Louisiana State University
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LSU Historical Dissertations and Theses
Graduate School
1990
Measurement of Positron-Electron Going to
Baryon-Antibaryon Forward-Backward Charge
Asymmetry.
Jit Ning Lim
Louisiana State University and Agricultural & Mechanical College
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Recommended Citation
Lim, Jit Ning, "Measurement of Positron-Electron Going to Baryon-Antibaryon Forward-Backward Charge Asymmetry." (1990). LSU
Historical Dissertations and Theses. 4999.
http://digitalcommons.lsu.edu/gradschool_disstheses/4999
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3 1 3 /7 6 1 -4 7 0 0 8 0 0 /5 2 1 -0 6 0 0
O rder N um ber 0112246
M easurem ent o f e+e
-*
bb forw ard-backw ard charge asym m etry
Lim, Jit Ning, Ph.D.
The Louisiana S tate University and Agricultural and Mechanical Col., 1990
UMI
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Measurement of e +e
—> bb forward-backward
charge asymmetry
A Dissertation
Submitted to the Graduate Faculty o f the
Louisiana State University and
Agricultural and Mechanical College
in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
in
The Department of Physics and Astronomy
by
Jit Ning Lim
B.S., National University of Singapore, 1984
M .S., Louisiana State University, 1986
August 1990
A c k n o w le d g m e n ts
For the education which allows me the freedom to pursue my hopes, dreams and
aspirations, I owe a great debt to my family. My sincerest thankB to my parents,
Lim Heng Say and Tan Tew Hiew, who devoted their lives to their children; to my
sisters and brother who sacrificed their education and took early work so that I
might continue, Tuay Cheng, Toi Ming, Mui Kim and Boon Tong; to my professors
Richard Imlay, Bill M etcalf and Richard Haymaker who made it possible for me
to come to America to study; to my thesis advisor, Professor Roger M cNeil, for
his encouragement, guidance and immense patience in reading this thesis countless
times over and giving valuable insights into the various aspects of the analysis; to
Dr. Kazuo Abe and Dr. Hiroyuki Sagawa who taught m e much about Experimental
Physics while I was in Japan so I didn’t sink into total “whale shit”; to Professor
Stephen Olsen and Dr. Aki Maki for their leadership in providing an excellent
enviroment for serious research; to all the members of AMY who built the detector
and wrote the detector-specific software; especially Roger M cNeil, S. Igarashi, S.S.
M yung and N.M. Shaw for the work they have done on the muon analysis, T.K um ita
for his work on punchthrough, H. Sagawa and T. Mori on their work on total
hadronic cross-section; my analysis is built upon a part of theirs. My wife and
I give thanks to Professor Stephen Olsen who allowed the graduate students the
use of “Rochester” truck for survival; to Yosida-san who kept my wife and I alive
clearing red tape at the hospital; to Dr. Aki Maki who called the ambulance when
I was ill and for staying many hours with us, and to Delores Hart who made all
arrangements at LSU on our behalf. Finally and m ost dearly I thank Eden, my
wife, lover, teacher and companion of life, for her support and love and for sharing
the good tim es and the hard tim es. She is the “wind beneath my wingB.”
To Victoria Mai-Ying Eden Elizabeth Mountbatten-Lim
iv
Table o f C ontents
1
I n tr o d u c tio n
1
2
T heory
8
2.1
Electrom agnetic t h e o r y ................................................
9
2.2
Weak I n te r a c t io n ...............................................................................................
10
2.3
Electroweak T h e o r y ...........................................................................................
13
2.4
Differential cross s e c t i o n .................................................................................
18
2.5
Topless M o d e l......................................................................................................
23
2.6
B ° — B ° mixing and its effect on A b ........................................................
25
3
T h e A M Y E x p e r im e n t
28
3.1
The TRISTAN e +e “ co llid e r .........................................................................
29
3.2
The AM Y D e t e c t o r ...........................................................................................
31
3.2.1
Inner Tracking Chamber ( I T C ) .....................................................
33
3.2.2
Central Drift Chamber ( C D C ) .........................................................
34
3.2.3
X-Ray Detector ( X R D ) ........................................................................
39
3.2.4
Barrel Shower Counter ( S H C ) .........................................................
40
3.2.5
Super Conducting M a g n e t .................................................................
46
3.2.6
Muon D etection System ( M U O ) ......................................................
47
3.2.7
End Cap Detector
..............................................................................
58
Triggering and D ata A cq u isitio n ..................................................................
61
3.3
v
3.4 Monte Carlo Simulation
4
..................................................................................
62
3.4.1
Event G e n e ra tio n ..................................................................................
65
3.4.2
Detector Simulation
66
I n c lu s iv e M u o n E v e n t S e le c tio n
67
4.1
Multi-hadronic e v e n ts .........................................................................................
69
4.2
Inclusive Muon S e le c tio n ..................................................................................
75
...................................
75
4.2.1
4.3
4.4
4.5
4.6
5
...........................................................................
Matching the muon track to a CDC track
B a c k g r o u n d ...................................................................
4.3.1
Cosmic ray muons and accidental h i t s ............................................
82
4.3.2
P u n ch th ro u g h .........................................................................................
85
4.3.3
Muons from decay of tt* and K*
...................................................
85
Efficiency for selecting promptm u o n s ............................................................
91
4.4.1
92
MUO and CDC efficiency
.................................................................
D ata S a m p le............................
95
4.5.1
Composition of inclusive muon d a t a ................................................
95
A check for detector b i a s s e s ...........................................................................
97
A n a ly s is
5.1
82
101
Enrichment of the b —» ft f r a c t io n .....................................................................105
5.2 The Unfolding F a c to r ............................................................................................. 108
5.3 System atic E rro r s.................................................................................................... 113
5.4 R e s u lts ......................................................................................................................... 117
vi
5.5
6
5.4.1
Obtaining Ab and R b using minimum x 2 fit
5.4.2
A b and R b from form ulae....................................................................... 123
5.4.3
Final R e s u l t s ............................................................................................ 125
Limit on B° — B° mixing
..........................................................
F u tu r e m e a s u r e m e n ts
6.1
.................................. 117
. 125
130
Matrix transformation m e th o d ..........................................................................131
7
C o n c lu sio n
135
8
B ib lio g rap h y
137
0
A p p e n d ix
143
9.1
The AMY C o lla b o r a tio n .................................................................................... 143
9.2
Monitoring the performance of the MUO
9.3
Where was I in the Scheme of th in g s ? ............................................................147
............................................ 144
List o f Tables
2.1
The Z° —» ff vertex factors in the standard model with sin 20\v —0.234. 21
2.2
Weak isospin and hypercharge quantum numbers of leptons and
quarks in standard model
..............................................................................
22
4.1
Decay Amplitudes of Heavy and Light M e s o n s ........................................
68
4.2
Number of events passing each hadronic selection stage................
4.3
Efficiency for selecting prompt and fake m u o n s ........................................
4.4
Summary of inclusive muon data with center-of-mass energies be­
tween 52 and 57 G e V
4.5
74
92
98
Summary of inclusive muon data with center-of-mass energies be­
tween 57.25 and 61.4 G e V
98
4.6
Integrated luminosity of the data s a m p l e .........................................
99
4.7
Number of inclusive muon e v e n t s .........................................................
4.8
A check for detector b i a s s e s ....................................................................100
5.1
Rb and Ab for various P t c u t s ................................................................ 119
5.2
Comparison of Rb and Ab using hand calculation and minimum \ 2
100
f i t t i n g ............................................................................................................. 124
5.3
Final Results for Rb and A b ....................................................................125
C .l Responsibilities for fabrication and funding of A M Y ......................149
-i
{
A b str a c t
T h i s d is se r ta t io n de sc r ib e s t he m e a s u r e m e n t of t he f o rw ar d -b a c kw ar d charge
a s y m m e t r y , Ai,, for e ' e - —►bh at T R I S T A N by t he A M Y d e t e c t o r .
m e n t o f t h e ratio, R|,, o f t h e cross s e c t i o n for e +e cross s e c t i o n for e ' e
-> / t ' >
is also o b t a i n e d .
A measure­
bb to t h e t h e o r et i c a l Q E D
A|, is an efTect of t h e weak-
e l e c t r o m a g n e t i c i nt e rf e re n ce . T h e m e a s u r e m e n t o f A], is the re for e a dir ec t test of
t h e s t a n d a r d m o d e l e l e c t r o w c a k theory. T R I S T A N is t h e o n l y e + e “ collider in the
world t o e x p l o r e t h e c e n t c r - o f - m a s s e ne rg y region o f 50 G e V t o 62 G e V , whe re
t he effects o f w e a k - e l e c t r o m a g n e t i c int er f er en ce b e c o m e s m a x i m u m . T h e d a t n were
c ol l e c te d b e t w e e n J u n e 1987 and J u l y 1989 with a total i n t e g ra t e d l u m i n o s i t y of
Xl.U pb'"1 a nd c e n t e r - o f - m a s s e n er gi es ranging from 52 G e V to G l ^ G e V . Multihndronic. e v e n t s wi t h a m u o n were used for t he a nal ys is . T h e m e a s u r e d values were
ix
A,,
0.R2 :l; 0 . 2 5 ( s l a . l ) I O. H( .s y sl ) mid It,.
0.-17 I 0. 12 :!: 0.12 ftl an average
c e n t e r - o f - m a s s e n e r gy of 57. 2 ti V\ ' . T h e s e results were c o n s i s t e n t wit h t h e s tandar d
m o d e l c l e c l r o w e a k t h e or y p r e di c ti on s o f Ai, =•■ - 0 . 5 8 and R|, — 0 . 5 6 at. this energy.
T h e m e a s u r e m e n t of the charge a s y m m e t r y is used to s e t a limit on 11" — B* mi xi ng
o f y ■„ 0 .2 0 at t he 9 0 c,’f c o n f i d e n c e level.
x
Chapter 1
Introduction
According to the standard model, the fundamental particles of the universe
consist o f spin-half quarks and leptons which come in at least six “flavors”. Each
particle has an anti-particle counterpart which has the same mass, but opposite
quantum numbers. The quarks and leptons form left-handed doublets and right
handed singlets as shown in figure 1 . 1 .
Interactions among these fundamental particles are of four types: strong, elec­
tromagnetic, weak and gravitational.
The strong interaction originates from a hidden “color” charge carried by quarks
and the theory of the strong interaction is known as Quantum Chromodynamics
(QCD). Leptons do not carry color charges and therefore are not affected by the
strong interaction. The weak and electromagnetic interactions are low energy man­
ifestations o f a single unified electroweak interaction. The electroweak theory is
1
2
t
u
\
I
\
quark doublets
\ d >L
(u)„ («•), (0. (a)„ (0„ (*),
I
T
‘ in s te t‘
\
lepton doublets
\ U‘ } L
\ V» ) L
\
t L
Figure 1.1: Families of quarks and leptons
based on the SU(2) x U (l) gauge group. QCD combined with this electroweak
theory is referred to as the “standard model”.
In spite of its remarkable successes in explaining a wide range of experimental
phenomena, the standard model still has many problems. It is complicated and
unable to predict fundamental constants such as masses of quarks and leptons, nor
is it able to explain the fact that electric charges of the electron and pToton have the
same magnitude but opposite sign. The family classification of quarks and leptons
is not well understood since m atter is made almost entirely of particles from the
first of the three families, nor is it understood why there are three families of quarks
and leptons. It does not explain the one to one correspondence between the quark
and lepton flavors. Also, the t quark and vT which are required to complete the
third quark and lepton family have yet to be observed experimentally.
Thus experimental tests of the standard m odel are extrem ely important and are
carried out at all the major accelerators today.
The standard electroweak model makes an absolute prediction for the forwardbackward charge asymmetry ( A f ) for the process e+e “ —* ff (where f is a quark or
lepton). Af is due to the interference between the weak interaction mediated by
the neutral boson
and the electromagnetic interaction m ediated by the photon
(figure 1 .2 ). Therefore a direct measurement of Af is an unambiguous test of the
standard electroweak theory. A r is energy dependent and is defined by
*
Nf - N
b
A' - n T + n ^
<»-l >
4
7
Figure 1.2: Feynmann diagrams for e+e~ —> ff: The forward-backward asymmetry
is due to the interference between these two contributions.
where N b- and N» are the number of f ’s produced in the forward and backward
region respectively (figure 1.3). The forward direction is defined by the direction
of the e~ beam.
This dissertation describes the measurement of the forward-backward charge
asymm etry (A b) for the process e+e _ —» bb at TRISTAN by the AMY detector.
A measurement of the ratio of the cross-section for e +e - —> bb to the lowest order
theoretical QED cross-section for e +e~ —> fi+ fi~ (R b ) is also obtained. Rb is given
by
Rb =
<r(e+e “ —►
( i . 2)
)q
ed
Measurements for e +e~ —* bb made at center-of-mass energies of 29 - 43 GeV at
5
Backward
Forward
Figure 1.3: Forward-Backward region
P E P and P E P T R A [l] are shown in figure 1.4. T he best results were obtained by
th e JA D E and MAC collaborations. J A D E ’s result of Ab = —0.228 ± 0.06 ± 0.025
agrees w ith the standard m odel prediction o f —0.252. However, M A C ’s m easure­
m ent o f A|, = 0.034 ± 0.070 ± 0.035 differs from th e standard m odel prediction of
—0.16 (unless substantial B° — B° m ixing is assum ed).
An independent m easurem ent o f Ab by A M Y is therefore tim ely and im por­
tan t. T his m easurem ent by A M Y is also interesting since T R ISTA N operates in
th e center-of-m ass energy region where Ab is exp ected to be at its m axim um neg­
ative value (figure 1.4).
T o p le s s m o d e ls
T h e standard m odel assum s that th e b and t quarks are m em bers of a left-handed
6
1.0
—
_
0.5
TA& O
•
•
*
e
TA #0
ft
ft
♦
dELLO
•Jt
X JADE
ft
«
MAd
ft
X MARK J
ft
8
HRd
•
X PLUTO
ft
■ LB
4 TPd
“
□ TPd
r~
-
-
ft
JO
<
0.0
- 0 .5 I
I
TO0TAN‘0
energy range
-
1.0
—
40
60
80
center-of-m apfp energy (GeV)
Figure 1.4: Forward-Backward asym m etry m easurem ent for e+e" —» bb by previous
experim ents
weak isospin doublet since all the other observed quarks and leptons belong to lefthanded doublets. Hence it is generally accepted th at th e t quark will eventually be
found as higher energy accelerators becom e operational. M eanwhile, th e absence of
the t quarks in experim ental searches has sustained interest in five quarks models.
In the sim plest alternative m odel w ithout a t quark, th e left- and right-handed b
quarks are assigned to weak isospin singlets [2]. Such a m odel predicts Ab to be
zero. T he standard m odel prediction for Ab at a center-of-m ass energy of 57.2 GeV
is —0.58. Therefore the m easurem ent of Ab is also a direct test o f th e viability of
this alternative m odel.
The data were taken betw een 1987 and 1989 w ith an integrated lum inosity of
33.3 p b ~ '. This data sam ple contains 197 m ulti-hadronic inclusive muon events
which were used for the m easurem ent of Ab and Rb .
Chapter 2 gives a short description of the electroweak theory. Chapter 3 de­
scribes the TRISTA N e +e “ accelerator and the A M Y detector. Chapter 4 gives
details of th e selection o f e +e~ —> bb events. Chapter 5 describes the m easurem ent
of Ab and Rb . Chapter 6 talks about future m easurem ents. Conclusions are drawn
in chapter 7.
Chapter 2
Theory
T he electroweak theory is based on the gauge group SU (2) x U ( l) first pro­
posed by S. Glashow [3] to account for the electrom agnetic and weak interactions.
