.

7.5.

7.6.

Chapter 8.

Beam Line . . . . . . . . . . . . . . . . .
The Trigger . . . . . . . . . . . . . . . .
Angle Resolutions . . . . . . . . . . . . .
Energy Resolutions . . . . . . . . . . . . .

The Experiment . . . . . . . . . . . . . . . . .
Beam Line . . . . . . . . . . . . . . . . . . .
Monitoring. . . . . . . . . . . . . . . . . . .
WBB Flux. . . . . . . . . . . . . . . . . . . . .
6.3.1. Monte Carlo Simulation.

6.3.2. Comparison With Data. . . . . . .
Event Triggers. . . . . . . . . . . . . . . . . .
Gating. . . . . . . . . . . . . . . . . . . . .

Data Analysis. . . . . . . . . . . . . . . .
Purpose . . . . . . . . . . . . . . . . . . . . .
Data Analysis Software. . . . . . . . . . . . . .
Data Cuts . . . . . . . . . . . . . . . . . . .
NC/CC Ratio . . . . . . . . . . . . . . . . . .
7.“.1. Monte Carlo . .

7.“.2. Antineutrino Distributions. . . . . .

7.“.3. Correction of Data. . . . . . . . . .

Determination of NC Structure Function Parameters .

7.5.1. Parameterization. . . . . . . . . . . .
7.5.2. Analysis Approach . . . . . . . . . . .
7.5.3. Systematic Error Approximation. . . . .
7.5.“. Results . . . . . . . . . . . . . . . .
Comparison With Other Experiments . . . . . . . .

conCIUSionS. O O O O O O O C O O O O O O O O O 0

vii

.page

73
75
76
85
85
87
91
91
92
95
98
103
103
10“
113
11“
118
120
126
130
130
131
132
1“1
1“1

1“6

Appendix A. The E59“ Monte Carlo Program.
A.1. Electromagnetic Showers .
A.2. Hadronic Showers.
A.3. Non-Catastrophic Processes. .
A.“. Flash Chamber Data. . . . . .

A.5. Proportional Tube Data.

A.6. Comparison With Calibration Data.

Appendix B. Derivation of E02 .

List of References . . . . . . . . . . . .

viii

.page

1“9
1“9
150
152
152
153
153
166

170

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

2.1.
5.1.
6.1.
6.2.
7.1.

7.2.

7.3.

7.“.

7.5.

LIST OF TABLES

Quark Quantum Numbers. .

Hit Cell Enhancement for 10 Cell Regions .
Run Type Triggers and Gate Scheme.
Total Triggers by Trigger Type .

Variation of A8 to 8CC .

Fitted Values of Bnc for Simulated Data.

Results of Two-Parameter Fits.

Summary of N88 Analysis.

Summary of CHARM Analysis.

Angular Profile Comparison .

Magnitude of (W/Eh)2

ix

.page

211

81
101
102
139
1110
1112
1113
1115
165

169

Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure

Figure

1.1.
2.1.
2.2.
2.3.
3.1.
3.2.
3.3.
3.“.
3.5.
3.6.
3.7.
3.8.
3.9.
3.10.
3.11.
“.1.
“.2.
“.3.
5.1.
5.2.
5.3.

5.“.

LIST OF FIGURES

Deep Inelastic Neutrino-Nucleon Scattering.

Parton Scattering (Breit Frame)

Lepton-Parton Scattering. . . . . . . .

Neutrino-Nucleon Scattering (CC and NC Case).

The E59“ Detector . . . . . . . . . . .

Construction of Flash Chamber Readout .

Voltage Output from Magnetostrictive Amplifier.

Flash Chamber Efficiency and Hit Cell Multiplicity.

Efficiency Stability During WBB Run .

Efficiency and Delay Measurements - June 1981

Schematic of Gas Recirculator . . . .
PFN Circuit and High Voltage Pulse. . .
Schematic of High Voltage System. . . .

Schematic of Regulator Circuit. . . .

High Voltage Pulse Monitoring system (PQD).

Flash Chamber Coordinate System . . . .

Single View Deviations (in clock counts).

Three View Deviations (in clock counts)
Calibration Beam Line . . .
Muon Angle Resolution . . . . . . . . .
Electron Angle Resolution .

Hadron Angle Resolution .

1“
16
18
3“
39
“O
“3
“5
“7
50
53
5“
56
59
67
70
71
7“
77
78

79

Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure

Figure

.10.
.11.
.12.
.13.
.1“.
.15.
.16.
.17.
.18.

Electron Energy calibration and Resolution. . . .page
Hadron Energy Calibration . . . . . . . . . .

Hadron Energy Resolution. . . . . . . . . . .

NO Wide Band Beam Line. . . . . . . . . . . .

POT Distribution for HORN ON/OFF. . . . . . . .

Muon Counter Distribution for HORN ON/OFF . . .
Energy Spectrum from Quasi Elastic Data . . . . .
Energy Spectra from Charged Current Data. .

Schematic of WBB Gating . . . . . . . . . . . . .
Data Analysis Flow Diagram. . . . . . .

Typical CC Event. . . . . . . . . . . .

Typical NC Event. . . . . . . . . . . . . .

Blow-up of CC Event . . . . . . . . . . . . . . . . .
NC/CC Ratio - Data. . . . . . . . . . . . . .
Contours of Constant E02. . . . . . . . . . . . . . .
NC/CC Ratio - Data and Monte Carlo. . . . . . . . .
CC Misclassification as Function of E02 . . . . .

'CC Misclassification as Function of E02 .

fCC(EO’).

fnc(E02). . . . . . . . . . . .

Corrected NC/CC Ratio - Data. . . . . . . . .
Corrected NC/CC Ratio - Monte Carlo . . . . . . . .
Stability of fine to E02 Range . . . . . . . . . .
Effect upon Bnc to Variations in a and B. . .

Effect upon fine to Variations in 5 and Y. . . . . .
Effect of Hadronic Energy Resolution and Offset . .

Effect of Hadronic Angle Resolution .

xi

82
83
8“
86
89
90
93
9“
99
105
107
108
109
115
117
121
122
123
12“
125
127
128
133
13“
135
137

138

Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure

Figure

Energy Comparison - 10 GeV. . .
Energy Comparison - 35 GeV.
Energy Comparison - 100 GeV .
Monte Carlo Energy Difference .
Density Comparison - 10 GeV .
Density Comparison - 35 GeV . .

Density Comparison - 100 GeV.

Shower Length Comparison - 10 GeV .
Shower Length Comparison - 35 GeV .

. Shower Length Comparison - 100 GeV.

xii

15“
155
156
157
159
160
161
162
163

16“

CHAPTER 1. INTRODUCTION

1.1. WEAK INTERACTIONS

Weak interactions were first studied via nuclear B-decay
experiments. The B-particle was known to be an electron. What puzzled
experimenters of the 1920's was that the electron's spectrum was
continuous rather than discrete. In 1930 Pauli suggested that there was
a very light, uncharged, penetrating particle call a neutrino which
shared the decay energy with the emitted electron. The existence of
this electron-type neutrino (actually antineutrino) was confirmed by
Reines and Cowan1 in 1959 using the antineutrino flux from a nuclear
reactor.

Fermi took Pauli's idea and began the first steps towards placing
the Weak interaction on a firm theoretical basis. Fermi2 described the
interaction in terms of a four-fermion point interaction, whose strength
was given by a single constant. It is also possible to describe the
Weak interaction as the interaction between two currents, mediated by a
weak-interaction quantum. Since the Weak interaction in the B-decay
interactions changes charge, the quantum must be charged (Wi). Thus the
B-decay interactions are described as a Charged Current (CC)
interaction.

Experimentally, during the late 1950's it was discovered that the
Weak interaction does not conserve pari ty,3 the neutrino's helicity was

measured,“ and the space-time nature of the Weak interaction was

2
deternnxuui.5 The experiment which determined the space-time structure
did so by analyzing the decay branching ratios of pions and muons.
Muons, which are like electrons only more massive, were found to have an
associated neutrino.6

With the advent of large accelerators in the 1960's and 70's, it
was possible to perform experiments utilizing intense beams of muon-type
neutrinos (and antineutrinos). One of the biggest surprises was the
discovery of weak-neutral current (NC) interactions in a bubble chamber
in Europe.7 Since then, over the last ten years, many experiments have
probed the nature of the Weak interaction in neutrino-nucleon and
neutrino-electron interactions.

Theoretically, the original description by Fermi was shown to cause
problems beyond the leading order in perturbation theory. In 1967.
Weinberga and Salam9 purposed a model for the Electro-Weak interactions
of leptons, This so called "Standard" Model was extended to hadrons
(quarks).10 The data are consistent with a single value for the only
parameter of the model, sin’Ow = 0.23 i 0.01.11

The Standard Model has had many successes, including the prediction
of the existence of neutral-current interactions. Recent discoveries of
the W1 and 2° bosons”’” add credence to the Standard Model. Despite
its successes, some of the basic assumptions remain untested or poorly
constrained. The limits of the Standard Model are being tested in some

of the current European experiments.‘“

1.2. KINEMATICS
A schematic of deep inelastic neutrino-nucleon scattering is shown

in Figure 1.1. K and P are the four-vectors (E,P) of the incoming

 

 

N(P)

DEEP INELASTIC NEUTRINO SCATTERING

Figure 1.1. Deep Inelastic Neutrino-Nucleon Scattering

u
lepton and target nucleon. K' and P' are the four-vectors of the
outgoing lepton and hadronic system X. The momentum transfer via the
intermediate boson is q (v.6). The interaction can be defined 1J1 terms
of Lorentz-invariant variables:

Q2 = _q2 = ’(K _ Kv)2 = ’(P' _ p)2

 

v a
W2 = (P')2 = (P + q)2.
In the laboratory frame, neglecting lepton masses, we can write the
variables as:

Q2 = 2E E (1 - cos 0

A 2' 22')

v = E a E - M
x

2 ’ Ei'
W2 = M2 + 2Mv - Q2

where M is the nucleon mass. Alternatively, one can use the

dimensionless Bjorken scaling variables x and y, defined as:
Q:
2Mv ’

Mv
Y'fi,osy31o

 

x = 0 S x S 1

In the laboratory frame, y - (E - E£,)/E£ . Ex/E .and is the fraction

2 A
of the incident lepton energy transferred to the hadronic system.
The scaling variables are useful, and in particular, it is common

to write the cross section in terms of x and y. For

(anti)neutrino-nucleon scattering:

do(“'V) g GZME (v.5)

dx dy n

1
'5 Y2JF2

 

1 ,“
[(1-y+ (x) 1 (1--§ y)ny,‘V V)(x)].
F} and xF3 areluunnias the weak-nucleon structure functions and (to
first order) are functions only of the scaling variable x. (At higher

orders, they depend upon both x and Q2.) These structure functions are

a result of the nucleon being an extended system of quarks, exhibiting

5
complex structure to the Weak interactions. In general, the structure

functions will differ for Charged and Neutral Current interactions.

1.3. NEUTRINO BEAMS AND DETECTORS
In order to perform an experiment using neutrinos, it is necessary
to have both an intense beam of high energy neutrinos and a detector.

‘38

Since neutrino cross sections are very small, (=10 cm2 at a neutrino
energy of 1 GeV) the neutrino beam must have a high intensity in order
that the interaction rate in the detector be reasonable. Ideally, a
good detector should be able to measure the energy and angle of all
particles in an interaction. Also, because of the small cross section,
neutrino detectors must be massive, usually anywhere from a few tons to
several hundred tons.

High energy neutrino beams are made using a standard technique. A
proton beam from a large accelerator is extracted and is directed toward
a target. The target material is usually a low atomic number metal such
as Aluminum or Beryllium. Secondary particles, mostly pions and kaons,
are formed from interactions between the protons and the target. The
secondaries travel through an evacuated region, allowing time for decay,
with decays dominated by two-particle decays of a muon and a muon-type
neutrino. Following the decay region is a large amount of absorber
material to filter out all other particles except the neutrinos. Most
high energy neutrino experiments are done at one of two laboratories:
the Fermi National Accelerator Laboratory (FNAL, Fermilab) in Batavia,
Illinois, and the European Organization for Nuclear Research (CERN) in

Geneva, Switzerland.

6

There are two main types of neutrino beams, Wide Band (WEB) and
Narrow Band (NBB). In a Wide Band Beam, the secondary mesons are sign
selected before the decay region. The sign selection is done by using a
magnet element. Mesons of a given sign are focused and collimated
toward the decay region, opposite sign mesons are defocused. Upon
decay, the neutrinos are predominately muon-type neutrinos (or
muon-antineutrinos). This provides an intense beam of neutrinos over a
wide spectrum of energies. If the secondary mesons are both sign and
momentum selected, then a Narrow Band Beam is the result. Neutrino
intensity is decreased, but since the neutrinos come from the two-body
decay of a parent of known momentum, the incident neutrino's energy is
approximately known. The neutrino spectra vary, in a calculable manner,
as a function of the transverse distance from the beam axis. Both FNAL
and CERN can produce either Wide or Narrow Band Beams.

Neutrino detectors can be classified into two main types: bubble
chambers and electronic calorimeters. There are other detector types,
such as photographic emulsions, large tanks filled with cleaning fluid,
etc. Bubble chambers, filled with a heavy, cold liquid, offer good
particle identification and small background, but because of their low
mass (=3-5 tons) suffer from low event rates. Electronic calorimeters
offer excellent event rates due to their high fiducial mass (2100-300
tons, and up to 1000 tons) but have decreased particle resolution and
minimal particle identification. In general, most electronic
calorimeters are designed to offer a compromise between pattern
recognition capability and measurement resolution in return for target

mass.

1.“. REVIEW OF EXPERIMENTS

This section will serve to give a brief overview of
neutrino-nucleon experiments which have taken place over the last
decade. This will not be a comprehensive review (there have been
roughly 20 experiments in the last 10 years) but will focus upon the
experiments which have contributed significantly to the measurement of
Neutral Current interactions and to the measurement of Charged and
Neutral Current structure functions.

1.“.1. GARGAMELLE. In the beginning, there was Gargamelle. This
was a bubble chamber, cylindrical in shape, filled with either Freon
(CFaBr) or a propane-Freon mixture. The chamber was “.5 meters long,
with a diameter of 1.85 meters.

In 1973, a collaboration discovered the existence of
neutrino-nucleon neutral current events15 and neutrino-electron elastic

scattering.“

The experiment used a WBB at the CERN Proton Synchrotron
(PS) for both neutrinos and antineutrinos, with neutrino energies in the
range of 0.5 to 15»GeV. The experiment measured the total cross
sections for both v and 6 CC interactions,17 thus establishing the
linear dependence of the cross section upon the incident energy. The NC
to CC ratio was determined,‘5 placing limits upon the value of sinzew.
1.“.2. HPWF/HPWFRO. A collaboration of Harvard, Pennsylvania,
Wisconsin and Fermilab first detected neutrino-nucleon Neutral Current

events18

in a large, electronic calorimeter. The detector consisted of
altarget-detector calorimeter followed by a muon spectrometer. The
calorimeter used liquid scintillation counters for the target material

and calorimetry, and wide gap spark chambers for muon tracking. The

muon spectrometer consisted of “-12' diameter Iron toroid magnets,

8
interspersed with spark chambers. The experiment used several types of
WB Beams at FNAL. The total cross section19 (for CC). x and y

° were measured for

distributions for CC interactionsz° and NC/CC ratiosl
both neutrino and antineutrino beams with energies up to 160 GeV. The
experiment also detected opposite sign di-muon events,“ which provided
the first evidence of charm production and decay via neutrinos, same
sign di-muon events,21 and tri-muon events.22

In 1977, the detector was upgraded to include an Iron target,
liquid scintillator and an Iron calorimeter. The muon spectrometer was
also upgraded to include 3-2“' diameter toroids. Rutgers and Ohio State
joined the collaboration (HPWFRO). This group measured the x and y
distributions, F,(x), xF,(x), and quark fractions within the nucleon,

2’ Di-muon events were also measured.’“

using the CC events.

1.“.3. CITF/CITFR/CFRR/CCFRR. The CIT-Fermilab and the
CIT-Fermilab-Rockefeller groups used a new NBB at Fermilab. Various
momenta of the secondary mesons were used for both neutrino and
antineutrino beams. This group used a detector consisting of a Iron
calorimeter and a muon spectrometer. The calorimeter consisted of 1“0
tons of steel plates (3 m by 3 m cross section) with spark chambers
every 20 cm and scintillation counters every 10 cm. The experiment
measured total cross sections for the CC interaction,25 NC/CC ratios:6
(as well as sinzew), and integrated values of the CC structure
functions,“ for neutrino energies from “5 to 205 GeV. The space-time
structure27 of the Weak interaction was determined.

The cahndmeter size was increased to 690 tons, with a “20 ton

spectrometer. Rochester joined the collaboration (CFRR). Continuing to

use a N88 for both v and I), the experiment measured total cross

28729 8

sections, y distributions2 for CC events as well as NC cross
sections“ to determine sinzew. The x and Q2 dependence of F2 and xF,
were measured for CC events."o With the inclusion of Columbia (CCFRR)
the group measured total CC cross sections and searched for evidence of
neutrino oscillations."

1.“.“. CRS-BNL/CR-BNL. Two bubble chamber experiments are worthy
of mention for measuring the x distributions of neutrino NC
interactions. The Columbia-Rutgers-Stevens-BNL group measured x and y
distributions for vNC and vCC interactions using a NBB at Brookhaven
National Laboratory (BNL).’2 Neutrino energy ranged from 3-9 GeV. The
seven foot bubble chamber was filled with a Ne-H2 mixture, providing a
fiducial mass of 3 tons. This group measured x and y distributions, as
well as the quantity <xy> for both NC and CC interactions. They
determined (with 23 NC and 73 CC events) that the the NC y distribution
was consistent with the space-time nature of the CC interaction, as well
as concluding that <xy>no . <xy>cc.

The Columbia-Rutgers-BNL group used the 15' FNAL bubble chamber, in
a NB neutrino beam.’3 This group measured x and y distributions for
both vNC and vCC interactions, measured NC/CC ratios and NC structure
functions. The collaboration obtained 151 NC and 683 CC events.

1.“.5. CDHS. The CERN-Dortmund-Heidelberg-Saclay collaboration
probably is the preeminent neutrino experiment to date. Primarily using
the N88 at the CERN Super Proton Synchrotron (SPS), the group has also
taken data using the CERN WBB. With an event sample of 35.700 v (807“
NC and 27603 00) interactions and 8600 {3 (2203 NC and 6367 CC)

interactions, CDHS has made precise measurements of many of the

quantities already discussed.

10

The detector consists of a magnetized Iron calorimeter. The
detector is constructed out of 3.75 meter diameter Iron plates, each
plate either 5 cm or 15 cm thick. Between each plate are scintillator
planes. The plates are grouped into modules, with each module weighing
about 65‘mmuh for a total weight of 1235 tons. Triple plane drift
chambers are sandwiched between modules, with wires at 0°, i60° to the
horizontal.

Given the vCC and CCC data, with neutrinc>energy from 30 to 200
GeV, CDHS has measured the total cross section, x and y distributions,
1F, and xF3 as functions of x and Q2, as well as individual quark

3“ When neutrino and antineutrino

distributions and momentum fractions.
NC events are included, the group can measure NC/CC ratios, sin’Ow, the
space-time nature of the NC, as well as a comparison of Charged and

Neutral Current hadronic energy distributions.’5

The group has also
measured opposite and like sign di-muon events.’°

1.“.6. CHARM. The detector of the Amsterdam-CERN-Hamburg-Mosc0w-
Rome collaboration sits just downstream of the CDHS detector. The two
detectors were used together to measure the polarization of the muon.37
The detector consists of a "sandwich" of scintillator plane-marble
(Caco,) target-proportional wire drift-chamber. There are 78
"sandwiches" in the detector for a total of 180 tons with a 3 m by 3 m
cross section. Surrounding the marble is a "window frame" of magnetized
Iron and scintillator. CHARM took v and (a data in both Narrow and Wide
Band Beams. With NBB neutrino energies in the range of 30 to 200 GeV,
they obtained 8553 v (6271 CC and 2282 NC events) and 3578 5 (2536 CC

and 10“2 NC events) interactions. They measured total CC cross

sections, NC/CC ratios, sin’Ow, CC structure functions, antiquark

11
distributions, gluon distributions and x and y distributions for CC
interactions.”3 Most importantly, they measured the NC x distributions
and fitted the NC structure functions to a parameterized functional
form.39 With larger numbers of NC events, they can achieve a better

measurement than either the CRS-BNL or CR-BNL groups.

1.5. THE E59“-FMMN EXPERIMENT

A collaboration of Fermilab, MIT, MSU, and Northern Illinois built
a large, fine-grained calorimeter and muon spectrometer in the LAB C
building at FNAL. The collaboration took data using a WBB (first half
of 1981) and a NBB (first half of 1982) for both neutrinos and
antineutrinos.

The detector calorimeter consists of acrylic sheets filled with
either steel shot or sand as target material, plastic flash chambers,
sandwiched between the target planes, and proportional wire chambers
every 16 target planes. The muon spectrometer consists of 3-2“'
diameter and “-12' diameter magnetic toroids (inherited from the HPWFRO
group). Proportional chambers were inserted in two of the four 12'
toroid gaps for the WBB. During the WBB running, the calorimeter had a
f‘iciucial mass of 2“0 tons with a 3 m by 3 m cross section. For the N88,
the detector length was increased by 50% (2100 tons), and the muon
SDectrometer was upgraded.

