MICMWW

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

M WWWV'WES V WC '
M3\\\\1\\g\\9\gkums\ mm \M firm...
University

 

 

 

This is to certify that the

dissertation entitled
(DMPARISON OF POLARI ZATIONS OF

INCLUSIVELY PIODIIIED LANBDAS AND ANI‘IIAMBD‘XS
BY PIO'IONS, ANTIPRD'IONS AND KAONS

presented by

HARRY L. MELANSON

has been accepted towards fulfillment
of the requirements for

PH .D . degree in PHYSICS

WM; «my

Major professor

Maris A. Abolins
Date 51-3" 8{

 

M3 U is an Affirmative Action/Equal Opportunity Institution 0-12771

 

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

DATE DUE DATE DUE DATE DUE

    

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MSU Is An Affirmative Action/Equal Opportunity Inditution

 

 

COMPARISON OF POLARIZAIIONS OF
INCLUSIVELY PRODUCED LAMBDAS AND ANTILAMBDAS
BY PROTONS, ANTIPROTONS AND KAONS

By

Barry Louie Melaneon

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics

1985

in loving memory of my parents,
Roger and Virginia Melanaon

ii

ACKNOWLEDGEMENTS

I would like to thank my adviser, Maris Abolins, for his support
and encouragement of this work. Above all, I would like to thank him

for his caring and friendship in both good times and bad.

Thanks to Steve Gourlay, for sharing this experience with me. The
most important result of this experiment is our friendship, and I

cherish it.

To Hans Kobrak, who showed me how to do things correctly, and to
Phil Yagsr, who showed me new approaches to solving problems, I extend
my appreciation. Thanks also go to the rest of the £663
collaboration - Bob Swanson, Bill Francis, Randy Pitt, Ken Edwards and

Werner de Rosario.
Thanks to the Meson Dept., the Computing Dept. and the entire
Fermilah staff for their crucial support in this work. Special thanks

go to Lisa Dillingham and Debbie Robbins back at M.S.U., for their help.

Finally, thanks to Vense, whose love I value above all else.

iii

TABLE OF CONTENTS

LIST OF TABLES 0.00.0... ....... O ....... 0.0.0.0... ......... O. ......... Vi

LIST or FIGURES ............................... ..... . ............... vii

1.

Introduction ........ . ............ .... ............. ............... 1
1.1 Introduction .. ................ . ........ ...... ................ . 1
1.2 Background ..... . ................................... . ...... .... 2
1.3 Polarization Physics ................ .......... .. ...... . ..... .. 5
lJiflmmy..u.. ......... ..H.”.u.n.u.u.n.u.n.n.u.u.u.6
Apparatus ............. ..... .... ...... ........................... 10
2.1 Fermilab M4 Beam Line ............. ..... .. ............. ....... 12
2.2 Cerenkov Counter . .......... . ........... ............... ....... 13
2.3 Beam Spectrometer .................... ...... .................. 15
2.4 Sweeper Magnet . ................................ . ............. 18
2.5 Target ........................ ................. .............. 18
2.6 Forward Spectrometer . ...... .................... ....... ....... 19
2.6.1 Proportional Wire Chamber System ........................ 20
2.6.2 Drift Chamber System ... ............................... .. 23
2.7 Trigger ......... ......... .... ...... ...... ....... ............. 27
2.7.1 Fast Trigger ... ....... ......... .............. ........... 27
2.7.2 Trigger Processor ............. ........ ... ............... 31
2.7.3 Auxiliary Triggers ...................................... 34
2.8 Data.Acquisition ............................................. 35

iv

3. Analysis ...... ..... . ........................... . ...... . ..... .... 36

 

3.1 Pattern Recognition ................................ . ......... 36
3.2 Data Reduction ... ............... . ............ . ............. ... 38
3.3 Polarization Analysis .... ....................... ... .......... 56
3.3.1 Monte Carlo ............. ............................... . 58
3.3.2 Calculation of Polarization .. ..... . ....... . ..... ........ 67

4. Results and Conclusions .. ......................... . ....... . ..... 70
4.1 Bias Studies ...... ........... . ..................... .. ........ 70
4.2 Polarization Results ............ ....... ... ........ ...... ..... 77
4.3 Systematic Errors and Backgrounds ....... ..................... 86
4.4 Conclusions ......... ............ .................. ....... .... 88

Appendices

 

I. Pattern Recognition Algorithm ................................... 9O

 

 

II. Drift Chamber Alignment ............................ .......... .. 98
III. The Polarization Fit ................. ..... . ....... ........... 101
LIST OF REFERENCES ............. ............ ............ ..... ....... 104

Table

Table

Table

Table

Table

Table

Table.

Table

Table

Table

Table

Table

LIST OF TABLES

Comparison of Polarization from Various Reactions ........
Theoretical Expectations of Polarizations ..... .-...Q .....
Negative Beam Composition ......... . ........ .............
PVC Information ........ ..... ........... ......... ........
Trigger Counter Sizes ...... .......... ...................
Trigger Rates ......................... ..... .............
Breakdown of Losses due to Cuts ........... ...... ........
Summary of Final Event Sample ... .......... ..............
Measured Lifetimes of A, I, K: . ..... ..... ....... . .......
Polarization Results for p‘9 A ..........................
Polarization Results for S 9’] ............. .... ..... ....
Polarization Results for K' 9*A .. ..... ..................

vi

12

21

29

29

44

56

71

78

78

78

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

Figure

2-6.

2-7.

2-8.

2-9.

2-10e

2-11.

2-12.

3-2 a

3-3.

3-4.

3-5.

LIST OF FIGURES

Plan View of the Apparatus ... ......... ..... ............ 11
Cerenkov Counter ................. ................... ... 13
P Pulse Height versus K Pulse Height ........ ........... 14
Beam Spectrometer .. ............... .... ...... ........... 17
Beam Chamber Readout ............... .................... 17
Forward Spectrometer ...... . ............. ............... 19
PVC Readout System ..... ......... ..... .................. 22

Drift Chamber Cell ..................................... 25
Drift Chamber Readout System ..... ..... ................. 26

Drift Chamber Time StretChet ...VOOOOOOOOOOOOOOO...-.... 26

Fast Trigger Logic .. ............ ....... ...... .. ..... .. 30
Trigger Processor .................. ..... . ...... ....... 33
A Direct Interaction in the Target ..... ................ 41

The Z of the Direct Interaction Vertex (ZI ) .......... 41

NT
X Intercept and Slope of Beams at Target ............... 45

Y Intercept and Slope of Beams at Target ............... 46

Momentum of Beams ..... ..... ............................ 47
leDOF of Forward Tracks ..... .. ....... .......... ...... . 48
Track Intercepts at 438 ....... ..... .................... 49

x and Y Of the meay vertex 0 O O O O I O O O O O O O O O O O O O O O O O O O O O I 50
X and Y of the Production Vertex ..... ' ......... . ........ 51
Z of Production and Decay Vertices .................... 52

vii

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

Figure

Figure

Figure

3-11.

3-12.

3-13.

3-140

3-15.

3-16.

3.17.

3—18.

3-19.

4-1e

4-2.

4.10.

II-l.

Distance of Closest Approach at Vertices .... ..... ..... 53
Invariant Masses before Cuts .......................... 54
Invariant Masses after Cuts ................. ........ .. 55
Center of Mass Coordinate System .......... ........... . 57
Decay Pl Distributions ....... ........ ............. ... 60
Momentum of A, A, K: ........ ..... ....... ..... ......... 61
Pl of A, A, K: ................. ................... .. 62
XF of A, A, K: .. ...... ......................... . .... 63
Number of PVC Hits in A, I, K: Decays ............ .... 66
Decay Asymmetry of K: from K’ 9 K: ........ ...... ....... 72
X Polarization for p 9 A, 5 Q‘A, K’ 4 A ................ 73
Y Polarization for p Q'A, p'Q‘A, Rf 9 A ................ 74
P2 (Up - Down) for p 9A, 39A, K" 4A 76
Polarization Results for p 9’A ......................... 79
Polarization Results for S 9’1 . ......... ............... 80
Polarization Results for K’ 9'A ................ ........ 81
Linear Fits of Polarization versus P‘L ........... ....... 83
Comparison of Results to Previous Experiments
(vs. Pi) ....................................... ....... 84
Comparison of Results to Previous Experiments
(vs. XF) ............. ..... ............... ..... ........ 85

Position versus Time for a Drift Chamber Cell ......... 99

viii

CHAPTER 1

Introduction

 

1.1 Introduction

 

This experiment measured the polarization of lambdas inclusively
produced by protons and kaons, and antilambdas inclusively produced by
antiprotons at a beam momentum of 176 GeV/c using a liquid hydrogen
target. In particular, the processes studied were

p + p 9 A + X

E +p-bl +X

K' + p 9 A + X,
where X represents the collection of all other possible final state
particles. This data represents the highest energy, fixed target study
of K“9 A and E 9‘] to date. It is also the first experiment to measure
hyperon polarizations using three such beams with the same apparatus,

and it allows for direct comparisons of the results.

Also studied was the process
K' + p a K: + x.

This last reaction was used as a bias check since the K: has spin zero,
and thus cannot be polarized. The decay modes that were used were

A e p + 1' (0.642)

I -> 5 + 1“ (0.642)

x: -> a" + r (0.6861).
The branching ratios for these decays are given in the parentheses.
Data were collected in the range

0.2 < XF < 1.0

0.0 < P; < 1.5 GeV/c,
where XP is Feynman X and Pi is the transverse momentum of the produced
particle with respect to the beam particle. A total of 8,250 lambdas

from K"s, 10,480 lambdas from p's, 4,800 antilambdas from 5's, and

16,685 Kg's from K"s were used in the analysis.

1.2 Bagkground

 

Because of the high charged particle multiplicities at high energy
(<nch> 8 7 at Plab - 176 GeV/c), it is very difficult both theoretically
and experimentally to study any reaction in detail. To simplify the
situation greatly, inclusive processes like a + b‘9 c + X are used. If

any of the particles in the above reaction have spin, then polarization

effects can occur.

3
Polarization measurements provide a method of detecting small
spin-dependent terms in the reaction amplitude that cannot be detected
by cross section measurements. Before 1976, it was known that
polarization effects in elastic scattering experiments became small as
the energy increased, which was in agreement with simple Regge pole

[1]

. Perturbative QCD calculations have also shown that there are

[21.

models
no expected large polarization effects for high-P; hadron reactions
The report of substantial polarization for inclusively produced lambda's

[3]

by 300 GeV protons on Beryllium was therefore somewhat surprising.
Since that time, it has been determined that many hyperons produced
at high energy have non-zero polarizations. These measurements all seem

to be consistent with the polarization being

3

_ [a]
a+A9b+X

A
fa,b(xF’Pi’A) n,
where A is the atomic weight of the target nucleus, and h is the normal

to the production plane. The function fa has the properties :

,b

0.

V

1. df/dXF

2. df/dP‘L > 0 for PL < 1.0 GeV/c.

3. df/dP& 0 for P4 ) 1.0 GeV/c.
4. The polarization is smaller for heavy nuclei than for light
nuclei,
e.g. f(0.35,1 GeV/c, A-9) z 1.5 f(0.35, 1 GeV/c, AP136).
From a large data sample for p + p 9 A + X, an empirical fit has been
made to
cpiz).

[5]

fp,A(Xi,P;,A=1) - ( a XF + b XF3 ) ( 1 - e

with a I 0.295:0.010, b I 0.18:0.04 and c - 2.48:0.12 , for the range

4

of Pi up to 5 GeV/c. Table 1-1 shows the general relationship between

4
Pp A and the other measured channels.

Table 1-1. Comparison of Polarization from Various Reactions

 

Channel Polarization
_ [3,6-11]

p 9 A P 3P,A
5 9‘] _
p 9 8' 3 g 3 [12 14]
p950 p,A

+
p42 -
p 9 2° 3 g _ 3 A [15 17]
P92- P,
K' 9’A g _ [18-23]
K+-)A 3' Engu)”

- 9. ~ [24]

K»... infra“ (;>1)
p *K
1"9 A
750) z A
K 911

Several theoretical ideas have been proposed to explain these

[27]

features. One, by Andersson, Gustafson and Ingelman , suggests that
polarization comes from the soft, semi-classical process of
quark-antiquark pair production via tunneling in a confined color field.
Another, by DeGrand and Miettinen [28], uses the parton-recombination
model plus 30(6) to relate the polarization to a Thomas precession like

term in the recombination process. Both of these models will be

described in more detail later in this chapter.

1.3 Polarization Physics

To determine the polarization of a sample of lambdas, consider the
weak decay mode
A 9 p + a".
To conserve total angular momentum, the p-s system must be in a L-O or
L-l state. For a lambda with its spin in the +2 direction, its decay
amplitude is
+ _ +
F - a8 Y2 x + ap [Jf Yi x + J? Y2 x ]
where as and ap are the S and P wave amplitudes, x: are the proton spin
states, and the J? and J? are Clebsch-Gordon coefficients. The angular
distribution is then
'1:
Y? - ( a2 + a2 ) ( 1 + u cosG )
s p A
where

2 a8 Re(ap)

“A - [a2 + 82] ’
3 P

 

and 9 is the angle between the pion and the lambda spin. Previous

measurements have determined aA to be

«A - -0.642 r 0.013 [29].

Finally, the angular distribution of the pion in the lambda center of

mass is

S)
v

-— - -l- (1 + a 2 .

d9 4 1 A

. . . A
where a is a unit vector in the pion direction, and s is a unit vector

in the lambda spin direction.

6
For an ensemble of lambda spins, we can integrate over all spin

directions to get

dN 1 9 A
d9 I 4 I ( 1 + “A P - w ) (1-1)

where

is the polarization vector. The measurement of lambda polarization can
therefore be accomplished by determining the angular decay distribution
of pions from lambda decays. The above analysis holds for antilambdas
as well, with the assumption that

ax'C - GA.

This assumption relies on CP invariance for the lambda decay.