S. Weinberg [4] and A. Salam [5] independently introduced th e Higgs m echanism
to generate m ass for the gauge bosons, thereby making th e gauge theory more
realistic.
This chapter gives a brief description o f the electrom agnetic and weak inter­
actions, their unification, derivation of the differential cross-section and prediction
o f the e +e “ —►bb forward-backward charge asym m etry, Ab . B° — B1* m ixing and
topless m odels are also discussed.
8
2 .1
E le c tr o m a g n e tic th e o r y
Q uantum electrodynam ics (Q E D ) is the quantum theory o f th e electrom agnetic
interaction and its basic form ulation was com pleted by 1930. However, th e calcula­
tion of higher order term s which involve divergences was not resolved until the late
1940’s. T he problem o f divergences was solved by rescaling th e fields so that all the
divergences occur in th e renorm alization o f th e mass and charge o f the electron.
This means that th e terms for the electron m ass and charge were replaced by their
experim entally m easured values.
QED is a guage theory w ith the Lagrangian invariant under gauage transfor­
m ations. A local gauge transform ation is given by
V»(®) -* e,a(lV(*)
ip(x)
—> e~,a^ i p ( x )
( 2 .1)
T he Lagrangian of a free particle
C i = vtpdrf/ — mifiip
(2.2)
is not locally gauge invariant since
=
C\ — iJ>'ytiTf)dtlat(x) = Ci — J ^ a
(2.3)
where J'1 is th e conserved particle current. A dditional term s are needed in order
10
to m ake the Lagrangian gauge invariant. Letting
—> Dp = dp + te J4 M(x )
A tl
►A^
(2.4)
~~9ftOi
(2.5)
where A ^ x ) is som e vector field. T he lagrangian w hen w ritten aB
C = £ l - e J ,,A„
(2.6)
is invariant under gauge transform ation (2.1). T h e gauge field A tl is identified with
th e electrom agnetic potential and e w ith the electric charge.
QED is a theory th at has been vigorously tested by m easurem ents o f Lamb
shift, the hyperfine splitting in hydrogen, the m agnetic m om ents o f the electron,
etc.
2 .2
W ea k I n te r a c tio n
T he weak interaction is responsible for such processes as th e /0-decay observed in
radioactivity.
T he energy spectrum of th e j3 rays (electrons)
was bound
continuous, violating th e conservation of energy and m om entum
to be
if it were a two
body decay phenom enon. W . Pauli (1931) suggested that an unobserved massless
particle m ust be em itted along with the f3 rays (n —►pe" + m assless particle).
E. Fermi (1933) nam ed the m assless particle the “neutrino” and formulated a
weak interaction theory of the form
M =
(2.7)
where A i is the invariant am plitude and G is Ferm i’s constant. J,J and J* are the
charged vector currents which describe th e transitions involving a charge of one unit
in the electric charge (n —♦ p, */«, —►e~ ). Fermi theory is a four-fermion interaction
that does not have a propagator term . T h e am plitude for /9-decay is given by
M = --^=G (p7''n)(l7e7M e)
(2.8)
Observations of th e kaon decays
K —►2 tt ,3tt
led T .D . Lee and C .N . Yang (1956) to propose th at th e weak decay violates par­
ity since these two final states have opposite parities. This was confirmed within
m onths by C.S. Wu. Subsequent experim ents showed th at only left-handed neutri­
nos, 17,, and right-handed anti-neutrinos,
V r ,
participate in th e weak interaction.
If the vj, and v r are the only ones to ex ist, neutrinos m ust necessarily be m assless
since th e scalar m ass term is given by
mipip
IU l +
2
=
m tp
-
m (V'fiV’L + i ’L'Plt)
2
f! U
J I 2
.51
l , I - 7
(2.9)
where 7 5 is the eigenvalue o f chirality with 7 s = 1 corresponding to right-handed
and 7 s = —1 to left-handed. T he “elem entary en tities” o f weak interactions are
therefore m assless and have definite chiralities.
An eigen -state o f finite mass is
obtained by a superposition of the left- and right-handed states w ith equal weight
(2.9). It is possible for electrons to have m ass since left- and right-handed e " ’s exist
12
(figure 1 . 1 ) but neutrinos m ust be m assless if vr does not exist. Charge conjugation
is then also violated because a v L sta te is transformed by charge conjugation to a
V t state. Taking parity violation into consideration, th e am plitude for /?-decay is
re-written as
M (p -> n e+i/t.) =
[p 7 " (l ~ 7 S)n] [?e7i*(l ~ 7 S)e]
(2.10)
I n t e r m e d ia t e v e c t o r b o s o n m o d e l
The Fermi theory violats unitarity (th e requirement that probabilities add up to
unity) in the high energy lim it. A m odification to correct this was first proposed
by Hideki Yukawa (1935). This is the interm ediate boson m odel that was improved
upon by J. Schwinger (1957). T he m odel introduces m assive spin-1 charged bosons,
W + and W “ , to m ediate the weak interaction. T his gives a /3-decay am plitude of
M (n -
p e - P. ) =
(1 - 7 ») n )
(> - V ) ' )
P -H )
where g f y/2 is a dim ensionless weak coupling, and q th e m om entum carried by the
weak boson, which has a m ass of m \y. Comparison betw een ( 2 . 10 ) and (2.11) for
low energies (q 2 <§; m 2v) gives
G
g2
VS “ s k
(212)
T h e fact that a weak decay is weak can now be explained by th e large mass o f the
interm ediate boson. However, at high energy, th e am plitude for e+e “ —» W + W ~
diverges. This problem can be solved by introducing a neutral vector boson W" to
cancel the divergence figure 2 . 1 .
13
a)
b)
e+
W+
W-
e
e
w+
W~
Figure 2.1: Feynman diagrams for e+e" —►W +W"
2 .3
E le c tr o w e a k T h e o r y
S.L. Glashow (1961) proposed using an SU (2) x U ( l) gauge group such th at the
necessary relations betw een the W * and W ° couplings would em erge autom atically.
In doing so, he also unified the weak and electrom agnetic interactions.
Quarks and leptons were assigned weak iBospin and weak hypercharge inter­
nal sym m etries. T he left-handed com ponents of the particles in each fam ily form
a doublet representation of the weak isospin group SU (2) and the right-handed
com ponents are SU (2) singlets (figure 1 . 1 ).
The generators of SU (2) sym m etry obey the algebra
[ T \T j] = i e ijkT k.
(2.13)
T he weak hypercharge denoted by Y has a U ( l) sym m etry and is defined such that
Q = T3 + |
(2.14)
where Q is th e electric charge and T 3 the third com ponent o f th e weak isospin.
T he S U (2) gauge group has 3 generators and U ( l) has 1 generator. So using
S U ( 2 ) x U ( l) introduces 4 gauge fields naturally, one for each group generator. The
gauge fields for SU (2) are
( i= l,2 ,3 ) and U ( l) is BJ,1. T he electroweak interaction
am plitude is then
M = - i g ( j i) " w ^ - i ^ ( j V)', B„
(2.15)
T he isotriplet vector field Wj, is coupled to the weak isospin current Jj, w ith strength
g and
a single vector field B,, is coupled to the weak hypercharge
w ith strength
g '/2 . T he fields
( 2-16)
=
describe m assive charged bosons W ± .
WjJ and B^, are neutral fields.
T he SU (2) x U ( l ) sym m etry introduced by Glashow describes m assless gauge
bosons interacting w ith massless fermions. T his cannot be used to describe the
physical world since th e gauge bosons are m assive. H ence S. W einberg (1967) and
A . Salam (1968) were m otivated to use the Higgs m echanism to generate guage
boson and fermion m asses w ithout destroying the renorm alizibility o f th e theory.
S p o n t a n e o u s s y m m e t r y b r e a k in g
Consider the Lagrangian for a scalar particle
c
=
r - V=
+ JA*')
where A > 0. For ft 2 < 0, th e potential has 2 m inim a satisfying
(2.17)
15
at <f> = ± v with v = y j —fi2f A. In order to use th e perturbation theory, th e expansion
has to be m ade at one o f th e m inim a
4>(x) = v + ij(x)
(2.19)
where rj(x) represents the fluctuations around th e m inim un <j> = v. Expanding the
Lagrangian around <}>{x) gives
£ —
d„i})2 — \ v 2t)3 — ^ V 4 + co n sta n t
( 2 .2 0 )
with th e “generation” of a mass term
m„ =
y/~ 2 p 2
T he physics is not changed by using £
( 2 .21 )
instead o f C. T his process o f using the
expansion o f £ in tj around th e <f> — v m inim um to “generate” m ass is referred to
as “spontaneous sym m etry breaking” .
H ig g s M e c h a n is m
To generate m ass
for th e W ± and TP bosons, the Higgs scalar is introduced. A
lagrangian for the scalar fields is given by
Ci =
j^
+ »pT ■W , , + t t f 'y Bp'j <fr|
( 2 .2 2 )
The sim plest choice o f th e Higgs scalar <j> which is an SU (2) x U ( l ) m ultiplet is
(
4>+
\
(2.23)
<f> =
\*°
/
16
where
4> —
*^2)
<ft° = ^ = (^ 3 + i<f><i)
(2.24)
and 4>, are real.
The Lagrangian can also contain a self-interaction term betw een the Higgs fields
c 2 = - V{<f>)
(2.25)
where
(2.26)
w ith A > 0. For fx2 < 0, th e potential V{<f>) has its m inim um at a finite value of
.2
— 2^
+ $1 + 4>l + <i>4 ) = ~ 2 \
(2.27)
<f>, can be chosen such that
4>i
— <f>2 = <f>4 = 0
(2.28)
<f>(x) is then expanded about
(2.29)
VV /
Due to gauge invariance, the expansion
«*>
=
T 2
(2.30)
{ V + h(x) }
17
can be su bstitu ted into the lagrangian C = C \ + C 2. The relevant term s are [6]
l( - * 9 §
| B M 1
\
9
= (jv a fw jw
“ + £ » “ ( WJ
f W 3" '
-9 9
(2.31)
B„ )
/
t B#1 J
where
W± = f y Wl * lW2)
(2.32)
T h e first term (2.31) is the mass term for the charged bosons W ±
Mu = -vg
(2.33)
T h e term which is off-diagonal in the W 3 and B^ basis is
\ v 2\g2( W 2)2 - I g g 'W 'B " + g'2B„\ = ^ { g U * - g 'B ,} 2 + 0 |j'W « + gB,.)2 (2.34)
R otating to fields given by
A„
=
Z„
=
9 ‘W i + g B , ,
\''g2 + grl
gW Z - g 'B ,
V g i + gn
(2.35)
leads to m ass term s
M. 4
=
0
Mz
=
^ v \J g 2 + g'2.
(2.36)
T h e m asses of the W * and Z° bosons are related by
M \y
g
Mz
g 2 + g'2
=
C O80 ir
(2.37)
18
b
e
Figure 2.2: Feynm ann diagrams for e +e
—* bb
where 6\y is W einberg angle, m easured experim entally to be sin20ir ~ 0.23 [7]. A,,
is identified with the electrom agnetic potential.
2 .4
D iffe r e n tia l c r o ss s e c tio n
The differential cross-section for e +e
d<r
dcos#
—» bb is given by
1
32tts
IM t + M z?
(2.38)
T he invariant am plitudes M 1 and M -z correspond to the Feynm an diagrams in
figure 2.2.
( 2 .3 9 )
19
3g 2
My = —
4 W ^
lb 7 K
~ w
) bJ
gflA— q^qA/M | 0 \ f . A/ (
, n\ 1
+ iMz-rz) l e7 V y ~ ^
) eJ
U a” M|o
(2.40)
The invariant am plitudes M z and M y can also be expanded in term s of rightand left-handed spinors since j ( l ± 7 s ) are projection operators.
Mz
= - W 0 w ( , - Ml. +irz) ^ ( W > » ) + < i L f e W ) ] *
(e/i7^e/?) + 9 l { e Ll 0 e L)]
(2.41)
M ~> = ~ ~ j r [(bK 7 3 b R) + (bi/y^bi,)] ((cRTflen) 4- ( e ^ e t ) ]
(2.42)
where g H = g v - g A, g L = g v + g A and
9v ~ 3.»7r> = ( 9v ~ £. 1) 2(1
T ’) + (£ '’ + £. 1) 2(1 — T5)- H ence the differential cross
sections for definite helicities are
dtr
_ p+
dcos£ Cl e H
3ffct2
(1 4- cos£)2 |Qb + 4x g l;|!
2s
(2.43)
3xa2
d o . _ p+
elt -* bHb L) = 2s ( 1 - cos£)2 |Qb + 4 JC*t|I
dcos£
(2.44)
d<r (
dcos£
d<T
dcos£
where %
bLbH) =
e L -> b |{bL) =
3ttq 2
(1 + cos£)2 |Qb + 4 * g t |2
2s
(2.45)
—►bLb R) =
1e L
3?ra2
cost?)2 |Qb + ^ g u f
2s ( 1 -
(2.46)
a function of s
* (s) =
16cos20\vsin2£\\
s -M |o + irz
(2.47)
T he average over the four allowed L and R helicities com binations then gives
der
dcosd
7TQ2
[R (l 4- cos20) + AcosflJ
2s
(2.48)
20
w ith
R
_
3{Qb — S Q s^ v ^ v R efx ) +
16[(jJ-)2 +
A
=
+ (jJ )2]lx |2}
8 [-6 t? l5 )<,5Re(x) + 48? E,S‘l, J; s i | x | !J.
(2-49)
(2.50)
Integrating (2.48) over dcosd gives,
A'jr/y'^
o,(e+e “ —4 bb) = ( — — )R = <r0R
oS
(2.51)
w here er(J is the lowest order QED cross section. R is then identified as Rb.
T he forward-backward charge asym m etry, Ab is defined as
Ab = —
( 2. 52)
+ <rb
where a> and <rp are the forward and backward cross-section respectively and are
defined as
fO=ir/ 2
<rp=
j
-dcosfl
Jo=u dcosp
f 0=7T der
<*B = I
-j
-zdcosB
J0=jtt/2 dcosv
dcosO
(2.53)
S ubstituting erf and er# into (2.58) gives
A
-
!
b
A
8 Rb
=
3 [ - G Q bg A
e gkAM x ) + * * g v 9 v 9 A9AIxl2] /R b.
T h e differential cross-section for e +e
d(T
7TQ
dcosf?
2s
(2.54)
—» bb then becom es
Rb [(1 + cos2<?)
^ A bcosd .
(2.55)
21
f
Qr
9a
9v
0
2
1
1
2
-1
1
2
+ 2sin 20w ------0.03
u ,c,t,...
2
3
1
2
\ — jjsin20\v ~ 0.19
d ,s,b ,...
1
3
1
2
—5 + §sin 20\v ~ —0.34
Table 2 . 1 : T he Zw —►ff vertex factors in th e standard m odel with sin 20\v = 0.234.
T h e Z° —> ff vertex factors for th e standard m odel are shown in table 2.1. The
weak isospin and hypercharge quantum numbers are shown in table 2 .2 .
Rt, is m odified by QCD term s corresponding to a contribution from gluons
(figure 2.3). T he result in (2.49) is then increased [8 ] by a factor of
1+ ^ + C ,
(2* iy
(2.56)
a„(s) is the “running” strong coupling constant, which is given by [9]
f.
/ t = _________________
12
« s(s)
(33 - 12N r)ln (s/A ! ) ~ \
153 - 19Nrln |li(./A * )n
.
.
(33 - 2N r)Jln (« /A ! ) /
l
)
where A is the QCD scale param eter and Nf is th e number o f available flavors at
the center of m ass energy ^/s. T he constant C 2 is given by C 2 = 1.986 — 0.115Nf
[10]. Nf = 5 for T R IS T A N ’s energy range and the effect of this QCD correction is
to increase Rb by about 5%.