Significant physics from the WBB consists of neutrino-electron
elastic scattering, deep-inelastic NC and CC interactions and analysis
of the quasi-elastic interaction: MC) + N + u-(u+) + N'. The N88
analysis will include: x and y distributions and structure function

measurement for both NC and CC interactions, total cross section

 

 

’(5

12
measurement, measurement of sinzew, analysis of neutrino-electron
scattering and a search for neutrino oscillations.

The scope of this thesis is to present the NC and CC analysis, from
data taken in the WBB, and in particular, to determine the NC structure
functions relative to the CC structure functions given an explicit
parameterization for the CC functions. A Wide Band neutrino beam is not
ideal for this analysis. Since the incident neutrino energy is unknown,
it is not possible to explicity determine either x or y for Neutral
Current interactions. We will show, however, that it is possible to
calculate a quantity, say u, which is a function of both x and y. Using
both NC and CC distributions of the quantity "u", and given certain
assumptions about the CC structure functions, it will be possible to
make certain statements about the NC structure functions. Given the
higher event rate (factor of 10) of the WBB over the N88, a larger data
sample should compensate, in part, for the inability to directly compare
x distributions.

The theoretical background for neutrino-nucleon interactions is
discussed in Chapter 2. Chapters 3-5 will discuss the E59“ detector:
its construction, operation, alignment and calibration. Information
Concerning the neutrino beam, as well as experimental gating and
tF'iggering is presented in Chapter 6. Data analysis and conclusions

will be found in Chapters 7 and 8.

CHAPTER 2. NEUTRINO-NUCLEON INTERACTIONS

2.1. THE PARTON MODEL

The parton model was developed as a result of ep scattering
experiments at SLAC in 1968."0 The data showed electrons scattering
from protons at large energy and momentum transfers with significant
probability; The data suggested that the proton's charge was localized
on a few, small scattering centers. Energy and angle distributions of
the scattered electrons suggested that the scattering centers were
structureless, spin-one-half Dirac particles. Because the scattering
centers (partons) seemed to be structureless, the energy and angle
correlations exhibit "scaling" as described by Bj orken,” Feynman,"2
and Bj orken and Paschos.” Scaling refers to an interaction which is
independent of any mass or energy scale.

2.1.1. Assumptions. Scaling suggests that the current-target
interaction is governed by incoherent (free) scattering. The Parton
Model contains implicit assumptions which must be satisfied for the
incoherent impulse approximation to be valid: (1) the current-parton
.hiteraction time is small, so that interactions between partons can be
neglected and (2) final state interactions can be ignored. Intuitively,
the parton is struck so violently that it is removed from the nucleon,
independent of the other partons. Figure 2.1 shows a diagram which
illustrates the scattering. In the Breit frame, before interactions,

partons have essentially all longitudinal momenta, each parton carrying

13

14

 

 

 

 

 

(1
WP) 21% (— 1111111011
1 ' UP
BEFORE
41 > 21+ 1
in .
11111

Figure 2. ttttttttttttttttt g ( rrrrrrrrrr )

15
some fraction 21 of the parent's momentum. After interaction, the
current momentum has removed one of the partons kinematically from the
target with the non-interacting partons continuing on undisturbed.
Kinematically, the Parton Model is satisfied if interaction energies
(e.g. 2M0, Q2, W) are very much greater than the square of the parton
state's effective mass, Mgff.
2.1.2. Lepton-Parton and Lepton-Nucleon Scattering. In order to
make the connection between lepton-parton and lepton-nucleon scattering,
it is necessary to calculate the diagram(s), illustrated by Figure 2.2,
for an N parton configuration, summing incoherently over all N partons,
and summing incoherently over all final state hadrons which result from

the non-interacting partons. The four-momenta of the states shown in

Figure 2.2 are as follows:
M2

P - .__
P ' (P + 2P, 09 P) P2” (Ptoyp) (23)
p2 +u2
u 1T 1 8
pi (ziP +-—§E;F—, piT’ ziP) Pia (ziP, 0, ziP) 21? (2b)
p'“-.- p“ (20)
1": T T 2 2
p1 (/(pi+q) +111 . piqu' ziP+qL) (2d)
where )1 21 = 1, and pi is the mass of the ith parton.
Let
f?(z) dz (3)

represent the probability distribution that parton 1 out of N has
longitudinal momentum fraction 2 between 2 and z+dz. Since the parton
must have some momentum, then

Jlf?(z) dz = 1, (“)
0

and let PN be the probability of finding N partons within the nucleon

1 (p’)

 

 

 

 

 

 

 

, >

HADRONS

 

 

 

NUCLEON

Figure 2.2. Lepton - Parton Scattering

17

with
The hadronic tensor for the interaction becomes:
N f N
Wuv(P,q) ZN PN {i=1 J fi(zi) dz wpv(pi.q) (6)
where Wuv(pi,q) is the interaction tensor for the ith parton.

Equation 6 can be written in expanded form:

 

1 1 - 1 __d____’P' 1 N
w P. = - -- d f‘
uv( q) 2“ 2” Epins Xvi J (21) 29o EN “J 2 1(2) (7)
* (pilju(o)|pi><pi|Jv(0)[pi>(%§—JP (2n)~5~(pi+q-Pi)

by following standard procedures given in texts.““ Note that Equation 7
contains no cross terms, implying incoherent scattering.
In order to proceed further, it is necessary to define the matrix
element:
<pi|Jv(0)|p1>. (8)
‘We will come back to this point later within the context of

neutrino-nucleon scattering.

2.2. CHARGED CURRENT NEUTRINO‘NUCLEON SCATTERING

2.2.1. Structure Functions. A diagram for deep inelastic CC
neutrino scattering is shown in Figure 2.3a. The four-momenta K and K'
refer to the incoming and outgoing leptons, P and P' to the target
nucleon (we will assume proton) and outgoing hadronic system.

The space-time properties of the current could, in general, contain
terms which transform as Scalar (S), Pseudoscalar (P), Vector (V), Axial
vector (A), and Tensor (T). Early B-decay experiments determined the

current as V - A for neutrinos and V + A for antineutrinos.

18

'11. (K’)
V ‘K’ A.

 

V (K )
V ‘K’ A.

 

N(P)

 

NEUTRAL CURRENT INTERACTION

Figure 2.3. Neutrino-Nucleon Scattering (CC and NC Case)

19

Given V - A coupling, one can write the differential cross section

for up CC interactions as:
_ 1 d3K' 1 1 f , , _ ,_ ,
do - 2K,ZK 23 (2“) 25, 2 {P 2?, 2M J Hn(2n) 6 (P+K P K ) (9)
d3p'

n

(211)32p5n

 

IMIZ

where
_ G - . _ . u
M --75 u(K )Yu(1 Y5)u(K)<P |Jw|P> (10)
(Muon masses and W propagator terms have been ignored.). lkiEnuation

5

10, G is the Fermi coupling constant, 0210- /M;, the /2 is a historical

artifact and J: is the weak current operator. We can write MHZ in
terms of a leptonic and a hadronic tensor. The lepton tensor is:
G - , _ t G - , _
Luv ZK'XK[72 u(K ”6“ Ys)u(K)] [75 u(K Hum 75mm] (11)

and the hadronic tensor is:

up 1 1 uT v
w “§?R'ZPEP'J nn(2w)“ 6“(P+K-P'-K') <P|Jw (0)|P'><P'|Jw(0)|P> (12)
d’P'
n

x 3 ' _
(2n) 2Pon

 

The leptonic tensor can be evaluated using standard techniques and is

a ,8
VKK ] (13)
aBYd

L = “02[K K' - g K-K' + K K' - is
w u v w v 11 (1118
uv . . . . uv u v
where g 13 defined in terms of the Y matrices, 2g = {Y ,Y } and e

is a totally antisymmetric, fourth-rank tensor with
E:0123 = -60123 :1.
The hadronic tensor cannot be evaluated directly because of the
unknown weak-hadronic matrix element. What is known, is that wuv is a

second rank tensor and must be comprised of P and q (cn~1>') which are

the only two independent variables. In general:

 

 

u v . uvaB u v
uv uv P P IE 9
W = '8 w] T M2 ' w2 " 2M5 Paq8w3 + qu W“ (1)4)
u v u v u v _ v u
+ (P q + qu ) W5 + i(P g P q ) W

M2 M2 6

20

where the Wi's are, in general, functions of v and q2 (or Q2). Current

conservation, quW1W 0, requires W“, W5, and W6 be zero. This leaves:

PuPV ie“V“B

\) \)
_gu W1 + 'fi?"w2 -.§fi7——— Paq8w3. (15)

WU

Contracting the lepton and hadron tensors (Equations 13 and 15),
and writing the differential cross section in terms of the scattered
muon energy and angle (in the laboratory frame) yields:

dov G’E'2

______., _____. 29f.§1§i
dE'dQ' 2N2

2 2 )w?] (16)

I V
[(coszg-)W: + (2sin2%-)WY + sin
for the neutrino case. Similar calculations for the antineutrino CC
case yield the same equation for the cross section except for a sign

change on the W3 term.

Under the assumption of Bjorken scaling:

MW,(v.q2)q2?v+mF,(x) (17a)
Vw2(qu2)q2?V+mF2(X) (17b)
VW3(Vvq2)q2?v+mF3(x) (170)

where v and q2 approach infinity in such a way, that their ratio remains
finite. We can define x (x=Q2/2Mv) and y (yap/EV) and perform a change
of variables in Equation 16 from (E',9') to (X.Y). Under the assumption

of scaling, the cross sections are given in their familar form:

(v.5)

(v.9) - -
d° GZME [(1—y)F. (x) + xyzrfv’”)(x) i (1—1 )ny§“’“)<x>. <18)
2

dx dy ‘ 6
Notice that do has the form:

 

do = E : Zi[f(x)]i ° [g(y)]i.
which is factorized into equations of x and y, a consequence of scaling.
The F1 (Equation 18) are known as the neutrino-nucleon structure
functions. Over the last decade, much experimental work has been done

to determine the nature of their x dependence.

21
2.2.2. The Parton Model, Quarks, and Structure Functions.
2.2.2.1. Parton Model for up Interactions. Returning to
Equation 8, it is now possible to specify and calculate the matrix
element within the context of up CC interactions. 'We will assume: (1)
the V - A structure of the current, (2) J: as a weak, isospin raising

operator, and (3) parity non-conservation. The equation can be written

as:
,W 3-! _
(pilJu(O)lpi> u(pi)Yu(1 Y5)u(pi). (19)
Squaring, and then summing over initial and final states yields:
1. .1 v- 0'98
8Epiupiv guvpi p 1 I pivpiu ieaqupipi 3' (20)

.Substituting this into Equation 17, we then integrate over d’p',

rewriting the energy part of the delta function in terms of z and x and

 

obtain:
2? P z
_ N T N u v ____ a 3
wuv(P’q) ’ Xn Pn Zi=1 sz f1(2) ME; [ Mv Mv ieuvaBP q (21)
_ - 2
guv] xP 6(z x) ii
for up interactions. The factors A1 and 111 are explicity shown in order

to account for the V - A, isospin raising nature of the current, where

11 = +1, for any I3 = -1/2 parton
= 0, otherwise
for up scattering,
xi + I1 = +1, for any I3 = 1/2 parton

0, otherwise
for 0p scattering, and
"i = +1 for partons

= -1 for antipartons.

22
Comparison of Equations 15 and 21 allows us to make the connections

between vp structure functions and parton probability densities:

N
MWY(v,q’) = 2N PN Z?=1 f1(xi)li = F¥(x) (22a)
0W¥(v,q2) . ZEN PN Z?=1 f?(x1)xixi = F:(x) (22b)
vw§(6,q=) . zszNz?rf(xi)nix; . F§(x). (226)

Notice that 2xF,=F,, which is the Callan-Gross"s relationship, a result
of the assumption that the partons are spin-one-half. Also implicit in
this analysis is that the masses of the partons are negligible. In the
case of heavy partons, the "scaling" variable is no longer x but 5,

where:

mh is the mass of the heavy parton. The relationships in Equation 22
still hold, but the cross section in Equation 18 no longer factors.

:2.2.2.2. Parton-Quark Relationship. What are the partons?
In 196“, Cell-Mann"6 and Zweig“’ proposed that the hadrons were made up
of "quarks". The quark model had some success, especially in making
sense of the large number of meson and baryon states which existed at
that time. Only three quarks were needed to explain the existing mesons
as quark-antiquark systems and baryons as three-quark systems.

When the SLAC ep data was combined with neutrino data from CERN, it
was discovered that the quantum numbers of the partons matched those of
the quarks. A fourth quark (charm) was predicted and was discovered in
197“. Since then a fifth (bottom) has been found and a sixth (top) is

being sought and has probably been recently found. There is now firm

theoretical and experimental evidence that the partons which participate

23
in the EM and Weak interactions are the quarks. Table 2.1 lists the
quantum numbers of the first four quarks.
2.2.2.3. Quark Density Description of the Structure
Functions. With these quantum numbers, we can write out the structure
functions in terms of the quark densities. Let
{N PN 2?.1 f?(x) + u(x). d(x), s(x), c(x)

represent the probability of finding a given quark at momentum fraction

x, then
pr(x) = d(x) + u(x) + s(x) + c(x) (23a)
F2p(x) = 2x[d(x) + 6(x) + s(x) + E<x>3 (23b)
F¥p<x) = 2[d(x) - fi<x) + s(x) - 5(x)] (23c)
for neutrinos, and
pr(x) = u(x) + d(x) + c(x) + 5(x) (23d)
F2p(x) = 2x[u(x) + 5(x) + c(x) + 5(x)1 (23e)
F¥p(x) = 2[u(x) - d(x) + s(x) - 0(x)] (23:)

for antineutrinos. The extension to vn and (in scattering is performed
via the isospin relationship between protons and and neutrons:

u - d . u, etc.

p n

Since most experiments are done using a (nearly) isoscalar target,

the cross sections are written as in Equation 18:

do(v,v)
dx dy

where

 

- 02:5 [(1-y)F§v’v)(x) + xyZFSV'V)(x) i (1- %)ny§V'V)(x). (18')

2foV'V)(x) = FEV'V)(x) = x£(x)

ngv,v)(x) = xV(x) : xA(x)

24

 

 

 

 

 

 

_ o T: o O Q? o
o _- Q: o o m\_. m
o c Q: N\_. N\_ ms- a
o o Q: Q: N\_ TN... 3
o m m m. _ o #230

 

 

 

 

 

 

 

muonasz aaucmso xwmao

.H.N mHan

 

25

and,
xZ(x) = xq(x) + xd(x)
xV(x) = xq(x) - xd(x)
xA(x) = -[xs(x) + xs(x)] + [xc(x) + x6(x)]
q(x) = u(x) + d(x) + s(x) + c(x)
6(x) = {i(x) + d(x) + £6.) + Em.

The elementary cross sections for neutrino- and antineutrino-quark

2

 

 

interactions, in units of ,are:
do --
dxdy - 1, for vq, vq (2“)

= (1-y)2, for 06, Cq.

This is a consequence of basic helicity arguments.
2.2.2.“. Sum Rules. Various sum rules can be formed from
the structure function-quark relationships. The Gross-Llewellyn-Smith

sum rule“° defines the quark-antiquark difference in the nucleon:

l
T xF,(x) dx = 3
O

and indicates a nucleon carries three valence quarks. All other quarks
in the nucleon come from a "sea" of quark-antiquark pairs. The Adler
ennniuile“9 exploits the isospin symmetry between protons and neutrons.
Ignoring strange and charm quarks:
J1: % [F‘,m(x) - F§p(x)l dx = 2
and indicates that the proton's quark content is uud. Finally, the
Callan-Gross relationship is:
2xF,(x) = F,(x).

This is a consequence of the spin-one-half nature of the quarks.

26
2.3. THE STANDARD MODEL.

Even though the quark-parton model has had some success, it
remains, nonetheless, a phenomenological model. Work was done in the
1960's and early 70's to place weak interactions on a strong theoretical
footing. At that time, a very good theory existed for Electromagnetic
interactions, Quantum Electrodynamics (QED).

There existed many simularities between the EM and Weak
interactions. Both processes involved the interaction of two currents.
EM interactions also contained the effects of the photon propagator,
whereas Weak processes resemble a four-particle point vertex (Fermi type
interaction). In an attempt to gain a resemblance to the EM process,
one could imagine that the Weak process is mediated by a heavy
weak-boson. This would add a propagator term to the interaction. Then,
in the limit of q2 << ”174’ the propagator term would be close to unity
and the interaction would resemble a Fermi type interaction.

The Weak current in neutron decay is a charged current. Feynman
and Gell--Mannso showed that the vector part of the current (the third
component) is related to the isovector part of the EM current.

Finally, QED is a renormalizable theory. Weak interactions at the
Fermi level are not. The dimensional coupling, GF’ with a dimension of
inverse mass squared, gives rise to incurable divergences at higher
orders of perturbation theory. Even adding a single heavy boson
propagator "by hand" does not help.

2.3.1. The Weinberg-Salam Model for Leptons. The original
conjecture of WeinbergE51 and Salam$2 gained possible relevance as a

physical theory when it was shown by t'Hooft"’3 that only if the

27
propagator acquires a mass through the spontaneous symmetry breaking“
of the underlying theory can the theory be renormalizable.

An immediate prediction of the theory was the existence of weak
neutral currents. Experiments at CERN55 in 1973 discovered
neutrino-nucleon neutral current interactions. Further experiments with
CC, NC and neutrino-electron interactions, as well as recent discoveries
cfi‘the charged56 (Wi) and neutral“’ (2°) heavy bosons yields further
credence to this model.

The Weinberg-Salam (WS) Model is based upon the SU(2) X U(1) gauge
group. The leptons are organized into left-handed doublets:

L = (2),.
and right-handed singlets:
R = (e)R.
the projection operators are defined as:
L - -;-(1-Y5)[:)
R - -;-(1+v,)(:).
For complete generality, we should include a sum over all lepton
families:
L = 21 L1, 1 = e,u.'r
but for simplicity, we will only consider the electron family. The
extension to other families is simple and obvious.

The generators of the gauge group are E, the electronic isospin and
Y, the electronic hypercharge. Hypercharge is related to the electric
charge via Q = T, + Y. The interaction Lagrangian is constructed out of
L and R, an isovector, spin-1 field, An and an isoscalar, spin-1 field,

811' (which couple to ‘1’ and Y, respectively), plus a spin-zero doublet

field 0, where

0
¢ 3 (00).
This "Higgs" field has a non-vanishing vacuum expectation value,
<0|¢|0> = v, and will spontaneously "break" the underlying gauge
symmetry.

The complete Lagrangian can be found in literature.51 The

interaction Lagrangian for the lepton fields is:

a-“ ' -111" __1_.+.->
Lint iRY (ig Bu)R + iLY (21g Bu 21g1 Au)L (25)
l. __1_.->.-> 2_ -1- _
+ [(3p + 21g Bu 2igt Au)¢| G£(R¢ L + LcR).

By proper mixing of the massless boson fields, A“ and 811’ we can form

the real, physical boson fields:

i 1 2
wu(x) = 72 [A;(x) 1 iAu(x)] (26a)
Zu(x) = [-gA:(x) + g'Bu(x)]// g5 + g'2 (26b)
Au(X) = [gBu(x) + g'A:(x)]// g2 + g'2 (26c)

for the charged and neutral bosons and photon, respectively. Masses are
assigned via the Goldstonesa mechanism, which breaks the symmetry.
The couplings g and g' are related by:
=.§:
tan 0w 8 (27)
where OH is called the "weak mixing angle" by Weinberg and the "Weinberg

angle" by everyone else. The lepton Lagrangian can be written for a

generic lepton field, "A" , as:

 

=- _u 8-u_ 4"
int 831” 9w 17 2A“ +'§7§[1Y (1 Y,)qu + H.C.] (28)
Z
-_8_ u1-u_ _1-u_ .2-“
2 COS GW[EVY (1 Y5)V E£Y (1 Y5)£ + 281n Ong 2].

The EM and weak coupling constants are related by:

e = g sin Ow.

29

The CO weak coupling constant, the Wi mass, and the Fermi coupling GF

are related by:

SF .61
7'2' ' 8142w

The NC weak coupling is g/cos e" and the Z° mass is predicted, in the
"minimal" theory (one Higgs doublet), as:

M; = M: / coszew.
The theory predicts left- and right-handed couplings of fermions as:
6L = 1, - Q sinzew (29)
6R = -Q sin’Ow
where Q and 13 are the particle's charge and third component of isospin,
respectively.