1.4 Theory

.As mentioned earlier, simple Regge models and perturbative QCD
calculations have failed to explain the measured polarizations. Attempts

[30]. More recently, two

to apply triple Regge theory have also failed
semi-classical models have been suggested that yield some agreement with

the data.

Andersson, Gustafson and Ingelman propose that the polarization of
hadrons can be understood through the soft process of quarks tunneling

through a confined color field. They assume that baryons can be

7
described as bound states of a quark and a diquark (the diquark is made
up of the two quarks with the most similar wave functions). In this
framework, the lambda is made up of a ud singlet diquark, and an s
quark, with the lambda spin being defined by the s quark. They first
consider the channel p 9 A. During beam fragmentation, the diquark of
the incoming proton continues on as a unit. A color dipole field is
stretched between the diquark and the central collision region. This
color field is assumed to be confined, without any transverse degrees of
freedom (like a 1-dimensional string). It is assumed that transverse
momentum is locally conserved. To produce a lambda, an a? pair is
created on the string. This pair will now have some orbital angular
momentum. To conserve angular momentum, the spins of the quarks must be

polarized in a direction opposite to the angular momentum.

The proposed method through which the spins become polarized is a
Thomas precession during the production stage. In order to get the sign
of the polarization correct, the color fields must be assumed to be
confined, so that there is no interaction between the quark's magnetic

[31]

moment and the color field . A Monte Carlo involving the above model

has given general agreement for low Pl, p 9 A data.

They apply the same proton fragmentation model to other channels,
and give their expected signs for the polarizations (see Table 1-2).

These signs are in agreement with the data.

8
For the reactions K’ 9 A and K+ 9 A, the s quark comes from the
incoming beam particle, and thus these channels cannot be handled by

their model.

Table 1-2. Theoretical Expectations of Polarizations

 

 

Channel Degrand and Miettinen Andersson, er a1.
P94 s. P>O
p9£+, 2-, 2° -(1/3r+2/36) p<0

p 9 5°, 8’ 1/3 c + 2/3 6 P > 0
n,K+9A 5/2

K“ 9 A -c

The model by Degrand and Miettinen is proposed within the framework
of the parton-recombination model, assuming minimal complexity for quark
transitions and uses 80(6) symmetry. They propose the following rule to
describe the data - "slow partons preferentially recombine with their
spins down in the scattering plane while fast partons recombine with
their spins up". Here, as in Andersson, er a1., a baryon is considered
to be made up of a quark and a diquark. This assumption implies that
their model has two parameters - one for how single quarks combine, and
one for how diquarks combine. To extract these two parameters, they use
the results of p 9‘A (where ud is the diquark), and p‘9 I+ (uu is the
diquark). By applying their rule and the two extracted parameters they
make predictions for several other reaction channels. Table 1-2 gives a
review of these predictions. The signs of these predictions are all in
agreement with the current data. The relative magnitudes are in general

agreement, with the exception of the K' 9 A channel. Their model

9
predicts the polarization for K’ 9 A to have the same magnitude as that

for p 9 A. The data show K‘ 9 A has a much larger signal than p 9 A.

To explain the dynamical origin of their rule, they propose that
the spin of the parton undergoes a Thomas precession during
(recombination. This comes about because the force on the parton is in
general not parallel to its initial momentum. Because slow partons are
accelerated but fast partons are decelerated, the Thomas precession term
in the Hamiltonian will be of opposite sign. By using this model and
semi-classical arguments, they predict that the polarization should be
approximately linear in P4 and weakly dependent on XF' This is in

general agreement with the low P‘L dependence of the data, but disagrees

with the XF dependence.

.Although this model contains some interesting agreements with‘ the
current data, it is in no way a satisfactory explanation of the observed

polarization signals.

CHAPTER 2

Apparatus

In order to satisfy the goals of this experiment, the apparatus had
to determine the type of incoming beam particle and measure its vector'
momentum, identify events containing final state A, A or Kg's and
determine their vector momenta, and measure the vector momenta of their
decay products. The apparatus used in this experiment satisfied these

requirements, and is shown schematically in Figure 2-1.

A Cerenkov counter was used to tag the incoming beam particle. Its
vector momentum was measured by a beam spectrometer. The beam was then
focused onto a liquid hydrogen target to produce the A, A and Kg's.
Located just downstream of this target was a 6' long magnet with a
0.8 GeV/c P; kick which attempted to sweep out any charged particles
produced in the target, while leaving all of the desired neutral
particles uneffected. Following the magnet was a 14.6 m long evacuated
region where most of the neutrals decayed. Finally, a forward
spectrometer was used to measure the momenta and positions of their

decay products. The lab coordinate system was defined such that X

10

11

measured horizontally (+X was beam left), Y measured vertically (+Y was

up) and 2 measured along the beam (+2 was in the beam direction).

Each section of the apparatus will now be described in detail.

 

 

 

 

x
' 7
I %
2 ~
(+Y UP) 7/ ‘”‘
BCI %
all |
J'Z'l—‘h—l 1
LI —.1 l U i U
7
cream v / (NOT TO SCALE)
° %
435
BEAM SPECTROMETER
I I l I I
2 (In): -ss.5 -45.7 -2s.3 -26.1 -24.0

[’
f
I

I

1

DECAY REGION

 

I
\ ---fi’

"1

FORWARD SPECTROMETER
l l l I ll
-7.4 -1.8 0.. 2.2 7.6 8.4

 

 

 

 

 

 

 

 

 

 

Figure 2-1. Plan View of the Apparatus

12

2.1 Fermilab 55 Beam Line

This experiment was performed in the Fermilab M4 beamline [32]

during the period from March, 1980 to June, 1980. The beam was made from
primary, 400 GeV/c protons incident on a 1.5 mm x 1.5 mm x 203 mm
Beryllium target. Particles coming off at a 6.8 mrad production angle
were selected by a 10' long steel collimator located 200 m from the
target. This selection had the effect of lowering the total possible
hadron flux. The lowered flux was necessary to allow the tagging of each
beam particle by the Cerenkov Counter. The beamline was able to be tuned
to select either positive particles (for protons), or negative particles
(for kaons and antiprotons). To change from a positive beam to a
negative one, the magnetic fields of the beam magnets were reversed. The
6.8 mrad production angle also had the effect of increasing the K“ and 5
fraction in the negative beam. The composition of the negative beam is
given in Table 2-1. The positive beam was dominated by protons. The beam
line was tuned to have an average momentum of 176 GeV/c with a spread of

2.8 %.

Table 2-1. Negative Beam Composition

Particle Fraction
- 0.91

‘l
K’ 0.06
33 0.03

13

2.2 Cerenkov Counter

[33]

A differential Cerenkov counter was used to identify protons
in the positive beam and kaons and antiprotons in the negative beam.
Figure 2-2 shows a schematic of this counter. By adjusting the pressure
of the gas in the counter, She threshold was set so that particles with
a mass less than or equal to that of a proton would radiate light. The
radiator consisted of a 75 m beam pipe filled with Be. Light from a
particle above threshold was reflected by the primary mirror (M1) onto
the secondary mirror (M2). The secondary mirror had a hole in its center
and a mask around its outer rim. Light from protons would go through the
hole in M2 and be detected by the photomultiplier tube P. Light from
kaons would be reflected by M2 into the photomultiplier tube K. Pion
light would fall on the masked region of M2, and would not be detected.
The pressure in the counter was adjusted to maximize the separation
between the proton and keen signals. Figure 2-3 shows the P pulse height

versus the K pulse height. The overlap between protons and kaons is very

small (less than 0.05 Z). The counter was operated at 0.55 atm.

 

 

 

---d

 

 

 

 

 

 

 

 

Figure 2-2. Cerenkov Counter

P Pulse Height

14

 

 

 

280 1‘—
240 a"
200 .— -
s-“.
I.‘.'
160 —'«_"
120 L522:
- a-~'
80 ...
40 b: II.-
.-'.'-.'.I:‘. Wamwx- - .. . , .
0 4‘1." ’ ' ”l" s ' i l
0 40 ' 120 160 200 240 280

K Pubs Hebht

Figure 2-3. P Pulse Height versus K Pulse Height

 

15

2.3 Beam Spectrometer

 

A spectrometer consisting of small proportional wire chambers [34]

was used to determine the position and momentum of the incoming beam.
This system is shown in Figure 2-4. It was composed of four statiohs,
each station made up of an X and a Y chamber. Each chamber contained 64
sense wires spaced 1.0 mm apart. The sense wires were 12 um gold plated
tungsten. The gas. used was CO2 (20%), Freon 13B] (0.15%) and Argon
(balance).

[35] (Figure 2-5) utilized a digital delay-line

The readout system
scheme. Each chamber was connected to separate 64 bit, 16 word memories.
Every 50 ns, the condition of each wire was recorded into its memory.
The words in each memory were addressed in a circular fashion with the

newest information overwriting the oldest. At any one time, there was

50 x 16 I 800 as of wire history stored in the memories.

Upon receiving a fast trigger signal (to be described later), the
storing of information in the memories was halted, and a selected word
from the memory was loaded into a shift register. The particular word to

be loaded was determined by the timing requirements of the trigger.

.After the data had been loaded, the shift registers were read out
serially by a CAMAC scanner module [36]. The scanner used a 10 Mhz clock
to read out all eight chambers in 51.2 psec. Since the number of hits

expected in each chamber was small, the scanner only reported the

16
location and size of clusters of hits, ignoring sections of unhit wires.
This cluster information was stored in a 16 word memory in the scanner.

Each word could report the location of a cluster up to 7 wires long. The

- location of a cluster was defined as the address of the last wire hit in

that cluster.

The magnet used to determine the momentum of the beam (4B5 in
Figure 2-4) had a Pl kick of 1.6 GeV/c. A second magnet (4B6) was used
to straighten out the beam after it passed through the beam spectrometer
system. This magnet was identical to and was run in series with the
first magnet, its current running in the opposite direction to insure
that the two magnetic fields were equal in magnitude and opposite in
direction. The fields were measured with a Hall probe and were found to

be equal to within 0.4 %.

The average position resolution for a beam chamber was 265 pm, and

the average momentum resolution of the system was 0.4 %.

17

 

 

 

 

 

é
H/Im:

V

6

 

 

 

 

 

 

 

BZY 33x
485
BIX BIY 82X V B3Y I
CERENKOV _ / \ 84X B4Y
‘ fl V

 

 

 

 

 

 

f1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2-4. Beam Spectrometer

INDIVIDUAL CHAMBER LOGIC

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

r ........
I i
: BEAM I
I CHAMBER [

I

I
i 12 53 64 l
I }
' I
' l
u: SPA—91 a MAIN ADDRESS: ’ i
A 555’ CONTROL LOAD j MEMORY ,
RESET——-> LOGIC ' i :
LOAD i s IFT [

H \

85211-2," '.> i REGISTER I ’
L_.__._”_ ....__..

CLOCK —.'>— e

 

 

Figure 2-5. Beam Chamber Readout

T0 SCANNER

18

2.4 Sweeper Magpet

Located just downstream of the target was a magnet (4B7) used to
sweep out charged particles produced in the target, without affecting
the trajectory of the A's, A's and Kg's. It was run in ramped mode, and
the PL kick at the top of the ramp was measured with a Hall probe to be
0.85 GeV/c. The magnet was intended to be operated at this maximum field
during the spill, with the ramping occuring before the spill. However,
by using reconstructed, non-interacting beam tracks, it was determined
that the magnet was still ramping during the spill. The average kick was
determined to be 0.78 GeV/c, with a difference between the beginning and
end of 'spill of 8 %. It was assumed during the data analysis that the
field was a constant 0.78 GeV/c. The effect of this assumption is

discussed in Section 4.2 under systematic errors.

2.5 Target

A liquid hydrogen target built by the Hydrogen Target Group at
Fermilab was used. It consisted of two flasks, one 25.4 cm long and the
other 45.7 cm long. Their diameters were 5.1 cm. The flasks were made
out of 0.127 mm Mylar. The two flasks, a reservoir, and a refrigerator
were all enclosed in a foam vacuum vessel. This vessel had a 0.127 mm

Mylar upstream window.

19

2.6 Forward Spectrometer

The forward spectrometer was composed of four stations, with two
stations upstream and two stations downstream of the analysis magnet
(Figure 2-6). Each station was identical, consisting of a preportional
wire chamber (PVC) section and a drift chamber section. The PVC section
contained X and Y planes, and the drift chamber section contained X, Y,
U and V planes. The U,V planes were oriented at 3 45° with respect to
the X,Y planes. The analysis magnet was operated at a constant current
to maintain a 0.2 GeV/c Pi kick. Its field was in the Y direction. The

average momentum resolution of the system was 2 %.

 

37 5676 8765

1.2134 4132 1

 

 

 

bdp-hdp-—---------gp-----

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

// ICOUNTERS
l. SMALL X PVC 5. SMALL X PVC
2. SMALL Y PVC 6. SMALL Y PVC
3. SMALL X.X’.Y.Y’ DRIFT CHAMBER 7. LARGE X,X’.Y.Y’ DRIFT CHAMBER
4. SMALL U.U'.V,V’ DRIFT CHAMBER 8. LARGE U.U’.V.V’ DRIFT CHAMBER

Figure 2-6. Forward Spectrometer

20

2.6.1 Prgportional Wire Chamber System

 

The PVC system [37]

consisted -of eight chambers. Each chamber
included one plane of sense wires located half way between two planes of
high voltage wires. The high voltage wires were oriented perpendicular
to the sense wires. The spacing between the sense wires was 2.0 mm. The
spacing between the high voltage wires was 1.0 mm. The sense wires were
either 20 or 25 pm gold-plated tungsten and the high voltage wires were

64 pm phosphor-bronze. The windows were made of 0.051 mm Aclar (type

3C). The gas used was CO2 (20%), Freon 1331 (0.15%) and Argon (balance).

There were two sizes of proportional chambers - their dimensions
are listed in Table 2-2. Each chamber had support wires made out of
AVG 30 wire wrap wire running perpendicular to the sense wires, attached
with glue to each wire. These were included to eliminate
electromechanical vibrations in the sense wires. The number of support
wires per plane is listed in Table 2-2. They were equally spaced
throughout each chamber. They also had the undesirable effect of
deadening about a 7.0 mm region of the chamber running along each

support wire.