Substituting for the variables in (2.49) and in th e QCD correction (2.56) gives
the standard m odel prediction for Ab and Rb at y/s = 57.2 GeV as —0.58 and 0.56
22
Lepton
T
T3
Quark
t'c l'v jV r ,...
0
-1
eL i/i L irL r
-1
-1
e U i Mi l > r R > '
0
0
•1
-2
T
1
T3
Q
Y
2
2
1
2
a
I
3
dL,SL,bL, ...
1
2
1
2
l
3
1
3
U|1, Cjt^tK,...
0
0
2
3
1
3
dR ,Stt,bR ,...
0
0
1
3
_ 2
3
Table 2.2: Weak isospin and hypercharge quantum numbers o f leptons and quarks
in standard m odel
gluon
Figure 2.3: QCD correction to e +e
—» bb
23
respectively. Here Mz = 91 G eV and Tz = 2.5 G eV .
2 .5
T o p le ss M o d e l
The sim plest m odel w ithout a top quark has the left- and right-handed b quarks as­
signed to singlets. Such an assignm ent for the b quarks is allowed in the SU (2) x U ( l)
m odel. A direct consequence o f this is that g \ becom es zero. Substituting this into
(2.49) and (2.54) gives Aj, = 0 and Rt, = 0.38. This can b e checked experim entally
by the present analysis. A nother distinctive feature o f this m odel is th at the flavor
changing neutral current decay m odes [11 ], B —* X t + l~ where Z* = e± or ji* , are
predicted to have branching ratios of 2%. T his is above the experim ental upper
bound o f 1.3% at 90% confidence level set by the CLEO collaboration [12 ].
A more sophisticated topless m odel was proposed by Ernest M a [13] using Su­
perstring theory. This m odel uses as its gauge group S U (3) x S U (2 )t x S U (2 ) 2 x U (l)
subgroup of E0. T he usual doublet assignm ent is given to (u,d)/, and (c,s)/, under
S U (2 )i. A new doublet is assigned to (c,b )« under S U (2 )2. b/, is assigned a singlet
under both SU (2)j and S U (2 )2. b n is a singlet under 811(2)!. There is no need for
a top quark in this m odel. T he flavor changing neutral current m odes are greatly
reduced by this enlarged m odel [14] and th e decay m ode B —» XZ+ Z” is consistent
with experim ental upper lim it. T he axial-vector coupling gb is zero in this m odel.
T he observed forward-backward charge asym m etry in e +e “ —> bb is explained by
introducing a new neutral scalar boson <f>and a new heavy charged lepton E . These
24
r,b
E
<f>
t
r ,b
,
b
r,b
T ib
r,b
*
Figure 2.4: One loop am plitudes contributing to e +e
—►bb
new particles contribute to e +e~ —►bb as shown in figure 2.4.
T h e asym m etry At, is given by [15]
=
©
© (s^y
(®) - ® &
where p i, g2 and p3 are Yukawa couplings and m £• = m^ = m.
)
<*•«>
s is the square
o f the center-of-m ass energy and G f is the Fermi constant. T he phenomelogical
requirement is for
© ©
^
~1
<«•>
T he m asses of cf> and E are exp ected to be much less than 100 G eV , otherwise the
Yukawa couplings plt g2 and pa would have to be very big to be consistent with
(2.59). A search for <f>and E were m ade at TR ISTA N [16] but they were not found.
T he charge asym m etry, Ab, for this Superstring m odel can still agree with the
d ata depending on the as y et undeterm ined param eters in (2.57).
2 .6
B ° —B ° m ix in g a n d its e ffe c t o n Ab
T h e neutral B° m esons are m ade from charge-conjugate quark-antiquark pairs
(BJj (bd), B^j (b d ), B ” (b s), B^ (b s)). So flavor-changing neutral current weak
interactions can m ix these states. T he box diagrams for B° — B ° m ixing are shown
in figure 2.5. The eigenstates are
B,
=
B2 =
- j = [< B'J > + < BU > ]
and
- ^ [< BS > - < BS > ] .
(2.60)
T he m ass difference between these two eigenstates is A M . For sim plicity, the
lifetim e and total decay w idth T o f B t and B 2 are assum ed to be equal. T hen, for
a sy stem w hich is en tirely B ” a t tim e zero, I b (0) = 1, th e in te n sity I |j( t) to find it
!■| |
in a B s ta te a t tim e t is
(2.61)
M O = 2 e ~ '(1 - c o s A M t )
W
Bd
u,c,t
u ,c,t
u ,c,t
W
Bj
b :i
u ,c , t
Figure 2.5: B ox diagrams contributing to B j — Ifj m ixing
26
A m ixing param eter is defined by * = A M /I 1. Appreciable mixing only oc­
curs for large x. T he integrated transition probabilities are given by th e mixing
parameter r.
r(B S _ BS)
d
r(B 3
BJ)
2 + *=
1
’
where 0 < r < 1. Frequently the param eter x >s used instead of r where
r ( B 3 — j% )
r(B;i
BJ) + r<B 3
r„
b ;)
1 + Id
where 0 < x</ < 0.5. The standard m odel predicts [17] rj ~ 0.02 — 0.05 and r„ ~
0.12 — 0.75 (r„ is for B's’ — B^,' m ixing).
E ffect o f B ° — 1? m ixing on Ab
The ratio of production o f B * : B[j : B , is exp ected to be about 3:3:1 in e +e~
annihilation at TR ISTA N energies. This is deduced from th e 3:3:1 ratio for the
production o f quark pair (uu : dd : ss) from color fields.
T he B° — B° m ixing
param eter x is defined by
r(B“ —►Bj —►X)
Xd ~
Xd
T(B[] ^ X or X ) '
The average x is then
X = jX d + yX»
(2.64)
Charge conservation dem ands that there is no m ixing for charged m esons. The
range of possible values for Xd and x» is from 0 to 0.5. T he best m easurem ent of
X,i are given by CLEO [18] (xd = 0.123 ± 0.048) and A R G U S [19] (xd = 0.167 ±
0.055 ± 0.046).
27
In the presence of B° — B° m ixing a fi~ is som etim es produced from an initial
b-quark, thereby confusing th e quark identification.
C onsequently th e observed
numbers o f forward and backward events becom e
N | 7bs = N f - X N f + X N b
N'b1" = N b - XN b + X N f
and the observed asym m etry is
'b s
]tfr>bs
Ab>, = i # T N ?
= ( 1 " 2 x )A b -
(2 '65)
If one varies Xs from 0.0 to 0.5 and varies Xd within errors given by th e A R G U S and
CLEO results (0.075 <
< 0.239), the effect of B u — B^ m ixing is to reduce the
m agnitude of th e observed asym m etry by 6 % to 36%. Conversely, by measuring
and using th e standard m odel predicted value o f Ab, one can m easure or set a
lim it on x .
Chapter 3
The AMY Experiment
T he A M Y [20] experim ent is a collaboration o f physicists from five countries',
th e U SA , Japan, the People’s Republic of China, Korea and from 1989 the Phillipines (see appendix A for list of collaborators). A M Y is one o f four collaborations at
T R ISTA N (Transposable Ring Intersecting STorage Accelerator in N ippon) which
is an e +e - collider located at KEK (Kou Enerugii Butsuri-gaku K enkyuu-jyo or
N ational Laboratory for High Energy Physics) in T sukuba City, Japan. T he other
three collaborations at T R ISTA N are th e V E N U S and TO PAZ general purpose
e +e" experim ents and the specialized SHIP detector. T his chapter gives a brief
description of T R IST A N and the AM Y experim ent.
28
29
3.1
T h e T R I S T A N e+e" c o llid e r
TR ISTA N [21 ] consists o f a positron generator, an electron linear accelerator
(L IN A C ), an accum ulation ring (A R ) and a m ain ring (M R ). Figure 3.1 shows the
site layout of TR ISTA N .
Positrons are generated by e +e - pair creation processes when a 200 M eV , 10 am ­
pere, electron beam strikes Tantalum . The positrons are collected and accelerated
to 250 M eV , then transferred to the LINAC.
The 400 m long LINAC accelerates the electrons and positrons to 2.5 GeV
where they are injected into th e A R . T he A R has a circum ference of 377 m. It
accum ulates the electrons and positrons and when currents o f about 10 mA of
electrons and positrons are accum ulated, the A R accelerates them to 8 GeV and
feeds them into the MR; first the positrons then th e electrons.
The M R is buried 11 m underground and has a circum ference of 3 km . It consists
of 4 straight sections of 200 m each and four curved sections o f 550 m each. The
center o f each straight section is where the beam s are m ade to collide. T he A M Y
detector is built around one such collision point in th e OHO experim ental hall. T he
three other experim ents, V E N U S, TOPAZ and SHIP, occupy th e FU JI, T SU K U B A
and NIKKO experim ental halls respectively.
In th e M R, electrons and positrons are grouped into two bunches. A typical
bunch size is about 2.3 m m along the x axis, 0.023 mm along th e y axis and 1.17 mm
along the z axis. The z direction at the A M Y detector is defined as th e direction of
30
TRISTAN MAIN RING
NIKKO EXP. HALL
(S H IP )
TSUKUBA EXP. HALL
(T O P A Z )
TRISTAN
ACCUMULATION RING
OHO EXP. HALL
(A M Y )
A
12 GeV PS
FUJI EXR
HALL
(VENUS)
BOOSTER
UTILIZATION
PHOTON FACTORY
2.5 GeV
ELECTRON
STORAGE RING
FACILITY
2 .5 GeV
ELECTRON LINAC
POSITRON GENERATOR
300 M
Figure 3,1: T h e site layout of T R IST A N
31
the e~ beam and the y direction is perpendicularly upward. Beam crossings occur
once every 5.0 /ts and the beam energy spread iB cte/E = 1.64 x 10 - 3 (r.m .s.). This
rather large beam spread is due to the small bending radius at th e curved sections.
The first electron-positron collision occured on Novem ber 14, 1986 at a center
o f m ass energy o f 50.0 G eV . Since then a center of m ass energy of 61.4 GeV has
been achieved and an integrated lum inosity of 33.3 pb -1 was accum ulated by July
1989.
3 .2
T h e A M Y D e t e c to r
Electron-Positron annihilation at high center of mass energies results in the pro­
duction o f m any particles which are either charged or neutral. T hese particles m ove
away from th e interaction point in all directions. T he short-lived ones quickly decay
into more stable particles within a few m illim eters.
A M Y is a general purpose particle detector that tracks and m easures the energy
and m om enta of the particles em erging from the interaction point. Figure 3.2 shows
the isom etric and cross-sectional views of the AM Y detector which is optim ized for
lepton identification. It is an extrem ely com pact detector (about 120 m 3 compared
with 600 m'* for V E N U S .) The z direction at th e A M Y detector i 6 defined as the
direction o f th e e~ beam and the y direction is perpendicularly upward. T he r, <j>
and 6 coordinates are define for the cylindrical coordinate system .
T he tracking of the charge particles in th e barrel region is done by the central
AMY DETECTOR AT TRISTAN
NU UM
M
IT
(b)
Muon Chombcr
’f i r
Vacuum Pim p
-Bam Plpa
-O b M M ad Ian fta a p
‘ ' i Untocrty UonDar
■law TmUni
f
S j b e
Qantmt
■ N l Tip Courtr
■CaM (Ml (Tartar
■X-i*f O artar
■Ah* W i C a rta
'Show Couilir
■ iw rnrtlrtn j U n U Call
-M op* YtM/Hrtan Abwbar
Figure 3.2: (a ) The isom etric and (b ) cross-sectional view s o f AM Y
33
drift cham ber (C D C ) and th e charge particle m om enta are calculated from the de­
flection in the 3 Tesla m agnetic field produced by the superconducting m agnet. The
electrom agnetic shower counter (SH C ) provides energy m easurem ent for gam m as
and electrons, and also identifies the electrons.
T he m easurem ent o f Ab described in this thesis depends on th e detection and
identification of m uons. This is done by th e muon identification system (M U O )
com prising th e thick hadron absorber, muon chambers and counters.
T he following sections give a brief description o f the various com ponents of
A M Y and its principle o f operation.
3.2.1
In n er Tracking C h am b er (IT C )
T he IT C is a drift cham ber located ju st outside the beam pipe, which detects
charged particles after they have traversed only 1.7% radiation lengths o f m ate­
rial. T he ITC is designed to determ ine the vertices o f charge tracks and also to
help provide an efficient trigger for events of interest while m inim izing triggers on
background. T he ITC consists of four layers of cylindrical plastic tubes. The in­
nerm ost and outerm ost layers are 12.2 cm and 14.2 cm from the beam axis (z-axis)
respectively. Each of the tubes is 55 cm long with a radius o f 3m m and is aligned
parallel to th e beam axis. At the center of each tube is a 16/xm diam eter anode wire
stretched th e length of th e tube. A voltage of - f 1700 is applied to th e anode wire.
The inside surface o f the tube is coated with aluminium to provide th e cathode.
W hen a charge particle passes through th e gas in a drift chamber, it liberates
electrons by ionisation. T he electrons drift towards the anode wire and the position
of th e ionisation is calculated from th e tim e it takes for th e electrons to drift to the
anode wire. Position m easurem ent in the ITC is therefore achieved in th e plane
perpendicular to the beam axis (r — <j>) and has a spatial resolution of <r ~ 80/im .
T he staggered arrangement of the layers makes it possible to determ ine whether a
charged particle passes by the right or left of a hit wire. This is com m only called
th e resolution of left-right ambiguity. T he ITC is filled w ith 50% Ar and 50% C^Hr,
and th e gas is pressurized to 1.48 k g /c m 2.
T h e signals are read by tim e-to-analog converters (T A C ) and analog to digital
converters (A D C ). TAC signals are used to determ ine th e hit position and ADC
signals are used for rejecting noise signals in the TAC. A cross-sectional view o f the
ITC is shown in figure 3.3.
3 .2 .2
C en tral D rift C h am b er (C D C )
T he C DC is th e main com ponent of the A M Y detector for tracking charged parti­
cles. Figure 3.4 shows a schem atic diagram o f the CDC. T he CDC consists o f 40
cylinders of wires forming six bands. It is outside the ITC radially and extends to
a radius of 65 cm . T he length of the bands increase radially outwards to m aintain
an angular coverage of |cos0| < 0.87. There are 9,106 sense wires and 22,966 field
wires. Each sense wire is in the m iddle o f a cell surrounded by six field wires in a
^ 8 ure 3-3: Cross-sectional view of ITC
hexagonal arrangem ent. T he advantage o f th e hexagonal arrangement is th at the
contours o f equal drift tim e around a sense wire are concentric circles even in a mag­
netic field as shown in figure 3.5. T h e sense wires are m ade o f gold plated tungsten
w ith a radius o f 10 fim and the field wires are m ade of gold plated alum inium with
a radius of 80 fim. There are two kinds o f sense wires; axial and stereo. The axial
wires are arranged parallel to the beam axis and th ey track th e hit positions in the
r-<f> plane. T he stereo wires are strung at an angle of 4° to th e axial wires, enabling
th e tracking o f charged particles trajectories in the z direction. Altogether there
are 25 cylinders o f axial and 15 cylinders of stereo wires in the CDC. The CDC
was filled with HRS gas (89% Ar, 10 % C O 2 and 1 % C H j) at atm ospheric pressure.
The gas was changed to n eon /eth an e (50%:50%) after th e installation of the x-ray
detector in May 1989. (A ll data accum ulated after run 6899 were taken with the
n eon /eth a n e m ixture. This includes som e of th e 60 G eV data, and all o f 60.8 and
61.4 G eV d ata.) Neon absorbs fewer of th e synchrotron x-rays than argon due to
its sm aller atom ic mass number. The switch to n eo n /eth a n e was therefore m ade to
increase the effeciency of th e X-ray detector. T he 50%:50% m ixure of n eon /eth an e
is chosen so th at th e drift velocity and gas gain characteristics are similar to those
for HRS.