2.3.2. Weinberg-Salem Extension to Hadrons. Based upon the sucess
of the WS model for leptons, attempts were made to incorporate the
hadrons (quarks). At that time, there were three quarks (Lh.<1, and s)
and they were incorporated into a left-handed isodoublet and three
right-handed isosinglets:

qL ‘ (EJL’ ”R' dR’ SR' (30)
This model correctly predicted all strangeness conserving semi-leptxnmic
jprocesses but predicted strangeness changing decays at a rate higher by
a factor of 20. This led Cabibbo59 to propose that the weak current
contained a mixture of strangeness conserving and strangeness changing
pieces:
do = d cos so + s sin 00 (31)

s = -d sin 0 + 3 cos 0 ,
c c c

30
where 00 is the "Cabibbo" angle, sin’Oc . 0.05. This gave the correct
form of the CC processes but predicted strangeness changing neutral
currents at an unobserved rate.
A "minimal" model, proposed by Glashow, Iliopoulos, and Maiani,‘so
(GIM), suggested a fourth quark, called "charm", which added a new

isosinglet and an isodoublet:
c
' 8
qL (s )L. ca. (32)
c
This new quark leaves the CC processes unchanged and adds a new piece to
the NC Lagrangian but with the opposite phase with respect to the
original strangeness changing piece thereby cancelling exactly (in the
limit M . M ).
u c
The CO interaction Lagrangian for hadrons can be written as:
. 8 ' u+
Lcc m [ WUJ + H.C.] (33a)
. 8 ' ‘ u _

the EM piece as:

Lem - qJSmAu --§ fivuuA“ --% avudA“ + ... (33b)
and the NC piece as:
L --——§§i——— [ J3 - sin20 Jem], (33c)
nc cos 0w u w u
where
J’ - 1-6 Y u --1 5 Y d + ...
u 2 L p L 2 0L u cL

The addition of the fourth quark was justified by the discovery of the
W/J meson in 197“. This scheme is easily extended to more quark
families (we now have three) and it is possible to determine generalized

Cabibbo matrices to mix the I, - -1/2 quarks.

31
2.“. NEUTRAL CURRENT NEUTRINO-NUCLEON SCATTERING.
A diagram of neutrino-nucleon neutral current scattering is shown
in Figure 2.3b. As in the CC case, we can write this process as the

interaction of a lepton and hadron current. The lepton piece is:

I.“ =%§v“(1-1,)6 (314a)
and the hadronic piece is:
1 - 1 -
Hu = 2 GuL uYu(1 Y,)u + 2-6uR uYu(1+Y,)u (3“b)
1 - 1 -
+ ‘2- (SOL (”11(1 Y5)d 4' '5 GdR dYu(1+Y5)d

which, in general, may contain both left- and right-handed pieces. For

clarity, only u and d quarks are shown and (as in the CC case) we set

00 -- 0 for simplicity. The couplings are defined in the WS-GIM model
as:
GuL =-1§--§-sin20w (35)
5dL = --% +-% sin’Ow
GuR = --§ sin20w
6dR --% sin’O .

We could then proceed and calculate the cross sections as before,
however, by using the elementary cross sections already developed,

(Equation 2“) we can write (for an isoscalar target):

 

 

u
do GZME 2 2 _ 2 2 2
dxdy fl {xq(X)[(6uL + ch> + (1 y) (GuR + GdR)] (36)
’ _ 2 2 2 2 2
+ xq(x)[(1y )(suL + 561.) + (éuR + 561:)“-
In terms of the structure functions:

V 2
6:3,: " "“6 :EW'WEW * xyzF‘flx) + <1-15y)xyF§’(x)]. (37)

 

where:

v = V g 2 2 2 2
2xF,(x) F,(x) x2(x)[auL + a dL + cuR + 6d,]

2 2 _ 2 _ 2
+ XA(X)[6uL + 6uR 6dL 6dR]’

32
va(x) = xV(x)[62 + 62 - 62 - 62 ].
3 uL dL uR dR

Similar equations can be written for antineutrino scattering.
Within the WS-GIM model, certain predictions can be made about CC
and NC interactions. Of particular interest are the ratios:

R \)N -> VX ("N -> 3x

=-————-—-—, R- = .

- - +

V vN+ux V vN+uX
The standard model predicts, with sin20w = 0.23, and minimal Higgs
symmetry breaking, Rv = 0.30 and R; = 0.38. Current data are in

excellent agreement with these predictions. (See Baltay61 for an

excellent review.)

CHAPTER 3. THE E59“ DETECTOR

3.1. GENERAL OVERVIEW

The E59“ detector is a fine-grained, massive detector suitable for
neutrino calorimetry. The fine-grain nature is usefuli%n'measuring
both the energy and direction of showers, as well as differentiating
'between hadronic and electromagnetic showers. Since neutrino reactions
are rare, especially neutrino-electron elastic interactions, the
detector must also be massive. The detector is based upon plastic flash
chambers and aluminum-extruded proportional tube planes. These devices
allow us tr>1Miild a detector with excellent pattern recognition at an
acceptable cost.

The detector has two parts: a flash chamber calorimeter and an iron
toroidal spectrometer (see Figure 3.1). THdis Figure illustrates the
configuration of the detector during the N88 run period. For the 1981
Engineering run, the active area of the calorimeter was 12 ft X 12 ft in
cross section and “0 feet in length. It consisted of “16 flash chambers
and 25 proportional tube planes. One module of the detector consisted
of four, “ inch wide steel box beams with “ chamberslxn'beam. The
chambers1unwain sequence U-X-Y-X, where X chambers have horizontal
cells and Y and U chambers have cells oriented 110° from vertical,
respectively. Flash chambers have 5 mm X 5 mm cell size and each
chamber contains approximately 635 cells. Each chamber is read out,

using magnetostrictive techniques, from both ends of a wand placed

33

34

b 40' Lb no' u
l‘ ’1‘ V r]
MUON SPECTROMETER TARGET-CALORIMETER
24' DIA. Fe TOROIDS
12' DIA. Fe TOROIDS ‘

1I1I1 11

1 1 - 38MODULES ‘
PROPORTIONAL 37 PROPORTIONAL PLANES
PLANES e 24'x 24' 608 FLASH CHAMBER PLANES
PROPORT'ONAL 340 TONS SAND/STEEL SHOT

 

 

E U
BEAM

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PLANES

MODULE OF FLASH CHAMBER mm
4 L 3 2 1 J
=_ 1

 

 

 

 

 

 

 

SAN D
_\

D

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

STEEL g
SHOT

.- ‘2' u .
DJ... ,_ . o. _ o c
. I," .

V £5$°c
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(“76 . ”£19.19 1 02°. - 5}. °‘

an

 

. F
P :I
U 3;."
f'a
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m w.

3-
8 a.
o
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1 fl

 

Figure 3.1. The E594 Detector

35
across the cells. The flash chambers are sandwiched between 5/8 inch
thick acrylic extrusions which are alternatively filled with sand or
with steel shot. These filled extrusions form the target mass of 2“0
metric tons.

The proportional tube planes alternate X-Y (wires running
horizontally and vertically) throughout the detector and are placed
after each flash chamber module (16 chambers). The proportional tubes
have 1 inch cell size and provide both a trigger and an independent
measure of the shower energy. Liquid scintillation counters are placed
every five modules (80 chambers) and provide a muon trigger for
calibration purposes and software alignment of the flash chambers. A
liquid scintillation counter was placed in front of the calorimeter to
veto on incident charged particles.

The iron spectrometer followed the calorimeter and consisted of
three, 2“ foot diameter toroids and four, 12 foot diameter toroids.
Proportional tube planes with a one inch cell size were placed in the
toroid gaps. For the 1981 Engineering run, only the second and fourth
12 foot toroid gaps contained proportional tube planes. Each gap
contained both X and Y planes. These planes were "double" planes. Two
layers of cells, with the second layer offset by 1/2", comprised one
"double" plane. Large 2“ foot planes were installed behind the last
2“ foot toroid but were not operational during most of the 1981 run.

The average sampling step of the flash chambers is 3.6 g/cm2,
corresponding to 22% of a radiation length and 3% of an absorption
length. The average distributed density of the calorimeter is

1.“ g/cm3 , and the average Z is 19.1. This construction offers a good

36
compromise for angular and energy resolution and neutrino event rate,

optimized for the physics we studied.

3.2. THE FLASH CHAMBERS

,3.2.1. Constructiorn Each chamber was constructed from three, “
foot wide black polypropylene sheets to form an active area of
12' X 12' . The three sheets are fastened together with mylar tape to
prevent sparking through the seams between the polypropylene sheets.
Aluminum foil sheets, 5 mil thick and 36 inch wide by 1“ feet long, are
glued to each side with a water based latex contact glue to the
polypropylene to form the high voltage (HV) electrodes. The foil is
overlapped and is fastened together by conductive aluminum tape. The RV
electrodes are cut back 12" from the gas manifolds to quench the plasma
discharge before it reaches the gas manifolds eliminating cell-to-cell
cross talk.

The gas manifolds are made by welding translucent polypropylene
strips around the ends of each of the “ foot wide polypropylene sheets.
The ends of the gas manifolds are fused together by heat to form a
complete seal. The use of a polypropylene manifold avoids outgassing
problems as well.as avoiding strength uncertainties associated with
adhesive bonding to the polypropylene.

Standard 90% Ne-10% He gas, with small amounts of Argon and other
impurities as quenchers, is used in the chambers. The gas flows through
the chambers at the rate of 1.5% of the chamber volume per minute. The
gas is continously purified, replenished and recirculated using a
molecular sieve gas purification system. This gas purification system

is detailed later.

37

To achieve good efficiency independent of location on the chambers,
the high voltage pulse must have a duration of approximately 500 usec at
a voltage of 5 kV. The HV rise time is critical in initiating the
plasma discharge within the chamber cells. Measurements“ show the
chamber efficiency degrades by 1“% if the high voltage rise time is
increased from “0 to 100 nsec. The duration of the pulse is critical in
sustaining the plasma discharge long enough for it to propagate through
the cell to the readout section. At 5 kV, the propagation speed is
roughly 10 nsec/foot“2 and this speed has a weak dependence on the
applied voltage.

The high voltage pulse is produced by a pulse forming network
(PFN). Each chamber has its own PFN. The PFN has a capacitance of
roughly 100 nF, with the capacitance distributed in three stages to
insure a fast rise time and a sustained pulse. The RV system and RV
monitoring is detailed later. The RV pulse is fed into the chamber by a
30" wide HV tongue at the lower corner (for X chambers) or at the side
(for U and Y chambers) and is terminated by two 10 $2, 2 Watt carbon
resistors. No significant variation of the HV pulse is observed at
different locations on the chamber.

The flash chambers are read out using magnetostrictive wire
techniques to detect the current pulse induced by the plasma discharge
in a struck cell. The current pulse is induced on 0.118" (3 mm) wide
copper strips about 20" long and glued to the outside surface of the
polypropylene sheets about one foot from the edge of the polypropylene.
These copper strips are connected to the chamber ground plane and form a
set of capacitors (one for each cell) with the chamber HV plane acting

as the other side of the electrode. The plasma discharge, once it has

38
propagated along the length of the cell causes the capacitance between
the copper readout strips and the HV plane to change. This induces
about a 0.5 A current pulse to flow through the copper strips to ground.
The copper strips are made of photoetched copper clad mylar sheets with)
appropriate cell-to-cell spacing. On the photoetched mylar, each strip
is connected to a ground bus via a narrow "sense wire".

A 5 X 12 mil Remendur 27 magnetostrictive wire is laid over the
sense wire region. The current pulse from a struck cell causes an
acoustic:;nilse to propagate down the magnetostrictive wire. The
acoustic pulse propagates at approximately 5000 m/sec, corresponding to
a 1 usec separation between adjacent hit cells. Figure 3.2 shows a
schematic diagram of this construction.

When the chamber operates in the plateau region, the plasma induced
current pulse is roughly five times larger than the no plasma induced
current pulse. To improve this signal to noise ratio a type of ac
bridge is made which balances the current through the sense wires. 'Nie
bridge is produced by a 1:1 inverting transformer connected to the HV
plane of the chamber. The inverting transformer applies an opposite
polarity pulse to a 2" wide Aluminum "bucking:flxdp" laid
perpendicularly across all of the read out strips (see Figure 3.2). The
pulse is Optimized by input resistance (R,) and output resistance (R,).
This reduces unwanted capacitive pickup by a factor of 3 to “. Since
the operation of the bucking strip is determined by geometry, no chamber
to chamber tuning is necessary. Figure 3.3 shows typical pulses from
the magnetostrictive amplifier with the bucking current turned on and
turned off. A typical signal to background ratio of 10:1 to 20:1 is

achieved when using a properly tuned bucking circuit.

39

READ OUT SCHEME
TOPVIEW

Copper Pickup Strips
3mm x 508mm

. %////1// ///////
1‘

/) R,

R From Hot Plane
1

7

 

Bucking
Transformer

 

A Fiducials

I/IIII)ILIJ II

Magnetostrictive Wire
Bucking Slri p

 

 

 

 

 

Ground Bus

Polypropylene

SIDE VIEW OF READOUT

MOQI‘IBIOSII’ICIIVB Wand Polypropy gene
Bucking Strip Spacer

IO mils Mylar

] ‘1‘

MS. Wire

Ground Bus

 

 

 

 

 

 

 

  
     

 

 

 

 

 

 

i< I 5-—_8mm . \ >11/
Ground Plane
Gas Manifold /
Photoelched Mylar Hoi Plane

Sense Wire Region (PICk UP region)

Polypropylene of Chamber
(Cells run left to right)

Figure 3.2. Construction of Flash Chamber Readout

40

WITHOUT BUCKING

11111 WWII

WAIIWNI:
min“, I III I:
11'

"'1
—->l K—
IOp. sec

 

WITH BUCKING

 

 

Figure 3.3. Voltage Output from Magnetostrictive Amplifier

“1

The magnetostrictive wire is held in a 10 mil deep grove in a long
extruded aluminum bar (wand). A solenoidal coil is wound around the
entire length of the wand to periodically magnetize the magnetostrictive
wire. During data taking the wire was magnetized every 200 events (one
event per accelerator cycle). We found that there is an optimum
magnetization of the wire which minimizes dispersion and limits the
attenuation of the acoustic pulses down six feet of wand to less than
20%. Amplifiers with a gain of approximately 103 at each end of the
wand provide analogue signals for the readout system.

Three fiducials, one at each end and one in the middle of the
chamber calibrate the wand. Typical amplitudes from the flash chambers
are in the 100 to 200 mV range. Using two amplifiers on each wand
limits the number of cells which must be monitored by each amplifier.

Each wand amplifier feeds a discriminator circuit which in turn
clocks a 102“ X 1 memory. The discriminator threshold is programmed
with an exponentially decreasing function to compensate:fin~the 20%
attenuation of signals from the middle fiducial regions. The clocking
of the memory advances at a frequency such that 2+E (E is a small
number) counts occur per microsecond. The use of this clock frequency
avoids synchronization problems caused by slight variations in the cell
separation. The memory boards are read out asynchronously into CAMAC to
a PDP 11/“5 computer.

3.2.2. Performance.

3.2.2.1. Efficiency. The chambers were tested using cosmic
ray muons and "beam" muons from upstream neutrino interactions. Initial
tests of the chambers' performance were performed using the standard

90% Ne-10% He gas. The high voltage characteristics are shown in Figure

“2

3.“. The chambers roughly follow the same curve and reach an efficiency
plateau of 90% in the range from 3.75 kV to 5 kV. Roughly half of the
10% inefficiency is due to the inner wall thickness which separates
individual cells. The remaining 5% inefficiency is thought to be due to
recombination of the initial ionization electrons and due to the
sweeping of these electrons by the HV pulse before the avalanche
mechanism begins. Multiplicity is defined tolxzthe number of
neighboring cells which fire due to the ionization in one cell. The
multiplicity per trigger is shown in Figure 3.“ and is a slowly
increasing curve.

The uniftnunity of the high voltage response of a chamber has been
tested by measuring the HV plateau of selected chambers at various
locations on each chamber. The results of the study show that the
chamber is uniformly efficient over the entire 12' X 12' active area for
a high voltage 23.75 kV.

The chamber efficiency vesus trigger delay has been investigated.62
The sensitivity is dependent upon gas flow, but at a flow of 1.5%
volume/min, the efficiency drops roughly 16%/usec. Higher flow allows
higher efficiency. Flash chamber recovery time is measured as the
probability for a given struck cell to reignite as a function of the
time between triggers. The reignition probability is roughly 6-8% after
a 10 second repetition rate.

Extensive tests were begun to determine if the refire probability
could be decreased even more by the addition of a small amount of
electro-negative gas. The gas chosen is umuflly 0,,cw C0,. In our
case, a fraction of the recirculating gas is reinjected into the

chambers without passing through the purification sieves. Refire

43

 

 

 

 

 

 

 

EFFICIENCY
VERSUS HV
IOO"
A" 33—.
... 80- if E a x
.\° A
v D
>.
L2) 60"- - 3
E
9. A t
tt:‘4()"' <3—“——'!3 -22 g;
LIJ l ‘IQ/ .J
I /§/o &'
20- " ~2/f’ \ - I .34
r 2
OPERATING POINT
O I 1
3 5

4
HVIkV)

Figure 3.4. Flash Chamber Efficiency and Hit Cell Multiplicity

““

depends upon both the amount of "dirt" and upon the applied high
voltage. It was decided63 to reduce the appliedlnigh voltage from 9kV
to 8.5kV as our gas sample changed from Ne-He to a mixture of Neon,
Helium, and dirt. Unfortunately, these two changes reduce the
efficiency of the flash chambers. The impure gas contains water vapor.
The water vapor diffuses through the chamber walls and its amount is
strongly correlated to the absolute humidity in Lab C. Since water is a
strongly polar molecule, the ionization electrons are attxwurted to the
water vapor and this depletion reduces the chances for the plasma to
develop. To compensate for this efficiency drop, a small amount (=0.2%)
of Argon is added to the gas. Argon increases the primary ionization
which in turn increases the chances for the plasma to develop.

Thus, starting in January 1981, the standard gas running conditions
were: 96% Neon, “% Helium, =0.0“% Oxygen (and Nitrogen), 0.17% Argon,
and =0.05 to 0.08% water vapor (depending upon humidity). As a result
of these changes, the refire probability was reduced from 6-8% to 1-2%
at a 10 second repetition rate. The efficiency does not suffer too
badly, and is =70-7“% at the minimum delay of approximately 700 nsec.
This delay is the time between the muon transversing the chambers and
the HV being applied to the flash chambers. It has been found that
doubling the gas flow rate does not improve the efficiency appreciably.

3.2.2.2. Stability. The stability of the flash chambers was
nunaitored during the WBB run. Runs in which we used the scintillation
tanks to trigger on beam and cosmic muons were used to determine
efficiency and refire probability. Figure 3.5a shows the efficiency as
a function of thma. The error bars shown are all equal to 20.6% as

derived from data. It is evident, however, that the graph shows a

“5

 

EFFICIENCY (7.)
.4
L”
I

 

 

IIIIIIIIIILJIII
102030102030102030102030102030
JAN FEB MAR APR MAY

EFFICIENCY VS. TIME

 

 

 

 

.3-
>_
2
E 75— II I
e 1:: I! ,1 ...I
E IIII|| I II I I
70" ”
l I l I l I l

 

 

 

2 4 6 8 IO l2 I4
WATER CONTENT (C/M’)

EFFICIENCY VS WATER VAPOR

Figure 3.5. Efficiency Stability During WBB Run

“6

greaten~<iispersion of the data than suggested by the error bars. This
dispersion reflects the variation of parameters which affect the chamber
efficiency. The amount of water vapor in the chambers is one of these
factors. The average efficiency is shown in Figure 3.5b. The average
efficiency drops about 0.15% per 0.01% of water vapor by volume. Since
(unethird of the recirculating gas was reinjected into the chambers
without filtering, the actual proportion of water at the center of the
chamber is less by a factor Of two thirds.

The high efficiency region in Figure 3.5a from April‘fiithrough
May 20 is in part due to low atmospheric humidity, but two other factors
were involved. On April 18, a high voltage monitoring system was
installed. With monitoring, it was possible to identify chambers with
low efficiencies due to HV pulse problems and to correct the PFN. Also,
the muon trigger was changed. The change allowed for muons which were
Imore perpendicular to the chambers. The chambers are more efficient to
these types of tracks. Figure 3.5b shows the correlation between
absolute rnmudity and the amount of water vapor in the gas. Apart from
one possible mismeasurement, and a few temporary leaks in the gas cart,
the correlation is strong. The refire probability during the five month
running peroid was 1.5 i 0.25%.

A quick check was made at the end Of the run on the operating
characteristics of the flash chambers. We checked the efficiencies and
Inefire probabilities as well as the reproducibility of the delay curves
and the HV plateau curves. The chambers were tested using the standard
high voltage and gas mixture given above. The humidity in LAB C was
constant and high 6:10-11 g/m’). Figure 3.6 shows the delay curves and

PiV plateau curves from the test. For comparison, the curves from

A7

 

 

 

 

 

 

 

 

g-
*' .A
(J
E 70 — Q Q X
52 A.CD
t x
L” 60 — A A JAN
A X X MAR
X 0 JUNE
50'—
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6 7 8 9
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HV PLATEAU
E;
g A A
I: TO — O 0 JUNE
2 3
n.
III:
60__
50 — $
I I I
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y.SEC

DELAY CURVES

Figure 3.6. Efficiency and Delay Measurements - June 1981

N8
earlier tests are shown. The curves are stable within the rtmning
peroid within the fluctuations noted before. The efficiency drop is
approximately 12% per microsecond in the region from "minimum delay" to
"minimum delay" + 700 nsec. The average efficiency was approximately
70-7uz, and the average refire probability was 1.5 i 0.25% at a 10

second repetition rate.