Each sense wire was connected to an amplifier, and the amplifier
was connected to the input of a one-shot (Figure 2-7). The one-shot was
used as an adjustable delay. If a fast trigger secured, the trailing
edge of each one-shot output would be latched into a single, long shift

register. The shift registers for each plane were read out serially by

21
individual CAMAC scanner modules. These scanners were of the same type
as the one used to read out the beam chambers. It took about 100 usec

for the scanners to read out the information in the shift registers.

The average position resolution obtained was 533 pm. The average
efficiency was 96 %. A lower efficiency was found in the center of each
chamber, coinciding with the region through which the beam passed. This
region was approximately 5 x 5 cm in size, and the average efficiency in

it was 73 %.

Table 2-2. PVC Information

 

Support

Chamber Size Wires
P1X 1.2 x 0.8 m 1
P2X 1.2 x 0.8 m 1
P3X 1.5 x 1.2 m 2
P4X 1.5 x 1.2 m 2
PlY 1.2 x 0.8 m 2
P2Y 1.2 x 0.8 m 2
P3Y 1.5 x 1.2 m 3
P4Y 1.5 x 1.2 m 3

22

FROM PREVIOUS CHAMBER

 

LOAD (FAST TRIGGER)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

, DATA IN

“RE i - one an H 3.9
I
E
3 z z 3 ii 2 :5” g

0 O O O

o g. g
[ - {I
"IRE " We“ snot I 3—9 '55
U)

 

(ADJUSTABLE DELAY)

 

 

 

CLOCK DATA OUT

 

 

 

\ 10 scamsR

 

Figure 2-7. PVC Readout System

23

2.6.2 Drift Chamber System

 

[38]

The drift chamber system consisted of four stations, each
station containing eight planes labelled X,X',Y,Y',U,U',V, and V'.
Primed planes had wires parallel to unprimed planes of the same type,
but offset by one cell length. The cell length (defined as half the
distance between adjacent sense wires) was 5 cm. The active area of the
chambers was matched to those of the PWC's. The X,X' and Y,Y' planes
formed a common gas enclosure, as did the U,U' and V,V' planes. The gas
used was CO2 (10%), Freon 1331 (0.15%) and Argon (balance). The windows

of the chambers were made of 1 mil Aluminum, 3 mil Mylar laminate. A

cross section of a package is shown in Figure 2-8.

The drift field in a cell was generated by 30 field wires divided
into two parallel planes of 15 wires each. These two planes were
separated by 9.52 mm, with the sense wire plane centered between them.
Located at the interface between two cells were 3 additional field
wires. Two of these wires were in the plane of the field wires, and the
third was located in the plane of the sense wires. These last 3 wires
were included to improve the definition of the electric field at the
interface between adjacent cells. The voltages on the field wires were
supplied by a 15 resistor voltage dividing chain (one chain per plane),
and were set so that the average field in the cell was 1200 V/cm. The
field wires were 100 um beryllium copper, spaced 3.18 mm apart. The

sense wires were 20 um gold plated tungsten.

24
The output of each sense wire was amplified and sent to a time to
digital converter (TDC). The TDC system contained a separate scaler for

[39] for each station (Figure 2-9)-

each wire, and a shared clock module
The signal from the sense wire was used to reset the scaler. A fast
trigger was used to stop the scaler. The scaler determined the time

between these two signals by counting the number of clock pulses between

them. All scalers were stopped by the same signal (common stop).

In order to increase the precision of time measurement
(see Figure 2-10), the time between the reset and the following rising
clock transition (Ta) was stretched by 16:1 and digitized for each
channel. The time between the first rising clock transition following
the reset and the first rising clock transition following the stop (Tb)
was then digitized by counting clock transitions for each channel. The
time between the stop and the following rising clock transition (Tc) was
stretched 16:1 and was digitized at twice the clock frequency in the
clock module. This time was later subtracted from all channels that

shared that clock module. The clock frequency was 20 MHz.

The single hit capability of the drift chamber system prevented it
from working at the high rate of the incoming beam. To solve this
problem, the region of the chambers where the beam passed through was
deadened. This was accomplished by placing plastic sleeves over sections
of wires that would have been exposed to the beam. The average deadened
area was 10.0 cmz. Unfortunately, these dead regions were positioned for
a previous experiment and did not correspond to the location of the beam

in this experiment. To correct for this, hits on wires that were

25
affected by our beam were totally removed by software prior to pattern

recognition.

The drift chambers were used to measure the intercept of a
transversing particle by relating the clock time to the spatial position
of the intercept. A linear relationship was assumed for most of the
chamber. The functional form used was

x-xotviflo-T)
where T is the clock time, X5 is the wire location, To is an offset
time, V:t are drift velocities (one for either side of the wire), and X
is the position of the hit. The constants X0, To and V+ were obtained
for each wire using the PVC system as a reference (see Appendix II for
more details). The chambers were aligned to within 3 25 um and had an
average position resolution of 510 um. Their average efficiency was

65 %.

3.18 mm

WGQOOGOOOOOOOGOOOO-G-G'G-O-G-GW

4.76 mm

...9: .... _ g 43..-. i

 

MGOOOOOOOOOOOOOO‘GGGGGGGW

'6—- 4921 mm —§i O 20 MICRON GOLD-PLATED TUNGSTEN SENSE HIRE

o 100 MICRON BERYLLIUM COPPER FIELD HIRE
Figure 2-8. Drift Chamber Cell

26

.1
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
l
I
I

INDIVIDUAL. CHAMBER LOGIC

 

RESET
CHANNEL 1

 

5
r?
000 :7

HIRE n

 

V ‘
E

 

CAMAC INTERFACE

 

 

 

 

 

 

STOP (FAST TRIGGER)

 

 

 

RESET RESET

 

 

 

Figure 2-9. Drift Chamber Readout System

-- ----
----
----

 

 

CLOCK : g :
RESET an 5 5 1*
(FROM EACH HIRE) : 5 5 5
STOP 5 J;
(FAST TRIGGER) : g : ; To
:To u 9: I?
‘<—— Tb -9'

T=Ta+Tb-Tc

Figure 2-10. Drift Chamber Time Stretcher

27

2.7 Trigger

Since the inclusive cross sections for producing a A, A or K: are
much smaller than the total cross section, most of the interactions in
the target were not pertinent to this experiment. In order to avoid
wasting time analyzing these interactions, a trigger was set up to

attempt to identify only events that contained a A, A or K: decay.

This trigger was composed of two parts - the fast trigger and the
slow trigger. The fast trigger was constructed of signals from various
scintillation counters, and was used to insure that a beam particle had
gone through the beam spectrometer, and had then interacted in the
target. The slow trigger was issued by a trigger processor. It tried to
identify these interactions that contained a A, A or K: decay. The two

parts of the trigger are discussed in more detail below.

2.7.1 Fast Trigger

The logic used in the fast trigger is illustrated in Figure 2-11.
The locations of the scintillator counters used as input to this logic
are shown in Figure 2-1. The counters 3:, Ba and B3 were used to detect
the passage of an incoming beam particle. The counter B had a hole in it
for the beam to pass through and was used to veto any beam halo. The

sizes of these various counters are given in Table 2-3. The signals from

28
these counters, along with a signal from the Cerenkov counter (either K

or P) were used in coincidence to define the valid beam signal

Beam I Bl - B2 - B3 ° 3 - (K + P).

To detect interactions in the target, a counter hodoscope (I) was
located just downstream of the forward spectrometer, and was used to
identify events with at least one charged particle (other than a beam
particle) exiting the apparatus. Two holes were provided for the beam to
pass through - one for for running with the positive beam and one for
running with the negative beam. The signals from the I counters were

logically summed together to form the signal

I-ZIi.
In addition to these counters, a small counter (3,) was positioned just
upstream of the first chamber, centered on the beam. Its purpose was to
veto diffractive events that would have triggered the experiment if only
the I counters were used. The I counters and the B, counter signals were
combined to form the interaction signal
IT - I . B4.
To prevent triggers from occuring during data acquisition, a level
called "Dead" was generated by the data acquisition computer, and was

used as a veto.

These signals, in coincidence with the valid beam signal, formed
the fast trigger
Fast I Beam - IT - Dead.

Table 2-4 gives some typical rates for these various signals.

Signal

29

Table 2-3. Trigger Counter

Counter

H(hole)

Siz

oewww
L‘NNOOO
NXNNXN

NH

.5

6
6
6
3
3
2

e

O‘COO

Sizes

C1!)
C1!)
cm
CI!

0.5 cm
.54 cm

Table 2-4. Trigger Rates

Incoming Beam

Bx . Bz .
BI ' B2
Beam

BI ' Bz
Fast
OK

Ba

9 B3 0

.33

ml
Uil
I

Average Rates (per spill)
Positive

XMMM

x
638
75

10‘
105
10s
10*
10*

Negative

30

POSITIVE
BEAM

NEGATIVE
BEAM

   

K
p

81

82

83
H

11

D6
B4

DEAD
(FROM COMPUTER)

FAST

Figure 2-11. Fast Trigger Logic

31

2.7.2 Trigger Processor

In order to enhance the number of A, A and Kg's in the event
sample, a second, slower level of selection was incorporated into the
trigger. A simple device was built to supply this secondary trigger
requirement - the trigger processor. This home built, TTL device
attempted to identify events containing two tracks (hopefully from a A,
A or K: decay) by counting the number of hits in the PWC's, and
selecting those events whose hit pattern was consistent with the two
track topology. It succeeded in increasing the good event to trigger

ratio by a factor of four.

If the PWC's were 100% efficient, a good event would cause each PWC
to contain two hits, one from each track. With the actual PWC
efficiencies, requiring each PVC to contain two hits would make the
probability of triggering on the event 0.52. (By relaxing this
requirement to allow one out of the eight PWC's to miss a hit, the
triggering probability becomes 0.87. Because of electronic noise and
extra, unrelated tracks within good events, each chamber generally
contained more than the two hits associated with the actual decay. The
hit pattern requirement that was used for data taking required at least
seven out of the eight PVC planes to have two or more hits in them, and

allowed the eighth to have one or more.

32

A schematic of the trigger processor is shown in Figure 2-12. The
clock and data lines from each PVC went to separate hit counter boards,
one board for each plane. The hits were counted here, and a two bit
result was obtained for each plane. In order to help eliminate the
effects of spurious hits and tracks not associated with real A, A or K:
decays, only the central region of each chamber was examined by the hit
counters. These regions were defined by the window boards. The circuits
on the window boards counted the incoming clock pulses, and only
activated the hit counters when the desired regions became available.
The windows were obtained from a Monte Carlo study, and were stored by
computer into the window latches at the beginning of each run. The
latches were read back at the beginning of each spill, and checked to

see if they were correct.

The eight 2 bit numbers from the hit counters formed a 16 bit
address that was used to reference the 64k x 1 memory. The memory was
used to determine whether the hit pattern in that event should be
accepted. The memory was downloaded by the computer with the desired hit
pattern requirements at the beginning of each run. It was monitored

throughout the run to make sure it did not change.

The fast trigger initiated the trigger processor operation. After
about 100 usec, the processor decided if the event had a proper hit
pattern, and if it did, a slow trigger (OR) was issued, and data
acquisition proceeded. If not, a clear signal was generated to reset the
experiment for the next fast trigger. The speed of the trigger processor

was dominated completely by the scanning rate of the PWC's.

33

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'::[D———>o

 

 

 

 

 

 

 

 

 

DATA (ID BITS) DATA I16 BITS)
COMPUTER
INTERFACE W
LOAD
J— =-
ADDRESS
IN/IJUT
WINDOW LATCHES
sTssossx LOAD/RUN
e e o e e e 0 64K X 1
3 3 3 3 3 3 3 HE’IDICYDDNUTER MEMORY
HgochS'pEmr- ”I- - -- '"7 DATA OUT (1 BIT)
I
: DATA .
. Long; mom I
I ENABLE : mg
m“
I I g“
I I 82:
I
I G
FROM SCANNERI HIT A I
oATA COUNTERg :
FROM SCANNER; 3““ )
I
I- _ ., ......... I

\m
0

 

FAST TRIGGER -—)

RESET——)l

 

LOAD

TRIGGER
INTERFACE

 

SCAN DONE

 

 

.0.

(B HIT COUNTERS TOTAL)

 

 

 

 

Figure 2-12. Trigger Processor

I

K
TRIGGER EXPERIMENT)

34

2.7.3 Auxiliary Triggers

In addition to the trigger described above, two other auxiliary

triggers were used:

The first was the straight through trigger (identical to Beam
described previously) :
ST-B, -B2-B3-fi-(K+P).
It consisted mostly of beam particles that did not interact in the
target, and was used to align the beam chambers, as well as to align the

beam spectrometer system with the forward spectrometer system.

The second auxiliary trigger was a muon trigger. It used a counter
hodoscope (the Mn counters in Figure 2-1) which was situated downstream
of the rest of the apparatus, behind 3 m of steel. The logic used to.
define this trigger was

MuIZIi-ZMui.
The muon trigger was run with 4B5, 4B6, 4B7 and 4B8 turned off, and with
a 1.37 m long piece of steel lowered into the beam 290 m upstream of the
Cerenkov counter. Muons from pion decays were selected by this trigger.

They were used to align the chambers within the forward spectrometer.

Both of these auxiliary triggers were run with the trigger

processor set to accept any fast trigger.

35

2.8 Data Acquisition

The fast trigger initiated the latching of information from the
various parts of the apparatus into their respective CAMAC modules. The
slow trigger initiated the readout of this information through the CAMAC
highway. It consisted of seven standard crates, each controlled by type
A-l crate controllers. The highway was interfaced to the data
acquisition computer, an Eclipse S/200, through a modified BIRA 1251 BD
branch driver. The information was read in using direct memory access,
and was written onto 800 BPI magnetic tape. The dead time during this

read was approximately 10 msec.