Charged particles follow a helical path in the presence o f the 3 Tesla m agnetic
field.
T he CDC track finding software reconstructs the trajectory o f a charged
particle by grouping th e hit positions in the C D C . T he m om entum and charge of
Myl ar foil
Romacel
foam
A l u m i n u m foil g r o u n d p l a n e
4 .9 '
( 6 Cor bon Fi ber
su p p o r t p o s t s - n o t shown)
4 .5 ‘
O':
-.4m
4.B'
O*
i t t r t o 4.1*1
Axiol 0*:
1.5 m m C a r b o n F i b e r i n n e r t u b e
+ -
IP
- +
—
.2 m
• 4- —
- + —
.4 m
i6 m
,8m
Figure 3.4: Schematic Diagram of CDC
.+
Im
38
(*) B = 5 Teals (10 w ee drift lime contours)
(b ) B - 3 Tesla (10 nsec drift tim e contours)
Figure 3.5: Countours o f equal drift tim e for CDC
39
these particles are determ ined from the curvature o f th e reconstructed trajectory
in the i-</> plane. T he tranverse m om entum is given by
p, = 0.29979qBR
(3.1)
where q is th e charge of the particle in units o f electron charge, B th e m agnetic
field in tesla and R th e radius of curvature of th e fitted trajectory in m eter. The
minim um p t required of a charge track to reach the outside o f th e CDC is of the
order of 300 M eV.
The software includes the effect of non-uniform ity in the m agnetic field. The
spatial resolution was a ~ 170/xm and m om entum resolution was A p ,/p , — 0.8%p,
( p, in G e V /c ). p, is the com ponent of the m om entum in the r-^ plane.
3 .2 .3
X -R a y D e te c to r (X R D )
The X RD is designed to d etect synchotron x-rays produced by electrons as they
pass through the 3 Tesla m agnetic field. Energy em itted in synchotron x-ray is
inversely proportional to th e fourth power o f the charged particle’s m ass,
I
Radiated power o c
E 2B 2
—m*
T he electron being the lightest charge particle em its m ore energy than other charge
particles and the X R D [22] provides a m eans for distinguishing electrons from
hadrons. For exam ple, a 10 GeV electron em its 1.3 M eV /m in th e 3 Tesla m agnetic
field while a 10 GeV pion only em its 2 x 10- ,e v /m .
40
T h e X R D consists o f 3 m odules, covering polar angles from 37" to 143". It oc­
cupies th e space betw een the CDC and SHC. Figure 3.6 shows a schem atic diagram
o f a m odule o f the X R D . This detector was not installed until th e spring of 1989
and was not used in this analysis.
3.2 .4
B arrel Show er C ou n ter (S H C )
T he SHC is an electrom agnetic calorimeter which m easures th e energy deposited
by electrons, positrons and photons. It is comprised o f tw enty layers o f gas pro­
portional tubes interposed with lead. W hen a charged particle passes through the
gas, it causes ionization and produces electrons. Charged and neutral particles can
also interact w ith the lead to produce secondary charge particles which can ionize
the gas. The electrons from the ionisation drift towards th e anode wire which is
m aintained at a high voltage. These electrons gain kinetic energy T from the elec­
tric field and when T is greater than th e ionization energy o f th e gas, fresh ions are
produced. A chain of such processes leads to an avalanche o f electrons and ions.
The total num ber of secondary electrons reaching th e anode is proportional to the
num ber of initial ions, hence th e nam e proportional counter. T he secondary ions
produced have lower mobility. T hey drift toward th e cathode and do not cause an
avalanche. This signal induced on adjacent cathode strips can be used to determ ine
the position o f the avalanche.
41
999999
Figure 3.6: Schematic Diagram of XRD
42
P article Identification
Electrons and photons
An electron or photon loses energy quickly in m atter by C om pton scattering,
brem sstrahlung (e —♦ erf) and pair creation (7 —►e +e" ). T hese process repeats itself
until there is no longer enough energy left for further reactions. This cascade is
called an electrom agnetic shower and th e electron or photon deposit eventually all
o f their energies in the SHC. A “good” SHC particle is one w ith energy greater
than 200 MeV and with not more than 95% of its energy deposited in any one of
th e five longitudinal layers. A “good” SHC particle which is m atched to a CDC
track within 2 ° is considered to be charged shower, otherwise it is a neutral shower.
Electrons are charged particles, hence an electron shower can be m atched to a CDC
track. Photons, being neutral, do not leave any track in the CDC.
Electrons and charged pions
Electrons and charged pions are distinguished by their shower energy to CDC m o­
m entum (E /p ) ratio and by their shower developm ent profile. T he developm ent
of an electrom agnetic shower is a statistical process. T he radiation length for an
electrom agnetic shower in lead is 0.56 cm whereas the nuclear absorption length in
lead is 17.09 cm [23]. One radiation length is the distance over which th e electron
energy is reduced by a factor of e (67%) due to radiation loss (brem sstrahlung)
only. One nuclear absorption length is the distance over which a particle such as a
pion loses its energy by a factor of e by nuclear collisions. Hence electrons tend to
43
deposit their energies in th e first few layers o f the SHC while pions tend to shower
deeper into the SHC. E /p for electrons ~ 1 due to electrom agnetic shower in the
SHC while for pions E /p
1 (unless th e pion charge exchanges: jt^ —* 7ru).
Neutral pions and photons
Neutral pions decay to two photons which cause electrom agnetic showers. In the
case o f low energy pions, th e pion invariant m ass can be reconstructed from the two
showers produced. T he showers from high energies pions are not easily resolved, but
are characterized by a large lateral spread. This can often be used to distinguish
th e pion showers from single photon showers.
D escription o f SHC
Figure 3.7 shows an overview o f the SHC. Figure 3.8 shows th e detailed view of
one layer, figure 3.9 shows th e longitudinal segm entation and figure 3.10 shows the
layout of the phi and th eta pads.
T he SHC consists of six sextan ts which form
a cylinder with an inner and outer radius o f 79 cm and 110 cm respectively. It is
220 cm in length covering the polar angle of |cosfl| < 0.74. Each sextant has twenty
layers of gas proportional tubes m ade of resistive plastic material interposed with
lead. The first sixteen layers o f lead are 3.5 m m thick and the last four layers are
7 m m thick. T he total thickness corresponds to 14.4 radiation lengths. The gas in
the proportional tubes is 49.3% Ar, 49.3% CjHe and 1.5% C 2H 2OH, m aintained at
atm ospheric pressure.
SHC signals are read from both the anode wires and cathode pads which are
Figure 3.7: Overview of th e SHC
3.5 mm
LE A D
CATHODE R E A D O U T L I N E S
G-IO
£
JJO. 86mm
^
P A D S " ''
RESISTIVE
PLASTIC
TUBES
t
anod; wire
I
I
7 mm
1
^B PADS-^
6-10 [
L 0 .8 6
CATHOOE R E A D O U T L IN E S
3.5m m
LEAD
F ig u r e 3 .8 : D e t a il e d v ie w o f o n e la y e r o f S H C
45
■ ^ o p tim ized
4 layers
4 layers
4 layers
4 layers
4 layers
optimized
for 7r/e
j
for y / i r °
optimized
for 7r/e
Figure 3.9: A longitudinal segm entation o f SHC
110cm
11Ocm
^
60'
(8 3 .7 cm)
mrad
0 .3 8 4
rad
0 .3 8 4
Phi Pads
60"
(8 3 .7 c m)
2 2 0 cm
Th«ti Pads
F ig u r e 3 .1 0 : T h e p h i a n d t h e t a p a d s o f S H C
46
etched on G10 boards. Four layers o f cathode signals are ganged together to give
a total o f 5 gangs per sextant. T he anode signals in each layer axe also ganged
together to give a total o f 48 azim uthal towers. High voltage is applied to the
anode wires.
There are tw enty four 55Fe sources em bedded in th e SHC. M onitor tubes are
used to read their signal. This data is used to correct for fluctuations o f SHC signals
due to changes in gas pressure, tem perature and com position.
T he cathode pads measure the shower position with a precision o f 3 m m or
about 4 mrad in angle. T he electron identification efficiency is 87% for isolated
electrons and 70% for electrons in a jet. T he energy resolution is
~
4 . Q%
(E is in G eV ). T he minim um energy for a “good ” shower cluster is 0.2 GeV.
3.2.5
S u p er C o n d u ctin g M agn et
T he high field 3 Tesla superconducting m agnet (24] allows the A M Y detector to
be com pact while achieving good m om entum resolution for charged tracks. The
com pactness of A M Y also m inim izes th e number o f muons from the decay of pions
and kaons. T he probabity of decay is proportional to the path length and is given
by
Prob ~ 5 2 ^
for m 0L <
(3.2)
rE where L is th e average distance th e pion or kaon travels before
interacting, r the m ean lifetim e, E and mo the energy and invariant m ass of the
47
decaying m eson.
The m agnet coil was m ade with a superconductor (N b T i) wound into an 8 layer
cylinder. T he inner radius is 1.195 m , the outer radius is 1.29 m and the length
is 1.54 m . The m agnet weighs 17 tons and is cooled by liquid helium . During
operation, a current o f 5,000 amperes runs through th e coil producing a 3 Tesla
field in the central region.
Figure 3.11 shows the NM R m easurem ent of the m agnetic field in the central
region.
Figure 3.12 shows the deviation of th e m easured field from th e field as
calculated by the com puter program, PO ISSO N , and figure 3.13 shows the m agnetic
flux lines as calculated by PO ISSO N .
3.2.6
M u on D e te c tio n S y stem (M U O )
The Muon D etection System is the primary responsibility of the Louisiana State
U niversity group. The author was responsible for its m aintenance and repair from
March 1988 to January 1990.
The muon identification system consists o f the hadron absorber, a high efficiency
muon drift chamber for position m easurem ent and scintillator counters for time-offlight m easurem ent.
48
30000-
2 29000 -
20000
•soo
500
-250
Z (Ml
Figure 3.11: NM R m easurem ent of the m agnetic field in the central region
i.o0. 3 -
Z (an)
Figure 3.12: D eviation o f th e m easured field from th e field
I
uotus la I
2
F ig u r e 3 .1 3 : M a g n e t i c f l u x li n e s a s c a l c u l a t e d b y P O I S S O N
49
H adron A bsorber and Drift Cham ber
M uons do not interact strongly like hadrons nor produce electrom agnetic show­
ers like electrons.
T he design o f a m uon d etector is therefore based on muons
penetrating thick m aterials w ithout interaction, other than ionization. A hadron,
on the other hand, tends to undergo inelastic nuclear collisions w ith nuclei in the
m aterial resulting in the production of secondary hadrons. T he secondary hadrons
can again interact inelastically to produce more hadrons. One interaction length
for a hadron in iron is about 16.8 cm . Few hadrons therefore will penetrate a thick
iron absorbere.
Electrons are even less likely to p enetrate because o f the short
radiation length of iron ( 1.8 cm ).
T h e hadron absorber, consisting o f the SHC m aterial, the superconducting m ag­
net coil and th e return yoke, has an average thickness o f 165 cm equivalent o f iron.
This corresponds to over 9 nuclear absorption lengths. Figure 3.14 shows th e thick­
ness o f th e hadron absorber in term s of absorption length.
There are six sextants of drift cham bers and scintillation counters located ou t­
side th e m agnet return yoke. Figure 3.15 showB th e m uon chamber configuration.
There are a total of 1,184 drift tu b es, each w ith a wire at th e center. T he chambers
were assem bled from alum inium m odules. Each m odule consists o f 4 tubes m ade by
K obe Steel using the extrusion m ethod. T h e m odules were welded together to make
th e different planes. Figure 3.16 shows an endview o f tw o m odules put together.
Each tube has a cross-section of 10cm x 5cm . At its center is strung an anode wire
ABSORPTION
LENGTH
50
X
I
O.l
0.3
0.5
0.7
lcos£l
F ig u r e 3 .1 4 : T h ic k n e s s o f h a d r o n a b s o r b e r i n t e r m s o f a b s o r p t io n l e n g t h
o f gold plated tungsten. T h e anode wire has a diam eter o f 100 m icrons. M odules
on adjacent planes are w elded together w ith a 5 cm (half-cell) offset. This offset is
necessary for determ ining w hether a m uon passed to th e left or right side o f a wire.
T he m odules are welded together to form each sextant. Each sextan t has 4 layers
o f drift tubes with layer 1 and 2 having anode wires strung perpendicular to the
beam axis. T hese m easure the z position of the hits. Layer 3 and 4 have wires in
th e direction along th e beam axis. T h ey m easure the x position o f the hits. The
y position o f the hit is determ ined from th e geom etry o f the M UO. Layer 1 and 2
have 64 wires each. For layers 3 and 4, sextants 1 and 3 have 36 wires per layer,
sextan ts 2 and 5 haVe 40 wires per layer and sextants 4 and 6 have 28 wires per
layer. Each sextant o f drift cham ber is 6.5 m long and 2.8 m to 4.1 m in width.
T h e drift cham bers cover a polar angle o f |cos0| < 0.74.
H igh Voltage an d . Threshold Voltage
T h e high voltage here refers to the potential difference betw een the anode wire
o f th e m uon drift cham ber and th e alum inium wall which provides the ground.
Threshold voltage refers to th e m inim um voltage required of a signal on the anode
wire before it can be considered a hit. A stud y was m ade o f chamber efficiency as
a function o f high voltage and threshold voltage [25] using cosm ic rays. T he results
are given in figure 3.17 which shows (a ) th e wire hit efficiency and (b ) the hit-pair
efficiency. T he wire hit efficiency is the efficiency of a single wire to register a hit
w henever a cosm ic ray particle passes through, and the hit-pair efficiency is the
52
r
i
Figure 3.15: Muon chamber configuration
400mm
cJ /EXTRUDED ALUMINUM
100
*-2.3 •
CELL
F ig u r e 3 .1 6 : E n d v ie w o f t w o m u o n c h a m b e r m o d u l e s w e ld e d t o g e t h e r
53
efficiency of a pair of adjacent wires in different layers (layers 1-2 or 3-4) registering
hits whenever a cosm ic ray particle passes through. T he wire hit efficiency levels
off at nearly 100% and the hit-pair efficiency at 98.5% at a high voltage of around
3,000 volts with a threshold voltage of 0.8 volts. T h e wire hit-pair efficiency can
never be 100% due to the finite size o f the cham ber cell walls which are 2 m m thick.
Because a low threshold voltage tend to introduce m ore noise in th e signal, the
high voltage and threshold voltage were set at 3,100 volts and 1.5 volts respectively
during data taking.
Finding a muon track
A muon track is defined as one which has hits in at least three of th e four layers of
th e muon drift cham ber, w ith two of the layers (1-2 or 3-4) having adjacent hits.
Allowed com binations are shown in figure 3.18. T he position of a m uon track is
determ ined from th e hits and their drift tim e. Consider th e z position o f the track
which is determ ined for the hits in layers 1 and 2. Since the distance betw een two
anode wires in this direction is 5.0 cm , th e z position o f th e m uon track is defined
as z = z\ 4- zcor where
+5-0 x
if », > *,
zcor =
(3.3)
“ 5-0 x
if z 2 < z i,
where Zj and z 2 are th e position of the hit wire in layer 1 and 2 respectively, and
t ( and t 2 are the drifttim es
o f the hits in layer 1 and 2 respectively. The positions
of the anode wires are obtained from
a survey o f th e detector. T h e x position
is
54
Hit efficiency
M .9%
100
efficiency %
H it-p air efficiency
'
100
80
80
80
80
40
40
20
20
2.8
2.8
3.4
HV (KV)
2.8
3 .2
HV (KV)
Figure 3.17: W ire hit and hit-pair efficiencies for M UO
3.4
similarly determ ined. In th e case of only one h it wire in layer 1-2 or layer 3-4 pair,
the hit position is taken as the position of the hit wire.