3.3. THE GAS CART

3.3.1. Gas Flow. The H16 flash chambers represent a volume of
about 37 m3 (1300 ft’). From the chamber efficiency studies, the
efficiency plateaus, at fixed trigger delay, occur at a flow rate of
about one volume change per hour.

Two gas.rechwnflators were built. Each recirculator has a flow
capacity of about 900 l/min. Although one recirculator would have been
sufficient, two were built to provide an extra margin of safety in case:
higher gas flows were required and to serve as a backup in case of
mechanical failure. The basic system is an upgrade of the recirculator
used at SPEAR on the Mark II experiment.‘“

With the addition of "dirt" into the standard gas mixture, both
recirwmilators were used. One "gas cart" would purify a fraction of the
total volume (13.3 ft’/min) while the second merely recycled the
icemaining gas (10 fta/min) back into the chambers.

The rugged flash chamber construction eliminates the need for
deelicate pressure regulation. The overall system pressure reference
POint is established by a regulator on an NeHe backfill bottle. This
8855 reservoir makes up for any system losses due to leaks or diffusion.

Ovencall flow rate is controlled by a variable feedback adjustment on the

N9
two-stage blowers by means of a butterfly valve which routes a
percentage of the gas into the flash chambers. The blowers themselves
run at a constant rate. A M-D Pneumatics rotary blower model 57/81 with
a butterfly valve controlled feedback loop was used.‘55 More detailed
adjustment was possible using individual flowmeters which serviced
combinations of four chambers.

3.3.2. Gas Purification. The gas is cleansed by passing it
through two molecular sieves, one operating at room temperature, the
other at liquid Nitrogen temperatures. Two pairs of sieves resided on
each cart, one undergoing cleansing by being baked and pumped with a
vacuum pump while the other was on-l ine. Details of the plumbing is
shown in Figure 3.7.

The molecular sieves consist of two stainless steel cylinders of
66.7 liter volume, filled with N1 kg each of 3 mm Linde 13X molecular*
sieve pellets. One sieve is run at room temperature to trap water vapor
and.the other at liquid Nitrogen temperature (~T96°C) to remove Oxygen
and Nitrogen. Argon was also trapped out in the cold sieve and had to
be continously added to the purified gas going back to the chambers.

In normal operation, the sieves are cycled from temperatures of
-196°C to 290°C. Heat shields were placed surrounding the heating coils
to prevent uneven heating of the dewars. Temperature regulation during
the heating cycle inside the dewars was accomplished by a chromel-alumel
thermocouple control device66 and temperature was monitored with a
commercial iron-constantan thermometer.

At a flow rate of 600 l/min, nearly 1H.3 kcal/min of heat is
removed from the incoming gas to cool it to liquid Nitrogen

temperatures, Vflllle the same amount must be added to the outgoing gas.

50

w111
.823 z a

206:3; o»

>¢ 24 53%

 

~¢

 

.896 26

 

 

mu ...
2.2m

 

 

 

 

 

 

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2.25390 2 So can

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51

If this were accomplished simply by boiling off Nitrogen with no
recovery, the useage of LN2 would be large. Internal heat exchangers
were used in the dewar to (1) facilitate faster cooling/warming of the
gas and (2) to reduce Nitrogen consumption. After the WBB, large
external exchangers were added.66

3.3.3. Gas Monitoring. Under normal conditions, the gas is pushed
through the chambers where it picks up Oxygen, Nitrogen and water vapor.
A small quantity of gas is lost through leaks in the chambers and some
Helium is lost due to diffusion. The gas returns to the cart at a small
overpressure (ll-6 mm of Hg) carrying about 600 ppm each of O2 and N2.
The amount of water vapor varies with the absolute humidity, but can
approach 600 ppm. After purification, the 0,,/Ar/N2 content drops to
less than 30 ppm. The operation of the system was checked three times
daily by means of a two column chromatograph. We used a model 69-550
gas chromatograph manufactured by Cow-Mac Instrument Company.67

Under normal conditions, with our standard gas mixture, a sieve
would become saturated after about three days. Saturation is detected
by an increasing 02 content in the post sieve gas which grows to about
20% of the input level within 12 hours. The cleansing cycle takes about
four days: one for boiling, two for evacuation, and one for cooldown.
Since we had four sieves on two carts, one sieve would be on-line, two
being cleansed, and the last cooled down and ready to come on-line. The
presence of Argon in the gas greatly reduces the saturation time as it
is trapped out in the cold sieve. Had we run with straight NeHe gas

With no bypass, the saturation time increases to 7-10 days.

52
3.A. THE HIGH VOLTAGE SYSTEM

3.”.1. Overview. Each chamber had its own pulse forming network
(PFN) to produce the HV pulse. A schematic of the PFN circuit is shown
in Figure 3.8a. Direct current high voltage (DCHV) charged up the
capacitors. The spark gap acts as the switching element and uses a
spark plug in the gap. High voltage thyratrons provided the trigger
pulse. Upon receiving a trigger, the charge stored on the capacitors is
switched to the chamber. The chamber has a capacitance of roughly
100 nF, so half of the charge on the PFN is transferred to the chamberu
A typical HV pulse is shown in Figure 3.8b.

A mini-computer controlled monitoring system (PQD) was installed to
check the PFN performance on a pulse-by-pulse basis. The PQD monitors
the total charge applied to the chambers, the timing of the HV pulse and
verifies that no spurious pulsing occurs between triggers. The
monitoring system is detailed later.

.A block diagram of the high voltage system is shown in Figure 3.9.
Multipurpose distribution panels service 8 PFN's. The panels provide
DCHV, the HV thyratron pulse, dry N2 gas for the spark gaps and bulkhead
lemo feed-through connections to link the HV monitor signals from the
PFN's to the POD. One thyratron pulser usually serviced 10 distribution
panels, with a single power supply (Hipotronics, model 815-75.
15 kV-15 mA) for all of the thyratrons. There are 8 PQD units, each
servicing up to 80 chambers and interfaced to an L81 11/23 computer.
Two nuthi DCHV power supplies (Hipotronics, model 815-335, 15 kV-335 mA)
supplied up to 9 kV to one half of the 608 N88 detector, one supply was
used for the 1116 WBB detector. Each supply feeds a fan-out box, each

box supplying up to #0 distribution panels.

53

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55

Safety circuits, "Droege Boxes" were installed to monitor the total
current in the ground return of the main power supplies. The Droege Box
trips the main power supply and the Key Tree safety circuit when the
current exceeds preset limits (typically 2 mA). After a trigger has
caused the PFN's to discharge, a dead time is allowed to accomodate the
high recharging current. After this tdmua, typically u-s seconds, a
current in excess of 2 mA will cause a trip.

Override switches were available. A "dead man" switch.pnNivided a
high current (10 mA) trip and required the switch to be continuously
depressed. Releasing the switch caused a trip. This override satisfied
a "two man" safety rule when it was necessary to work near Unerngh
voltage. A second override "blanked out" current monitoring for a
preset time, typically 20 seconds, to facilitate turning on the HV
system.

3.11.2. The High Voltage Regulator. Fluctuations in the ac line
voltage, due to the power drain by the accelerator magnets, created a
need for better regulation in the HV power supplies. Two silicon
controlled rectifier (SCR) based regulators were built and installed in
each of the HV supplies. A block diagram of the regulator circuit is
shown in Figure 3.10 and consists of a comparator card, phase card, gate
card as well as low voltage dc supplies, transformers and SCR's.

Inside of the HV power supplies, the 3 phase 2H0 VAC line is
continuously varied from 0-2A0 VAC by means of a VARIAC, enters a
HV tank where it is transformed and full wave rectified and then emerges
as DCHV from 0-15 kV. The regulator was inserted electronically between

the VARIAC and the HV tank. Taps were taken off of the input voltage to

56

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provide 2UO VAC to the transformers and 120 VAC to the low voltage dc
supplies.

An SCR behaves like a "triggerable" diode. In the regulator, an
SCR will hold a positive voltage between the anode and cathode until the
gate receives a pulse. Upon receiving a gate pulse, the SCR triggers
and allows current to flow winch is proportional to the voltage
difference between the anode and cathode. The power diodes, in parallel
idith each SCR, short out the negative phase (with respect to the anode)
of the ac cycle.

In actual operation, the DCHV from the output of the main supply
is picked off and voltage divided via a resistor chain and used as input
to the comparator card. This low sense voltage (typically .5 volts) is
compared to an internal preset voltage. When the sense voltage is
greater than or equal to the reference, the comparator card output is
high (off). When the sense voltage is less than the reference voltage,
the output is low (on).

It is this change in output states which adjusts the tuning of thel
gate pulse within the ac cycle. The SCR can fire early fim~nmximum
current or late for minimum maintenance current. On the phase card, the
voltage from the comparator card is seen by the emitter of a transistor.
The base of the transistor sees the 12 V, half wave rectified, ac
voltage fiwnn the transformers. When this base voltage exceeds that of
the emitter, the transistor fires, discharging a capacitor. This
discharge pulse travels to the gate pulse card where it is shaped,
acceptable to the main SCR's.

On the comparator card, the difference voltage between the sense

and reference voltages originally had a gain of unity with respect to

58
the output voltage. The gain was changed to 30, providing faster
switching between the high and low output states.

The HV regulator was easy to build and debug. The phase and gate
pulse cards were used in accelerator magnet power supplies, the rest was
assembled using easily obtainable components. The regulator provides at
least a factor of 40 improvement over no regulation. At 9 kV output, a
20% change in the input voltage resulted in a 20% change in the output
voltage without regulation and a 0.5% change with regulation. The
regulator provided faster recharge times, roughly by a factor of two
over no regulation.

3.”.3. High Voltage Pulse Monitoring System. The system, shown in
Figure 3.11, has a capacity of monitoring 6110 channels and consists of
up to 8 special crates of electronics controlled by an L81 11/23
computer. Each crate contains a crate controller and five data modules.
Each data module contains the electronics to monitor 16 PFN's as well as
an 8-bit serial shift register readout system.

Upon receiving a trigger, the pulse monitor system (POD) checks
whether the front edges arrive in proper synchronzation with the
trigger, determines whether there is spurious pulsing and measures the
total charge in each pulse.

The front edge arrival time is considered satisfactory if the pulse
amplitude exceeds a preset comparator level by the time a preset timing
signal is received from the controller. Any channel with a bad front
edge is flagged by setting a bit in a storage register.

To check for spuriously firing (run-on) spark gaps, each 16 channel
data module contains two, H-bit "run-on" counters. Each counter is the

logical OR of the eight PFN's serviced by a single multi

59

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60
purpose distribution panel. The run-on counters contain a count of one
if all the PFN's worked properly. In the event of a spurious discharge
in any one of the 8 PFN's being monitored, the run-on counter is
increased by one.

To measure the total charge of the high voltage pulse, the monitor
signal for each channel is integrated with a resistor-capacitor
combination and then digitized using an 8-bit analog-to-digital
converter (ADC). The voltage across the 16 integrating capacitors is
digitized in succession with each conversion taking about 100 usec. The
capacitors are allowed to discharge throughout this process with a time
constant of 50 msec, allowing for complete discharge by the time of the
next trigger. No dispersion in the measured pulse-heights is introduced
by the capacitor discharge since digitization occurs at the same time
relative to the monitor pulse.

The information from the three pulse analysis sections is read into
the computer by a single shift register bit serial path connecting all
the modules. The details of the data transfer are given elsewhere.”
The program used for data acquisition and display is an RT-11 version of
MULTI69 with special data handlers to accomodate our hardware
configuration. Once all the data has been read in, it is written into a
CAMAC memory module in the data acquisition system of the main computer
and combined with the rest of the event's data and written onto magnetic
tape. The monitor computer then unpacks the data, displays it via
standard MULTI commands and statistically analyzes the data for an end
of run summary. Poor PFN performance can be easily determined either on
an event-by-event basis or from the end of run summary. PFN maintenance

is then performed based upon the information.

61
3.5. PROPORTIONAL TUBE PLANES

3.5.1 Construction. The proportional tube planes provided the
trigger:fim~the experiment as well as provide energy measurement at
higher energiens (above =100 GeV). The calorimeter contained 25 planes
for the WEB (36 for the N88), with each plane containing 1AM cells. The
planes were made of extruded Aluminum. Each cell measures 1" X 1" X 12'
and is strung with a 50 micron diameter Gold-plated Tungsten wire. Four
cells are connected to one amplifier to reduce the cost of the
electronics while still maintaining adequate granularity for triggering
purposes. An Argon-Methane (90%-10%) gas mixture is used to give the
fast drift time (S 200 nsec at 1650 volts) needed to form the trigger
within the flash chamber sensitive time. The planes arecxflibrated
using Cd”9 sources which are mounted on the planes.

3.5.2. Trigger Electronics. The amplifiers are charge-integrating
vflth a risetflme of 180 nsec. The gain is 1 mV/fC within 22%. The
calibration, gain, and operation is discussed elsewheref”o The four
cell wires were capacitively coupled in parallel to the amplifier input.
The amplified output signal passed through a 600 nsec delay line. This
delay lnuavms tapped at 250 nsec and subtracted from the undelayed
signal. This differential pulse, called FAST-OUT, was sent to other
electronic boards in the planes. These boards are the Sum and
Multiplex Board (SMB), the Electron Logic Board (ELB) and an Interface
Card (IFC). Two signals labeled B (Before) and A (After) were generated
to sample and hold, on capacitors, the delayed amplifier output voltage.
In normal operation, the delay between B and A was set to N00 nsec. The
SLOW-OUT pulse height was the difference of the capaciUM‘voltages,

PH = VA - VB.

62

Each of‘tflne 36 FAST-OUT signals were terminated into a comparator
culthe ELB. The comparators discriminated at programmable threshold
levels. These levels were externally adjustable in 5 mV increments,
from 5 to 128 mV. The comparator output was logically TRUE whenever the
input voltage exceeds the threshold. THualogical state of each
comparator was stored in a latch, called RITBIT.

The comparator outputs were processed further by the ELB. Three
fast signals were constructed which contained information about the
pattern of energy deposition in the plane:

1) Single (8), the logical OR of the 36 comparator outputs.

2) Analog Signal (A): the multiplicity of comparators above
threshold in units of 50 mV per channel ON.

3) Fat Shower Veto (FSV) , indicated that the shower width was
greater than a preset span of amplifier channels.

The ELB operated in either of two modes, EVENT or CALIBRATION. In each
mode comparator thresholds were automatically adjusted. In EVENT mode,
the ELB responded to an external trigger, in CALIBRATION, an internal
trigger. At the end of each trigger cycle, a RESET cleared the HITBITS
and reenabled the circuits.

The SMB performed four functions. First the 36 FAST-OUT pulses
were summed to create an analog signal, SUMOUT, which corresponded to
the total energy deposited in the plane. Second, the A and B switching
signals were made when a trigger was received and smuzto the
amplifiers. Third, the trigger and RESET signals were sent to the ELB.
Finally, the 36 SLOW-OUT pulse heights and the 36 HITBIT latches were
multiplexed through the SMB for digitization.

During EVENT mode, the FSV, the discriminated SUMOUT and the Analog

Signals are gated into CAMAC latches. The discriminated SUMOUT rates

63
were stored in CAMAC sealers. All information was read out by the
computer and added to the event record on tape.

3.5.3. Trigger Logic. Since many processes deposit energy in the
detector, it is necessary to develop a trigger which can discriminate
the interesting processes from the uninteresting (Cosmic Rays, beam
muons, noise). Even wiUmUxthe interesting interactions, it is
desirable to determine whether the energy being deposited is from final
state electrons, muons or hadrons, especially when searching for rare
processes.

In forming a trigger, some constraints are imposed by the
detectors. The proportional tube response to an ionizing transversal is
delayed by the time for electrons to drift to the anode. Full
informatdxni is typically available 300 nsec after a transversal. Time
is needed to develop the SLOW-OUT voltages, but not so much time as to
degrade flash chamber efficiency.

A two-stage trigger was developed. First, a pre-trigger gave early
indications of activity and second, after’a.fixed delay for electron
drift and signal development, higher level conditions were interrogated.
The pre-trigger chosen required a coincidence of any two SUMOUT signals
above a<xmmwn threshold. A new pre-trigger could not be generated
until after a fixed delay (1 usec), resulting in dead time.

The second level was then checked. Cable lengths from the
individual planes were tailored so that the signals frmntflmaplanes
generated by a particle traveling at the speed of light in the direction
of the neutrino beam would all arrive simultaneously.

The analog signals were discriminated for use in multiplicity

decisions. The A(c) of a plane was ON if at least c channels were above

6A
the ELB comparator threshold. The single plane SUMOUT was (Mdiwhen the
pulse height was above 50 mV (corresponding to (30% efficiency for a
single minimum ionizing particle). Each SUMOUT was included in a total
energy sum, SUMSUM, which was discriminated at several levels.

Due to saturation of linear summing electronics and minimum voltage
threshold of discriminators (30 mV) the SUMOUT pulses were divided
resistively into a 901-10% split. The 90% parts were discriminated at
50 mV and the 10% parts were summed to give SUMSUM.

When any two SUMOUT's were ON in coincidence (600 nsec window) the
pre-trigger, M condition (WAIT). was generated and other conditions were
tested after the signal development delay. These conditions were:

1) N(n) was TRUE when >n SUMOUT's were On.

2) AM(c,p), at least p planes satisfied the A(0) condition.

3) FM(w,p), ON if, from the FSV conditions, at least p planes
had greater-than-w-wide patterns.

u) L(k), the length, measured in SUMOUT's above threshold,
exceeded a length k.

5) From the muon spectrometer, the logical OR of discriminated
SUMOUT signals in the FRONT (F) set and BACK (B) set of
planes indicated penetration through the toroids.

Specific triggers for various neutrino induced interactions were formed

from these signals. Further descriptions will be given when data

acquisition is discussed.

3.6. TOROIDS

The toroids consist of three, 2u' diameter and four, 1:2' diameter
magnets. The toroids are constructed of 20 cm thick toroidal disks,
three disks for the 211' toroids, six disks for the 12' toroids. Inner

diameters are 30 cm and 15 cm for the 24' and 12' toroids, respectively.

65
The magnets are energized by hollow, water cooled copper conductcn~, and
driven into saturation at 800 A by standard beam line power supplies.
Low conductivity cooling water circulates through the conductor. Each
disk had 3 mm gaps for field measurement. The fields have been measured

using a Hall probe, and are reasonably well understood.71

3.7. ONLINE COMPUTER

The detector was interfaced via CAMAC standard data bus hardware to
a PDP 11/“5 computer. All on-line data handling was controlled by
MULTI, a Fermilab supported software package and was installed under the
RSX-11 operating system. Data from the CAMAC bus were stored on disk
and written onto magnetic tape each event. The MULTI system then made
event information available for diagnostic histogramming and evaluation.
The computer automatically performed certain tests, such as rate checks
and run-summary calculations, to inform the experimenters of equipment

failure and beam status, and to simplify the operation of the detector.

CHAPTER 11. SURVEYING AND ALIGNMENT

14.1. OVERVIEW

The alignment of the flash chambers and proportional tube planes
affects the experimental resolutions (vertex, hadronic shower angle and
muon track angle), thus understanding and correcting for chamber to
chamber variations is important. Muon momentum depends upon the
Iaroportional tube planes in the toroid gaps. Our alignment consisted of
two parts: (1) a physical survey of selected flash chambers, toroids,
and toroid proportional planes and (2) software track fitting. The
survey endeavored to provide direct measurement of the chamber to
chamber variations as well as provide an external coordinate system for

the flash chambers, proportional tube planes and toroids.

11.2. SURVEYING

An external coordinate system was used and was based upon the
direction of the NO beamline, distance from the target in the N0 line
and absolute elevation above sea level. During the surveying, I
assisted a pair of on-site, professional surveyors.

The flash chambers measure a coordinate along the direction of the
”and. X chambers measure the vertical coordinate, the U and Y can be
C30mbined to provide a horizontal coordinate. The origin of the
measurement is chosen to be at the pick up coil within an amplifier at

One end of the wand (see Figure 24.1). The survey measured groups of six

66

67

 

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68
chambers per group (two of each of the three views),aflJ.members of a
group within a space of 20-30 cm. The selected groups were spaced
uniformly throughout the detector. Measurements in all three spatial
coordinates were taken at the "origin" coil and a single coordinate was
measured at the opposite end of the wand to determine the angular
deviation from vertical (or horizontal) of the wand.

Since the wands were glued to the plastic flash chambers, Unawa
existed some variation in the angle between the wand and the chamber
cells. Random cells on the surveyed chambers were selected and the
angular direction, relative to the external coordinate system was
determined. Angles between cells and wand could then be calculated.

The toroid proportional chambers were surveyed. Measurements were
made to determine position and angle of the chambers. Since these
chambers are rigid structures with fixed wire spacing, it was possible
to determine the position and angle of each wire within a given chamber.

Finally, the Iron toriods were surveyed and their center point
determined. Relative position of the calorimeter center to the toroid
centers could be determined. Measurements showed that the toroid center
is roughly a foot lower than the calorimeter center. Since the WBB has
only a very small variation with radius, the offset is not a serious

problem.