Data acquisition only occurred during beam spills. A spill was 1
second long, and the time between spills was 10 seconds. During this
intermediate time, events were analyzed by the Eclipse to monitor the

behavior of the apparatus.

A total of 135 tapes was written, corresponding to 2.7 x 106

triggers.

CHAPTER 3

Analysis

The analysis of this data was divided into three distinct
steps - pattern recognition, data reduction, and polarization studies.
The pattern recognition phase converted the digital information on the
data tapes into spatial tracks. The data reduction phase used these
tracks to identify events containing the decay of a A,.A or Kg. These
selected events were then studied to see if any polarization effects
could be found. Each of these three steps will now be described in

detail.

3.1 Pattern Recognition

The pattern recognition was performed by a computer program that
used the digitized information on the data tapes to construct
3-dimensional space tracks which corresponded to the passage of charged

particles through the experiment. It attempted to locate all the tracks

36

37
in the spectrometer system regardless of the kinematic configuration of

the event. The following is a summary of the algorithm used.

First the information from the various chambers (drift times for
drift chambers, wire numbers for PWC's, etc.) was converted into spatial
coordinates. It was at this point that hits associated with drift

chamber wires in the beam region were removed (see Section 2.6.2).

Next, a search was made for tracks in the Y view. This view was
chosen first because it was the non-bending view (except for a small
vertical focusing component), and thus tracks in this view should be
straight all the way through the spectrometer. To find these tracks, all
combinations of Y PWC hits forming straight lines were considered. Hits
in the Y drift chambers that lay close to these lines were added to
them. Any of these hit patterns that passed a set of minimal
requirements (such as the total number of hits, or the x2 for a straight

line fit) were then considered as Y track candidates.

Finally, a search was made for track projections in the other views
that could be linked up with these Y candidates. In each of the X, U,
and V views, the particle tracks are bent by the analysis magnet. The
projections in these views will thus consist of straight lines upstream
and downstream of the magnet, which meet at its center. Because of this,
the algorithm handled the upstream and downstream sections separately
(and identically). Pairs of XU, XV and UV hits were formed. The Y
position of each hit pair was calculated, and if a Y track was found

close to that position, the hit pair was combined with that Y track.

38
Each combination was then used to predict hit positions in the other X,
U and V chambers. Hits found close to the predicted positions were then
included in those combinations. Upstream and downstream hit combinations
that passed another set of minimal cuts were then combined, and pairs
that matched up at the center of the analysis magnet were considered
spatial tracks, to be used in further analysis. For a very detailed
description of the pattern recognition program (including all cuts

used), see Appendix I.

Inefficiencies of this algorithm could be caused by several things.
Chamber inefficiencies could lower the number of detected hits on the
track below the minimum required. Two tracks close together might not be
resolved, because of the single hit capability of the drift chambers.
Finally, extraneous hits (noise) not associated with real tracks could,
when combined with real hits, cause the misidentification of tracks.
While the first two inefficiencies can be handled with our Monte Carlo
studies, no attempt has been made to measure the third. After studying
by eye the behavior of the algorithm on a large number of real data

events, it was concluded that this inefficiency is small.

3.2 Data Reduction

In the data reduction phase, previously found tracks were used to
reconstruct the decays of A, A and Kg‘s. The topology of these events is

two tracks in the forward spectrometer that are the decay products of a

39
single, neutral particle produced at some point in the target.
Accompanying these forward tracks must be an incoming beam track which
produced the neutral particle. To identify events consistent with these

characteristics, a set of cuts was applied to the data.

Each event was first required to contain one and only one beam
track. The beam track was required to have at least 6 hits, with hits in
B1X and B4X mandatory (these were the chambers that most strongly
affected the momentum and position resolution). In addition, the
reconstructed momentum of the beam track had to lie within the range

160 < PBeam < 200 GeV/c.
This cut removed small tails in the momentum spectrum that were not
modeled by the Monte Carlo. Finally, a unique particle identification by

the Cerenkov counter was required. These cuts eliminated 13 % of the

data, mostly due to an inefficiency in B1X or B4X.

Next, the quality of individual forward tracks was considered. The
x2 per degree of freedom from a fit to the hypothesis of a single kink
(including vertical focusing) at the center of the analysis magnet had
to be less that 2.5 for each track. The X and Y intercepts of the track

at the center of the analysis magnet (X ) had to lie within the

438’ Yang
magnet's aperture. .Also, the X and Y intercepts at each PVC were
required to be within the PVC windows that were used by the trigger

processor during data taking.

40

After passing these cuts, all pairs of remaining forward tracks
within each event were considered as possible products from the decay of
a single, neutral particle; that is, they had to form a neutral V. Each
pair of tracks was required to have a total charge of zero, i.e. the two
tracks had to be oppositely charged. The charge of a track was
determined by the direction of its hand in the analysis magnet. The pair
of tracks also had to form a well defined decay vertex. The location of
the vertex was defined as the point of closest approach between the two
tracks. The distance between the two tracks at this point (CDecay) was

required to be less than 1.0 cm. The vertex had to also lie within the

evacuated decay pipe region.

To eliminate neutral V candidates that were really by-products of a
direct interaction in the target, cuts based on the hypothesis
illustrated in Figure 3-1 were applied. Here, the two tracks were traced
back through the sweeper magnet, and a search was made for a new vertex.
For the undesired interactions, this vertex will be located within the
target. Since the P1 of the sweeper is so much greater than the decay P;
of a A, A or Kg, if the tracks from these decays are traced back through
the sweeper, they will form a false vertex at the center of the sweeper.
Figure 3-2 shows the 2 position of the vertex of all track pairs for the

direct interaction hypothesis (ZI ). A bump at the target from direct

NT
interactions and a bump at the center of the sweeper from actual neutral
decays can be seen. All events with ZINT less than -25.25 m were
rejected. This hypothesis successfully accounted for 49 % of all
triggers. Monte Carlo studies have shown that only 7 % of the A, A and

Kg's were lost by this cut.

41

4B7

 

ZINT

BEAM

TRACK TARGET \/

 

 

 

 

Figure 3-1. A Direct Interaction in the Target

#10

32)-

28—

 

24 r
20 '—
15 '-

Events per Bin

12-

 

 

0 I J J
-30 -28 -26 -—24 -22
(m)

 

Figure 3-2. The Z of the Direct Interaction Vertex (ZINT)

42
The trajectory of the potential neutral particle was then
reconstructed from each surviving pair of tracks. It was required to
have a production vertex within the target. This vertex was defined as
the point of closest approach between the beam track and the neutral
particle trajectory. The distance of closest approach at the vertex

(C Dd) had to be less than 1.0 cm.

Pr
The three hypotheses
A 9 p + 1‘
I '9 B + 1+
K: 9 1+ +'w'
were then tested on the surviving candidates. Lambda and antilambda
candidates were required to have
0.0 < P‘(decay) < 0.12 GeV/c,
while K: candidates were required to have
0.12 < Pi(decay) < 0.21 GeV/c.
Decay I“L is defined as the transverse momentum of a decay particle with
respect to its parent particle. Finally, invariant masses were required
to be
1.104 < Mai, < 1.128 GeV/cz (A)

1.104 < ”1+ P < 1.128 GeV/c2 (A)

0.46 < M + _ < 0.52 GeV/cz (K0).
1 ,x s

Because of the kinematical overlap between K: and lambda decays (K:
and antilambdas), it would be possible for an event to satisfy two

hypotheses. By setting the minimum decay I"L for a K: to 0.12 GeV/c, all

43
such overlaps were decided in favor of the lambda (antilambda)
hypothesis. This introduced a background of Kg's in the lambda and
antilambda samples, which was corrected for later by using the Monte

Carlo.

Finally, each event was required to be consistent with the trigger
used during data taking. The beam track had to pass through each beam
counter, but not through the H counter. None of the forward tracks was
allowed to pass through the B, counter, while at least one of them was
required to pass through an I counter. In addition, only one of the
possible 16 PVC hits in the 2 track decay was allowed to be missing.
This was a stricter requirement than what the trigger processor applied,
and was used to eliminate the effect of noise on the triggering scheme

(which was not modeled by the Monte Carlo).

Distributions of the variables used in the above analysis are shown
in Figures 3-3 - 3-12. Included are comparisons to the results of the
Monte Carlo (which will be described in Section 3.3.1). Figure 3-12
shows the invariant mass distributions obtained. They are all consistent

with previous measurements, within the resolution of our system.

Table 3-1 gives a breakdown of the losses due to the cuts described
above. It can be noted that most events failed due to more that one cut,
and the largest single contributing cut was the one on the invariant
masses, which eliminated only 4 % of the events. Only events passing all

of these cuts will be used in the polarization analysis.

44

 

Table 3-1. Breakdown of Losses due to Cuts
Cuts Used Events Lost (Fraction)
ZINT, Mass, cDecay 0.207
ZINT’ Mass 0.090
ZINT’ Mass, CDecay’ ZProd 0.084
Mass, ZProd 0.057
Mass 0.042
Mass, CDecay’ zProd’ CProd 0.038
“888’ zDecay’ CDecay’ zProd’ CProd 0'033
Mass, ZProd’ CDecay 0.030
Mass, ZINT’ zProd 0.020
“888’ ZINT’ CDecay’ ZProd’ CProd 0'019
zProd 0.019
Mass, ZINT’ CDecay’ CProd 0.016
Mass, ZDecay’ zProd 0.020
Mass, CDecay’ zProd’ ZDecay 0.019
ZINT 0.006
Any other combination ( 0.001

Events per Bin

Events per Bin

Events per Bin

45

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

~10 3 .10 3
2.8 ...
K.
2.4 10 - I
2. 8 ,—
1.6
6 1-
1.2
4 L.
0.8
0.4 2 i— ‘-
0 0 1 . 1 _ 1
'0.12 0.132 0.144 —400 —200 o 200 400
‘10 3 410 3
.1.
1.2 p
5 .—
1.
4 — "‘
0.8
3 1—
0.6
0.4 2 ”
o_2 1 h- . ....
o 0 1 1 1
'0.12 0.132 0.144 -400 -200 0 200 400
#10 3
500 _ 2.4 + _
P I P
500 -' 2 L- -+-
400 I— 1.6 )—
300 P 1-2 _
200 - 0.8 — r“
100 —- 0.4 - T
0 1 1 1 1 1 1 Hi 0. 1 1 1
0.12 0.132 0.144 -400 -200 0 200 400
(on) (Mad)
Intercept Slope

Figure 3-3. X Intercept and Slope of Beams at Target

Events per Bin

Events per Bin

Events psr Bin

.10
2.4

2.

1.6

1.2

0.8

0.4

O

'-20 ~16-12 -8

900
800
700
600
500
400
300
200
I 00

500

400

300

200

100

0

46

1:10

 

 

I J

 

IO

 

 

J I I I l 0

‘10

 

TFII

I

 

 

 

 

0
~20 -16-12 -8

 

 

1J1" 1

1.6

1.2

0.8

0.4

 

l I I l O

 

-20-16-12 -8 -4 D 4 8

(mm)
Intercept

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3

. -+—
_ K'
L-

1

—200 —100 0 100 200
3
— D
,_ ~1—
L.

r—

1-— ~4-

__ ,4

1 1: I "'"'L_J
-200 -100 O 100 200
3

+ ..
_ P
L—
.4.

F- -0-

1_ --1 1 1:7. 1
-200 -100 0 100 200

(Had)
Slope

Figure 3-4. Y Intercept and Slope of Beams at Target

s10

47

 

Events per Bin

nus-mood)
I

 

 

 

 

 

 

 

 

 

 

 

 

O)
O

D
_s
O

U

170 180 190 200

210

 

U1 0'
VTT

Events per Bin

01
TI

:‘NPPS‘P?

UI
I

 

 

 

 

 

 

 

 

 

 

 

 

I70 180 190 200

210

 

0.25 -

 

 

 

 

 

 

 

’UI

 

 

160

I70 180 190 200

Pu

Figure 3-5. Momentum of Beams

210
(GeV/C)

48

010

 

12

IO

 

 

 

 

 

 

 

 

 

'10
2.8

 

“OI

2.4

1.6

)2

 

0.8

0.4

 

 

 

 

3 4 5
x7001:
Figure 3-6. leDOF of Forward Tracks

Events per Bin

Events per Bin

Events per Bin

0110

49

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

9..

 

 

 

 

 

 

 

 

 

-0.4 -0.2 0.2 0.4 06 -0.4 -02
~10 3
1.2 1- - IOOO '-
P
1, )—
800 1-
0.8 -
600 -
0.6 -
400 -
0.4 1—
0.2 — 200 -
I I l _
. * 0
0 -0.4 -—0.2 0. 0.2 0.4 0.6 -O.4
x (m)

4B8

Figure 3-7.