T he spatial resolution
was measured by using vertical cosm ic ray tracks prior to in stallation and found to
be 1 m m . T he spatial resolution after installation will not be &b good since there
is no correction for tracks transversing the M UO at an angle. In th e w o n t case
(ii or t >2 = 0 and the track makes an angle o f 45°), the error can be up to 25 mm.
Gas System
P10 gas (90% Ar -f 10% CH i) flows through th e drift chambers at a total rate of
about 1 litre per m inute. Figure 3.19 shows a schem atic diagram o f the MUO gas
system . The P10 gas is passed through a high pressure regulator and a gas filter
to the input m anifold. From there, each sextant o f the M UO gets its gas from a
separate 1 /2 inch rubber tube. Figure 3.20 shows th e flow o f the gas within each
sextant. T he gas pressure inside the drift chamber is m aintained at about 2 inches
o f water above atm ospheric pressure.
M uon Scintillator Counter
T he scintillator counters are the outer-m ost com ponent o f the A M Y detector in
the barrel region. There are a total o f 159 plastic scintillator counters distributed
over six hexagonal sextants having the sam e geom etrical acceptance as the drift
cham ber. Photo-m ultiplier tubes m easure th e light produced by charged particles
passing through the scintillator counter. The output signal is fed into CAM AC
56
3 out of 4 layers
4 out o f 4 layers
3 out o f 4 layers
extra hits
F ig u r e 3 .1 8 : A llo w e d c o m b i n a t io n s o f M u o n t r a c k s
Flow m eters
High
Pressure
Regulator
P10 gas
Gas M onitor
Low
Pressure
Regulator
Filter
Gas Monitors
Input Manifold
half inch gas line
M UON
C H A M BE R
Gas Monitors
Flow M eters
Flow M eter
O utput Manifold
Out
Gas Trap
F ig u r e 3 .1 9 : S c h e m a t ic D ia g r a m o f M U O g a s S y s t e m
58
O ut to
next layer
Figure 3.20: Gas flow w ithin each sextant of MUO
discrim inators, those signals above th e discrim ator threshold are then fed toTim eto-A nalog Coverters.
The tim e o f flight of penetrating particles relative to the
beam crossing tim e is thus m easured. Using th e position inform ation from the drift
cham bers, a tim e resolution o f 3 ns is achieved. This tim e inform ation is used to
reject background from cosm ic rays.
3 .2 .7
E nd C ap D e te c to r
T he End Cap D etector consisting o f the Ring V eto Counter (R V C ), th e Pole Tip
Counter (P T C ) and th e Small Angle lum inosity M onitor (SA M ) covers both ends
of the A M Y detector.
T he PT C consists o f two lead scintillator calorim eters w ith a total thickness
o f 14 radiation lengths and on e.layer of proportional tubes sandwiched between
them . It is designed to measure the position and energies of showers in th e region
14.6" < 9 < 26.6°. The spatial resolution is 0.2° in th e th eta direction and 0.8°
in the phi direction. The PT C measures lum inosity w ith a 3% system atic error
using B habha scattering events.
m inim un ionizing particles.
I t’s efficiency is optim ized for th e detection of
T he lum inosity inform ation waB used to normalize
th e M onte Carlo sim ulated events that were used for comparison with the data
and also to obtain the cross sections of various processes.
Figure 3.21 shows a
schem atic drawing of the P T C and figure 3.22 shows the integrated lum inosity per
day collected by A M Y as m easured by the P T C during th e 1989 Bummer run.
The RVC was designed and built by P. Kirk of Louisiana State University. It
covers th e region 26" < 6 < 38". The RVC was m ade o f tw o layers o f lead sheets
and scintillators, w ith a total thickness of 3.6 radiation lenghts. The CDC covers
th e region 29.5" < 6 < 150.5" and th e SHC 42.3" < 9 < 137.7". T he RVC was
designed to provide shower inform ation for CDC tracks entering the region ju st
beyond th e reach o f the SHC. Electrons and m inim um ionizing particles can be
distinguished from a comparison of their deposited energy in th e RVC. The energy
resolution is 70%.
The SAM is used as an instantaneous lum inosity m ontior. It consists o f four
calorimeters made o f B aF 2 cystals. Each o f the calorimeter has a cross-section of
4 cm x 6 cm . A photodiode is attached to th e rear of th e B a F 2 crystals to collect
light from each m odule. T he geom etrical acceptance o f 4° < 9 < 6° is defined by
5 m m thick plastic scintillators located at the front o f th e calorimeter.
60
light f » H «
HLS bars
»tr
{ ran t ■action
»■ e t l o
n
viiiil wall
•clntlllator
laid
anoda w l r a
raaiatlva
p l a i t l o tuba
eathoda s t r i p b o a r d
u
poaltlon d a t a e t o r
Figure 3.21: Schematic plot of the PTC
INTEGRATED LUMINOSITY P E R DAY
AMY
1
(POLE TIP COUNTER)
L-
8B88.1 Bb~‘
200
160
100
60
/a
140
,6 /2 1
e/i
160
,7 /1
.7 /1
160
DATE (FROM l- J A N - 8 9 )
F ig u r e 3 .2 2 : I n t e g r a t e d L u m in o s it y p e r d a y d u r in g s u m m e r 1 9 8 9 r u n
61
3 .3
T r ig g erin g a n d D a t a A c q u is itio n
A beam crossing signal sent to th e Online com puter from TR ISTA N control “opens
th e beam ga te” for 1.5 ps from the tim e o f beam crossing. T h e triggering system
[26] is activated whenever the beam gate is opened so th at eventB o f possible interest
are stored. A beam off gate is opened for 1.5 fis after the beam crossing to provide
cosmic rays trigger for background studies.
Figure 3.23 shows th e list of triggers used for selecting data. The triggers that
are im portant for selecting m ultihadronic events are th e shower energy trigger (trig­
ger 8), CDC tracks trigger (17), ITC tracks trigger (16) and various com binations
of these three (13,15,19 and 14). T he overall trigger inefficiency for selecting m ul­
tihadronic events is estim ated to be less than 0.3% and has a negligible effect on
this analysis.
W henever an event satisfies one o f the trigger requirem ents, th e software begins
to save the even t. T h at takes tim e. W hile it is doing this th e detector is “dead” ,
being unable to read in another even t, even if it is an interesting one. T he primary
deadtim e is about 30 ms for an average size event. The online system is ready for
another event about 30 ms after it decides to save the detector inform ation for an
event. However th e deadtim e for the next event m ay be longer if it com es Boon after
th e first event. A lthough th e system is ready and can accept a trigger, it is has to
wait until th e information from the previously triggered event is read out before
th e VAX com puter is ready to read th e event. T his is the secondary deadtim e and
62
it can be up to 50 m s. At a trigger rate o f 1 H z, the dead tim e is around 3%.
T he m axim un data acquisition rate is therefore lim ited to around 3 Hz. At this
triggering rate about one event is saved out o f every 100,000 beam crossings.
D ata is accum ulated at about 6000 ev en ts/h o u r during normal operation and
from these only one or two inclusive m uon events per day are obtained.
A schem atic diagram of the data acquistion system is shown in figure 3.24. A
FA ST B U S and CAM AC system controlled by a V AX 11/780 was used to store
data from the detector; the FA ST BU S system for reading and digitizing o f detector
data and the CAM AC system for.m onitoring and control o f detector performance.
The VAX also performs online analysis and sends the data to a FACOM M382
com puter via an optical link. The data were rearranged on the FACOM into the
Tristan Bank System (T B S ) format and stored in a C assette Tape Library (C TL)
for further analysis.
3 .4
M o n te C arlo S im u la tio n
Electron-positron annihilation to hadrons is a com plicated process and usually
yields m any particles in the final state.
It is therefore very difficult to em ploy
a sim ple analytical formula to calculate the detector effects on inclusive m uon multihadronic even ts, especially since the A M Y detector itself is very com plex. M onte
Carlo (M C ) event sim ulation is therefore used to understand detector effects. There
are two steps to this MC simulation:
T rig g er Bit
N am e o f trig g e r
5
P T C trig g e r
8
Show er T o ta l E n erg y
11
RVC + P T C R e a r Inclusive
IT
IT'C 2 tra c k + C D C + Show er M in im u m Ionizing
11
i l C 2 tra c k b ack -to -b ack + C D C
15
1TC 2 tra c k + C D C + show er low M a j I
16
IT C M ulti T rack
17
C D C M u lti trac k
18
C D C lo o ser m u lti (rac k 4- show er M in Ionizing
19
(S h Hi M aj 1 a n d Sli Lo M a j 2) o r (S h Lo M a j 3)
20
(S h Hi M aj 1 a n d Sh Lo M aj 2) + C D C + N O T (T !9 )
21
IT C + C D C 2 trac k
22
C D C 3 o r -1 trac k
23
IT C 2 tra c k + M u
2-1
IT C 2 tra c k + C D C Sh M in I
26
C D C RV D iinuon
27
IT C RV D im uon
28
IT C 2 tra c k + C D C + RVC
30
C D C P e rfec t 2 tra c k
31
C D C P e rfe c t 1 tra c k , B ach elo r V
F ig u r e 3 .2 3 : L is t o f t r ig g e r s u s e d d u r in g d a t a t a k i n g
64
AMY DATA
ACQUISITION
SYSTEM
VAX M /T O O
P=
■w
isi wc
Ml
Ml
lit
DISC
M W W S C flM IIU W
HHt-vtrw m«i
ttn m iiri
DUWU
IMIAI
m-cmumu
I t'H c k l
mown auutxn »tTO PQLC nr llfU. I-*AT
«CI* M l JUNOU cawiei
mo sarin m u o u u ia
iw*i iiitki nut tin mmI nit
nti nrut
cmuc
Figure 3.24: D ata Aequistion o f A M Y
65
1. Event generation
2. D etector sim ulation
3.4.1
E ven t G en eration
LU ND 6.3 [27] was used for the generation o f partons (quarks and leptons) and the
String Fragm entation m odel [28] for the hadronization of th e generated partons.
In LU N D 6.3, the process e +e~ —> qq and e +e — —►qqg are sim ulated w ith the
m om enta of th e original partons obtained from a probability function determined
from th e Standard M odel. Each of the generated partons branches into two other
partons and each daughter parton branches into another two until a cut-off mass o f
about 1 G e V /c 2 is reached and the branching process stops. T he leading logarithm
approxim ation o f perturbative QCD is used to calculate th e branching probabilities
of each parton. This developm ent of a parton shower is called the “Parton Shower
M ethod” . A quark can branch into another quark and a gluon. A gluon can produce
two other gluons or a quark-antiquark pair.
T h e hadronization of th e quarks and gluons that were generated by th e par­
ton shower involves non-perturbative aspects of QCD and is done in the String
Fragm entation m odel which has been found to m odel th e processes e+e~ —> qq,
e +e~ —+ qqg rather well [29]. In this m odel, the quark-antiquark pair is stretched
out like a string.
As the quark-antiquark pair m oves further apart, the string
breaks. In this breaking, a new quark-antiquark pair is created depending on the
66
energy in th e string, giving two quark-antiquark pairs. The string fragm entation
allows th e quark-anti-quark pairs to keep dividing until there is not enough energy
for further division. T he short lived particles decay and at th e end of th e fragm en­
tation process, only the long lived hadrons (rr*, K s , K l , K * , p, n , A, £ * , £" , H"
and E~ ), electrons, m uons, neutrinoes and photons remain.
3.4.2
D e te c to r S im u lation
Each of the particles generated in the last section is traced through the detector
in small steps. A t each step, the particle m ay decay or interact with th e various
com ponents of th e detector m aterial. T he EG S4 [30] sim ulation program is used
to sim ulate th e electrom agnetic showers produced by electrons and photons in the
SHC and P T C . Hadronic showers are sim ulated by th e G R A N T [31] sim ulation
program.
T he software sim ulates actual detector signals and creates event data
records which can be analyzed using the sam e analysis programs as that used by
experim ental data.
A typical m ultihadronic event requires 12 seconds o f FACOM C PU or 180 sec­
onds of VAX 8800 CPU to sim ulate and requires 90 K bytes o f storage space.
Chapter 4
Inclusive Muon Event Selection
T he ob jective o f th e data selection is to obtain a sam ple enriched in e +e - —> bb
events. T his is done by requiring a muon in each m ulti-hadronic event. Muons in
e+e~ annihilation to hadrons occur m ainly from sem ileptonic decays o f heavy quarks
in th e processes, e +e “ —* bb (b —►o . f i ~ V t l ') and e +e _ -> cc (c —►
These
m uons are referred to as prom pt m uons. Figure 4.1 shows th e sem i-leptonic de­
cay of a B - meson resulting in the production of a prom pt m uon. T he charge of
the m uon is used to tag th e charge of th e parent quark (b —* fi~ and b —* n + ).
E vents th at originate from u, d and s quark pair production do not produce
many prom pt m uons (m uons w ith origin at the interaction point) because they have
smaller decay am plitudes as shown in table 4.1 [32]. Therefore m esons consisting
o f light quarks (u,d and s quarks) such as pions and kaons have longer lifetim e
( r •— 10-8 sec) than m esons containing a b- or c-quark ( r ~ 10-13sec.)
67
68
prom pt muon
irei
fi
Figure 4.1: Sem i-leptonic decay of B" —> D afi~P^
H1
"C
Decay A m plitude (sec *)
3.8 x 107
K * —> (tv
5.1 x 107
c /c —> fiX
7.6 x lO10
b /b —» pi/hadrons
8.4 x lO10
T a b le 4 .1 : D e c a y A m p li t u d e s o f H e a v y a n d L ig h t M e s o n s
69
T he requirement o f a prom pt muon (origin at interaction point) in a hadronic
event ensures th at the event sam ple consists m ostly o f e +e" —*
bE and
e +e “ —* cc
processes. Backgrounds to the muon signal (hadron fakes) arise principally from
hadron showers in the hadron filter, where the debris reaches th e m uon chamber
(punchthroughs), or from th e decay o f w* and K* m esons to muons that reach
th e muon chamber (decay). The background includes events w ith punchthrough
hadrons m isidentified as muons or with muons from th e decay of pions or kaons.
Hadronic event selection was done by the off-line analysis group. T he inclusive
muon events are selected from these hadronic events. This chapter gives a descrip­
tion of the selection criteria for hadronic events and th e m uon selection criteria.
T h e background and the efficiency of the event selection are also discussed.
4 .1
M u lti-h a d r o n ic e v e n ts
Electron-positron annihilation produce m ulti-hadronic events by the pair-creation
of quark-antiquark pairs (e + e~ —* qq). T he high center-of-m ass energy imparts
trem endous m om entum to th e quark-antiquark and forces them to m ove away from
each other.
The original quark (antiquark) excites th e vacuum and generates a
“sea” o f qq pairs [33]; it then captures a “sea” antiquark and becom es a m eson.
T h e remaining “sea” quark picks up another “sea” antiquark to becom e a meson
and this process continues until there is not enough energy to produce a “sea”
quark-antiquark pair. As a result many hadrons are produced. This production
70
o f hadrons from the original quark is called quark fragm entation.
The Lorentz
boost on the original quark tends to collim ate the resulting hadrons into a jet.
C onsequently, m ulti-hadronic events are often characterized by th e appearance o f
tw o jets. Som etim es there are more jets due to gluon production (e+e _ —* qqg) and
subsequent gluon fragm entation. Figure 4.2 give an exam ple o f a m ulti-hadronic
event with a muon as d etected by the A M Y detector.