A.3. ALIGNMENT
The software alignment used cell hits in the chambers from straight
throughrmxnitracks. The alignment followed a specific procedure to

obtain a set of software shifts and rotations for each of the chambers.

69

The orientation of the three flash chamber views is seen in Figure
11.1. The axes represent the coordinate along the wand by a particular
chamber type. The canonical three view relationship is easily seen to
be:

Y-U=2*TAN10*(XPw-X)
'where U, X, and Y are the coordinates measured.by each chamber type,
TAN1O is the tangent of the half angle between the U and Y chambers, and
XPW is the X position of the U and Y wands.

A shift and rotation of a given chamber represents the two degrees
«of freedom allowed for the fitting. A shift is a change along the axis
measured by the chamber and a rotation is an angular change of the
chamber about a perpendicular axis. The axis of rotation is arbitrary,
but by choosing the axis at beam center, the rotation corrections will
be small and the shift corrections alone will be sufficient for most of
the hits.

A least squares fit is applied to tracks in each of the three views
separately. Single view shifts and rotations are found by examining the
deviations between observed and predicted sparks and then minimizing
these deviations.

In order tc>obtain three view shifts and rotations, two views were
used to predict the hit position in the third view, deviations are
examined and then minimized. Three view corrections are not absolute,
so the survey information is used to estimate the corrections needed for
each chamber. A final pass through the data is made to determine any
remaining shifts and rotations. The residual deviations are shown in

Figure ”.2 the single view and in Figure N.3 for the three view fit.

7O

 

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14

12

10

 

 

 

 

 

 

 

 

 

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Single View Deviations (in clock counts)

 

 

71

 

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Three View Deviations (in clock counts)

 

 

72
This alignment procedure makes shifts both internallgr (within the
flash chambers) and externally (in relation to other elements of the
detector) consistent, but the rotations are only internally consistent.
Survey information was used to determine an overall rotation (= 2 mrad)

of the detector.

CHAPTER 5. CALIBRATION

5.1. BEAM LINE

A calibration run for the detector was done June 1980. Hadrons.
electrons and muons were transported through the Fermilab N5' beamline72
tx>the~detector. The beamline is shown in Figure 5.1. Particles with
energies from 5 to 125 GeV were transported. Beam momentum was selected
by two sets of bending magnets. The momentum resolution of the beam was
known to be dP/P = 0.5-1.0%."3 At low energies, it was necessary to
retarget the primary proton beam from the main ring to just upstream of
the second set of bend magnets. The momenta of the retargeted particles
is assumed to be at nominal value, but resolution and central value are
‘uncertainn The beam divergence was measured by hodoscopes and found to

be less than 1 mrad.

5.2. THE TRIGGER

The trigger for the run consisted of a hodoscope teleSCOpe (H1 and
112) and a threshold Cerenkov counter. The hodoscope telescope consisted
<3f two scintilator counters (2" X 3" X 1/16"), one (H,) set between the
(Serenkov counter and the calorimeter, the second (H2) roughly 25 meters
\Jpstream. The Cerenkov counter could be set to trigger on either
ealectrons (low gas pressure) or hadrons (high gas pressure). The
‘trigger demanded a coincidence in both hodoscopes and either coincidence

(Dr anti-coincidence in the Cerenkov counter depending upon gas pressure.

73

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75
The flash chambers were fired after a fixed delay. This delay was
approximately equal to the delay expected from the proportional tube
planes. Occasionally an absorber (Lead) was placed in the beamline to

filter out the electrons, enhancing the hadron to electron ratio.

5.3. ANGLE RESOLUTIONS

To obtain good angle resolutions, one must take into account (1)
the accurate determination of the shower vertex, (2) the best
calculation of the shower center of gravity at a given depth and (3) the
toest use of the centers of gravity as a function of shower depth taking
into account statistical shower fluctuations.

The lateral position of a shower or muon track at a given depth is
determined by calculating a center of gravity of hit cells within a
given flash chamber. A least squares fit is made to these centers of
gravity. This fit determines the angle of energy flow. Shower vertex
is determined by using the incident particle track before interaction
(in the case of electrons) or by using pattern recognition algorithms
(for hadrons). The pattern recognition algorithms are the same as was
leed to determine the vertex of neutrino induced interactions.

The center of gravity for a given flash chamber plane is determined
13y calculating a weighted mean of the coordinates of the hit cells. The
sveighting depends directly upon the deviation from the estimated shower
(firectnnn and upon the inverse one half power of the number of hit
cells within the chamber. As a consequence, the beginning of a shower
is weighted more. At the end of a shower, fluctuations controlling the

deviation from the estimated shower direction increase with increasing

76

shower depth. The length of a shower is somewhat arbitrary, but a
length was chosen which contained 80% of the total number of hit cells.

Muon angle resolutions are shown in Figure 5.2. The resolution
values are the rms deviation of a Gaussian fit1x>the~distribution of
computed shower angles. Separate data is shown for resolutions in the X
chambers, and for the view orthogonal to the X view, which is determined
by combining U and Y data. The solid curve is a theoretical
prediction’“ which takes into account multiple scattering and the finite
cell size.

Electron angle resolinions are shown in Figure 5.3 and the hadron
angle resolutions in Figure 5.“. Again, the resolutions plotted
represent the rms deviation of a Gaussian fit to the data. A functional

fit to the data yields

C(98) 3.5 + (52.5 / Ee) (mrad)

for electrons, and

c(eh) 6.0 + (6140.0 / Eh) (mrad)
for hadrons. Ekn'comparison, angle resolutions from the CHARM
collaboratjxni at CERN are shown. Our angle resolutions are better due

to the finer granularity of the flash chambers.

5.”. ENERGY RESOLUTIONS

The energy of a shower can be measured by counting the total number
cxf hit flash chamber cells (HITTOT). If all of the energy of a shower
\vere visible, the detector would show a linear response. Unfortunately,
tJie energy response is degraded by the fluctuation of the visible

fraction of the total shower energy, the effects of colinear

77

 

4.0 _

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A Y, VIEW

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MUON ANGLE RESOLUTION

Figure 5.2. Muon Angle Resolution

I50

78

 

0' (mrad)

|5.0

I0.0

5.0

 

 

I I J I I
0.05 0.10 0.15 0.20 0.25
l/Ee (GEV ")

ELECTRON ANGLE RESOLUTION

 

Figure 5.3. Electron Angle Resolution

 

79

 

     

0 AVERAGE OF x

AND YO VIEWS CHARM

80.0 '—

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60.0

 

40.0

20.0

 

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HADRON ANGLE RESOLUTION

Figure 5.4. Hadron Angle Resolution

8O
electron-positron pairs, and by saturation of the flash chambers in the
dense shower core.75

The effect of saturation can be partially corrected. Given a local
n cell region, with m cells (m S n) hit, statistical calculations can be
made to estimate the number of "effective" particles through the region,
and corrections are made to HITTOT. Table 5.1 shows the correctnni
applied for ten cell local regions. No corrections are made for the
factor of two arising from the colinear electron-positron pairs. The
corrections were optimized for hadron showers in the range of 20 tn) 125
GeV. The same corrections are applied to electron showers.

The energy calibration and resolution for electrons is shown in
Figure 5.5. The local density correction is nearly a factor of two at
75 GeV and improves the energy resolution somewhat. The resolution
degrades at higher energies due to unavoidable loss of information which
cannot be fully corrected by the local density effect.

The hadron energy calibration and resolution are shown in Figures
5.6 and 5.7. The energy corrections are smaller, due to the lower hit
density of hadron showers. The correction greatly improves the
resolution, especially at higher energies where a factor of two is

gained. A fitted curve to the data yields a hadron energy resolution of

0(Eh) / Eh = 80% / fir.
.Above 125 GeV, where flash chamber saturation begins, better resolution
can beauflueved by using the proportional tube information. Again,
energy resolutions from CHARM are plotted for comparison. The use of
scintillation counters yields better energy resolutions than our

detector.

81

Table 5.1. Hit Cell Enhancement for 10 Cell Regions

 

RAW CORR.

HITS

HITS

 

LO

LO

 

2.0

2.I

 

3.0

3.4

 

4.0

4.9

 

5.0

6.7

 

6.0

9.0

 

7.0

I2.0

 

8.0

I6.5

 

9.0

25.4

 

 

I0.0

 

42.6

 

 

HITTOT

4000

3000

2000

I000

Figure 5.5.

82

 

0 RAW HITTOT

A (er/E) 7.

I--

In

(B

a,

,o CHARM

 

l I I I I

— >< CORR. HITTOT -

 

 

25.0 50.0 75.0 I00.0 I25.0

E (GEV)
e

ELECTRON ENERGY RESPONSE

Electron Energy Calibration and Resolution

I0

83

 

HITTOT

7000 '— 0 RAW HITTOT
X CORR. HITTOT

6000 ’—

5000 —

4000 "—

3000 7'

2000 _ 0

I000 _ O

 

I I I I l

 

 

25.0 50.0 75.0 |00.0 I25.0

E h (GEV)

HADRON ENERGY CALIBRATION

Figure 5.6. Hadron Energy Calibration

84

 

x
{J
Bu 25 —O 0 RAW HITTOT
>< CORR. HITTOT
20 —
RAW
— O
'5 ‘X 3 .
‘3 I»
'0 _ CORR.
x x
5 CHARM'
I I I I I

 

 

 

25.0 50.0 75.0 I00.0 I25.0

E h (GEV)

HADRON ENERGY RESOLUTION

Figure 5.7. Hadron Energy Resolution

CHAPTER 6. THE EXPERIMENT

The 1981 WBB run was intended to be an "Engineering Run" in order
to gain an understanding of the detector, develop a trigger(s) and
understand the trigger efficiencies. Nonetheless, certain Physics goals
were set and achieved. The run was set up for neutrino running, but the
last two weeks were devoted to antineutrinos. For the analysis, only

the neutrino exposure is discussed.

6.1. BEAMLINE

The neutrino exposure for the February - June 1981 period used a
single HORN-focused wide band beam M11flmeFermilab NO line. The
beamline is shown schematically in Figure 6.1. The primary proton beam
of 400 GeV is targeted upon Beryllium. The target was cylindrical in
shape, 33 cm long with a radius of 1 cm. The HORN magnet, with a
current of 80 kA, sign selects and focuses the secondary particles,
nmstly pi-anKIK-mesons. These mesons traverse a decay region, 343
meters long, with decays dominated by 2-body decays, intormxnmsand
neutrinos.

The front face of the HORN is located 7.25 meters from the front of
the target. It is 2.42 meters long, with a conical section and a
cylindrical section. The conical section is 1.95 meters long, front
I"adius of 7.1 cm, back radius of 1 cm. The cylindrical section is 0.47

"Haters long, radius of 1 cm. The Iron is magnetized by a current

85

86

83 seem scam 2:: s2 .Hé 3%:

mmm2<zo DJEImafiwflw
Acmmmc mgmmnm ...womf. mmotzo:
«2.03m: ...oou m. mmmhzaoo ftmzmhz.
0 me... u m<._ 20:2 .5223... »<omo zmo: 22.01.;

 

QC __ I _ A1 at.

amp—m}. mm! 0:... 52. van _m mfi o

 

 

 

 

 

 

 

 

 

 

 

87
circulating around the outside surface of the HORN. A complete
discription of the HORN has been given by Nezrick and Mori.76
An antineutrino flux formed a significant background to the v WBB,
due to meson decays before the HORN and due to incomplete defocusing of
erng sign mesons in the HORN magnet. Three-body decays of charged and
neutral kaons account for electron type neutrinos, and occurred at thee

1-2% level relative to the Vu flux.

6.2. MONITORING
Monitoring of the primary proton beam is done before the target.

)77

Flux was monitored by a Beam Toroid (BMTOR and by a Secondary
Emission Monitor (SEM). These devices counted absoluteInmmmrs (hi
units of 101°) and agreed with each other to within 6% during the run.
A plastic scintillation counter was placed upstream of LAB C to measure
the muon flux through the berm. This counter was located 787 meters
from the target and was accessible via a beamline access enclosure. The
counter measured 1' X 2' and had a rate of 70-100 counts per beam spill.
This "HUNT counter also served to define the experiment's trigger gate,
discussed in detail latter. During the run, a second counter was placed
behind the first, and run in coincidence with the first. This counter
was used to lower accidental coincidences from Cosmic Rays and had
roughly half of the area of the first.

Information from the primary proton beam monitors, muon flux
counters, and HORN OFF/ON status was received and merged with the event
data records on tape. The muon counter information always arrived in

time to be included with the current event's data (in-phase). The

timing of the proton monitor information was such that it had to be

88

included with the next event's data record (out-of-phase). I While this
necessitated a certain amount of software data recombination, no
information was lost. From the period 5 April 1981 to the end of the
run, ("steady state" running conditions) the timing of the HORN
information was fixed and always arrived out-of-phase. Before this
time, the timing was uncertain. Information could arrive either in- or
out-of-phase, changing on an event-by-event basis.

This is a serious problem. The flux shape and the Su/vu ratio
change significantly between HORN 0N and HORN OFF conditions. We
analyzed the proton and muon monitor information during the "steady
state" running. Figures 6.2 and 6.3 show the proton-on-target (POT) and
muon counter information for the HORN OFF and HORN ON conditions for
this running period. The HORN OFF triggers represent 8.5% of the total
(2.3% of total POT). These triggers are clustered at low POT and muon
count. (In fact, the HORN was set to remain OFF for low intensity
spills.) Cuts on triggers with either less than 0.2 X 10” POT or less
than 20 counts in the muon monitor can eliminate most of the HORN OFF
pulses. The HORN OFF triggers remaining represent 3.0% of the total
triggers and 2.2% of the total POT flux. Since a large fraction of the
data occurs before the "steady state" running, these cuts were used to
reduce the uncertainties in flux shape and in the T)“ contamination
throughout the entire run period.

Very early in the run period, it was discovered that the HORN would
go OFF for a low intensity spill and then stay OFF until after a fixed
number of high intensity (=1013 POT) spills. To counter this condition,
we looked at the Charged Current data and noted the u+/u- ratio as a

+ -
function of run number (or time). Runs with a u /u ratio in excess of

89

 

 

 

I"
I I

 

 

O.

010

0.25 0.5 0.75

POT DIST - HORN ON

I
_.I I I LLLILLle I
1. 1.25 1.5 1.75

240 3

 

I I

 

 

 

 

 

0 __FcrfLrI~J1hJ~afiE4_—~—rrfr~limn

0.25 0.5 0.75 1. 1.25

POT DIST - HORN OFF

-2 __._.-. ..__- _._J

.._-fi -.-.— _. __-..

 

 

Figure 6.2.

POT Distribution for HORN ON/OFF

90

 

~10

 

 

 

 

 

 

 

 

O _I I I I I I
0 25 50 75 100 125 150 I75 200

 

3 MUON DIST — HORN ON

 

 

 

 

 

O W l l

0 25 50 75 100 125 150 175 200

MUON MST — HORN OFF

 

_ _.-I_.w-- __.-_.J

 

 

Figure 6.3. Muon Counter Distribution for HORN ON/OFF

91
roughly 10% were eliminated from the analysis. HORN trigger logic was

changed to make an ON/OFF decision every spill after this discovery.

6.3. WBB FLUX

6.3.1. Monte Carlo Simulatdtni. The characteristics of the WBB
neutrino flux have been calculated by Monte Carlo. The Monte Carlo had
to model both the single-HORN focusing system, and the production
spectra and angular distributions of secondary hadrons from protons on a
Beryllium target. The Monte Carlo considered production, absorption by
the HORN, and two- and three-body decays of wt, Ki, and KB as sources of
neutrinos. The Monte Carlo calculated the various spectra as a function
of the lateral (from the beam center) position for electron and muon
type neutrinos, as well as their antiparticles.

The standard beam Monte Carlo, "NUADA", performed flux calculations
for two-body decays. This Monte Carlo contained a model for the HORN.
A more sophisticated model was developed by Brock7a to account for
three-body decays, neutral kaon decays, and HORN OFF configurations.
Comparisons of the two Monte Carlo methods yield an estimation of the
uncertainty in absolute normalization of the integrated, energy-weighted
neutrino fluxes to be 110%.79

Several production models were used to estimate the production of
secondary hadrons. Measurements of pion production from thin films have
been parameterized by Wang,"0 while Stefansky and White,“ and Mori"2
considered the kaon production.

Given these~parameterizations, the comparison of the parameterized
neutrino spectra and the energy distribution of the Charged Current (CC)

events in the detector was poor. More recent particle production

92

measurements have been made at CERN by Atherton et al. ,°’

with targets
of varying thicknesses. These measurements have been parameterized by
Malensek“ to predict absolute numbers of each type of secondary meson,
by energy and angle, per POT. This new parameterization took into
account multiple proton interactions in the target. From calculations,
it was possible to fix the absolute ratio of each type of neutrino to
the number of POT.

6.3.2. Comparison With Data. The measured CC energy distributions
are in good agreement with the predicted shapes. The predicted flux
shapes are compared with the momentum distributions of u- from quasi
elastic data in Figure 6.4. The Charged Current energy spectra for v
and 0 are compared with prediction in Figure 6.5.

In all cases, the shapes are in good agreement with Monte Carlo
predictions. From the Monte Carlo, the energy weighted fraction of Cu
to VII in the WBB is predicted to be (In/V11 - 6%. Above 20 GeV in
neutrino energy, the antineutrino fraction increases to approximately
7.5%. This is in good agreement with the quasi-elastic muon data where
the (In/vu ratio is 8%.as

Initially, there appeared to be some discrepancy in the Charged
Current data. The antineutrino to neutrino ratio was 6%. This ratio
must be corrected for the relative acceptance (”C/”v - 0.8) and cross
sections (03/0V = 0.5). After corrections, the Charged Current data
indicated a 15% contamination, in disagreement with both quasi-elastic
data and Monte Carlo prediction.

This discrepancy was eliminated after observation of CC samples for
both neutrino and antineutrino events. There is an estimated "cross

over" error in the data samples of 224%. This error represents the

93

 

 

 

 

 

 

 

 

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r—
2 I—
D
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m — THEORY
m I'—
<
LIJ
U 2
z — +
‘O I.
10 .—
7 O
1 7 9
I J l 1 I I l
0 25 50 75 100 125 150 175 200
,, QUASI ELASTIC FLUX — 1937 EVENTS E (65V)

 

 

 

Figure 6.4. Energy Spectrum from Quasi Elastic Data

94

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95
probability that the muon momentum analysis routine does not find the
correct "hit" channel in the toroid proportional planes, thus
calculating an incorrect sign and momentum. Sources of these incorrect
"hits" are: random noise, "beam muons" from upstream neutrino
interactions (upstream of the detector), muons associated with meson
decays within the hadronic shower, and muons which penetrate the center
of the toroids where the field is small and uncertain. Since there are
a greater number of neutrino induced CC events, the "cross over" events
will have a larger effect on the antineutrino sample. Upon applying a
correction for this error, we determine the (In/v“ ratio to be in the
range of 1.8 to 4.0%, 4.5 to 10% after corrections for acceptance and

cross section differences.

6.4. EVENT TRIGGERS

During the first half of the WBB run, the response of many of the
trigger components was investigated. The toroid planes and some of the
calorimeter planes were either not yet installed or contained
non-functional electronics. All detector components were operational
during the "steady state" run conditions. The data during the "steady
state" period were logged with constant trigger conditions.

Nonetheless, it was possible to take data during the early setup
and studies period. A simple "low-bias" (PTH) trigger was set up and
used. The trigger consisted of a coincidence between the total energy,
SUMSUM, and the delayed pre-trigger, M(WAIT). The SUMSUM was
discriminated at 75 mV and the pre-trigger delay was set to 150 nsec:

PTH = M(ISO) ° SUMSUM(75).

96
From calibration data, it was determined that this trigger was 90%
efficient above 5 GeV, and 100% above 10 GeV. The SUMSUM threshold was
set at a compromise between minimum ionizing energies and reducing the
accidental trigger rate from Cosmic Rays and Cd109 source noise.

Interactions at the end of the calorimeter were not acceptable, so
the SUMOUT signals from the last five proportional planes did not
contribute to the M condition, but were included in all other trigger
components. In the WBB, a proton spill of 10” POT, within 600 usec,
resulted in roughly six PTH triggers per spill. The background from
non-neutrino sources contributed to about one PTH trigger. The neutrino
intensity was roughly Gaussian within the spill window, the background
flat, leading to a non-neutrino trigger fraction of roughly 16%.

The detector was limited to one event trigger per spill. The
low-bias PTH trigger gave a high (280%) dead time, which was
unacceptable. In order to be sensitive to rare events such as
neutrino-electron scattering, the PTH trigger was settu>in a
"pre-scaled" mode (PTH P/S). The PTH trigger was counted and allowed to
compete after every 25th satisfied trigger condition. After this, the
trigger was enabled and could compete with the triggers for the rare
interactions.

In particular, triggers for the quasi-elastic (QE) Charged Current

process 0“ + n + u + p, and the elastic neutrino-electron (ETRIG)
process vu + e- + v“ + e- were developed.