 

Track Intercepts at 4B8

50

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

~10 3 ~10 3
C
11’: 4.5 4 b ++ K-
L +
3 4. 3.5 r- +
{cf 3-5 .3. -- +
15 3' 2.5 ~—
2.5
2. 2. +
1.5 1.5 e ‘
1. 1 )— .
(15 (15 b 3-
O. 0 l l l l ‘
-0.08 0. 008
~10 3
.E
u) 1.6 -
3 1.4 ~—
' G)
‘g’ 1.2 ~—
>
“J 1. ~—
0.8 L
(16 P
0.4 —
0.2 -
0.
$1000
m 800 1 g,
L.
a 300 700 ~—
0)
‘5' 600 ~—
15 500 500 -
400 -—
400
300 r
200 200 h
100 -
o . 0 1
0. 0.1 0.2 0.3 -0.08 0. 0.08
m m
XDECAY ( ) YDECAY ( )

Figure 3-8. X and Y of the Decay Vertex

Events per Bin

Events per Bin

Events per Bin

51

 

 

 

 

 

 

 

 

 

 

 

 

 

 

III 0 3 ‘ 10
2.4
2.
1 .6
1 .2
0.8
0.4
0
11110 3
1 2 + 900
800
700
600
500
400
300
200
100
D
600
500
500 *-
400
400 1—
300 300
200 _ 200
100 b 100
I
O
0.1 2

 

 

 

K-

 

I I I l I l

 

'—20-16—12 -8 -4 0 4 8

 

 

 

 

 

-20—16—12 -8 —4 0 4 8

 

 

 

 

0 I I I I I I
-20-1e-12 -a -—4 0 4 s

YPROD

Figure 3-9. X and Y of the Production Vertex

s
O

 

Events per Bin
01
T

PNP‘P‘
U)
I

1.5 -

 

 

 

' l

 

-27.2 -26.4 -25.6 -24.8

 

 

 

 

’ l

 

-27.2 -25.4 -25.6 -24.8

 

Events per Bin
\1
o
O
I

 

 

 

I I I I I

 

-27.2 —2s.4 -25.6 :24.8

m
zpnoo ( )

 

0.5 _
o. ['1
-24

 

 

~10 3

 

I
-20

 

1 1-
-12 —8

111
—16

 

1.6 b,
1.4 —
1.2 )—
1. L-
0.8 —
0.6 -

 

 

 

 

 

800
700 ‘-
600 ’-
500 1-
400 '-
300 -
200 —

 

100 '-

 

      

 

 

I I ' I

 

~24

-15 -12 -8

2030.411 (m)

Figure 3-10. 2 of Production and Decay Vertices

Events per Bin

NP???

Events per Bin

gs

I
...
O

U!

U!

..s
0|

1.
0.5

\Im
CO
000

 

 

 

 

 

 

 

 

 

  

 

 

‘ P

__+

i—

_ Ti

r—u

I .
0 2 4 6 B 1 O
DECAY

53

.10

 

1 000

800

600

400

200

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3-11. Distance of Closest Approach at Vertices

 

Events per Bin

Events per Bin

~10

4.5

3.5

2.5

1.5

0.5

~10
2.4

1.6

1.2

0.8

0.4

 

 

 

 

 

 

 

 

 

 

 

 

54

~10

 

4.5

3.5 *-

 

 

 

 

K-

-)A

 

 

~10

 

20. -

17.5 *-

15. —

12.5 L-

10. '-

7.5 _

 

 

2.5 )-

 

 

 

 

 

3
-) A
,__ 1
I I I I I l
1.1 1.175 1.25
3 up!-
D91
1 1 1 J 4 1 I 4
1.1 1.175 1.25
111-4» (GeV)
p11

0.4 0.6

Figure 3-12. Invariant Masses before Cuts

(50V)

I
..a
O

55

 

Events per Bin
N
V

'o)
F

0.8 r-

0.4 *-

 

 

 

 

 

 

m

1000 1-

Events per 8

a:
o
o
I

500 -

400 '-

200 1-

 

——.—

 

 

I I J I I

 

I

 

1.1 1.12
111- 4
pi

1.14
(GeV)

~10

 

1.6 P-

1.4 *-

0.8 1—

0.4 +-

 

 

 

 

 

1.14
(GeV)

 

 

K'->1<°

 

 

O

I 1 [J11 I I

 

 

 

0.3

07

0.4 0.5 0.6 .
(GeV)

M+-
111

Figure 3-13. Invariant Masses after Cuts

56

3.3 Polarization Analysis

A summary of the final event sample coming from the data reduction
phase ‘is given in Table 3-2. This sample was used in the polarization

analysis.

Table 3-2. Summary of the Final Event Sample

 

Channel Number of Events
p '1 A 10,480
15 9 I 4,800
K' 9 A 8,250
K' 9 K: 16,685

As described in Section 1.3, the polarization of a sample of
lambdas can be related to the angular distribution of the pions from

their decays. Expanding Equation 1-1, we have

dN 1 , . .
d9 I 4 x ( 1 + GA [ PX Sine coso + PY sine sine + Pz c036 ] )
q
where PX’ PY and P2 are the components of the polarization vector P, and

9 and o are the azimuthal and polar angles of the pion in the center of
mass frame of the lambda (Figure 3-14). This distribution must now be
modified to accommodate the limited acceptance of the experiment, the
finite resolution of the apparatus, and the effects due to the

background of Ki's in the A and A samples.

57
The new distribution becomes

m'.

dN
d9 A(e.¢) d9

where A(9.¢) is the total correction to the raw distribution. In order
to extract the polarization from this distribution, we must determine

the function A(8,¢). This is the role of the Monte Carlo.

> N)
=1)

 

 

 

-<>

Figure 3-14. Center of Mass Coordinate System.

58

3.3.1 Monte Carlo

 

The Monte Carlo program attempted to simulate the behavior of the
experiment by modeling the production of particles from a given incoming
beam, the behavior of those particles after production and the response
of the apparatus to those particles. This was accomplished by a computer
program that was divided up into several parts - beam particle
generation and tracking, primary particle production and tracking,
primary particle decay, decay particle tracking and apparatus response

to these various particles. Each of these parts will now be described.

In general, six parameters are required to define the phase space
of the beam. Ve chose as these parameters the momentum of the beam, and
its X and Y intercepts and slopes at the first beam chamber (i.e.,
PBeam’ X0, Y0, X3, Y5, 20 I zBlX)° The problem of generating the beam
phase space is thus equivalent to generating PBeam’ X0, Y0, X6, Y3 at
201 remembering to include all possible correlations. To accomplish
this, the data was divided up into several momentum ranges, and
X0 vs. X0' and Ya vs. Yh' plots were generated for each range. The Monte
Carlo used the measured momentum spectrum to generate PBeam’ and then
used the appropriate Xa-Xo' and Yo-Yo' plots to generate the remaining
variables. The generated beam particle was then tracked through the two

beam magnets (4B5 and 4B6), until it got to the target. The K’, p and E

beams were handled independently.

59

The next step in the Monte Carlo was the simulation of the
interaction of the beam with the target. Several simplifications were
made here. Only one neutral particle was produced per incident beam
particle, and that particle was either a A, A or K:. The relative
probability of generating a A, A or K: in the Monte Carlo was adjusted
until the reconstructed decay P; distributions matched the data. Figure
3-15 shows the decay P.L distributions for events not consistent with the
lambda hypothesis and events not consistent with the antilambda
hypothesis. These plots allow the determination of the AIR: and AIR:
ratios respectively. The momentum and production Pl {of the given
particle were generated according to distributions that were adjusted
empirically until the reconstructed distributions matched the data
(Figure 3-16 and Figure 3-17). No attempt was made to fit these

production distributions.

60

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

~10 ~10
C
15 K-
2 2 2.
.3
5 1.6 1.6
>
U
1.2 1.2
(18 (18
(L4 - (L4 - .
o. 0. 1. 1
0. 0.24 0. 0.08 0.16 0.24
~10 3
.E
m 240 1'- p } 2 p
g o
,, 200 -
E 1.6 —
‘>’
U 160 ——
1.2 P
120 L- ,
80 _ 0'8 T
I
40 — 1* 0.4 -
1 ,.
o ' " I I J 0. j 1 1 M
0 0.08 0.16 0.24 0. 0.08 0.16 0.24
51000 1. - 120 ~ .-
3
A 800 P ‘00
’8
> 80
“J 600 »-
60
40
20
- ' 1 o
0. 0.08 0.16 0.24 0. 0.08 0.16 0.24
CeV c) (GeV/c)
PT”, (Not A) ( / PT”, (Not A)

Figure 3-15. Decay P.L Distributions

...

Events per Bin

Events per Bin

61

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

p -) A
000 *' 1000 —
800 *— 800 __
600 - 600 L
+
200 1- + 200 _
¢
0 25 50 75100125150175200 0 25 50 75 100125150175200
V
P(A) (GeV/c) 3 P(A) (Ge /c)
.10
1.75 F
400 —
1.5 1—
300 __ 1.25 L-
1. .—
200 1-
O.75 -
0.5 -
100 — .1
0.25 —
O 1 1 1 1 4 1 1 14 1‘11;

 

 

0 25 50 75 100125150175200 0' 0 25 50 7.5100125150175200
12(3) (GeV/c) POI: ) (CeV/c)

Figure 3~16. Momentum of A,I,K;

Events per Bin

Events per Bin

.10

700

600

500

400

300

200

100

62

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

J J 1 [Rm .1

 

 

 

0.5 1. 1.5 2.
11(1) (GeV/C)

 

Figure 3-17. P; of A,K.K:

63

 

 

 

 

 

 

 

 

 

 

 

 

 

.E
m K' —-> A
3 1
C
5 ’1
800 ._ 800 -
600 ~— 600 " FF 1
400 — 400 *-
+ +
200 - 200 h
+ + ++
O. 0 0.4 08
-1O
2.
500 1-

 

Events per Bin

4»
O
O

300

 

 

 

 

 

 

 

 

 

200 0.?5

0.5
100

0.25

0 .
. O 0. 0.4 0.3
x (K)
F xrmg >

Figure 3-18. XF of A,K,K:

64
The produced particle was then tracked through the apparatus, until
it decayed. ‘ Lambdas and antilambdas decayed eXponentially, with
CT I 7.89 cm. The K; decay distribution was an exponential with
c1 I 2.675 cm, modified by K: - K1 mixing. The only decay modes

generated were

K: decays were generated isotropically in their rest frame. Lambdas
and antilambdas were allowed to have a polarization, which was an input
to the program. Initially, the lambdas and antilambdas were unpolarized
in the Monte Carlo. The data was analyzed with this unpolarized model.
The polarization results from this analysis were then put into the Monte
Carlo, and the analysis was repeated. It was found that the results did

not depend on the polarization models used.

If a lambda or antilambda passed through the sweeper magnet, its
spin was precessed. The amount of precession was determined by the
f B d1 the particle experienced, and the orientation of the spin with
respect to the field direction. The ramping effect of the sweeper

discussed in Section 2.4 was included.

The generated decay products were then tracked through the rest of

the apparatus. Moliere multiple scattering [40]

of the particles was
included, as was pion decay. The response of the apparatus to these

particles was then modeled.

65

The PWC's were assumed to have 2 mm wire spacing (1 mm for the beam
chambers) throughout each chamber. The wire closest to a particle's
traversal was considered hit. In addition, if a particle went into a
region half way between two wires, both wires were considered hit. The
size of this sharing region was determined from the rate of adjacent
wire hits in the data. With this procedure, the resolutions of the PWC's
in the Monte Carlo matched those of the data. For the efficiency of the
PWC's, the chambers were divided up into 3 separate regions - the
support string region (100 % inefficient), the central beam region
(~ 73 % efficient) and the rest of the chamber (~ 96 % efficient). Each

chamber was handled independently.

For the drift chamber system, each wire was handled independently.
The location, efficiency and resolution for each wire was obtained from
the alignment data. The resolution was modeled by simply doing a
Gaussian smearing of the track intercept in the chamber. Also included

were the deadened central regions of the drift chambers.

Monte Carlo events were only considered if they would have
triggered the experiment. At least one of the two decay particles was
required to pass through an I counter. During data taking, ,the trigger
processor required at least 2 hits in 7 out of the 8 PWC’s, and at least
1 hit in the other PVC. However, these hits did not have to belong to
the tracks from the A, I or K: decay. The distribution of the number of
PVC hits in these decays is shown in Figure 3-19. The Monte Carlo events

were generated with this distribution.

66

 

 

 

 

CLS r-

Probobility of Triggering

0:4 *-

 

 

O.2 '-

 

 

 

0 1 1111
'1011121314151617

Number of PWC Hits

 

Figure 3-19. Number of PWC Hits in A, I, K: Events

The Monte Carlo events were written onto tape with the same format
as the data events, were processed through the same pattern recognition
program, and were required to pass vthe same cuts as described in
Section 3.2. Comparisons of the Monte Carlo and the data have been shown

in Figures 3-3 - Figure 3-18. Excellent agreement was obtained.

67

3.3.2 Calculation g: Polarization

 

 

By using the Monte Carlo, the function A(9.¢) described in
Section 3.3 can in general be calculated. It is simply the number of
events reconstructed after all cuts with a given 6 and 0, divided by the

number of events generated with that B and ¢.

Re

NGen(9.¢)

N c(9.1)
A(6,¢) I --—--—
It is convenient to convert these continuous functions into discrete
functions by binning over 6 and 0. This is done by integrating over bins

of solid angle A9, and yields

 

f N (9.¢) d9
A(91’¢j) . A9 Rec
IAQ NGen(e’¢) d9
AN' dN
35 - .A(ei.¢j> j;n 3516.1) (3-1)

which are now functions of the binning.

In general, AN'IAQ is a function of other variables as well, such
as I"L , XF’ etc.. However, statistical error considerations require the
data be analyzed only as a function of a limited number of these

variables. To measure P P and P simultaneously, 9 and 0 are

X’ Y 2

required. Previous measurements indicate that the polarization is a
function of I"l and XF’ and thus they should be included. The limited

statistics of the data constrain the analysis to either P1 or X and

F!
effectively eliminates the possibility of including any other variables

68
in the analysis. It is believed that all suppressed variables have been
correctly modeled by the Monte Carlo, and thus integrating over them to

calculate.A(6.¢) should be correct as well.

In order to use Equation 3-1, we must define the coordinate system
in Figure 3-14. Our choice is motivated by noting that parity is
conserved when A and A's are strongly produced. This implies that their
spins must be perpendicular to the production plane, and thus their
polarizations must also be perpendicular to the production plane. To
utilize this, the coordinate system was defined such that the Z axis was
normal to the production plane and the X and Y axes were in the plane.

In particular,

 

 

33
A A x Beam
2" 3 3
I A x Beam '
2 x Q
A Lab
x . A A
I z x zLab l
A A
z x x
A
y . A A
I z x x I

With this definition, A and A spins must be in the. :2 direction.
Since the A's and A's have non-zero magnetic moments, their spins will
precess as they pass through the sweeper magnet. The amount of
precession is determined by the magnitude of the field, and the
orientation of the spin with respect to the field. Assuming the magnetic
moment of the A is

“A . (-0.6138:0.0047) “N [41].