M ulti-hadronic event selection
Hadronic events tend to be collim ated into jets w ith an angular distribution
approxim ately o f the form (1 + cos20). T he total energy deposited in th e barrel
region o f the detector is therefore expected to be nearly equal to th e center-of-m ass
energy, y/s, for many of the events. T he m om entum o f all the particles should
also be balanced. An extrapolation from lower energy data o f other experim ents
indicate that the charge m ultiplicity at T R IS T A N ’s energy region is expected to
be about 15. T he final corrected charge m ultiplicity at 56 GeV m easured by A M Y
was 17.27 ± 0.16 [34].
Raw data were collected at a trigger rate o f up to 3 Hz and betw een 5000 to 6000
events were collected per hour, w ith only one or two events that eventually pass
all o f th e hadronic event cuts. About 80% o f th e triggers were background from
interactions betw een beam particles and the wallB o f th e beam pipe (beam -wall)
or with the residual gas in th e vacuum (beam -gas); and 20% of th e triggers are
from cosm ic rays events. The interesting events, about 1% of the triggers, consist
71
Rwrv. 3447. Ev: 1B86, Ebeow: 26.0Q(Govl, Bfld: 3.03«T), D ot*:87-07-18, Ttnwil4:16:3£
ARRM.HADMUMAR3J3A74
TRGbltl 2 8 ,2 4 .IB, 17,L5.14,13,12, 8, 7, 0.
OETbiti 7, 5 . 3. 2. L,
>
A
j -
S H O IV *
ll* x
Figure 4.2: A multi-hadronic event with a muon
0
200H «V ( 4 1
72
o f multi-hadronic events, lepton pair production (e +e “ —+■ t + t ~, e +e “ —* p +ft~y
e +e" —* e +e “ ), two photon collisions (e +e “ —►e +e “ -f hadrons, e +e “ , p +/r“ , r +r _ )
and radiative bhabha events ( e +e" —» e +e" -f 7 ).
In order to sort through this enorm ous am ount o f raw d ata for the one or two
hadronic events, the hadronic event selection is accom plished in three stages: [35 ]
• F ir s t s ta g e : T he first stage filter is designed to reject events which are obvi­
ously not from e +e “ annihilation. Charge track segm ents were reconstructed
and the cluster finding algorithm for the SHC was applied. Events th at passed
th e following cuts were accepted:
1 . Total energy deposited in SHC, EBt,c > 2.8 GeV or
2 . at least 2 charge tracks in the CDC and
E sh c
> 1 .5 GeV
This filter rejects more than half the recorded events which are m ainly from
beam -wall and beam -gas interactions.
• S e c o n d s ta g e : T he trajectories and m om enta of the charged tracks were
determ ined using a fa 6t tracking algorithm nam ed ACE [36] (A m y CDC Event
tracker). To survive this stage, the events m ust satisfy th e following cuts:
1. V ertex cut: At least 3 good vertex tracks are required. A good vertex
track is defined to be a CDC track with |Zo| < 10 and |Ro] < 5 cm . Z0
and Ru are th e z and r com ponents o f the distance of closest approach to
73
the interaction point. In addition to the vertex requirem ent, a “good”
CDC track m ust also have at least 8 axial and 5 stereo hits.
2. Shower energy cut: T h e total shower energy, E sjic is at least 2.8 GeV.
O f the events that passed the first stage, less than 0.5% survive the second
stage. Even w ith such a high rejection factor, th e data sam ple is still dom i­
nated by background events.
• T h ir d S ta g e : A more sophisticated tracking program is used to im prove on
the track reconstruction. This algorithm , D U E T [37], was adapted from the
original version developed for th e CLEO detector at CESR e +e “ storage ring.
T he shower cluster finding algorithm is used again, this tim e with a more
accurate SHC calibration.
T he following hadronic cuts were developed in order to select hadronic events
with a good efficiency and a high rejection for background:
1. Total energy deposited in the SHC greater than 5 G eV ( 3 GeV for
y/s = 50 and 52 G eV ).
2. T he sum of th e absolute m om enta o f all th e “good" CDC and SHC
particles,
E vis ,
greater than half the center o f m ass energy.
3. Five or more “good ” C DC particles.
4.
T he sum of th e z-com ponent of th e 3 m om enta of all the “good”
and
S H C
particles (m om entum balance) less than
0 . 4 E v jF.
C D C
74
(G eV )
raw data
1 st stage
2 nd stage
3rd stage
52
1637857
839054
4027
490
55
1926857
1126649
2458
376
56
2452022
1553682
5300
735
56.5
617819
405324
1343
131
57
1291053
865023
3902
495
scan
726413
466706
2073
317
60
931046
526200
1798
405
60.8
2775822
1562678
6147
368
61.8
1555472
842892
4555
431
Table 4.2: Num ber o f events passing each hadronic selection stage.
A “good” SHC particle is one w ith energy greater than 0.2 GeV and the
energy deposited in any one of the five longitudinal layers o f th e SHC less
than 95% of th e particle’s energy.
A M onte Carlo study shows th at 64% o f the m ultihadronic events pass th e final
hadronic cuts [38], T he background from e +e" —» r +r “ , 7 7 and beam gas adds up
to about 1.9%. Table 4.2 shows th e num ber of eventB passing each selection stage.
75
4 .2
I n c lu s iv e M u o n S e le c tio n
T he inclusive m uon event sam ple consist o f those events th at pass the final
hadronic event cuts and have at least one muon track. A m uon track is defined by
hits in th e muon drift chamber in at least three out o f a to ta l of four planes and
with at least one set of adjacent wires having hits in either o f the double layers of
th e drift cham ber. The tim ing measured by the muon scintillation counters m ust be
consistent with the beam crossing; muon tracks with tim ing less than zero, counting
from beam crossing are rejected.
The hit position in th e m uon chamber must
m atched the extrapolated position of one o f th e CDC tracks within a m om entum
dependent m atching distance cut (R C U T ) described in the next section.
4.2.1
M a tch in g th e m uon track to a C D C track
CDC track extrapolation
T he D U E T track finding program provides information about the initial position
and m om entum of each CDC track. Using this inform ation, the m agnetic field map
and d E /d x losses, the extrapolation program [39] calculates and extrapolates the
trajectory o f all CDC track with m om entum greater than 1.0 G eV /c.
T he CDC tracks are assum ed to be possible muons and th e extrapolation is
accom plished using the sam e routines as those used in th e M onte Carlo simula­
tion of muon tracks in A M Y . Uncertainties in the track extrapolation arise from
m ultiple scattering, d E /d x losses, survey, drift tim e, m agnetic field and CDC track
76
reconstruction uncertainties.
RCUT
T h e m atching distance (R D IF ) is defined as th e distance betw een th e m uon track
and the charged track extrapolation at the muon chamber. In th e local co-ordinates
o f the m uon cham ber, the z axis is defined as th e direction parallel to the electron
beam . T he x axis is perpendicular to the z axis and lies in th e plane o f the muon
sextant. In this co-ordinate system , all muon hits lie in the x-z plane.
X D IF and ZDIF are defined as the distance betw een the positions o f the muon
hit and the CDC extrapolated track along the x and z direction. T he m atching
distance is then
R D IF = \/X D I F 2 + ZD IF 2
(4.1)
Figure 4.3 shows X D IF and ZDIF in an inclusive muon event. T he R D IF cut is
m om entum dependent because the trajectory o f a m uon through iron is affected by
m ultiple Coulomb scattering; a high m om entum muon tends to suffer less m ultiple
scattering and therefore has a sm aller R D IF. Figure 4.4 show that the R D IF distri­
bution o f th e M onte Carlo sim ulted events closely resembles that for th e inclusive
muon data.
T he distribution o f the m om entum o f M onte Carlo sim ulated inclusive muons
at the muon chamber versus its R D IF is shown in figure 4.5. T he three plots in
figure 4.5 show that the decay-in-flight muons and fake muons from punchthrough
77
xxur
ZDDF
VJ
3
5>
Figure 4.3: X D IF and ZD IF in an inclusive m uon event
78
20
AMY
No. of inclusive muong
Data vg. M onte Carlo
0
10
20
30
40
50
RDIF (c m )
Figure 4.4: R DIF distribution for inclusive muon data and M onte Carlo
60
79
generally have bigger R D IF compared to th e prom pt m uons. T he distributions also
show th at R D IF tends to b e smaller for higher m om entum particles. A suitable
m om entum dependent R D IF cut (R C U T ) is therefore more effective in enhancing
the prompt muon fraction.
T h e m ost logical way to determ ine thiB m om entum
dependent R C U T is to use a sam ple o f real m uons. Fortunately such a sam ple is
available from th e acollinear muon events (e +e - —> e +e~fi+fi~).
Figure 4.6 shows th e m om enta (P p ) of the m uons from e+e “ —» e +e~fi+fi~ events
at the muon chamber versus R D IF. Pp is th e final m om em tum of a charge particle
at the MUO obtained by extrapolating its initial m om entum with muon energy
loss as it traverses through th e detector m aterial. T h e accollinear muon sam ple
was collected from e +e~ —* e +e~fi+ fi~ processes for 50 G eV < y/a < 61.4 GeV.
T he muons tracks were divided into seven P p bins o f 1 G eV w idth. T h e last bin
consists of P p greater than or equal to 6 G EV . T h e m om entum dependent R C U T
is designed to accept 96% o f the muon in each P p bin, as shown by the solid line
in figure 4.6. Muons w ith m atching distances (R D IF ) less than the R C U T were
accepted. The statistical error for the efficiency o f selecting accollinear muons using
this R C U T is 0.6%. T h e event shown in figure 4.3 did not pass th e R C U T .
M om entum cut
T h e m inim um energy required by a m uon track to penetrate th e detector from
the interaction point to M UO is at least 1.9 G eV . H ence any muon tracks w ith
m om entum less than 1.9 G eV are m ost likely to be from decay-in-flight or mis-
80
PROMPT
B V Id aa
PUNCHTHROUGH
m
i
n i | i i n p T Trj m
i
I
4.
'B
I
t
IDIT In
DECAY
16.0
ia.6
?
10.0
I
U
%
u
t
7.0
60
0.0
00
100
Figure 4,5: D istribution of final m om entum o f m uons from M onte Carlo simulated
events
81
■ i i i 1—i—i— i—r —j1 i- r i—r
30
A M Y d a ta
MOMENTUM OP MUON AT MUO (dEV)
25
52 G eV - 81.4 GeV
**"%
* *i
20 1 * a
*• *
/ £d t = 33.3 p b "1
•
I*JT*
• a *
15
HmU* •
“V* /*«
*
10
A
h •**♦.
« • ■
\ : j .... * ./) .
60
40
80
RDIF (cm )
Figure 4.6: Final m om entum o f muons from e +e
m atching distance (R D IF )
, ,‘ t . l
100
—* e +e fi+(i
events versus
82
identification.
A m om entum cut o f 1.9 G eV was therefore applied to the muon
selection.
Figure 4.7 shows th e efficiency o f selecting muons from e +e - —+ e +e - #i+p.events as a function o f the m om entum o f the m uon track. As can be seen, the
efficiency is very low for m om entum less than 2 G eV and levels off at an average o f
96% for m om entum greater than 3 G eV .
4 .3
B ackground
The principal background to th e m ulti-hadronic inclusive m uon sam ple are events
with:
1 . Cosm ic ray muons and accidental hits.
2. Fake muons from hadronic punchthrough.
3. Muons from pion and kaon decay.
4.3.1
C o sm ic ray m u on s and a ccid en ta l h its
This is th e background where a cosm ic ray or accidental hits make a muon track
in coincidence w ith a hadronic event.
T he probabilty o f such background was
studied using a sam ple of bhabha events (e +e - —> e +e “ ). B habha events were used
because they do not have any real m uon tracks. Any m uon track found in this
sam ple m ust therefore com e from cosm ic ray muons or accidental h its. T he bhabha
83
120
(%)
80
efficiency
100
60
40
20
0
0
5
10
15
20
25
m o m e n t u m in GeV
Figure 4.7: Efficiency for selecting muons from e +e~ - * e+e~fi+fi~ events as a
function of m om entum
84
events usually have only tw o visible charged tracks. T h e criteria for th e selection
o f Bhabha events is given by:
1 . A t least two
S H C
showers with energy greater than
E b eom / 3 .
2. Tw o of th e largest SHC showers m atching CDC tracks w ithin 2°.
3. T he m atching CDC track has m om entum greater than E benm/ 3 .
4. T h e acollinearity angle betw een the two m atching tracks is required to be less
than 10 ".
There were 7,079 Bhabha events from th e 52 G eV to 60 G eV data sam ple. O f
these there were 138 events w ith muon tracks. N one o f the events has tracks that
passed th e m om entum dependent R CU T.
The probability of a cosm ic ray or accidental hits in coincidence with a hadronic
event is therefore
2.3
Probability < ■—-j— - = 0.016% at 90% confidence level.
• v Iy x &
(4 .2 )
There were 2 tracks per bhabha event. T h e background exp ectation is given by
the total number o f C DC tracks with m om entum greater than 1.9 G e V /c m ultiplied
by th e probability o f a cosm ic ray or accidental hits given above. On the average
there are 5 CDC tracks in a m ulti-hadronic events with m om entum greater than
1,9 G eV. T he 52 GeV to 57 G eV d ata sam ple has 2192 m ulti-hadronic events. This
gives an expectation o f less than 1.7 cosm ic ray events at 90% confidence level.
85
4 .3.2
P u n ch th ro u g h
Punchthrough arises from th e products of hadron interactions in th e SHC or iron
that m anage to reach th e muon chamber, thereby giving a fake muon signal. A
study of pion punchthrough by Harris et.al. [40] using data taken at th e SLAC
20 GeV Spectrom eter is shown in figure 4.8. The A M Y M onte Carlo estim ate [41]
is compared with this data in figure 4.9. T h e 96% m uon circle m entioned in the
plot is the circle within which 96% of the muons will pass. G R A N T /A M Y in the
plot refers to the result obtained from the M onte Carlo sim ulation using G R A N T
on th e A M Y detector. T h e result as shown in th e plot indicates that G R A N T
system atically overestim ates pion punchthrough by a factor o f 2. T he contribution
from punchthrough as obtained by the M onte Carlo sim ulation events has therefore
been reduced by a factor o f two in this analysis.
There are no data on kaon punchthrough to com pare with those obtained by
M onte Carlo sim ulation. Figure 4.10 shows th at th e M onte Carlo punchthrough
from K + is much higher than th at from K" and pions. This is due to the smaller
K + cross-section for interaction in iron because K~ (u s) can cause uu annihilations
wiht nucleons whereas K + (u s) cannot.
4.3.3
M u on s from d ecay o f 7r± and K*
T he probability of decay of tt* or K* is given by
Probability ~ ——— ~
fl-ycr
Er
(4.3)
v ’
86
10
Ji
X
X
X
A
+9««Wk
+ 3J90eV A
OF RONS IN 9 6 % CIRCLE
JZ
J
JM
JM
FRACTION
JOZ
O
19
90
49
90
79
THICKNESS OF IRON (cm)
Fraction of the Incident pion* surviving within a multipleCoulomb-scattering circle containing 96% of the Incident muons,
plotted as a function of the thickness of Iron In cm.
Figure 4.8: Study of pion punchthrough by H arm s et.al. using d ata taken at the
SLAC 20 GeV Spectrom eter
87
In cid e n t 7T+ w ith in 96% m u o n c ir c le
10°
T
I
*1---1---1—1---f—Z
™
* \
D
*
JO - 1
Punchthrough
*
x
o
\
f
\
*
io ~ 2
dRANT/AUY
H a rris a t a l. (n + )
H a rria a t a l. ( n - ) —
\
\
•
10"3
t\
*
\
tt
\
\
ic r 4
-I
0
I
I
I
I
60
L
..................................................