The quasi-elastic event signature was little or no hadronic energy,
with muon penetration in the toroid spectrometer. The trigger required

coincidence from both sets of toroid proportional planesznuienergy

deposition in the calorimeter below a set maximum threshold:

97

 

QE = M(150) - F . B . SUMSUM(250).
The rate for this trigger was too high, so it was pre-scaled by a factor
of six (QE P/S).

Fbr the electron trigger, differences in topology between electron
and hadron showers were exploited. Electron showers are narrower,
denser and shorter than hadron showers at fixed energy. Since no
electron event could have an associated muon, the Single signals from
the last two proportional planes in the calorimeter were used as a veto.
A maximum shower length condition of six planes was set up.fi%m1the
SUMOUT signals. Six planes represented roughly 25 radiation lengths.

A width condition was investigated using the FSV component. This
component required longer drift time, so WAIT was set to 400 nsec. The
FSV was not efficient in rejecting hadrons, since hadron showers were
similar to electron showers at the proportional plane sampling
frequency. Even though the FSV was not used, the 400 nsec delay was
kept since all trigger studies had been performed at this delay. A
higher energy threshold and an AM condition were used to reduce

background rates. The final trigger was:

 

ETRIG = M(400) - AM(1,1) . SUMSUM(ISO) - [5(39) + 5(40) + N(6)].
A special High Energy trigger (PTHHIE) was also used. This trigger
was identical to the PTH trigger but had a higher threshold:
PTHHIE = M(150) - SUMSUM(1580).
This trigger had a threshold of roughly 130 GeV for full efficiency.
Since only one out of every 100 PTH triggers satisfied the PTHHIE

condition, no pre-scaling was necessary.

98
6.5. GATING

The detector was triggered only during the "fast spill"<fi‘the
accelerator cycle. The gating scheme is shown in Figure 6.6. The beam
spill arrived a pre-determined (PRE-DET) number of accelerator clock
cycles after a START signal.

The START signal had a certain amount of jitter<m1the order of
tens of microseconds and tended to drift in time relative to the spill
time. To obtain a gating system which would be insensitive to this
drift, a dynamic beam gate (DBG) was established. The PRE-DET was used
to Open a 2 msec gate (BGATE) and a coincidence between the first signal
from the upstream muon counters and the BGATE started the D80. TNae DBG
remained open for roughly 0.6 msec. In order to avoid prematurely
starting the D80 from a Cosmic Ray coincidence, the PRE-DET was lunat as
close to the start of the spill as possible.

Neutrino triggers were enabled during the D80. If a trigger did
not occur within the DBG, a one second gate was opened to allow a Cosmic
Ray (M - Liquid Scintillator u) or a pulser trigger. It was necessary
to trigger every spill in order to record beam monitor information. The
cosmic ray triggers and pulser triggers were used for alignment studies,
and to measure flash chamber refire probabilities, no-event'fimuse"
pedestals, and single-muon efficiencies.

All triggers (PTH P/S, QE P/S, PTHHIE, ETRIG) were enabled during
the entire DBG. A gate (20% GATE) was established, which occurred
during the last part of the D80. During this time, the non-pre-scaled
"low-bias" PTH trigger was enabled and allowed to compete with the rest.
‘The start of this gate was controlled by the number of hits in the muon

counters.

99

 

 

AMUON
COUNTER
INTENSITY
I I 5>
START PRE-DET 'nME

 

 

' I BGATE 2 msec

 

 

 

 

 

' 080 0.6 msec
+ 20x w
PEDESTAL .'5

 

 

 

 

 

 

Figure 6.6. Schematic of WBB Gating

100

It is asswmxithat the number of muons scales linearly with the
proton spill intensity. This is roughly true to within i15%. The
average number of hits in the muon counters was 97 1 18. TTna 20% GATE
‘was opened after roughly 80% (70 hits) of the total number of muon hits
had been recorded. The 20% GATE ended with the D80. Measurements of
the 20% GATE, during the "steady state"1nuvung, indicated it was open
during the last 25% of the integrated muon flux.

Once a trigger occurred, the detector was dead for the rest of the
beam spill. Scalers recorded the number of muon hits during each of the
gates, up until a trigger occurred (i.e. the "live" time). The dead
time due to the pre-trigger(s) and due to charged particles traversing
the front veto scintillator wall were also scaled in coincidence with
the muon scalers. This allowed us to determine the intensity-weighted
live fraction on an event-by-event basis. Measurements Uuficate an
average live fraction of 240% during the WBB run.

Events were recorded in sets called "runs". Each run allowed
certain combinations of triggers to be enabled during the DBG and
20% GATE. The type of trigger(s) enabled as well as the type of
trigger(s) responsible for a particular event were recorded on tape with
each event record. Table 6.1 indicates the various run types, and the
trigger types and gating scheme for each run type. Run types for both
the setup and steady-state periods are shown.

With an integrated intensity of 31X 1018 POT during the neutrino
running and 0.5 X 10” POT during the antineutrino running, Table 6.2

shows the number of triggers of each type we recorded.

101

Table 6.1. Run Type Triggers and Gate Scheme

 

RUN e TRIGGER (GATE)

 

 

LABEL PTH I P/S I 0E IETRICI HIE

 

(SET UP)

 

HRUN DBG — — — —

 

ERUN — -— —- DBG —-

 

 

 

 

 

 

ORUN -— — DBG — --

 

(STEADY STATE)

 

GRUN 20'/. DBG DBG DBG —

 

GGRUN 20'/. DBG DBG DBG DBG

 

 

 

 

 

 

 

 

102

Table 6.2. Total Triggers by Trigger Type

 

TRIGGER z/ EVTS E EVTS

 

PTH, P/S 82,|00 l9,200

 

ETRIG 58.300 3,700

 

 

 

 

0E 28.300 6,500

 

 

CHAPTER 7. DATA ANALYSIS

7.1. PURPOSE

The goal of the analysis is to determine the NC neutrino-nucleon
structure functicnus (see Equation 37, Chapter 2). The Standard Model
predicts (ignoring the strange-charm asymmetry) that the CC and NC
interactions couple to the quarks in exactly the same manner. It is
desirable to test the Standard Model's prediction of the NC coupling.
In particular, it is possible that the NC interaction couples to neutral
partons within the nucleon which would be "invisible" to the CC
interaction.

To date, only CHARM and our own collaboration, using the NBB data,
have measured the NC x and y distributions with a large amount of
data. It is hoped that by analyzing the WBB data, we can offer a
complimentary method in determining the NC structure mummions. In
particular, with roughly twice the neutrino data as CHARM, we may have
greater sensitivity to differences in the low x region.

Measurement of the NC structure functions in a Wide Band Beam must
be made indirectly by comparing kinematical quantities of the NC
interactions relative to the CC interactions. This is accomplished by
analyzing NC/CC ratios as functions of the kinematical quantities.
Also, by analyzing the data as a ratio, any flux uncertainties, in

either shape or in absolute number, will cancel.

103

104

The CC structure functions have been measured86 as functions of x
(x=02/2mv) and y (y=v/Ev). The structure functions are typically
parameterized using a polynomial form such as Axa(1-x)8. Using a
parameterization, fits are made to the data and the individual
parameters are determined.87 For this analysis, a particular CC
parameterization hull be assumed. Fits to the NC/CC ratios will
determine (assuming the NC parameterization has the same form as the CC)
the relative difference between NC and CC parameters.

In narrow band neutrino beams, x and y can be determined for both
In a wide

NC and CC interactions using the quantities Ev’ E , and 0

h h'
band neutrino beam, EV is unknown. Whereas xIand y can still be
determined for CC interactions using the information from the muon
energy and/or angle, this is impossible in the NC case. It can be shown
(see Appendix B) that the product of the hadronic energy and the square
of the hadronic angle (E02) is a function of x and y, E02 - 2mx(1-y),

where m is the nucleon mass. The quantity E02 has, of course, the

advantage of being calculable for both NC and CC neutrino interactions.

7.2. DATA ANALYSIS SOFTWARE

Analysis software was developed and maintained by the collaboration
.as a whole. Thais approach has several advantages: (1) a single set of
routnmm aretmmd to create, read, and unpack magnetic data summary
tapes (DST's). (2) standard routines use standard variables and
communication between these routines is well documented, and (3) this
approach provides ready access to software updates and modifications.

A flow diagram of the data analysis is shown in Figure 7.1. We

start with a set of nearly 250,000 triggers. Those triggers which

 
 

~250.000 TRIGGERS

 

  

 

 

REOUIRE PTH TRIGGER

 

 

 

48.000 TRIGGERS

 

 

FIRST PASS

 

VERTEX
FIDUCIAL VOLUME CUTS
SHOWER LENGTH
CC. NC CLASSIFICATION
HADRON ANGLE
HADRON ENERGY

 

 

 

I

 

SECOND PASS

 

MULTIPLE VERTEX
INFORMATION
(BOTH NC AND CC)

 

105

CC ONLY

 

 

 

 

  

5324 NC
"838 CC

Figure 7.1. Data Analysis Flow Diagram

 
   
 

>1

 

MUON MOMENTUM
MUON ANGLE

 

 

106

satisfy a PTH type trigger (PTH, PTH20%, PTH P/S) are selected out for
further analysis. This filtering leaves approximately 48,000 triggers
(events). These events are analyzed via software routines. A first
pass analysis program determines the following quantities: interaction
vertex, shower length, event classification (NC or CC event), and
hadronic angle and energy. Once an event vertex is determined, fiducial
volume cuts are made (to be described later) before subsequent analysis.
During the second pass, triggers with multiple interactions are:
identified and the individual interaction vertices are determined. If
an event is classified as a CC event, the muon angle and (if possible)
momentum are determined.

Figures 7.2 and 7.3 show computer reconstructions of both 3 (X3 and
NC event. Each picture is dominated by the flash chamber representation
of the event. The neutrino beam enters from the left, and the event is
shown in each of the three flash chamber views (U, Y and X). The
proportional tube information is displayed above and below the flash
chamber display. This shows energy deposited in each proportional tube
amplifier for each of the horizontal and vertical views. To the right
of the calorimeter displays are the 24' and 12' toroid displays. The
struck wires for the 12' toroid proportional tube planes can be seen
(for the CC event) in both horizontal and vertical views. As an example
of the fine granularity available form the flash chambers, Figure 7.4
shows a blow-up of the CC event in Figure 7.2, about the region of the
event vertex. At this level, each individual hit cell is clearly
‘visible. All analysis software is designed to analyze the data at the

level of the individual hits.

107

 

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108

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110

The off-line software determines basic event characteristics: event
vertex, hadronic shower energy and angle, event classification (NC or CC
event type), shower length and density, and (in the case of an CC event)
muon track angle and (if possible) muon momenUun. (fiven basic event
quantities, it is possible to determine the characteristics of the
physical interactions of interest.

Vertex identification was a particularly crucial quantity since
angle calculations and resolutions depend strongly upon its correct
identification. The vertex finding routine initially uses the
proportional plane information to localize the initial occurrence of the
shower. The proportional tubes contain only information from the
interaction responsible for the trigger. The flash chambers, with their
long memory times, occasionally (roughly 10% of the triggers) contain
information from another previous interaction within the same spill
(cnmrof-time event). Once the vertex area has been determined both
longitudinally and laterally from the proportional tubes, Unafiash
chamber information is examined. A weighted fit is performed in a
dynamic window in order to determine the vertex location.

Vertex resolution is roughly 5-7 clock counts (one clock count
equals.().23 cm) laterally and 2.2 flash chambers longitudinally. These
resolutions are determined by comparing the calculated vertex to the
selected vertex in the case of Monte Carlo generated showers, and by
comparing calculated vertex to the vertex found by professional (runman)
scanners.

A separate software package was developed to look at triggers with
Inultiple vertices. bhfltiple vertices have a tendency to "confuse" the

hadron shower energy and angle routines, giving erroneous values. 1TH:

111
rmiltiple vertex finder (MVX) locates all vertices within a given event
frame, demands a good, 3-view match and then identifies a given vertex:
as either in- or out-of-time via the proportional tube information. The
vertex algorithm is similar to the one already described. The number of
good vertices (NGM) is always equal to or greater Unnmthe number of
in-time, good vertices (NTM).

Hadronic energy and angle are determined by routines already
discussed in the calibration section (Section 5.3). Angle is determined
by calculating a center-of-gravity for hits within a given chamber, and
then using the centers-of-gravity to determine shower direction. Energy
is determined via enhancement of the "raw" hits. Shower length is
somewhat arbitrary but usually chosen to be the point which contains 80%
of the total number of hit cells. Since this procedure is applied for
both CC and NC interactions, the arbitrariness is unimportant. Shower
density is calculated by determining the number of hits within a
triangular shaped area about the shower. Density is a useful parameter
to separate hadronic and electromagnetic shower54muiis described n4
detail elsewhere.°°

In the case where the muon track penetrates through1x>the 12'
toroid planes, the muon momentum can be determined. The algorithm
requires an accurate determination of the track angle within the
calorimeter, information on the position and magnetic field of the
toroids, and position of the toroid proportional planes. Given the hits
in the proportional planes, the tracking package can determine txflfli the
sign and momentum of the particle (muon) taking into account multiple
scattering, ionization loss and curvature of the particle's path due to

the magnetic field. Muon calibration data fruntflme1982 NBBrnuuung

112
period shows resolutions typically on the order of 10%. The muon angle
calculation uses an algorithm similar to the hadron angle routine.

Most important, for this analysis, is the determination of an
event's classification (NC or CC). Since the analysis will depend upon
NC/CC ratios, misclassifying an event will contritnnne to larger
systematic errors. Classification depends upon the ability to identify,
within the calorimeter, tracks which have a high probability of being
muons.

The routine created an angular histogram about the vertex of the
hits from the interaction. The bin which contained the largest number
of hits formed the basis for the determination of the longest track.
The routine deterndned the angle of the track, required a 3-view
constraint for the track, and calculated track length, track efficiency,
and the track intercept at the vertex. Tests were performed to
determine if the track left the side of the calorimeter or stopped in
the calorimeter.

A matrix of criteria was used to determine if the track was a muon.
'The specific criteria.have been listed elsewhere.as If a muon was not
found, the event was "contrasted", that is, hits with nearest neighbors
were removed, leaving only isolated tracks. A second pass was
performed, and good hits in the toroid chambers were considered” 4After
two passes, the events were classified as "CC" if a muon was found, "NC"
otherwise.

Classification efficiencies were determined by comparing the
algorithm's classification with either the classification from scanned

data, Monte Carlo simulations, or from calibration interactions.

113

Average CC misclassification is 11.4 i 0.3%, determined from Monte
Carlo analysis. This value has a strong kinematical dependence,
especially upon y. High y events have lower muon energy, thus tluetnuon
has a greater probability of being hidden within the shower, or to
traveleniinsufficient distance beyond the core of the shower to be
considered a muon by the software.

Neutral current misclassification is 5.“ i 0.3% and is nearly
independent of kinematics“ Of this 5.”%, 2-3% comes from decay muons.
This number was determined from Monte Carlo, analysis of calibration
data, and from analysis of CC events where the true muon track is
eliminated. 'Nuerest of the misclassification is due to long,
non-interacting hadron tracks, or tracks which leave the side of the

detector.

7.3. DATA CUTS

Cuts are necessary to obtain a good, clean data sample. In all
cases, care was taken to insure that the cuts were not biased toward
either NC or CC events. As is the case with most experimental work, a
compromise must be made between a very clean data sample and a
sufficiently large data sample.

From an initial sample of 118,000 events (18,000 NC and 30,000 CC)

the following cuts were applied in the order listed.

1) The low bias trigger (PTH 20% or PTH P/S) was satisfied.

2) Fiducial volume cuts: the vertex was required to lie within the
first 320 chambers and within a radius of 130 cm from the
detector center. This allowed at least 96 chambers
longitudinally and at least 50 cm laterally for shower

development.

3) Hadronic energy must be greater than or equal to 8 GeV.

11“

N) The POT, muon counter and run cuts (see Chapter 6) were made to
eliminate triggers with the HORN OFF condition.

5) Multiple vertex cuts: NGM 2 1, NTM = NGM. This removed
triggers with one or more out-of-time interactions, but kept
multiple in-time interactions. Multiple in-time interactions
were primarily (911%) secondary interactions of a hadron from
the primary interaction.

6) A 3-view constraint on the primary vertex was imposed. The
3-view constraint condition is:

6 = U - Y + 2 * tan10 (XPW - X).
Data analysis revealed an rms value for 6 of :15 clock counts.
The primary vertex was required to have a 6 5 N5 clock counts.
The final data sample after cuts yields:
532“ NC
11838 CC
events fxn~4an overall.NC/CC ratio of 0.USO i 0.007. The error at this
point is statistical only. The deviation of this value from theory
(Rv - 0.30) is mainly due to CC misclassification. Thisxnmmlem is
discussed in detail in subsequent sections.

The CC sample can be further divided into events whose muons
penetrate the toroids, facilitating momentum analysis (CC), and those
which have an identifiable muon in the calorimeter only (NC). (The "W"
stands for "without".) The Charged Current sample breaks down as:

6923 CC
4915 WC

events. The CC events are used to determine the neutrino and

antineutrino flux spectra (see Figure 6.5).

7.“. NC/CC RATIO
As stated in the preceding section, the integrated NC/CC ratio is;
0.H50 i 0.007. This ratio, as a function of E02 is shown in Figure 7.5.

As already mentioned, theory predicts this ratio to have the value

115

 

 

NC/CC

0.8 -

,5

 

 

 

 

E — THETA SOUARED - DATA

% CD
0.4 r- + +
0.2 4—
o. 1 1 1 1 J 1 1
0. 0.25 0.5 0.75 1. 1.25 1.5 1.75 2.
U?

 

Figure 7.5.

NC/CC Ratio - Data

 

 

116
Rv = 0.30, independent of x and y (and of course E02). Ihi the figure,
there is a hint of the ratio being flat for E02 > 0.“, but increases to
roughly 0.6 at E302 near zero. This rise is primarily due to CC
misclassificatitni. Although CC misclassification is, on the average,
10%, it has a maximum at E02 near zero of 25% and decreases to near zero
beyond E02 = 0.75.

Charged Current misclassification at high y is a problem. In a
narrow band neutrino beam, it is possible to make a cut for both the
neutral and charged current events, say y > 0.8, to greatly reduce or
eliminate CC misclassification. Since neutrino-nucleon interactions are
nearly independent of y, this reduces the sample size by approximately
20%. In a wide band neutrino beam, a y cut is not possible for the NC
events. By making a low 802 cut, it is possible to eliminate many -of
the high y events, decrease the CC misclassification and achieve
(hopefully) a cleaner sample. As an illustration, Figure 7.6 shows an
x,y plot indicating contours of constant E02. The curves shown
represent the "theoretical" values of E02 and do not include resolution
smearing or geometric acceptance effects.

Cuts of E02 < 0.2, 0.25, and 0.3 will eliminate 87%, 91%, and 95%
of the data above y = 0.8. Without an E02 cut, 18% of the events would
fall above a y of 0.8. Unfortunately, the given cuts would cause the
loss of 50%, 60%, and 65% of the data. Given the possibility of large
data loss, an attempt was made to understand the misclassification
probabilities and the effect of the antineutrino contamination via a
Monte Carlo simulation, thereby regaining all or most of the data

sample.

117

 

 

0.8 +-

0.4 -

 

 

 

 

ET2=O.40
ETZ-OJO
ET2=O.25
' —' — ET2=O.20

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l
0.8

l
0.6

l

—‘
.

 

 

0.2 0.4
CONTOURS 0F CONSTANT E—THETA SQUARED

 

 

Figure 7.6.

Contours of Constant E0

118
7.A.1. Monte Carlo. The experiment measures the NC/CC ratio, and

this ratio can be written as:

 

(3g) =NCQ+NEO+aCCQ+EEEO_-8NCD-Efi6,
CCexp cc,+'€6,-acc,-&‘C'EO+BNCO+§—E, (1)
where:
6002: the number of true (anti) neutrino CC events
(NCz: the number of true (anti) neutrino NC events
(a?) 4 the (65) misclassification probability ((236) + (146))

H: <>

6 the NC' misclassification probability [(NCO + (ECO).
In general, all these quantities may be functions of E62. Since we rely
only on calorimeter pattern recognition, it is not possible tc>
differentiate between neutrino and antineutrino induced CC events.

A1Mnfie Carlo program was used to simulate the physics and the
detector. The Monte Carlo could (in principle) reproduce the
experimental resolutions, acceptance loss due to geometry, and
misclassification effects. If done correctly, the Monte Carlo could be
used to determine the various parameters in Equation 1.

The Monte Carlo had two parts. First, the physnxsof the
interactions had to be modeled, second, the average characteristics of
the detector (density, atomic number, size, placement, and response of
tflmaflash chambers, proportional tubes and scintillators) had to be
modeled.

For neutrino-nucleon kinematics, three quantities (typically EV, x,
and y) are sufficient to completely determine the interactnnn The

neutrino (and antineutrino) flux spectra used the Atherton/Malensek"o

parameterization, which determined the spectrum shape as well as the

119
integrated fluxrwudo of antineutrinos to neutrinos in the wide band
beanL. Distributions for x and y were obtained using a parameterization
by Buras and Gaemers.91

The detector Monte Carlo accepted as input, an interaction vertex,
invariant mass and 3-vector momentum of the hadronic system, and
3-vector momentum of the scattered lepton. Using a "fireball" method
for the hadronic system, the Monte Carlo "boils" away hadronic and
electromagnetic particles and then propagates all particles through the
calorimeter, taking into account the average calorimeter characteristics
and chamber responses. The Monte Carlo was written so that one could
use the same analysis routines used for the data. Details of the Monte
Carlo and comparisons to calibration data are given in Appendix A.