69
the precession angle is
0p I ~O.19604 I B dl sine (rad/Tm)

where f B dl is the field integral of the sweeper, and 6 is the angle
between the spin and the field direction. The maximum precession angle
in this experiment was ¢p I 29°. During the analysis, the coordinate
system was precessed by ¢p, and calculated for each event. The pion in
the decay was then boosted into this frame, and the pion angular
distribution was fit to Equation 3-1. Appendix III gives a detailed

description of this fit.

CHAPTER 4

Results and Conclusions

4.1 Bias Studies

 

Since the determination of a polarization involves the measurement
of an asymmetry in a decay distribution, it is important that no
apparatus induced asymmetries be present. Although we believe we have
modeled our apparatus correctly, it is useful to make independent checks

of this. Four such tests have been performed.

The first is a measurement of the lifetimes of the A, A and the K2.
These measurements are sensitive to the longitudinal acceptance of the
experiment. They were obtained by fitting the decay length distributions
to exponentials, correcting for acceptance by using the Monte Carlo. The
average results are listed in Table 4-1. They were found to be
independent of momentum, and are in good agreement with previously

measured values.

70

71

Table 4-1. Measured Lifetimes of A, A, K:

 

Particle Lifetime World Average
A (2.60:0.07) x 10"“ sec
(2.632010.0200) x 10"“ sec
A (2.44:0.11) x 10"“ sec
K: (0.87:0.01) x 10"“ sec (0.892310.0022) x 10"” sec

The second test is a measurement of the K: decay asymmetry. Since
the K: has spin zero, it must be unpolarized, and thus its decay must be
totally symmetric. The procedure followed to obtain the K: asymmetry was
identical to that for the lambda and antilambda (with the exception that
there was no precession of the coordinate system in the sweeper). Here,

the w' angular distribution was fit to

dN l A
an " 411(1*K"’)’

where X is the asymmetry. Only Kg's produced by the K‘ beam were used.
The results are shown in Figure 4-1. They are consistent with zero.
Although the K: asymmetry measurements are a stronger test for biases
than the lifetimes are, the kinematic differences between a K: and a A
or A implies the K: can not cover all possible sources of apparatus

induced signals for A or A's.

0.4
0.3
0.2

Asymmetry

0.1

-O.1
-0.2
-O.3

-O.2
-O.3
-O.4

72

 

 

 

 

 

 

 

 

 

 

% n 19.0, Noor 8 11 for P = O Q Ax
7‘— . . AY
L ‘ A,
1..
1 1 .. ,1
+ I
1. i
r.
r—
l J l l l
0. 0.2 0.4- 0.6 0.8 1.
PT (CeV/c)
{=12.9.Nw=sforp=0 .15‘
_ . AY
r- 1L ‘ Az
_ l
i. 1 ii
{I 37 II
I O
... 1
1..
J l 4 l l
O. 0.2 0.4 0.6 0.8 1.
Xr
Figure 4-1. Decay Asymmetry of K: from K' 9 K:

73
A stronger check for these channels is obtained by the parity
conservation requirement for A and A polarizations. This requires the X
and Y polarizations to be zero. The X and Y results obtained for the
channels p 9 A, E 4 A and K’ v A are shown in Figure 4-2 and Figure 4—3.

All are consistent with zero.

 

 

 

 

 

 

 

 

 

 

 

g (14
.g f-15,7,Nw-11forP-0 sK‘-—)A
.g (L3 -' IF>-> A
L. A "') A
g 0.2 - l + 5
n. 1 f *
01 —- 1
1+ 1 11 1
0. a
1 I 11
—0.1 L -
-02 - 6
-{L3 -
_ 1 1 1 1 1
0.40. 0.2 0.4 0.6 0.8 1.
PT (GeAO/c)
5 (14
:g f:8.1,Nw=-BforP=O IK'->A
E 0'3 ” ' p -> A
.g 0.2 1— ‘15 -> A
a.
0'1 ’— .1i 1 l 1_ 1
.1: ' =
...—0.1 r-
-o.2 .—
1—0431-
1 1 1 1 1
0.40. 0.2 0.4 0.5 0.8 1.

X:

Figure 4-2. X Polarization for p‘v A, 5 e A and K’ 9 A

Polarization

Polarization

0.4
0.3
0.2
0.1

-0.1
--0.2
—0.3

-0.4-

0.4
0.3
0.2
0.1

—0.‘1
-0.2
-0.3
-0.4

74

 

 

 

 

 

 

 

 

 

 

 

X’=9.3,NW=11forP=0 IK'->A
F . p —-> A
... AT: -> A
1+ 1 Ill 1+
1 11 1'
T 1
_.
1 1 1 1 1
0.2 0.4 0.5 0.8 1.
PT (CeV/c)
;.{=7.4N,or 8forP=O ,K-_>A
'- I p -—> A
i .15 -—> K
+1 111 +11
1 1 1 1 1
0.2 0.4 0.5 0.8 1.
x.

Figure 4-3. Y Polarization for p 4 A, E a A and K’ I A

75

Finally, a standard procedure, used in several of the previous
polarization. experiments, of flipping the direction of the magnetic
fields in the sweeper and analysis magnet was performed. This is
especially useful for fixed production plane experiments, where by
combining magnet up and magnet down data, apparatus induced biases can
be made to cancel. For this experiment, the production plane varied
event by event, and the bias cancelling procedure could not be used. The
main effect of reversing the fields in this experiment was to change the
area of the downstream two stations that were sampled by the protons and
pions from the A, A and K: decays. Reversing the fields therefore
primarily measured whether the downstream acceptance of the experiment
was modeled correctly. The differences between magnet up and magnet down
polarization results are shown in Figure 4-4. They are consistent with
zero. All other polarization results presented are for combined up.and

down data.

Polarization

Polarization

76

 

0.8
0.6 -
0.4 b
0.2 —

)( =12.9,N,,. - 11 for p _'o

515:3
1.11
>|>>

1.—

 

_o.2 1—
-0.4 —
—0.6 r-

 

 

 

-0.8

0.8 1.
PT (CeV/c)

 

0.8

0.4 1—
0.2 -

€15;
11¢
>l>>

 

..O.2 .—
-0.4 ~—
_0.6 .—

 

L

 

 

-0.8

0.4 -

0.6

0.8 1.
Xr

Figure 4-4. Pz (Up — Down) for p 9 A, E 9 A and K' 9 A

77
The above tests yield results consistent with zero systematic bias,
within the level of our statistics. However, there can still be
systematic errors in the Z polarizations of the A and A's. A discussion
of these errors will follow the presentation of the polarization

results.

5.2 Polarization Results

 

The polarization results for the channels p 9 A, E 9‘A and K” 9 A
are listed in Table 4-2 - Table 4-4, and are shown in
Figure 4-2 - Figure 4-4. The data have been binned both in Pl and XF'
The assumptions made in the analysis that define the sign of the
polarization were

a I -O.642 i 0.013

A

“71"“11

dN 1

d9 I 4 a (1 + a P cosB )

where 6 is the angle between the pion and the production plane normal in
the center of mass. Finally, the production plane normal was defined as
.A

PA x gBeam

A
z-

.A

I gA x PBeam '
The data presented here include both directly produced lambdas and
antilambdas, and those produced indirectly (such as from radiative
decays of Z°'s). A discussion of the contribution to the polarization

results from such non-prompt sources is contained in Section 4.3.

 

 

Table 4-2. Polarization Results for p 9 A

 

 

(Pl) (XF> P;
0.00 0 40 0.29 0.42 -0.012:0.047
0.40 0 52 0.46 0.50 0.073:0.055
0 52 0 68 0.59 0.54 0.15110.053
0.68 - 1.50 0.84 0.60 0.079:0.055

XF Bin (XF) (P > P;
0.00 - 0.45 0.36 0.43 0 04010.045
0.45 - 0.55 0.50 0.56 0 08930.055
0.55 - 1.00 0.68 0.64 0 07010.04]

Table 4-3. Polarization Results for B 9 A

 

 

 

 

Pl Bin (Pl) (XF> f;
0.00 - 0.40 0.30 0.46 -0.026:0.070
0.40 - 0.52 0.47 0.53 -0.031i0.083
0.52 - 0.68 0.59 0.56 0.117i0.076
0.68 - 1.50 0.85 0.63 0.17310.080

XF Bin (XF) (Pl) ‘3-
0.00 - 0.45 0.36 0.41 0.055i0.069
0.45 - 0.55 0.50 0.53 -0.064i0.081
0.55 - 1.00 0.70 0.61 0.174:0.056

Table 4-4. Polarization Results for K“ 9 A

 

 

 

P‘L Bin (Pl) (XF) . P;
0.00 - 0.40 0.28 0.39 -0.23430.052
0.40 - 0.52 0.46 0.46 -0.419:0.064
0.52 - 0.68 0.60 0.50 -0.438:0.058
0.68 - 1.50 0.85 0.57 -0.615:0.056

X? Bin (X?) (P&> P;
0.00 - 0.45 0.36 0.42 -0.32610.043
0.45 - 0.55 0.50 0.57 -0.466t0.057
0.55 - 1.00 0.66 0.66 -0.470:0.052

Polarization

Polarization

79

 

0.4
0.3 1-
0.2 1—
0.1 1—

 

-—0.1 -
-o.2 -
-O.3 L—

 

 

1 1 l i i

 

-0.4

0.2 0.4 0.6 0.8 1.
P, (GeV/c)

 

0.4

0.2 '-
0.1 -

 

-0.1 b

_O.2 —

 

 

1 1 1 l 1 1

 

-0.4

0.2 0.4 0.6 0.8 1.
X:

Figure 4-5. Polarization Results for p 9 A

Polarization

Polarization

99.0.0.0
AND);

1 I
o .0
L3 .1

-0.3
-0.4

0.4
0.3
0.2
0.1

-O.1
-0.2
-0.3
-0.4

80

 

 

 

 

 

 

 

 

 

 

Figure 4-6. Polarization Results for 5 9 A

L—
1 I '
t T 1
1 1 1 1 1
0. 0.2 0.4 0.6 0.8 1.
P1 (GeV/c)
1 1
~ 1
P
1 m 1 1 1
0. 0 2 0 4 0.5 0 8 1.
X:

.n.
a

9.0
(”Q
(11

Polarization

.0
N
u

—0.25
-—O.5
—0.75

m—J
.

Polarization
.0 .0
u: \1
01

.09
N
01

-0.25
-0.5
-0.75

81

 

 

 

 

 

0.6 0.8 'l

0.2 0.4 .
P, (CeV/c)

 

 

 

 

 

0.2 0.4 0.6 0.8 1.
X:

Figure 4-7. Polarization Results for K’ 9 A

82

As can be seen, the results for p 9 A and B 9 A are severely
constrained by statistics, and thus the possible conclusions are quite
limited. The two channels show positive polarizations, and are
consistent with having equal magnitudes. Using previous measurements as
a guide, the polarizations have been fit to linear functions of P;. The
intercepts for the fits have been constrained to go through zero at zero
Pi. The results are

p 9 A p - (0.136 1 0.046) p; (x2 - 3.46 with N - 3)

DOF

p a I p - (0.139 1 0.067) p* (x2 - 2.99 with N - 3),

DOF
and are illustrated in Figure 4-8.

Although the statistics for the K” 9 A channel are just as bad as
the other channels, the signal is much greater. The results of a linear
Pl fit yield

K’ 9 A P I (-0.756 r 0.049) P.L (x2 I 1.72 with N I 3).

DOF
Comparison of this result to the p 9 A and 5'9 A channels show a

polarization of opposite sign, with a slope larger by a factor of 5.6.

Also shown in Figures 4-5 - 4-7 are the polarization results as
functions of XF. All three reactions show non-zero results, however the

range of X covered by this experiment was not large enough to allow any

F

reasonable determination of the polarization's dependence on XF.

Comparisons with other experiments are shown in Figure 4—9 and
Figure 4-10. No attempt has been made to correct for the kinematical
differences between this experiment and the others. The data are in

agreement within errors.

83

 

0.4
0.3 r-
0.2 -

Polarization

SLOPE = .136 :t .046 x’ - 3.463

 

 

—0.1 1-
--0.2 1—
—0.3 1-

 

 

1 J

 

-0.4

0.2 0.4 0.6

0.8 1.
P, (GeV/c)

 

0.4
0.3 1-
0.2 r"
0.1 L

Polarization

ll

1"
(0
(O
.p.

SLOPE = .139 :1: .067 ;(

 

.../9”
1

13—97?

 

 

-0.1 +—
-0.2 r-
-—O.3 P

 

 

 

l 1

 

—0.4

0.8 1.
P, (GeV/c)

 

Polarization
.0 .0 7‘
01 \1

01
T l T

.0
N
U1
1

SLOPE = —.756 :1: .049 )6 1.717

 

-0.25 f
-0.5 r-
—0.75 —

 

0.2 0.4 0.6

Figure 4-8. Linear Fits of Polarization

 

1 J
0.8 1.
P, (GoV/c)

versus Pl.

84

 

0.4

__ O This Experiment
0'3 0 Ref. 6

0.2 *-

Polarization

0.1 '-

 

-0.1 1-
-0.2 1"-
_.0_3 )—

 

 

1 1

 

-O.4

0.4

0.6

0.8 1.
P, (GeV/c)

 

0.4

03 __ I This Experiment

0 Ref- 12
0.2 '-

0.1 P

Polarization

B-eK

 

-O.1
-0.2 P-
-03 ..