100
I___ I___ I___ L.
150
Iron D epth (c m )
Figure 4.9; Punchthrough: SLAC 20 GeV Spectrom eter pion d ata com pare with
M onte Carlo (G R A N T /A M Y ) sim ulated x + at a m om entum o f 3.75 GeV
88
punchthrough
0.10
0.08
o pi_
punchthrough probability
* pl+
• k -
d'k+
0.08
0.04
0.02
0.00
m omentum in GeV
Figure 4.10: Punchthrough stu d y using G R A N T
89
for m 0L C E r where m 0 is the mass o f the decaying m eson, L is th e path length,
r the m ean lifetim e and E the energy o f th e decaying m eson.
In order to confirm that the M onte Carlo is giving the correct am ount o f decay,
5250 7r“ events were generated using EPO CS [43] (E lectron P O sitro n C ollision
Sim ulator) and sim ulated by th e A M Y /G R A N T sim ulator. Each even t has 4 ir~
tracks with a center-of-m ass energy of 4.7 G eV and 0 o f 90". T he first tt~ track
generated was random in <j>. T he next generated track has 0 at right angles to the
first. T he third and fourth generated tracks have 0 at right angle to th e second and
first track respectively. A typical event is shown in figure 4.11. A total o f 21,000
ir~ tracks were sim ulated and o f these 51 ± 7.1 decayed to fi~ w ithin 67 cm . The
expectation from calculation was 53.5 ± 7.3.
750 K + events with th e sam e event topology and energies were also sim ulated.
39 ± 6.2 decays were found from the 3,000 K + tracks within 67 cm . The branching
ratio of K + —> (iv is 63.5% as given in the Particle Table and th e calculation using
(4.3) was therefore 36 ± 6 decays. Beyond 67/sin # cm , the particle enters th e dense
shower counter and iron yoke which tend to cause it to interact rather than decay.
The agreem ent betw een the MC and calculation for
and K* decay is therefore
good. T he total decay probability in an event also depends on the num ber o f tt*
and K* per event. L U N D was found to give a good agreem ent w ith data [44] for
producing the relative number o f pions, kaons and protons at 29 G eV . Prelimary
results from th e TO PAZ and V EN U S experim ents [45] also show good agreement
90
Figure 4.11: M onte Carlo 4 ir tracks event
91
w ith LU ND and data at T R IST A N ’s energies for th e 7T : K : p ratio.
4 .4
E ffic ie n c y for s e le c tin g p r o m p t m u o n s
T he com plex nature of A M Y makes it im possible to use a sim ple analytical formula
to calculate the efficiency o f detecting the inclusive muon events.
M onte Carlo
sim ulated events were therefore used to give an estim ate of this efficiency.
The acceptance for prom pt muons (b —►ft, b —►c —►p , c —►fi) is given by
number o f prompt muons reaching the M UO
acceptance = ------------- ;-------------------------------------------- :-------num ber of prom pt muons generated
and the efficiency for selecting prom pt muons is given by
_ .
efficiency
number of prompt muons found by analysis software
------------------------------------------------------------------------ -— —
number of prompt muons reaching the M UO
Figure 4.12 shows the m om entum distribution o f (a) the generated prompt m uons,
(b) prompt m uons reaching the M UO and (c) prompt muons found by the analy­
sis software for th e 67,400 five flavor m onte carlo sim ulated m ultihadronic events.
Figure 4.13 shows the (a) acceptance and (b) efficiency for selecting prom pt muons
as a function o f m om entum . T he study shows that the acceptance for selecting
prompt muons is 56% and the efficiency is 88 %. T he efficiency for selecting prompt
muons is lower than th e 96% efficiency for accepting accollinear
multihadronic inclusive muons usually lie within
muons because the
jets making it harder to recon­
struct the tracks. T he larger track reconstruction errors within jets thereby lower
th e selection efficiency of th e prom pt m uons. T he efficiencies for selecting prompt
92
efficiency
prompt (average)
88.4% ± 0.7%
b —* n
92.2% ± 1.0%
b —» c —+ fi
83.6% ± 1.9%
—> fi
87.8% ± 0.9%
decay
81.4% ± 1.5%
punchthrough
49.1% ± 2.0%
overall
82.0% ± 0.7%
C
Table 4.3: efficiency for selecting prompt and fake muons
and fake muons are summ arized in table 4.3. T he expression b —> f i is used for the
process B —►
4.4.1
where B is the b flavor hadron.
M U O and C D C efficien cy
T he MC sim ulation assum ed that A M Y is a perfect 100% efficient detector. This
is not true in practice. On top of th e efficiencies as found by th e MC sim ulation,
the factors of muon track finding efficiency and CDC efficiency need to be added.
The efficiency for CDC track reconstruction is 95% ± 0.8% [46] for multi-hadronic
events. T he muon track finding efficiency is the efficiency o f satisfying the tracking
requirements o f 3 out o f 4 layers discussed in section 3.2.6. T his has been deter­
m ined using cosm ic ray tracks. From penetrating cosm ic rays which satisfy the
93
(a)
generated
|)>)
eoo
simulated
900
260
800
o.
E
£
A.
400
i
200
too
ISO
100
90
20
a
momentum (d«V)
(c)
analysis
900
ao
200
IN
IN
N
0
o
10
18
a
momentum (deV)
Figure 4.12: M onte Carlo prom pt muon m om entum distribution (a) generated
prom pt m uons, (b ) prom pt muons reaching the M UO and (c) prompt muons
found by analysis software
94
(b) E fficiency
(a) A cceptance
1.0
0.0
V
u
a
m
aCi
O
0
■
k
o
a m
cV
o
e
CL
0 .4
0.0
0
fi
10
16
momentum (0«V)
0
0
10
10
20
tnomantum (OiV)
Figure 4.13: A cceptance and efficiency for selecting prom pt m uons using M onte
Carlo sim ulated events
95
m inim um 3 layer requirem ent, 98% of them have th e remaining 4th layer hit as
well. Therefore, the exp ected fraction o f muons which should satisfy the minimum
3-layer requirement is at least 98%.
4 .5
D a t a S a m p le
D ata taken from June 1987 to July 1989 were used for th e analysis o f bb asym m etry.
T he center-of-m ass energy y/s was from 52 G eV to 61.4 GeV and total integrated
lum inosity was 33.3 p b - 1 .
Tables 4.4, 4.5 and 4.6 sum m arize the data used for this analysis. T he scan was
a series o f runs betw een 57.25 GeV and 59.5 G eV.
4.5.1
C o m p o sitio n o f in clu siv e m u on d a ta
A sum m ary o f the com position for 67,400 M onte Carlo sim ulated m ultihadronic
events after applying the hadronic and m uon selection cuts is given in table 4.7.
M is-identified muons occur when th e muon analysis program m atches a muon to
the wrong CDC track. Figures 4.14 shows a few exam ples o f such events. This can
happen when th e CDC tracks are very close together. M ost o f th e mis-identified
tracks are from punchthrough and decay-in-flight fakes.
96
0 >)
Figure 4.14: m isidentified tracks (a) punchthrough track from m anget was
m istaken for a track inside the CDC. T h e plot on th e left shows the tracks as they
were sim ulated. T he plot on the right shows th e tracks as interpreted by the
analysis software, (b ) track 5 was the prom pt m uon. Track 1 was chosen as the
m uon candidate because it has a smaller m atch in g distance.
4 .6
A ch eck for d e t e c to r b ia ss e s
Checks were done to be sure th at th e detector is not biassed.
T he number of
muons of both charges in the forward and backward region as well as the number
o f positively and negatively charged m uon 6 is shown in table 4.8.
A j.'b is given by
r
A[rg
—
number of forward fi* — number of backward u*
—■1
1—
>■. i- ii
—■ —— —i
number of forward p * -f number of backward
and A± is given by
^
__
*
For
number o f fi+ — num ber o f fi~
number o f fi+ + num ber o f fi~
a sym m etrical detector A p g should be zero. A± will be zero forprompt
muons from bb or cc production but not necessarily for muons from ir*, K *
decay
or punchthrough. Since th e data is dom inated by the prom pt m uons, it iB therefore
expected that A± will also be close to zero. T hese tw o numbers were found to be
zero w ithin statistical errors.
98
52
55
56 + 56.5
57
hadronic event
482 ± 22.0
368 ± 19.2
850 ± 29.2
492 ± 22.2
MC expectation
475.6 ± 6.2
359.3 ± 7.1
752.6 ± 8.1
517.7 ± 5.1
inclusive fi event
28 ± 5.3
16 ± 4.0
49 ± 7.0
26 ± 5.1
MC expectation
25.0 ± 1.5
21.9 ± 1.8
46.0 ± 2.1
31.7 ± 1.3
\ / s (G eV )
Table 4.4: Sum m ary o f inclusive muon data w ith center-of-m ass energies between
52 and 57 GeV
scan
60
60.8
61.4
hadronic event
317 ± 17.8
405 ± 20.1
368 ± 19.2
431 ± 20.8
MC exp ectation
352.1 ± 3.3
387.5 ± 3.6
370.1 ± 4.1
458.2 ± 5.1
inclusive fi event
25 ± 5.0
9 ± 3.0
19 ± 4.4
20 ± 4.5
MC expectation
21.9 ± 0.9
24.0 ± 0.9
22.1 ± 1.0
27.4 ± 1.3
y / i (G eV )
Table 4.5: Sum m ary of inclusive muon data with center-of-m ass energies between
57.25 and 61.4 GeV
v^ (G eV )
Lum inosity (p b —1)
v/5(G eV)
Lum inosity (p b —1)
52.00
3.98 ± 0.04
55.00
3.27 ± 0.04
56+ 56.5
6.98 ± 0.05
57.00
4.40 ± 0.05
57.25
0.0582 ± 0.004
57.50
0.0803 ± 0.005
57.75
0.0781 ± 0.005
58.00
0.0772 ± 0.005
58.50
0.8010 ± 0.016
58.75
0.0865 ± 0.005
59.00
0.7210 ± 0.021
59.05
0.5040 ± 0.013
59.125
0.7560 ± 0.005
59.25
0.0984 ± 0.006
59.50
0.0724 ± 0.005
60.00
3.55 ± 0.04
60.80
3.49 ± 0.05
61.40
4.32 ± 0.05
Table 4.6: Integrated lum inosity o f the data sam ple
100
O.UU
0.50
0.70
1.00
1.50
to ta l rntu >n
3,110 (100% )
2,120 (100% )
1,631 (100% )
1,091 (100% )
576 (100% )
prom pt, iniion
2,130 (68.5% )
1,532 (72.3% )
1,220 (74.8% )
851 (77,8% )
457 (79.3% )
b - p "
682 (21.9% )
633 (29.9% )
583 (35.7% )
475 (43.4% )
264 (15.8% )
b — c —• p +
300 (9.8% )
193 (9.1% )
133 (8.2% )
68 (6.2% )
30 (5.2% )
1,112 (36.7% )
706 (33.3% )
504 (30.9% )
308 (28.2% )
163 (28.3% )
p tm rlilliro u g li
317 (10.2% )
20S (9.8% )
152 (9.3% )
97 (8.9% )
51 (8.9% )
d ecay-in-flight
521 (16.8% )
306 (11.-1%)
208 (12.8% )
12! (11.1% )
55 (9.6% )
in iftidentilicntion
1 12 (1.6% )
71 (3.5% )
51 (3.1% )
25 (2.3% )
13 (2.3% )
b -
, , ~
2 (0.06% )
1 (0.05% )
0 (0.00% )
0 (0.00% )
O (0.00% )
1) — c — p +
5 (0.16% )
1 (0.05% )
0 (0.00% )
0 (0.00% )
0 (0,00% )
c —
23 (0.7-1%)
10 (0.-l7% )
8 (0.49% )
2 (0.18% )
2 (0.35% )
pu n c llllllu u g ll
80 (2.57% )
49 (2.31% )
35 (2.15% )
19 (1.74% )
8 (1.39% )
dccnv-in-fliglit
32 (1.03% )
13 (0.61% )
8 (0.49% )
4 (0.37% )
3 (0.52% )
P t c u t (G e V /c )
C—
fi
fl
Table 4.7: Num ber o f inclusive muon events
v'S (G eV )
Backward /i*
52 to 61.4
102
95
- 0 .0 4 ± 0 .0 7
101
96
- 0 .0 3 ± 0.07
Forward
A fb
VS (G eV )
52 to 61.4
Table 4.8: A check for detector biasses
Chapter 5
Analysis
192 m ultihadronic inclusive muon events were found from the data sam ple accu­
m ulated betw een V s = 52 and 61.4 G eV. The data sam ple corresponds to an in te­
grated lum inosity o f 33.3pb-1 and contained even ts o f in terest, nam ely e +e - —> bb
with subsequent sem ileptonic decay either directly, b —* (i~ (b —» jt+ ), or by the
cascade decay, b —f c —> fi+ (b —♦ c —> fi~). (T h e expression b —►/i~ is used for the
process B —»
where B is the b flavor hadron. T h e other expressions follow
this notation.) It also contained additional prom pt muons com ing from e +e~ —♦ cc,
followed by c —►fi+ (c —> /i~ ), as well as non prom pt m uons from decay and non
prompt m uons. For the determ ination o f At,, the forward-backward charge asym ­
m etry in e +e “ —» bb and Rt,, the ratio of th e production cross-section of e+ e~ —> bb
to the theorectical QED expectation for e +e “ •—►
it was assum ed th at the
yield and asym m etry o f e +e~ —+ cc was correctly described by the standard m odel.
101
T he c quark form a doublet w ith the s quark w ith properties that are well es­
tablished. W hereas, since th e t quark has not been observed experim entally, the
sam e cannot be said o f th e (t,b ) doublet. An alternate m ethod o f measuring Ab
w ithout any assum ptions about the cross section and asym m etry o f e +e - —> cc is
described in chapter 6. The five free param eters fitting m ethod to obtain Ab, Ri„
A c, Rc and non-prom pt muons sim ultaneously discussed in that chapter requires
more data than presently available. T he estim ated contributions from cc production
and from non-prom pt muons were determ ined by using a M onte Carlo sim ulation,
where five flavors were generated according to the standard m odel using th e LUND
6.3 event generator [47]. These contributions were subtracted from th e inclusive
muon data in order to obtain the e +e - —►bb sam ple. E stim ation of th e fraction
o f non prom pt muons com ing from b flavored hadrons requires an assum ption of
e +e" —> bb cross-section and asym m etry which this analysis a ttem p ts to measure
and these quantities were assum ed to be given by the standard m odel. Although
such an assum ption is not strictly valid, it does not seriously affect th e analysis
because this fraction depends m ostly on the decay kinem atics o f th e b quark and
th e total num ber of non prompt muons com ing from the b flavor hadrons was only
about 1/10 of those originating from u ,d ,s, and c flavor hadrons. T h e M onte Carlo
was also used for estim ating the ratio o f muons from bb cascade decays to those
from direct decays. T his ratio depends only on th e decay kinem atics of the b quark
and not on th e dynam ics o f bb pair production. Cascade decays produce muons
103
w ith charge opposite to those produced by direct decay and hence have th e opposite
asym m etry. This effect was corrected during the unfolding o f th e d ata described in
section 5.2.