A set of events was generated via the Monte Carlo. Monte Carlo
showers are similar to real showers at the "macroscopic" level (i.e.
angle and energy resolutions, shower width), but Monte Carlo showers
tend to be narrower, denser and shorter than true showers. Single
tracks (i.e. muons) have slightly lower track efficiency (by :- 5%) and
hadron energy is overestimated by as much as 10-25%. Because hadron
energy is overestimated, shower energy and angle are not calculated via
software but derived from "smearing" the thrown (true) values. The 1980
calibration provided the resolutions as functions of energy, and so for
each shower, the true energy and angle is "smeared" using a Gaussian
distribution whose width was determined by the resolutions. Only the
classification and geometric acceptance of the Monte Carlo data set was
determined by standard software routines. Using the same fiducial

volume and hadron shower energy cuts as data yields a sample of:

120
7070 NC
15692 CC
Monte Carlo events. This gives a NC/CC ratio of 0.1451 :1: 0.007. This
ratio, as a function of 1320’, is shown in Figure 7.7, superimposed upon
the true data distribution. The comparison is reasonably good except at
low E62.

With the set of Monte Carlo data, it is possible to determine the
misclassification parameters ((5) and (§)) by comparing thrown event
type versus software classification. Figures 7.8 and 7.9 show a and a
as functions of E02. For the Neutral Currents, misclassification is
independent of E92 and is equal to 5." i 0.3% for both 8 and E.

7.11.2. Antineutrino Distributions. Recalling Equation 1, it is

necessary to deal with the CC, and NC, distributions. We choose to

parameterize them as:
'fiE,(Eoz) = anc(Be’)NC,(Eez) (2)

EE,(E@2) = vrcc(Eoz)cc,(Eoz)

where:
f ¢-(E-) dE-
v v v

Y ‘ f ¢ (E ) as °
V V V

(3)

 

The fno and fcc can be thought of as being the correlation
functions between the neutrino and antineutrino interactions.
Basically, they represent the difference in the y distributions between
the two types of interactions as well as the difference in flux shapes
between the two spectra. The f's are dependent upon the particular
structure function parameterization chosen. Figures 7.10 and 7.11 show

fCC(E02) and fnc(E92) using the Buras and Gaemers91 parameterization.

121

 

 

0 DATA

NC/CC

‘33 MCINTE CAR “(1:

3%

0.4 —

 

0.2 —

 

 

O. l l l l l l
O. 0.25 0.5 0.75 1. 1.25 1.5 1.

\jh—
01

E — THETA SQUARED - DATA AND MONTE CARLO

 

 

Figure 7.7. NC/CC Ratio - Data and Monte Carlo

 

 

122

 

MCL

0.28

C

0.2

0.08

0.04

 

 

 

 

 

0.25 0.5 0.75 1.

...o

\jr—
U1
POM

1.25 1.5

NEUTRINO CC MISCLASSIFICATION

 

Figure 7.8.

CC Misclassification as Function of E02

 

123

 

 

 

M C L

0.28 —

CC

0.24 —

0.2 —

0.08 r-
9

 

0.04 F Jr (D

 

 

 

 

 

 

 

 

 

 

l lnnlcl l l

 

O.

0.25 0.5 V 5775 1. 1.25 1.5

ANTI NEUTRINO CC MISCLASSIFICATION

 

Figure

7.9. CC Misclassification as Function of E0

 

 

124

 

 

FLUX)

0.8

(EQUAL

Hoe)

0.8

0.4

0.2

 

 

 

 

 

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ETZ

PARAMUEPIZATION or F(CC)

 

. 2
Figure 7.10. fCC(EO )

 

125

 

 

d
.

 

 

 

 

 

 

X
D
...J
L. 0 some A110 (3.251.135
.1 G FIELD AND FEYi-JMAH
<
D
O ' 1
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’7 0
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O. 0.25 0.5 0.75 1. 1.25 1.5 1.75 2.

PAPAMETERIZATION or F(NC)

 

 

2
Figure 7.11. fnC(E0 )

126
These1functions incorporate the effects of resolution smearing.
Overlaid on these plots are fCC and fno using a parameterizathnitw

Field and Feynman.92

There is very little difference between the two.
7.“.3. Correction of Data. Given reasonable understanding of the
quantitNfisin Equatnn11, we can rewrite the experimentally measured

distributions as:

NCexp = NCO(1-B) + ancm-smcO + cco(a+51fcc) (Ha)
= NC0[(1-B)(1+anc)] + cc,(a+&vroc)
ccexp = CC,(1-a) + chc(1-a)CC° + 8NC0(1+anC) (ub)

cc,[(1—a)(1+vrcc)] + Nc,e(1+vrnc).
Written in matrix form, Equations Ma and Nb are:

(NC (1-B)(1+anc) a+ancc NCO)

’ _ J ( (5)
CC exp 8(1+anc) (1 a)(1+chc) CCO

Inverting, we obtain:

NC 1 (1-a)(1+YfCC) -(a+&vrcc) NC
(CC, g'D -B(1+anc) (1-B)(1+anc)] (CC)exp (6)

where D, the determinate of the 2 X 2 matrix in Equation 5. is:
D = (1-a)(1-B)(1+anc)(1+chc) - 8(1+vrnc)(a+&1rcc).

Since all quantities are known as functions of E02, it is possible
to correct the data bin by bin in E02. Figure 7.12 shows the corrected
NC/CC ratio as a function of EO". The integrated ratio, in the range
of E02 from 0.0 to 2.0 is Rv = 0.302 t 0.007 (stat.). For consistency,
the same correction is applied to the Monte Carlo data.euui is shown in
Figure 7.13.

As already stated, there is good agreement between data and Monte
Carlo, as a function of 130’, except at E02 near zero. Because Monte

Carlo showers are denser and the muon track is less efficient, the Monte

127

 

 

 

 

 

Q 1.
O
\
0
2
0.8 ~—
0.6 -
D
0.4 —
0.2 —
o. 1 1 1 1 1 1 1
0. 0.25 0.5 0.75 1. 1.25 1.5 1.75 2
ET2
E -— THETA SOUARED — CORRECTED DATA

 

 

Figure 7.12. Corrected NC/CC Ratio - Data

 

 

128

 

 

N C ,:’ C C

0.6 r-

04 ~—

02 L—

 

 

.—.. -... --.-d

 

0. 1 1 1 1 1 1
o. 0.25 0.5 0.75 1. 1.25 1.5

E — THETA SQUARED - CORRECTED MONTE CARLO

 

—.

'\l""
U1

 

Figure 7.13. Corrected NC/CC Ratio - Monte Carlo

 

 

129

Carlo indicates a higher misclassification probability munidata at
E02 = 0.0. The showers in this E02 range have the muon track and
hadronic shower nearly collinear, so given the denser shower and less
efficient track, the pattern recognition routine has more difficulty
identifying the event as CC. The Monte Carlo indicates a 25%
misclassification for E02 = 0.0. Given the large correction and the
"microscopic" differences between the Monte Carlo and data, we choose to
avoid the full E02 range for the analysis.

By making a E02 out of 0.1, we can maintain 75% of the data, and
can apply lower corrections to the data due to CC misclassification (15%
for E02 = 0.10, 10% for E02 = 0.1", and 7% or less for E02 > 0.2).

There is a small amount of ve contamination in the WBB from 3-body'
kaon decays. From Monte Carlo information, the energy weighted flux is
estimated to be about 1.6% that of the up flux. Charged Current events
from Ve would appear as an overlapping hadronic and electromagnetic
shower and would be classified as a NC event by the pattern recognition
routine. Simulations indicate an overall ve CC/vu NC event ratio of uz,
with 50% of the events in the E02 range of 0.0 to 0.08. There is no
direct data measurement to confirm these numbers, so corrections to the
data for the Ve induced events are uncertain. This adds an additional
reason to avoid the E02 range below 0.1.

Given these problems, the rest of the data analysis will be
confined to the E02 range of 0.1 to 2.0. The integrated NC/CC ratio for

this region is Ru 2 0.323 t 0.007 (stat.).

130
7.5. DETERMINATION OF NC STRUCTURE FUNCTION PARAMETERS
7.5.1. Parameterization. Recall that the neutrino-nucleon cross
section can be written as:

do(V’V) a GZME

dx dy n

 

[(1‘y+‘% y21F2(x) i (1- é-nyxF3(x)]- (7)

The structure functions can be parameterized as:
F2(x) = Axm(1-x)B + C(1--x)Y (8)
xF3(x) = Axa(1-x)B

vmich separately accounts for the sea and valence quark distributions.

For the CC case:

F2C0(x)

CC(

F2(x) (9a)

xF3 x) xF3(x)

and for the NC case:

no = 2 2 2 2
(X) [6 uL + 6 dL + 6 uR + 6 dR]

=2 2_2-2
X) [5 uL + 5 dL 5 uR 5 an]

F2 F2(x) (9b)

nc( xF,(x)

xF3
1where the strange-charm asymmetry is ignored. For the analysis, the CC

parameters are fixed at:

ACC = 3.0 / E8(a,1+8) (10)
C = 1.0
cc
0 = 0.5
cc
Bcc = 3'0
700 = 7.0.

E8 is the standard Euler—Beta function, and the number 3 in the
expression for Acc is for the number of valence quarks within the
nucleon. Actual measurement of the CC parameters has been done by the

CHARM93 collaboration, and is in good agreement with the values in

131
Equation 10. The analysis will focus upon determining the NC parameters
relative to the CC parameters.

7.5.2. Analysis Approach. MINUIT“ is a minimization software
package written at CERN. MINUIT "steps" through an n-dimensional
parameter space. At each "step" a function (which depends upon the
parameters) is evaluated. MINUIT seeks to determine the parameter
values which minimize the value of the function.

For this analysis, for each "step" in parameter space, 100,000 NC
"events" are generated. Neutrino flux distributions are derived from
the Atherton/Malensek’° spectra. Events are weighted by the cross
section given above (Equations 7, 8, and 9). For eatni "step" if)
parameter space, the cross section will have a different x distribution.
Resolution smeared E02 values are calculated from the Ev’ x, and y
distributions. Misclassification and antineutrino contamination are not
incorporated.

A ratio between each set of NC events and a set of CC events
(generated only once) is calculated. A chi-square value is determined
between the simulated ratio and the (corrected) data ratio. The

chi-square (x2) is defined as:

x2 - Z, 102%?

m... ' ("C11

CC c,data

where 1 runs over the E02 bins, and 0; represents the statistical error

]2 / a; (11)
of the data ratio. It is this x2 which MINUIT will seek to minimize.
As the x2 minimum is reached, the parameter values at that minimum will
represent the best fit to the data.

Initial analysis will concentrate on a one-parameter fit, to Bnc'
The other NC parameters will be set to the following values:

AnC = 3.0 / E8(anc,1+8nc) (12)

132

C = C = 1.0
no cc

0 = a = 0.5
no cc

Ync = ch = 7.0

sin20w = 0.23.
For the given E02 range of [0.1.2.0], MINUIT gives a value of:
+
8no = 2'825 -g:§gi

where the errors correspond to a change of one in the chi-square per
degree-of-freedom. This fitted value is quite stable with respect to
the E02 range of the fit. Figure 7.111 indicates this stability as a
function of X, where X is the lower limit of the fit range (i.e. fit
range: E02 from X to 2.0). The points and error bars correspond to the
fitted value of Bnc’ and the crosses correspond to the fractional error,
68/8. The fractional error is seen to decrease as the fit range (hence
the number of data points) decreases. This is an artifact of the one
parameter fita. If both Ano and Bnc are allowed to be free parameters,
the fractional error increases as the fit range decreases. At any rate,
the fitted value of Bnc is quite stable, even out to an X of 0.11. For
reasons already discussed, we will continue to use E02 from 0.1 to 2.0.

7.5.3. Systematic Error Approximation. An effort was made to
determine an approximation of the systematic error. Clearly, to
determine the exact systematic error, a complete covariance matrix must
be determined. Here we take a simpler approach. The various parameters
(a, a, B, Y, etc.) are varied from their "nominal" value while all other
correction parameters are held constant. By varying each quantity in
turn, and noting its effect upon Bnc’ an approximation to the systematic
error can be determined. In Figures 7.15 and 7.16, the effect of

varying a, 0, 8, and Y are shown. As in the previous plot, the points

133

 

 

 

 

a... ”3
x B
...1 1111+ 1
x
2.0” X x x 70.09
x
L0' ‘003
o FITTED a...
X 818/0
I l I l
0.0 0.1 0.2 0.3 0.4 x

EFFECT OF E0” FIT RANGE

Figure 7.14. Stability of fine to E02 Range

134

 

 

 

.mmii

 

 

 

2.0—
1.0 '— O my...
< > X m
I l l I I
-202: 402 oz «ox +202
ccusaassnumu
In

 

 

2.0—
w_ Oman...
Xwn
< >
J L I l I
-20% 401 02 1H0: 0202

 

 

NCIflfllfiflflHCNflfll

Figure 7.15. Effect Upon Bnc to Variations in a and 8

(L09

(L09

GD.

20

L0

10

Z0

135

 

 

'—7\

22121?

AA '

 

 

4mm

 

 

QAAAAA

 

—7\

>
I I

I

22 ‘

‘

Osman...—

Xwa

 

 

Q04

Q06 0d” 01)
ANHNEUUHKIOUHIMNNHGN

(“2

Figure 7.16. Effect Upon Bnc to Variations in E and Y

Q09

Q08

Q09

00!

136
and enuwnc bars refer to the fitted value of Bnc and the crosses to the
fractional error. The double arrow at the bottom of each plot indicates
a reasonable variation in the quantity. As seen in Figure 7.15a,
changes in the value of a had the largest effect on Bnc'

Figure 7.17a shows the effect of changes in the magnitude of the
hadronic energy resolution, and Figure 7.18 shows the effect for the
hadronic argle resolution” Figure 7.170 shows the effect of a hadronic
energy offset as a function of the "nominal" value. In other words, if‘
a shower had an energy of 50 GeV, and there were a -10% systematic
offset, the shower energy would be measured as “5 GeV.

Since this analysis really measures the difference in 8 between the
NC and CC structure:finufidons, Table 7.1 lists the effect on A8

(A8 = B ) as the initial value of Bcc is varied. As can be

cc ' Bfit
seen, a 110% variation in ace results in less than a 13% change in AB.
Finally, "fake" sets of data were generated, and used in place of
the corrected, real data. This "fake" data contained the effect of
resolution smearing cnuyu For the "fake" data, the CC parameters were
set as given above (Equation 10) and the NC parameters were set to the
associated CC values except for Bnc which was varied. This data was
then fit, using MINUIT. The results of this analysis are summarized in
Table 7.2. The input value of Bnc is given in column one, and its
fitted value, via MINUIT, and error are shown in column two. In all
cases, the MINUIT fits agree with the data and change as the data
changes. The second entry gives the result from a set of "fake" data

‘with a factor of fOLH'better statistics. Notice that the fitted error

decreases by a factor of two, as expected.

137

 

 

 

 

 

 

 

‘1»
221121111111 °"°
Z0 " (L09
LO _' C) Fn1EDIh- Q00
1 Xv:
1‘1 1 1’1
-201 40% 0% «H01 2202
canesmmou
1.. xx
¢ X
“" 11112451115 °‘°
X
241" )< 009
X
L0 " >< C) FH1EDIW. '7 G00
, .Xwa
1 1‘ 1 ’1 1
-202 402 0% 1H0! *202

 

 

 

Figure 7.17.

2,, OFFSET

Effect of Hadronic Energy Resolution and Offset

u1hfl

unhl

138

 

 

 

 

 

13... x as
X
3.0 +++i駥+% '0.10
X
2.0 x X ‘ 0.09
I.O " 0.08
o FITTED 10...,
X W3
1 1< 1 >1 1
-207. -IO'/. 07. +407. +207.
HADRON ANGLE RESOLUTION
Figure 7.18. Effect of Hadronic Angle Resolution

139

Table 7.1. Variation of A8 to Sec

 

Boo

AB

 

2.7

0.|70

 

2.8

0.|73

 

2.9

0.|73

 

3.0

0.|75

 

3.|

0.|77

 

3.2-

0.|79

 

3.3

 

 

0.|80

 

 

140

Table 7.2. Fitted Values of Bnc for Simulated Data

 

 

 

 

 

 

 

INPUT 8 FITTED 18
3.0 2.93 t 0.27
3.0 2.95 i 0.|4

(4x DATA)

2.7 2.67 if 0.25
2.5 ' 2.42 i- 0.33
2.2 2.I3 4: 0.2I
2.0 L95 1‘ 0.20

 

 

 

 

1141
The changes in Bnc associated with each of the hufiyidual
variations are added in quadrature and give an indication of the
approximate systematic error.
7 5.u. Results. For analysis within the E02 range of [0.1.2.0],
we find an integrated NC/CC ratio of:
Ru = 0.323 1 0.007 (stat.) 1 0.025 (sys.).
With the structure function parameterization given in Equations 9a and
9b, and parameter values as given in Equations 10 and 12, a one

parameter fit to Bnc yields:

_ +0.292
Bnc - 2'825 -0.25u

+0.138
-0.122

Similar analysis was done to determine sin20w. All NC parameters were

(stat.) (sys.).
set to the corresponding CC parameter values and sinze)w was allowed to
vary:

sin20w = 0.217 1 0.032 (stat.) 1 0.021 (sys.).

We then tried simultaneous two-parameter fits. Table 7.3
summarizes the results. In the case of the first entry, Ano was not
defined in terms of the Euler-Beta function, but was allowed to be a
free parameter. Three-parameter fits were attempted, but all

sensitivity to variations in the fitted parameters was lost.

7.6. COMPARISON WITH OTHER EXPERIMENTS

The E59lI-NBB run took data at four different beam conditions. For
neutrinos, the secondary momentum was set at 165, 200, and 250 GeV, and
at 165 GeV’for antineutrinos. Table 7.4a lists the number of NC and CC
events at each beam condition. The analysis used the same structure

5

function parameterization9 (see Equation 8) and performed a

simultaneous fit to the x distributions of the four data sets. An

Table 7.3.

142

Results of Two-Parameter Fits

 

 

 

 

 

 

 

FITTED STATISTICAL SYSTEMATICAL
PARAMETERS ERROR ERROR
A = -1111 1111
1 -—= 111.6 11111
. = 1111 -1111
B = W? “58:88? 1'8: 888
“- = 0-432 8.161555 7:8. 888
1 = .111. -1111

 

 

143

Table 7.4. Summary of NBB Analysis

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1:11:11: 11c cc
+|65 873 2766
+200 590 I992
+250 548 I784
-|65 597 l563

CC NC
0. 0.5 0.53 1- 0.|0
18 3.0 3.l7 :1; 0.58
a/(q+5) 0.|36 0.|3 :1; 0.02
A 3.28 3.33 :1; 0.58
B 3.0 3.02 i- 0.34
EJ/(q+5) 0.|36 0.|4 1- 0.02

 

 

144

iJiitial fit to the NC/CC ratio yielded a value of the Weinberg angle of
sin20w = 0.243 1 0.014. Subsequent analysis, to determine other
‘parameters, set sin20w = 0.24 and the CC parameters to the values given
in Equation 10. Results are summarized in Table 7.4b. In all cases, NC
parameters which are not fitted are set equal to the corresponding CC
parameter values.

CHARM took data for both neutrinos and antineutrinos with a
secondary beam momentum of 200 GeV in each case. Event numbers are
summarized in Table 7.5a. CHARM used a parameterization93 similar to

the parameterization used for this analysis and is defined as:

3 a _ b
(X)=WX(1X)

qsea(x) = C(c+1)(1—x)c.

qval

where C is the integral over the sea quark content of the nucleon and is
used to determine the relative antiquark content, 0/(q+a). The shape of
the sea quark distribution is fixed by setting 0 = 6.18. Fits are
performed simultaneously to both sets of data.

Because of inherent beam momentum spread, ambiguity between
neutrinos from pion and kaon decays, and limitations in the experimental
resolutions, especially in the hadron shower angle, event-by-event
kinematical reconstruction of the NC events was not possible. Instead,
distributions of the measured quantities were unfolded to determine the
x distributions. This unfolding method was also applied to the CC

events to determine its validity. Fit results are shown in Table 7.50.

145

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

No.0.“ no.0 .1? Ed no.0 w. 2.0 mood H 2.0 Amtuvlm
mod“ vmd w 21d 9.0 M ~m.~ __.o HEN 0
mod». mod u. 3.0 mod .._.. mvd Nod ...u 2.0 o
mommm 025150.23 025151.23 hzmzmm3m<w2
.m>m 20mm 02 20m... 00 203.2 \3 00
9mm mow oow1
mvmm 5m. oo~+
Sum.
00 02 235.6:
>¢<ozooum
3.032... 25.5 «o 035m .95 033.