 

 

1 1

 

-—0.4 1

0.6

0.8 1.
P, (GeV/c)

 

..L
s

I This Experiment
0 Ref. 22

u
l

'01 \1
T

Polarization
0 P

.0
N
tn

1

 

-0‘.25 — +
-0.5 -
-0.75 —

 

1 +1

1 1

 

 

-1.
0. 0.2

Figure 4-9. Comparison

0.5 ‘l.
P, (CeV/c)

of Results to Previous Experiments (vs. Pl)

85

 

d
I

I 176 GeV/c (This Experiment)
0 32 GeV/c (Ref. 20)

o 10 + 16 GeV/c (Ref. 18)

A 14.3 GeV/c (Ref. 19)

0 8.25 GeV/c (Ref. 22)

.0
\l
m
T

Polarization

.0
U1
l

0.25 1—

0. A

1% + :1
1 +1 1 111 1 11

-0.5 1— 1

 

 

 

 

 

 

Xr

Figure 4-10. Comparison of Results to Previous Experiments (vs. XF)

86

4.3 Systematic Errors and Backgrounds

 

The errors quoted in Table 4-2 - Table 4-4 are statistical only.
Systematic errors have been estimated by using the Monte Carlo. As
mentioned in Section 2.4, a known source of systematic error was the
ramping magnetic field of the sweeper magnet. It was estimated that a
20 2 error in the sweeper field would cause less than a 1 % error in the
polarization measurement (due to improper precession of the A and A
spins). The field of the sweeper changed by only i 4 % during the spill.
Systematic errors have also been estimated for possible misalignments of
the apparatus and improper resolution modeling by the Monte Carlo. A
total systematic error of less than i 0.015 has been determined, which

is negligible compared to the statistical errors.

A known source of background in the lambda and antilambda samples
was due to the kinematical overlap between their decays and a K: decay.
As mentioned earlier, this background has been corrected for with the
Monte Carlo. The relative percentage of K: in the lambda and antilambda
samples was 11.2 %, 0.7 % and 0.8 % for the K', p and 5 beams
respectively. No other source of non-lambda or non-antilambda was

considered.

The other type of background in this experiment was due to
non-prompt lambda and antilambdas. One potential source for these
particles is the radiative decay of a X° 9 A 7 (2° 9 A 7). This

experiment was unable to distinguish such decays. The polarization of

87
these A's (A's) depends on the initial polarization of the 2° (:0)

according to

1
P101) ' ” ’3' P1200:"). “‘21

In order to correct for such non-prompt A's (A's), the polarization and
relative production rates for the 2° (2°) must be known.

Measurements have been made of the relative rates for and

K- 1221

p 143]

beams at lower energies. The results are consistent with
20

-—-—- z 30 %.

2“ + A
No data is available for B beams. The only 2° polarization
measurement [17] has been performed with a p beam. The results are very
limited in statistics, but they indicate
1391:" g " Pp9A ‘

With the above information, one can estimate the prompt A
polarization from p 9 A to be a factor of 1.3 greater than the measured
value (assuming the acceptance for non-prompt A's is the same as for
prompt A's). If we assume that Tn's and A's from E's behave the same as
2°‘s and A's from p's, the prompt A polarization from 5 9 A is also a
factor of 1.3 greater than the measured value. Although the relative
production rates are known for K” beams, it is difficult to make any

reasonable assumptions about the polarization for K” 9 2°, and no

correction for non-prompt lambdas in the K” sample has been calculated.

88
Other potential sources of non-prompt A's and A's, such as the
radiative decay 3° 9 A 7, have considerably smaller cross-sections, and

have been ignored.

4.4 Conclusions

 

The polarization of lambdas and antilambdas has been measured using
the reactions
p + p 9 A + X
E + p all + X
K" + p 41A + X,
at a beam momentum of 176 GeV/c, using a liquid hydrogen target.
Non-zero results have been obtained for all three channels. With the
sign conventions chosen (Section 4.2), the polarizations for p'9 A and
B 9 A are positive, equal in magnitude, with an average polarization of
0.063 t 0.022 within our kinematic range. The polarization for K”*9 A is
negative, with an average polarization of -0.419 t 0.029. All reactions
are consistent with a linear dependence on Pl.
When comparing polarization results from various experiments, it is

important to note the kinematical regimes of the data, since the

[51

polarization is a function of both P1 and XF

. The P and X
I F
distributions for p 9 A, 6 9 A and K” 9 A are so similar in this

experiment, that comparisons of these reactions are possible. While the

similarity between the polarization of p 9 A and E 9 A is perhaps

89
understandable, the large signal in K” 9 A is quite impressive. The
reason for the difference may lie in the fact that the s quark in K” 9 A
is a leading parton, where as the s quark in p 9 A (A in B 9 A) comes
from the sea. Future experiments are needed to study the reaction K” 9 A

in more detail, along with its companion K+ 9 A.

The only theoretical model which seems to be consistent with the
polarization data is the one by Degrand and Miettinen. It agrees with
the signs of the polarizations for all existing data, and except for the
signal in K” 9 A, is in reasonable agreement with the relative
magnitudes of the various channels. However, its method of determining
the actual magnitude is very non-rigorous, and does not seem to give the

correct (Pl, XF) dependences.

Polarization experiments yield sensitive measurements of spin
dependent terms in reaction amplitudes. Before any theory can be
declared correct, it must be able to explain such experiments. To date,

no theory successfully accomplishes this.

APPENDI CBS

APPENDIX I

Pattern Recognition Algorithm

The program used for the pattern recognition will be described in

detail here. A brief description can be found in Section 3.1.

The program first searches for tracks in the Y view. All possible
pairs of Y hits are considered, with the constraint that these pairs of
hits must be separated by at least one station. Also, the line defined
by the two hits must point back to a region near the target. These
constraints help eliminate fake tracks, and improve the speed of the
algorithm. Each pair of hits passing these requirements is used as a
seed to search for a potential track. Roads along the line defined by
the seed pair are searched to find the closest hit within the road for
each of the 12 Y planes. The road widths are i 3 mm for the PWC's and
i 6 mm for the drift chambers. These road widths are very conservative -
the PWC resolution is about 0.6 mm and the drift chamber resolution is
about 0.4 mm. The reason the drift chambers had such large road widths
was that their alignment was initially not as good as the PWC's. If a
total of 5 or more hits (including the seed pair) are found, the hit
pattern is declared a Y track candidate. Also accepted are roads
containing 3 or more PWC hits. No more than 40 such roads are presently

allowed. This is limited only by the dimensions of certain arrays in the

90

91
program. If more than 40 roads are found, the number of hits requirement
is increased by one and the previous steps are repeated. This continues
until less than 40 roads are found. This procedure is extremely
conservative and time-consuming, but also extremely safe. It could be

made much faster by reducing the number of seed planes.

Each track candidate is fit to a straight line. All contributing
planes are checked for hits which are closer to the fit line. If found,
the hit that was used is replaced. If a hit no longer lies within the
road, it is removed. If a plane did not contribute, but now has a hit
within the road, it is added to the pattern. The new track is refit, and
the replacing, removing and/or adding of hits is performed only once
more. A cut on the confidence level (probability) of the fit is made.
This cut is at 0.001. If the candidate fails the probability cut, the
hit with the largest contribution to the x2 is removed and the track is
refit. This continues until the track passes the probability cut, or
until it fails the number of hits requirement. The procedure followed is
probably good for tracks which have a large number of good hits and only
a few bad hits. It is certainly a bad procedure if the numbers of good

and bad hits are similar.

If the track candidate fails to pass these cuts, the above steps
are repeated using a fit that allows a bend at the center of the
analysis magnet. This is done to pick up tracks that pass near the outer
regions of the magnet, where there is a substantial non-vertical

component to the field.

92

No two Y-tracks are allowed to share a hit. If hit sharing is
detected, the shared hit is awarded to the better track. In order to
determine which track is the better one, a rather involved series of
criteria is applied. If both tracks have been fit the same way (straight
vs. kinked) and one has a probability that is 200 times that of the
other, that track is better. If one track is a straight track and the
other is a kinked track, and the straight track has a probability that
is 100 times that of the other, it is the better track. If neither of
these is true, then the track with the most Y PWC's is better. If this
doesn't work, then if one track has 2 more total Y hits on it than the
other, it is better. If none of the above is true, and if one of the
tracks is straight and the other one is kinked, the straight track is
chosen. Finally, if still no track can be determined as better, the
track with the highest probability is chosen. The candidate from which
the hit has been removed is refit and reconsidered with regard to all

Y-track cuts listed above.

This continues until no hits are shared. The above series of rules
were determined empirically by examining the behavior of the algorithm
on real data, and comparing the results to what the eye considered the
correct answer. Candidates making it this far are declared good Y-tracks

and will be written onto the output tape.

Next, correlations between Y tracks and hits in the X, U and V
chambers are searched for. Combinations of UV, U'V', XU, X’U', XV, and
X’V' drift chambers are used from each station. Other combinations are

possible, but were ignored to save time.

93

Hits from each combination are paired together and a Y coordinate
is calculated. If this Y coordinate is within the road around a Y track,
the pair is considered correlated with that Y track, and is stored. The
UV road width is i 4 mm and the X0 and XV road widths are i 14 mm. A
minimum road width is defined to be t 6 mm for UV and i 10.5 mm for XU
and XV, and it is within this window that most of the real correlations
are expected to appear. If a second pair of hits is discovered closer to
the Y track than the first, it will replace the first, unless it happens
to be within the minimum road. If more than one pair is discovered
within the minimum road, they are all recorded up to a limit of four. No
priority ordering is done for such multiple pairs. If more than four

pairs are found, only the best ones are kept.

Using the found XUV correlations and Y tracks, full space tracks
are now searched for. The spectrometer is first split at the magnet into
two symmetric halves - an upstream half and a downstream half, each half
containing two full stations. Each half is handled independently. If
both stations in a half have correlations in them, all possible pairs of
combinations are investigated. The program limits the number of such
combinations to 16. If a pair is contained in an already found track, it
is not investigated. A preliminary fit in the XUV-view to a straight
line is made combining these new pairs and the correlated Y track. The Y
track is fixed to its previous result. A cut on the probability at 0.001

is made.

94
If a combination passes this cut, a full XYUV fit is performed and
the result of this fit is projected into all planes not already
contributing to the space track. The replacing, removing and/or adding
of hits that was performed for the Y tracks is now done on the track
segments using all chambers. However, the hits forming the initial
correlation and the hits on the Y track are not allowed to change during

this process.

The track segments surviving the above procedure are stored. These
tracks are checked to make sure that no track is a subset of any other.

Any subsets are removed.

If no tracks were found in a particular half of the spectrometer,
all combinations of X PWC hits and previously found XUV drift chamber
correlations are used to form roads, up to a limit of 16 (any more are
ignored). These possible roads go through the same testing as previously

described. Any track segments surviving these tests are stored.

At this point, there exist possible upstream and downstream track
segments that are correlated to Y tracks. An attempt is now made to
connect these segments at the analysis magnet. In order to do this
matching, each segment pair is examined to see if its X mismatch at the
center of the magnet is less than 5 mm. If so, this pair is stored. If
not, it is skipped. If a second pair is found with an X mismatch less
that the first, but not less than 4 mm, it will replace the first. If
two pairs are found with mismatches less than 4 mm, then the pair with

the highest probability is chosen.

95

If no match has been found, the set of upstream segments is
compared to the set of downstream segments. The best set is determined
by a multi-step procedure. If only one half of the spectrometer has
track segments‘ in it, that set is the best. Otherwise, the highest
probability in one set is compared to the highest probability in the
other set. If one is a factor of 200 more than the other, that set is
the best. If a set has a track segment with more X PWC hits on it than
every track in the other set, that set is chosen. If this isn't true,
the set containing the track segment with the most X hits is picked.
Finally, if all else fails, the set containing the track segment with

the highest probability is declared the best.

A search for track segments in the non-chosen set that link up to
the track segments in the chosen set is now performed. Roads are formed
using the previously found XUV correlations in the non-chosen set and
the X intercept at the magnet of each track segment in the chosen set.
The usual filling in of the road, fitting it, checking its probability
(cut at 0.001) and refitting it (if necessary) is done for each road
found. Here a minimum of 3 XUV hits in 2 stations or 2 PWC hits is

required.

Any candidates passing these cuts are tested to see if the X
mismatch at the magnet between it and the track segment used as a seed
is within the cut described above. If a pair of upstream and downstream

segments have been found that match up, these segments are stored.

96
If a matching track has still not been found, a sweep search in X
is done, using the X intercept of each track in the chosen set as a
pivot. This sweep search forms roads using the pivot point and each X
hit in the station farthest from the magnet in the spectrometer half
being searched. These roads are filled, fit, checked for probability,

refit, and matched as previously described.

If there is still no matched track, the half of the spectrometer

that was not previously chosen is now used and the above steps repeated.

At this point, no two track segments are allowed to share even a
single hit. If such sharing is detected, the hit in question is awarded
to the better track. This is determined by another involved procedure.
If the probabilities of the two tracks differ by a factor of 20, then
the one with the higher probability is the better track. Otherwise, the
track with the most number of X PWC hits if the better one. If this is
not true, the track with the most number of total XUV hits is the better
one. Finally, if none of the above are not true, the track with the

highest probability is chosen.

An attempt is now made to use the X PWC's as seeds. All
combinations of X PWC hits that form 4 hit X tracks that meet at the
magnet are examined. Each X PWC track is combined with each Y track
previously found (regardless of whether that Y track has already been
linked to an XUV track). This XY track forms a road which is filled in,
fit, checked for probability, refit, and matched at the magnet. If this

XY combination fails to pass these cuts, it is ignored. If it passes

97
these cuts, it is required to have at least one UV hit or it is also
ignored. If the new XYUV track passes all of the above cuts, and no
previous XYUV track had been previously found, the new XYUV track is
saved. If an XYUV track had been found, it is compared to the new XYUV
track. The track with the most number of hits is saved and the other one

ignored.

Up to this point, XUV hit sharing has only been checked when
comparing track segments linked to the same Y track. An attempt is now
made to eliminate XUV hit sharing between different XYUV tracks. If
sharing is detected, the hits are removed from the worse track unless
the two tracks share 3 or fewer hits. If so, it is impossible at this
point to tell which track is worse, and they are allowed to keep these
hits. However, if the hits are to be removed, the worse track is
determined by the following series of tests. If one track has fewer X
PWC hits than the other, it is worse. Otherwise, the track with the
fewest total XUV hits is worse. Finally, the track with the lower

probability is worse.

After the hits are removed, the track is refit and tested to see if
it passes all of the cuts. If not, it is eliminated from the list. All
patterns of hits previously stored are written onto tape for later use

by the data reduction phase.

APPENDIX II

Drift Chamber Alignment

 

In order to determine spatial position from clock time in the drift
chambers, a set of alignment constants was needed. These constants were
determined offline by using the PWC system as a reference. Tapes
containing muon triggers (Section 2.7.3) were processed through an
analysis program that required each event to contain one and only one
forward track, with at least 7 PWC hits on that track. These tracks were
then fit to straight lines using the PWC's only, and the x2 per degree
of freedom was required to be less than 5.0. With these requirements,
220,000 muon events were obtained. They had the properties of being well
defined, straight spatial tracks that did not require any a priori drift
chamber alignment. For the purpose of the drift chamber analysis, only

these muon events were used.

By plotting the position of the muon given by the PWC track versus
the clock value for the cell that the muon went through, several
features were observed (See Figure 11-1). The expected linear
relationship between position and time can be seen (A). Also evident is

the dead time of the amplifier (B), and the noise in the system (C).

98

99

Finally, unexpected crosstalk between neighboring wires is seen (D).

POSITION

 

     
   
    

  
 
 
 

o o [Pfisz'e 9. o 9. O 0
9’ ‘dX’79l\o 0.9- O- 0 o . o .
009 o o [7'2790 4 o o
9‘ 0 0 '-I 0 017997'” e o u o
0.0.0. o )4)?! 700 u o o
9.} 0b.... a a c ff. 5’. O
9 )996000 0 o o \C’ 9 9O D o 9 09..
.0 09099.09 0 o o 6 :12, To \‘P9 . o
u . ”’1 a a" «a o. y «n I G or 7 0
0.0.0. 9 [a 09‘) o. -o o .7 ’7" o ‘0... .0
.09 oo 0.9: Q".\ .09 o o QII,Y?OO‘9OO . 3
...! oo o of f 9. oz 9 o 0.0 P ‘7""‘0 ,9 9. 0
000‘ 0 00.0 o .~2099\ Q. o 0 0‘2 0(979’... . .. .
o t' o 0 "so. 9.. .9'49f.‘ . 09.0 o yvnns . .
'° II ‘00 oo o 0:96 0 etc..! or“ o o 907979\o a o
- 900 0 o. ,0 0 ' 0‘. 0 019.6 00' O 0.0 "IYPIIOQ
o o 070 2: o 6 2,6027 o‘j,’9)§oooooo 0 ' 69777 ‘4 o
| o- o 0' 9.9.9 coco9‘6‘ gt] ao.oooOIO\o o O-ouoo 7
.9." 01 00 0 9649009.. e 0 72.099 ‘0999 9 o o o {7777' o o o o.
I o9 0.09 00.9 9 o. 9o at 0:4 2‘. to. o. o o. oo 9§7779fl99 9 .
‘90! ‘0. 9 9“‘.‘ OI 7o. ‘2, o oo ’ \o 999‘ 99 o. 0 ol”"" .0 I
\OQC‘.|J\Q :I‘IQ‘UQ: 20.9., .0 \Q Q o 9.. oz ‘\0‘ O ,0 0 OO."."'.'OO .9
\a?.oeeooxalathwoassaeg.egrsasan \ . .090 900999.! .00. 000370660979':
.. 0“ 0‘0!)Iav‘!zAcmafinlfeesaaQIa‘aaeageo 79.9. o to. (7:.e 00.1.5
090'.4¢'09fi~.¢9§$oo.|Q9|OCQPQO~§§Y“‘ o oo o . 000‘ o, 9o o. :A 7 '
907'9fiQQQSTOQAPB’9Yffio 9.) 09. o o 7‘ .09, 9ooo§oooo 90 \o : 7 I” o
’9; ° ’0 I 60‘. e. o. .00 o. .09. 0900 .09 $0.90. ‘0 :\:'9 79o.
o oo o oo 3 o9$9oooo o o 9 oo‘IC909ge o o o 9 7 9909 o: o
9 o 9o o 9 o 0.)). o ..9 o 7 9‘} 120‘ 9 i 0 999777".
see 9 . o (\M6077root ..‘B 4. .009 . yyyyyolo. .. . .
a - ° . o‘ . z 799' r . 92~ot¢tz . 9"'f" ‘ .° 9 ' °'
0 - De 1 o oo' o. ’. ’ o'ea‘n"oeyo o oo o o o a oo o
:'. - o. e a 09“ \oo£.\4991o 2 I777) ‘ o n ..
o o o o - o o 09 o o 0 0‘0... 9", o 0‘7'77“ 0 0
o 0 00.00090 .0 07‘ \ 9.? ’.,z) o 9.97 6.777" 9 cos
.9. o. o o ’9‘. 0‘ 6909 o 0 0‘4‘ 0' 7770‘ .0 O
o .0 ‘ 0,0. 0 oe9\oo\ a o o o: 7,:0 ’ o I
o. 9o..g 05" 0‘ o o 0" ' o o
o ‘: \ o oat 09. :0 o 0 00.7777 9 09“ ' ’ B
.0. ot.-.§o“2,ooo i’i’fifl’oo 0"4 0 O
09.09099e0990 o. 9 o 9 957777!” 0 o o 0",0 .
.' 9. n. ' ' . . - ‘gnyygs.s. o 3.0. ‘
.399\0' ‘ o o 90090 907799009 0 oo o 7?. z...
I“; a .. I I \"'Y.‘o .39.-. o o o o .. ‘ ‘
0.99. .0. -'7’7’\9 o z o 0 9 9. 9
0'0 o o.‘".‘.‘."¢ o o o o o o o C o A, .00 ‘0
9 oo o P?"'?‘.. 9 9. oooo o o so 000'
0 .0 .-"’,‘;. o O o O .0 O O O 0

' TIME
Figure 11-]. Position versus Time for a Drift Chamber Cell

Only those clock times that belonged to feature A were considered

valid. Upon closer examination of these times, it was found that a

nonlinear relationship existed between position and time for hits near

both the sense wire and the high voltage wires. The size of the

nonlinear region near the high voltage wires was ~ 5 mm and that near

the sense wire was ~ 3 mm. The nonlinearity near the field wires was

about a factor of 5 worse than near the sense wires. These

nonlinearities are attributed to large fluctuations in the electric

fields at these points.

100
In order to parameterise the linear region, the functional form
X I X0 1 Vi (To - T) (II-1)
was used where T is the clock time, X0 is the wire location, To is an
offset time, V+ are drift velocities (one for either side of the wire),
and X is the position of the hit. The constants X0, To and Vi were
obtained for each wire by fitting feature A to Equation 11-1 in the
linear regions. In addition, another parameter, 0, was ‘needed to
describe the rotation of each wire away from its nominal orientation
(i.e., vertical for X chambers). The average rotation of the wires was
1.4 mrad. The nonlinear regions were handled by creating lookup tables

which contained corrections to the linear function. A total of 25

alignment constants was used for each of the 418 wires in the system.

APPENDIX III

The Polarization Fit

 

The center of mass distribution of pions from lambda decays is

25 u —l— ( 1 + 0A [ PX sine coso + P sine sin¢ + P c089 1 7

d9 4 n Y Z

...)
where PX’ PY and P2 are the components of the polarization vector P, and

0 and 0 are the azimuthal and polar angles of the pion. This equation is

modified by the acceptance function A(6,¢) to become

92'.

d9 cosB ] ).

‘éi%:21 ( 1 + “A [ Px sine cos¢ + P sine 8109 * P

Y Z

The data were analyzed by binning over P; (XF) and then within each

PL (XF) bin, binning over c030 and 0. Each P.L (XF) bin was handled

independently.

The acceptance for a particular (cosB ,0 ) bin was calculated as

i J

cosBi+Acosel2 0 +A¢l2

j
NREC(cose.¢) dcosB do

cosBi-Acos0/2 oj-A0/2

 

l’J cosBi+Acosel2 ¢j+Aol2
NGEN(cose,¢) dcose do
cosBi-AcosGIZ oj-A0/2

101

102

where NREC(cosB,0) and N EN(cosG.¢) are the number of reconstructed and

G
generated events with (cos9,0) given by the Monte Carlo, and AcosB and
A0 are the bin widths used. Binning over cos0 and 0 changes the pion
angular distribution into

cosBi+Ac030l2 0j+A0/2

A

A113. _..11 ' as

A9 41 d9 dcosG d¢
cosOi-Acos9/2 0j-A0/2

51.1
. 1 2 3 1
4n ( Ii,j + “A [ Px Ii,j + PY Ii,j + PZ Ii,j 1 )
where
1 an

Ii,j Acose A0

Ii,j I i [ n2 7 1 - n3 + sin”1n2 - n, J 1 - nf + sin”1nl ]

x ( 2 c030 sinA0/2 )

J

Ii,j I f [ n2 J l - n: + sin'ln2 - n, J 1 - hf + sin"n1 ]
x ( 2 sin0j sinA0/2 )
~ -
Ii,j cosBi AcosB A0

n, I cosBi + AcosB/Z

n, I c030i - AcosGIZ .

103
A least squares fit of the data to Equation III-1 was performed.

The x2 that was minimized was

 

 

 

 

,. .2
__ 1 z 3 11
Did 11.111,j ( 11,1 +01A 1 PX 11,3..1 1311.3 + Pz 11.31)
x2-
7 D
_ 1.1 _,
11
where
2 ”1.1

 

N-
1 2 3 s
z Ai’j ( 11,, + 0A 1 Px Ii,j + PY xi’j + P2 11.1 1 )
normalized the Monte Carlo to the data. The program DUBNAL (originally
FUMILI) in the Fermilab Cyber Computer Library was used to minimize this
X’ PY and P2. The results did not depend on the
(cosB, 0) binning.

expression for P

LIST OF REFERENCES

LIST OF REFERENCES

1) A. Gaidot, et a1., Phys. Lett. 57B (1975) 389.
2) G. L. Kane, J. Pumplin and W. Repko, Phys. Rev. Lett. 61 (1978) 1689.
3) G. Bunce, et a1., Phys. Rev. Lett. 66 (1976) 1113.

4) L. G. Pondrom, Proc. of XIV International Symposium on Multiparticle
Dynamics, Eds. P. Yager and J. F. Gunion (1983) 563.

5) B. Lundberg, Ph.D. Thesis, University of Wisconsin-Madison
(unpublished).

6) K. Heller, et 31., Phys. Rev. Lett. 61 (1978) 607.

7) S. Erhan, et a1., Phys. Lett. 626 (1979) 301.

8) K. Raychaudhuri, at 31., Phys. Lett. 296 (1980) 319.

9) F. Abe, at 31., Phys. Rev. Lett. 66 (1983) 1102.

10) K. Heller, et 51., Phys. Lett. 666 (1977) 480.

11) F. Lomanno, et a1., Phys. Rev. Lett. 66 (1979) 1905.

12) P. Chauvat, et 81., Cern Preprint CERN-EP/83-104.

13) O. E. Overseth, High Energy Physics with Polarized Beams and

Polarized Targgts , Proc. of the 1980 International Symposium, Eds. C.
Joseph and J. Soffer (1980) 114.

 

 

14) K. Heller, et 81., Phys. Rev. Lett. 61 (1983) 2025.

15) C. Wilkinson, et a1., Phys. Rev. Lett. 66 (1981) 803.

16) P. S. Cooper, High Energy Spin Physics AIP Conference Proceedings
No. 95, Particles and Fields subseries No. 28, edited by G. Bunce (1982)
102.

17) E. C. Dukes, Ph. D. Thesis, University of Michigan (unpublished).
18) H. Grissler, et 31., Nucl. Phys. B136 (1978) 386.

19) H. Abramowicz, er a1., Nucl. Phys. B105 (1976) 222.

20) M. L. Faccini-Turluer, et 31., Particles and Fields (1979) 19.

104

105
21) I. V. Ajinenko, et a1., Phys. Lett. 121B (1983) 183.
22) H. Baubillier, et a1., Nucl. Phys. B148 (1979) 18.

23) R. Rameika, High Energy Spin Physics AIP Conference Proceedings No.
95, Particles and Fields subseries No. 28, edited by G. Bunce (1983) 77.

 

24) J. R. Bensinger, jbjdl, 126.
25) D. Aston, et 81., Nuc. Phys. B195 (1982) 189.
26) Barth, et a1., Z. Physik 619 (1981) 205.

27) B. Andersson, G. Gustafson and G. Ingelman, Phys. Lett. 66B (1979)
417.

28) T. A. DeGrand and H. I. Miettinen, Phys. Rev. D 16 (1981) 2419.

29) H. Roos, et 51. (Particle Data Group), Phys. Lett. 1116 (1982) 1.
30) F. Paige, D. Sidhu, Phys. Rev. 216 (1976) 2307.

31) G.‘ Gustafson, High Energy Spin Physics AIP Conference Proceedings
ggg 95, Particles and Fields subseries No. 28, edited by G. Bunce (1983)

32) H. Kobrak, R. Pitt and R. Swanson, Fermilab Technical Memo TM-597
(1975).

33) The Cerenkov counter was patterned after a design by S. Pruss of
Fermilab.

34) The beam chambers were constructed by the Research Services
Department of the Fermi National.Accelerator Laboratory.

35) M. Abolins et a1., Nucl. Instr. Meth. 121 (1982) 331.

36) Model WCS-ZOO Wire Chamber Scanner manufactured by Nanometric
Systems, Inc., 837 North Cuyler Avenue, Oak Park, IL 60302.

37) The PWC's were built by the Carleton University Physical Sciences
Shop. a

38) The Drift Chambers were built by Nanometric Systems, Inc..

39) T. F. Droege, H. H. Watson and T. R. Wesson, IEEE Trans. Nucl. Sci.
NS-23 (1976) No. l 248.

40) S. Goudsmit and J. L. Saunderson, Phys. Rev. 61 (1940) 24.

106
41) L. Schachinger, at 31., Phys. Rev. Lett. 61 (1978) 1348.
42) R. Gatto, Phys. Rev. 192 (1958) 610.

43) M. W. Sullivan, et 31., Phys. Lett. 1428 (1984) 451.