CHAPTER 8 . CONCLUSI ONS

We have shown that it is possible to make a detailed analysis of
the Neutral Current interaction in a Wide Band neutrino beam. Having
demonstrated a reasonable understanding of misclassification effects and
of the antineutrino contamination, we are able to apply corrections to
the data for these effects. With a proper choice of variable (E02).
which can be calculated for both Neutral and Charged Current
interactions, we are able to gain information about the NC structure
functions. In particular, given certain assumptions about the form of
the CC structure functions, differences between the Neutral and Charged
Current structure functions can be determined.

For an E02 range of 0.1 to 2.0, the (corrected) NC/CC ratio is:

RV . 0.323 1 0.007 (stat.) 1 0.025 (sys.).
This is compatible with a value of sin’Ow of:

sin20w = 0.217 1 0.032 (stat.) 1 0.025 (sys.).

World data96 indicate a NC/CC ratio of roughly 0.30 to 0.32 and a value
of’sinzew = 0.23 1 0.01. Both values are in good agreement with world
data. Assuming a structure function parameterization of:

F,(x) = [3.0/EB(01,1+8)]xa(1-x)B + C(1-x)Y

xF3(x) = [3.0/58(a,1+3)]x°(1-x)8,
and assuming parameter values for the CC structure functions, a one-
parameter fit to the value of fine is:

_ +0.292
8no - 2°825 -0.254

+0.138

(stat.) _0.122

(sys.).

146

147
T1“: parameter fits for Bno and one other parameter yield in turn (with

Ano replacing the quantity [3.0/EB(0,1+8)]):

_ +1.033 +0.402

AnC - 2.859 -0.764 (stat.) -0.387 (sys.)
_ +0.593 +0.284

Cnc ‘ 0.840 -0.572 (Stat') -O.286 (sys')
_ +0.165 +0.064

“no ’ 0.432 -0.115 (Stat') -0.060 (sys')'

The value of Bnc in each case is compatible with the value obtained from
the one parameter fit. All parameters are in good agreement with
results from boUT the NBB data and from CHARM. 0n the basis of the
analysis, within the errors cited, there is no difference between the NC
and CC interactions. The NC interaction couples to the quarks in the
same manner as does the CC interaction, and there is no evidence1mf
coupling to neutral partons within the nucleon.

Even though the WBB offers a higher interaction rate, and thus a
larger data sample, the WBB is not ideal for this type of analysis. It
is not possible to determine the variables x and y for NC interactions.
To minimize the CC misclassification, it is advantageous to make a high
y cut”. ‘Without a similar cut in the NC sample, the data sample becomes
biased. The detector, however, is well suited to analyze the NC
structure functions as the NBB analysis shows.

Despite the slightly larger data sample, the errors on the fitted
parameters are roughly a factor of two (or more) than the errors on the
values from the NBB or CHARM. The NBB had available four separate sets
of data, including a data set from the antineutrino running. Whereas we
used roughly 10 data points for the fitting, the NBB analysis had
roughly 40 points for analysis (10 from each run condition).
Incorporating both neutrino and antineutrino data adds an additional

constraint.1x3 the fitting by virtue of the sign change on the xF3 term

148
in the cross section. The CHARM group also could incorporate both
neutJdJua and antineutrino data. The antineutrino run period during the
WBB was short, and the neutrino contamination in the antineutrino sample
was significant, thus the sample was of too poor a quality to be
incorporated into this analysis. Had comparable neutrino and
antineutrino samples been available, we expect, based upon the NBB
analysis, that the errors would have decreased by roughly a factor of

two.97

Analysis based upon a Monte Carlo program suggests that a factor
of four more data would also reduce the errors by a factor of two.
Currently, (December 1984) the collaboration is preparing to take
data in a WB neutrino beam utilizing the Fermilab Tevatron. Primary
proton energy is doubled (800 GeV) and the neutrino beamline will use a
quadrapole magnet focusing system for the secondary mesons. Thais will
increase the average neutrino energy from approximately 20 GeV (for this
analysis) to roughly 120 GeV, a factor of six. .Average muon energy in
CC interactions will also be higher by this amount, thus greatly
reducing the CC misclassification problem. With the prospects of
smaller corrections to the data, and if comparable neutrino and
antineutrino samples can be obtained, the upcoming run period offers the
opportunity for significant contributions to the study of NC structure

functions. I, of course, offer this opportunity to the next generation

of students.

APPENDICES

APPENDIX A

THE E594 MONTE CARLO PROGRAM

The Monte Carlo package allows the user to simulate neutrino
induced electromagnetic and hadronic showers within the context of the
E594 detector. A user writes a control program and selects the
appropriate "physics" to be simulated. The user supplies the
interaction vertex, interaction "particle" (where the "particle" can be
a hadron, electron, muon, or even a hadronic "fireball") and three-
vector momentum of the "particle". In the case where a hadronic
"fireball" is selected, the invariant mass must also be supplied. The
Monte Carlo package will than control the interaction's propagation and
development through a model of the detector taking into account nuclear
interactions, particle decays, multiple Coulomb scattering, ionization
energy loss and bending in a magnetic field for all particles produced
in the interaction. Flash chamber and proportional tube data is

generated, with data organized in the same manner as the real data.

A.1. ELECTROMAGNETIC SHOWERS

Electromagnetic showers are generated by randomly generating hits
according to longitudinal and lateral distribution functions. These
functions have been parameterized, and the parameterization is based
upon our calibration electron data. The only adjustable parameters in

these functions are the critical energy and the radiation

149

150
length appropriate for the target material. One of the inherent
liJnitations1of this scheme is that there is no correlation in hits from
flash chamber to flash chamber (i.e. particle tracks are impossible).
Given that electromagnetic showers in our detector appear dense and
rmrrowly<xfllimated, the lack of hit correlation in the Monte Carlo
showers is not critical at the "macroscopic" level. The Monte Carlo
package does not handle large angle (with respect to the beam axis)
showers very well. Since electromagnetic showers from neutrino-electron
interactions occur at small angles to the beam dhcection, this also is

not a serious problem.

A.2. HADRONIC SHOWERS

The ability of the Monte Carlo package to simulate a hadronic
interaction is a more important consideration for this analysis.
Hadronic showers have far more detail, (i.e. individual tracks are
apparent) so hadronic interactions are treated in more detail. The
original "fireball" of the hadronic system is de-excited using an
isotropic cascade model."°"’9 Particles (which may be excited) are
propagated through the simulated detector. In hadron-nucleon
collisions, both non-resonance and resonance collisions are considered.

Resonance collisions are handled via a crude model. The Monte
Carlo utilizes information of the total cross section for production of
A's and N*'s. The Monte Carlo uses only the lowest lying resonance
(actually, the only large one) and assumes isospin symmetry. To decay
the state, a choice is made between treating it as a resonance or as a

normal cascade, with the relative probabilities given by the ratio of

151
the total cross section to the extrapolated cross section outside the
resonance region. Only de-excitation by pion emission is considered.

Non-resonance collisions are more complex. Initially, only hadron-
luuhwxlcollisions are considered, with a simple extension to hadron-
nucleon collisions. Hadron-hadron collisions are handled in a two step
process. First, a diffractive scattering model98 is used to select the
transverse momentum and mass of the outgoing particles (one or both of
which may be excited). Second, the outgoing fireballs (if any) are de-
excited, using the isotropic cascade model. This modelikm hadron-
hadron<xfliisions is tuned to give the correct elastic to inelastic
cross section ratios, x-Feynman distributions (including leading
particle effects) and particle multiplicity.

Extension to hadron-nucleon collisions is simple. The target
nucleon is given a random momentum to simulate Fermi motion. The energy
of the projectile-target system is reduced to remove the energy added by
the Fermi motion, and to simulate nuclear excitation.

After a hadron-nucleon collision, the forward going particle (or
fireball) has a probability of undergoing additional collisions.
Collision probability depends upon the target material andynnticle
type. With the hadron-nucleon extension, the model agrees with hadron-
nucleon data for nuclei with atomic mass greater than that of Carbon.‘°°
The model does not consider fission or particle emission of the target
nucleus. Two-body decay of hadrons is done exactly,1nn;three-body
decays are not considered. The interaction model does not produce
kaons, however, if kaons are initially supplied by the user, they are

propagated properly.

152

A.3. NON-CATASTROPHIC PROCESSES

N0n-catashwxflnc processes involve multiple Coulomb scattering,
ionization energy loss, and bending in a magnetic field. Coulomb
scattering uses a Gaussian probability distribution. Ionization loss is
energy dependent and does not involve any fluctuatnnux Energy
fluctuations cause large tails in the ionization energy loss
distribution. All three processes are integrated after amflitarget
plane (in the calorimeter) or at 5 cm intervals (in the toroids). Decay

and interaction probabilities are evaluated at each integration point.

A.4. FLASH CHAMBER DATA

Flash chambers are considered to be infinitely thin (so that no
single particle can strike two cells in the same chamber) and have cells
5 mm wide. Shifts and rotations, as determined from analysis of the
real flash chambers, are applied. For response, each chamber is divided
into 64 regions (along the length of the cell). with each region having
its own efficiency and hit cell multiplicity value which also is
determined from analysis of the real chambers. The cells "operate" at
nominal efficiency along the length of the cell, and at half-nominal
efficiency in the readout region. Multiplicity is modeled using a
binomial distribution in number of hits, with a spatial distribution
flat over about 5 cm (1 5 cells). Noise hits were scattered uniformly
across all chambers, with the total number set to agree with values from
pedestal rwuus. (These are runs where the chambers were pulsed out of

synchronization with the neutrino beam spill.)

153

11.5. PROPORTIONAL TUBE DATA

In the calorimeter, the pulse height (energy) per traversal is
thrown according to a distribution measured from calibration muons.
Difference in gain is accounted for and shows up as variations in HITBIT
and latch efficiencies. The AM and FSV latches are derived from the
HITBIT's without an additional inefficiency, although software
thresholds are variable. SUMOUT latches are generated by adding up the
software pulse heights in channels which have the HITBIT latch ON. For
toroid planes, the pulse height sum from a pair of channels is thrown
according to distributions measured from calibration muons (efficiencies
included). The fraction for each channel is set to give exact
reconstruction during analysis. No toroid latch bits are generated. No

noise is generated for any proportional tube planes.

A.6. COMPARISON WITH CALIBRATION DATA

The Monte Carlo package was compared with the 1982 calibration
data. Three of the (nominal) calibration energies are considered: 10,
35 and 100 GeV. Figures A.1, 11.2, and A.3 show the measured energy for
calibration data and Monte Carlo data. In all cases, the solid line
corresponds to calibration data, the broken line to Monte Carlo data.
Agreement is good. This is not surprising, since the Monte Carlo
package was "tuned" to the calibration data. Energy discrepancy occurs
when comparing the hadronic energy for simulated neutrino induced
showers. Figure A.4 shows the difference between calculated and
selected hadronic energy for simulated neutrino interactions as a
function of the selected hadronic energy. There is evidence that the

calculated energy is overestimated with increasing selected energy.

 

154

 

 

 

 

 

 

 

 

 

 

 

40 F
CMTA
SUM = 1200
35 __ MEAN = 12.325
SIGMA = 2.184
.30 _ __ MONTE CARLO
SUM = 1310
” T
I MEAN = t2685
I
l
25 _ : SIGMA 1.988
I
I
I
I
' I
20 — : I
.-J '
1 I
' I
I
' I
l
15*— *-’ -1
I
I
r—l
I
10 - I
I
I
I
I
I "' ‘I
I I
I I
5 ~ I
p .. .11.. ...I
l
I _1
."H“
I r————j
O I I 1 111 I I I I I
O. 2.5 5 7.5 10. 12.5 15. 17.5 20 22.5

ENERGY — 10 GEV

 

Figure A.1.

Energy Comparison - 10 GeV

 

155

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DATA
35 7 SUM = 77.0
MEAN = 36.795
SIGMA = 5.016
30 — 1‘"
I
I : MONTE CARLO
I
: I SUM = 113.0
I
I
I =
25 __ : | MEAN 38.579
1——' SIGMA = 3.986
——I
20 — :
I
I
I
I
I
I
15 ~— '
I
I
I
I
I
I
I --I
10 "' r—J I
I
I
I
I
I
I
.— I
5 I
I
I
I
_.J
I
I
O I I 1 I I I I
o 10 2o 50 4o 50 00 70
ENERGY — 35 GEV

 

 

 

Figure A.2. Energy Comparison - 35 GeV

156

 

 

 

 

 

 

 

 

 

DATA
60 - SUM - 111.0
MEAN = 112.942
SIGMA = 9.641
T“
50 *- |__ MONTE CARLO
I SUM = 116.0
I
I MEAN = 108.495
I SIGMA = 11.101
40 - 1
l
I
I
I
I
I
I
I
30 h l
I
I
I——
'.._
20 — ;
I
I ...—_—
I l
I I
I I
I I
I I
10 — I
I
I
o 1 1 1 7 I 1 I IF" I 1
0 25 50 75 100 125 175 200

ENERGY - 100 CEV

 

Figure A.3.

Energy Comparison - 100 GeV

 

 

157

 

 

50

40A

E(CALC.) — E(SELECT.)

30 —

20 —

 

 

 

 

 

 

-10 _

 

 

 

I I l I I I I
0 25 50 75 100 125 150 175 200
SELECTED ENERGY

 

-20

MONTE CARLO ENERGY DWFERENCE

 

 

 

Figure A.4. Monte Carlo Energy Difference

158

This problem is not well understood, and may be due to the de-excitation
model used for the initial fireball. (Calibration simulations use an
initial pion, which then interacts.)

Figures A.5, A.6. and A.7 show the density comparisons and Figures
A.8, A.9, and A.10 show the shower length comparisons for Unathree
nominal energies. Notice that the Monte Carlo data is denser and
shorter. Table A.1 compares the angular profiles of Monte Carlo and
calibration data for the nominal energies. For a given shower, the
angle (relative to the beam axis) of each hit is calculated and entered
into a histogram. All shower hits within 5 meters of the interaction
vertex are considered. When all showers, at a given energy, have been
analyzed, a Gaussian curve is fitted to the resultant histogram and an
rms width is calculated. Table A.1 indicates the values of the rms
undths for Monte Carlo and calibration data. Comparing Monte Carlo
Ienergy and.angle resolutions with calibration data show that the energy
resolution is roughly comparable, whereas, angular resolution is
slightly degraded.”1

In conclusion, the Monte Carlo package can generate electromagnetic
and hadronic showers which agree, at the "macroscopic" level, reasonably
well with the real data. At the "microscopic" level, some differences
exist, as seen by the density, shower length, and angular profile
comparisons, as well as the hadronic energy discrepancy in simulated

neutrino induced showers.

159

 

 

 

 

 

 

 

 

 

80 '-
DATA
SUM = 127.0
MEAN = 0.255
70 -
SIGMA = 0.041
MONTE CARLO
60 '-
SUM = 134.0
MEAN = 0.297
SIGMA = 0.051
50 *-
--I
I
I
I
I
40 "' ‘P—IF -]
I I
I I
I I
| I
I I
| I
I I
I I
I I
I I
I I
I I
I I
20 I" I I
.-J I
I
_I
--I
I
10 — I
I
I
‘-1
L] 1
I
r4 '
0. 0.2 0.4 0.6 0.8
DENSITY - 10 GEV

 

Figure A.5.

Density Comparison - 10 GeV

 

 

 

160

 

 

 

 

 

 

 

DATA
28 7 SUM = 77.0
MEAN = 0.347
SIGMA = 0.063
24 1—
MONTE CARLO
SUM = 113.0
20 MEAN = 0.407
.-- SIGMA = 0.083
I
l
I
I
I
16 — I
I
I__.I
I
I *‘1
I I
I --1
I I
12 "' I '
I I
I I
I I
I I
I I
I I
I I
8 '— I I
I I
I 1
I l
I I-
1 '1
_-J I
I
4 ” I
I
““1
I
“‘1
I
I
0 1 1 I 1
0. 0.4 0.6 0.8
DENSITY - 35 CEV

 

Figure A.6.

Density Comparison - 35 GeV

 

 

161

 

 

35*-

30—

25—

20—

15—

10-

 

 

 

 

 

DATA

SUM = 111.0

MEAN = 0.553
SIGMA = 0.076
MONTE CARLO

SUM = 116.0

MEAN = 0.565

SIGMA = 0.096

 

 

I I—I I

 

 

 

0.4 0.6
DENSITY - 100 GEV

0.8

 

Figure A.7.

Density Comparison — 100 GeV

 

 

162

 

 

 

 

 

 

 

 

 

90 ... DATA
SUM = 127.0
MEAN = 314.492
I...
80 SIGMA = 101.329
.-.-I
' I
1 MONT AR
70 _ : : E C LO
' , SUM = 134.0
MEAN = 300.252
60 — SIGMA = 140.546
50 —
40 —
30 -— ,—
20 b
10 —
o I I I I I— -I I
O. 0.25 0.5 0.75 1. 1.25 1.5 1.75
SHOWER LENGTH (CM) — 10 GEV

 

 

Figure A.8. Shower Length Comparison - 10 GeV

 

163

 

 

 

 

 

 

 

 

 

35 — DATA
SUM = 77.0
MEAN = 488.717
30 A SIGMA = 121.625
{-1
I
I : MONTE CARLO
I
: I SUM = 113.0
I
25 I : MEAN = 479.915
I
[_J SIGMA = 111.950
I
I
20 '
I
F I
I
1 --1
I _—
I
1. .. J
15 —
10 E
I
I
l-—
5 _-
-- .-—
I
I
I
O K I I I I I I I

 

 

 

 

0. 0.25 0.5 0.75 1. 1.25 1.5 1.75 2,10 3
SHOWER LENGTH (CM) - 35 GB/

 

Figure A.9. Shower Length Comparison - 35 GeV

 

164

 

35

30

25

20

15

10

 

 

 

DATA

SUM = 111.0
MEAN = 675.290
SIGMA = 139.095

I
---..I

MONTE CARLO

SUM = 116.0

—-———--

MEAN = 618.472

SIGMA = 156.711

—-———---_-———d

 

 

 

----—----—-———-——-‘

L 1
l

'—

I

..--_J

 

‘ —"I
I I I 1 III I I

 

 

 

0.25 0.5 0.75 1. 1.25 1.5 1.75

SHOWER LENGTH (CM) — 100 GEV

2.10 3

 

Figure A.10.

Shower Length Comparison - 100 GeV

 

165

Table A.1. Angular Profile Comparison

 

ENERGY (GEV)

CALIBRATION

MONTE CARLO

 

 

 

 

 

 

l0 0.330 0.3”
35 0.240 0.2l0
100 0.200 0.|73

 

 

APPENDIX B

DERIVATION CF E02
we whflito present a brief derivation of the quantity E02 from

basic kinematical identities. Remember that the value of 02, defined at
the lepton vertex is:

Q2 = 2E2E£,(1 - cos 0££,).
For small angles, it is possible to expand the quantity cos 0 as a
Taylor series:

cos 0 = 1 - —T-+ ET:— ~--.
IKeeping terms up to and including 02, and inserting into the expression

for 02, we obtain:

2 a: 2
Q 3222,0£1,

)2.

E
= ——-<

E2,
The transverse momentum, PT, of the outgoing lepton is just P2 sin 021,,

which in the limit of small scattering angles and negligible lepton mass

EI'GII'

is:
I _._ °

PT P2, Sln 0
a P

12'

219111 ‘ E11921"

This gives an expression for Q2 of:

E E

2 z _E_ 2 g___
Q ' (ER'ORL')

Ea
Also recall that:

Q2 = 2mxv 2 2meh,

166

167

and that:

so by substitution, we obtain:

023—811312: T

E2, T 1 - y ’

 

 

2 2meh.
Equating these two expressions for 02, we obtain:
PIZ
2meh a 1 _ y

Since transverse momentum is balanced:

P sin 0 = P sin 0 ,

TTPI' 111' 11 h

and can be written (in the small angle approximation) as:

P£,0£2, z PhOh 2 PT.
which yields (after substitution):
(P 6)2
2me a h h

h 1 - y '
Rewriting, we obtain:
22. _
Ph 0h 2mEhx(1 y).
The relativistic kinematical relationship between axxniicle's
energy, momentum and mass is (setting c=1):
E2 = P2 + m2.
For the hadron system:
2:2 2
Eh Ph + W ,

where‘W21h3the square of the invariant mass. This equation can be

written as:

Given this relationship, we can write:

168

 

w2
2 2 ___ 2 2 _ __ z _ .
P On Eh 0h (1 BE) 2mEhX(1 y)
Solving this equation for the quantity Eh 0;, we obtain:
2mx(1-y)
2 z z —

Where the quantity Wz/E2 is assumed to be small. Table 8.1 lists the

h

value of Wz/E; for various values of Eh and x. (kfly'fOr low Eh and/or

low x is Wz/Ezh greater than 5-10%. Thus, with the given

approximations, we can write Eh 0; as:

2 a _
Eh 0h 2mx(1 y).

169

Table B.l. Magnitude of (W/Eh)2

 

 

 

 

 

 

 

 

 

 

 

#1:?) X=0.| x=0.3 x=0.5 x=0.7
10.0 0.|8 0.14 0.10 0.06
20.0 0.09 0.07 0.05 0.03
30.0 0.06 0.05 0.03 0.02
50.0 0.04 0.03 0.02 0.01
70.0 0.03 0.02 0.01 0.01

 

 

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