The angle betw een the outgoing b quark and th e incom ing e - beam directions
is referred to as 9 (see figure 5.1a). In practice, it is not possible to find th e bb
quark direction. 9 is therefore approxim ated by th e angle m ade by th e thrust axis
and beam direction. The th rust, T , is defined as
T -—
m mn axt
v
T
N lt p .?l
£ i = i [pi I
(5-1)
where th e p i’s are the m om enta of the “good” C DC and SHC particles (see sec­
tion 4.1). T he unit vector t is chosen to m axim ize th e thrust. In an ideal situation,
th e thrust axis would be the sam e as the initial bb quark axis. However, one still
needs to know the direction o f the b quark. This inform ation is inferred from the
charge and location of the prom pt muon as follows: The particles are divided into
tw o hem ispheres by the plane perpendicular to th e thrust axis. T h e hem isphere
th at contains the
is associated with the b (b ) quark and th e angle 6 is the
angle m ade by the thrust axis in this hemisphere and the incom ing e ~ (e + ) direction
(see figure 5.1b). The thrust axis is a poor m easure of th e b-quark axis if m any
of th e particles are m issing. This can happen because o f the lim ited geom etrical
acceptance of th e CDC and SHC (|cos#| < 0.85 and |cos0| < 0.73 respectively). An
angular cut of |cos0| < 0.60 was therefore applied to th e data. Figure 5.2 shows the
good agreem ent between the th e thrust distribution of th e m ultihadronic events
(a )
8 d e fin itio n
in t h e o r y
e
(b) 9 definition in experim ent
Thrust axis
F ig u r e 5 .1 : D e f in i t io n o f f o r w a r d - b a c k w a r d d ir e c t io n
105
for th e 52 G eV to 61.4 GeV data sam ple com pared w ith th e thrust distribution
o f M onte Carlo sim ulated events norm alized to the sam e lum inosity o f 33.3 pb- 1.
Figure 5.3 shows that difference in cos# for the b quark axis and the thrust axiB
for the M onte Carlo sim ulted events [48]. T he results indicate that the difference
is less than cos# = 0.10 at 90% confidence level.
5.1
E n r ic h m e n t o f t h e b —►/i fr a c tio n
Sem ileptonic decays o f heavy quarks (6 —>
c —*
lead to prompt
muons w ith large transverse m om entum ( P i ) with respect to the event thrust axis.
T he average P x o f th e prom pt muon from a c quark generally is not as high as
th at from a b quark, reflecting the heavier m ass of m esons w ith b-quark flavor. An
enrichm ent o f b-quark events is thereby obtained by selecting m ultihadronic events
w ith high P i m uons.
T he distribution for m uon P x for th e d ata is shown in figure 5.4 together with
the estim ated contributions of cc , non prom pt muons and bb . Figure 5.4 shows
th at th e fraction o f events from bb can be increased by m aking a P x cut (elim inat­
ing events below a specified P x ). However beyond a certain muon P x (around 1.5
G eV / c) th e rate of rejecting b —►fi events would becom e bigger than the rate of
rejecting background. Thus the data sam ple can be enriched w ith b-quark events
by applying a suitable m uon P j cut. A study using M onte Carlo sim ulated events
indicated that the statistical and system atic errors for Ab were minimized by a cut
106
THRUST
number of even ts
AMY Multihadronic events
Total Luminosity = 33.3 pbCenter of maSS = 57.2 OeV
10°
0.6
0.7
0.8
0.9
thrust
F ig u r e 5 .2 : T h r u s t d is t r i b u t i o n fo r d a t a a n d M o n t e C a r lo s i m u l a t e d e v e n t s
1
107
600
Number of events
500
400
300
200
100
0
1
0 .5
0
0 .5
1
Figure 5.3: Acos#: The difference between cosd of b quark axis and thrust axis as
determ ined by M onte Carlo simulated events
108
of 0.7 G e V /c on th e muon P T (figure 5.5). H ence the Ab and Rb were extracted from
the distributions for P j > 0.7 G e V /c. For events w ith m uon P-j > 0.7 G e V /c , th e
non prom pt muons were estim ated to be about 25% o f th e inclusive m uon data sam ­
ple [see table 4.7]. A bout 50% of the non prompt m uons were from punchthrough
and the remainder from decays.
The distributions for cos0 of th e data and the exp ected background as deter­
m ined by M onte Carlo are shown in figure 5.6.
T he angle 8 used in figure 5.6
is defined as the direction of the thrust axis associated with
w ith respect
to the incom ing e ~ (e + ) direction.. As exp ected, the angular distribution for non
prompt m uons does not show any asym m etry, while the cc contribution has a pos­
itive asym m etry. A ctually e + e - —►cc also has a negative asym m etry. T he positive
asym m etry observed for e+e “ —►cc is due to th e convention of tagging th e c-quark
with a ti~ (rem em ber b —►p r but c —►fi+ ).
5 .2
T h e U n fo ld in g F a c to r
After subtracting cc and non prom pt muons from the d ata sam ple, the resulting
distribution was unfolded to give the corrected e +e “ —> bb differential cross-section.
M onte Carlo sim ulation studies show th at about 19% o f e +e “ —* bb events produce
prompt muons w ith P i > 0.7 G eV /c that are d etected by A M Y w ithin jcosfl| < 0.6.
Thi6 19% includes the average efficiency for detecting the b quark from inclusive
109
40
5 2 G e V - 6 1 .4 G e V
/ £dt = 33.3 pb~
No. of muoni
30
20
AMY data
1IC 4 fit
hadron faked
bb
cc
muon Pt (deV /c)
F ig u r e 5 .4 : P j d is t r ib u t io n s fo r d a t a a n d M o n t e C a r lo e x p e c t a t i o n
110
t
1—
i
1
i—
i— |
i— i
i---- i—
|—
i—
i
i
i " j—
i—
r—
t—
r
ptatiPtical e rro r
0.20
— —
pyptematic e rro r
0 .1 5
Error
1o
.
' •o
0.10
0.05
0.00
i —
I—
0
I—
I—
I—
1—
I .
0.5
I
I
. i
.
I
I
1
PI Cut (<JeV/c)
I
>
«
■
■
1.5
■
■
■
■
2
Figure 5.5: Errors on Ab as a function of P x cuts from a stu d y using M onte Carlo
sim ulated events
111
No. of even ts
30
(a) P t > 0.7 d e V /c
AMY d a ta
52
Md + fit
h a d ro n fa k e s
G eV - 81.4 G eV
JCAt = 33.3 pb"
b h
cc
20
(b) P t < 0.7 d e V /c
No. of events
25
20
10
J
-1
L
J
L
J
1- - - - - 1_ _ _ L
0.5
-0 .5
cos 0
Figure 5.6: cos# distributions for data and Monte Carlo
112
muon events and th e m uon detection effeciency of 82%. A sim ple way to unfold the
d ata is by m ultiplying the num ber of events in each cos# bin by a factor o f 1 /0.19.
B y doing this an asym m etry, Ab = —0.66 ± 0.36 is obtained, consistent (within
errors) w ith th e standard m odel prediction o f —0.58.
However this sim ple way o f unfolding the data does not account for: 1) th e effect
of different # definitions; i.e. th e theoretical (generated) angle 9 was defined by the
b quark axis while the d etected event angle 8 was defined by th e thrust axis and; 2)
the effect of th e cascade decay b —*■c —> fi. A more sophisticated unfolding factor
was obtained by dividing a M onte Carlo generated e +e “ —» bb angular distribution
by an angular distribution of sim ulated bb events with a d etected prom pt muon.
T he unfolding factor is a function o f cos# given by
Unfolding factor (cos#)
_
T otal num ber of e+e - —» bb events (cos#)
Num ber of b —» fi (cos#) and b —►c —*■fi (cos#)
The unfolding factor thus obtained is biased because the M onte Carlo sim ulated
events th at were used have the standard m odel predicted value for th e e +e “ —* bb
charge asym m etry built into it. However, this is justified in the present case because
the m easurem ent m ade by a sim ple unfolding factor of 1 /0 .1 9 described above
already show an asym m etry for e +e “ —♦ bb th at is consistent w ith th e standard
m odel prediction.
Figure 5.7 show th e M onte Carlo generated and sim ulated cos# distribution for
Pt
0*7 G e V /c of th e (a ) total num ber o f e+e _ —►bb , (b ) observed number of
113
b —> n and (c) observed num ber of b —►c —►fi events.
T he unfolding factor is shown in figure 5.8. This unfolding factor has an asym ­
m etry due to the contribution from the cascade b - t c - t ^ i events, where a muon
generated in a cos# bin is observed in th e negative cos# bin.
5 .3
S y s te m a tic E rro rs
There are two broad categories of system atic errors in this analysis arising from:
1. T he detector and data analysis
(a) lum inosity m easurem ent (3.3% )
(b) trigger inefficiencies (0.3% )
(c) detector acceptance (2%)
(d ) data recording failure (0.2%)
(e) CDC calibration/reconstruction (0.8% )
(f) background to m ultihadronic events from r r , two photons and beam
gas (0.3% )
(g) M UO inefficiency ( < 2%)
(h) selecting e +e _ —» bb, cc events by requiring a m uon ( < 1%).
2. T he M onte Carlo sim ulated events to estim ate data for
(a ) non-prom pt background: punchthrough and muons from decay of
pions and kaons (8%)
114
(a)
(b )
1600
I860
of e v e n t#
160
G enerated
e+e ~ — > b"&
1000
100
%
60
E
760
600
number
eo
a
O b serv ed
b — > n
E
860
-1
0.6
0.6
MfUlf
(e)
160
Observed
num ber
of muon#
126
100
78
60
86
0
-1
-0.6
0
0.6
I
a o e ih v
Figure 5.7: M onte carlo generated and sim ulated cos0 distribution
115
correction
factor'
15
10
5
0
-1
- 0 .5
0
copB
0.5
1
Figure 5.8: Unfolding factor for P j > 0.7 G eV data; determ ined by M onte Carlo
sim ulated events
116
(b) thrust axis angle calculation and sm earing o f 6 by using thrust axis
angle instead o f b quark axis ( ~ 0%).
3. Cross section and asym m etry o f e +e~ —♦ cc (assum ed standard m odel,
0 %).
T he system atic errors from th e detector and data analysis ( l a to If) have been
studied in detail (see reference [49]). Together with th e M UO inefficiencies (see
section 4 .4 ), this typ e of system atic error adds up to 4.5%.
Figure 4.4 shows that the R D IF distribution of the M onte Carlo sim ulted events
closely resem bles that for inclusive m uons, indicating that the efficiency for selecting
prompt m uons as determ ined by the M onte Carlo sim ulated events m ust also be
close to that for data, giving a very small system atic error.
T he m ain system atic uncertainty from the M onte Carlo sim ulated events was
from th e non-prom pt background.
Pion punchthrough is well understood since
there are data that can be compared to th e results o f th e M onte Carlo sim ulation[50].
As discussed in section 4.3.2, th e M onte Carlo system atically overestim ated pion
punchthrough by a factor o f two, hence the contribution for punchthrough as ob­
tained by th e M onte Carlo sim ulation was halved.
punchthrough in the T R ISTA N energy range.
There are no data for kaon
This was estim ated from M onte
Carlo studies to cause approxim ately half o f the punchthroughs, m ainly because
of th e sm aller absorption cross section for kaons in iron. T he M onte Carlo event
generator is in good agreem ent w ith measured results for th e pion:kaon:proton ratio
117
[51] so estim ates o f th e decay background are reliable. T h e selection o f e +e" —►bb
events by requiring a m uon depends only on th e decay kinem atics of th e b quark
and not on the dynam ics of the bb pair production and the M onte Carlo simu­
lation is therefore exp ected to be reliable. T he system atic uncertainty from the
non-prom pt background was taken to be 30% o f th e total non-prom pt events. At
a P x cut o f 0.7 G e V /c , this contributes to 8% o f the m ultihadronic inclusive muon
d ata sam ple (see table 4,7).
Figure 5.2 shows th e good agreem ent betw een th e
data and M onte Carlo sim ulated events for th e thrust distribution of m ultihadronic
events and figure 5.3 shows that difference in cos# for th e b quark axis and the
thrust axis is sm all. A lso, this sm earing was corrected for in th e unfolding factor.
Overall, th e system atic error for 2(b) is therefore very small.
T he system atic errors for Ab and Rb are obtained by repeating th e analysis
with the non-prom pt contribution varied by ±30% (corresponding to 8% of data
sam ple) and th e system atic errors o f the data sam ple by ±4.5% . T h e largest o f the
resulting shifts in Ab and Rb are used as estim ates for th e system atic errors.
5 .4
R e s u lts
5.4.1
O b ta in in g Ab and Rb u sin g m in im u m
x2
After subtracting cc and non-prom pt backgrounds from th e data sam ple, the re­
sulting distribution was unfolded to give th e corrected e +e~ —►bb differential cross­
118
section. T his was then fit to equation (2.55) w ith two free param eters (ie. Ab and
R b)
over th e angular range o f |cos0| < 0.6, allowing A b and
was accom plished using the Minuit x 2 program from th e
to vary. T he fit
R b
C E R N
Com puter Center
Program Library for function m inim ization and error analysis. T his program finds
the values of R|, and
Here
Xj
A b,
such that x 2 is a m inim um , where
is the value of the differential cross-section for cosflj and
Xj
value obtained from equation (2.55) for particular values o f Rb and
standard deviation o f
X j,
the expected
A i,.
<r\Kis the
including errors R om d ata and M onte Carlo.
T he results obtained for various P t cuts at an average center-of-m ass energy
o f v /s= 5 7 .2 G eV , are given in table 5.1. The results agree w ith each other within
errors for th e different P t cuts. The optim al P t cut for m inim izing th e statistical
and system atic errors as obtained using M onte Carlo sim ulated d ata is 0.7 GeV
(see section 5 .1 ). This is consistent w ith th e results shown in table 5.1.
T he final results are
A b
= - 0 .8 2 ± 0.25 ± 0.14 and
R b = 0 .4 7 ± 0 .1 2 ± 0 .1 2 ,
where th e errors are “statistical” and “system atic” respectively. T h e “statistical”
error includes the statistical errors o f the M onte Carlo as well as data.
contains th e errors in the unfolding factor.
It also
T h e results o f th e fit are shown in
119
Rb
Ab
X 2/ d . o . i .
0.0
0.35 ± 0.12 ± 0.20
- 0 .7 8 ± 0 .3 3 ± 0 .1 4
0.33
0.5
0.45 ± 0.12 ± 0.15
- 0 .6 8 ± 0.28 ± 0.14
0.36
0.7
0.47 ± 0.12 ± 0.12
- 0 .8 2 ± 0.25 ± 0.14
0.43
1.0
0.47 ± 0.13 ± 0.10
- 0 .9 0 ± 0.31 ± 0.16
0.84
1.5
0.49 ± 0.17 ± 0.07
- 0 .9 9 ± 0 .3 3 ± 0 .1 0
1.17
Table 5.1: Rb and Ab for various P j cuts
figure 5.9. No corrections were made for B ° — I?’ m ixing. The m easured results are
consistent with the standard m odel prediction o f Ab = —0.58 and Rb = 0.56.
Figure 5.10 compares the result for Ab w ith m easurem ents by other experim ents
[53] which were also not corrected for the effects o f B ° —B*' m ixing. Figure 5.11 shows
the results for Rb compared with the standard electroweak prediction including
QCD effects.
Since Ab and Rb are functions o f the center-of-m ass energies (>/s)) it would be
interesting to see the results if the d ata were divided into tw o sam ples, w ith each
sam ple having a smaller spread in y/s: 52 GeV < v/s < 57 GeV w ith an integrated
lum inosity o f 18.6 p b -1 and 57.25 GeV < y / s < 61.8 G eV w ith an integrated
lum inosity o f 14.7 p b - 1 . Using the sam e analysis procedures, th e extracted Ab and
Rb at an average y / s o f 55.2 GeV were
A,, = - 0 .7 2 ± 0.28 ± 0.14 and R b = 0.57 ± 0.16 ± 0.15.
—r —1---- 1
—
"
1----1---i— i— 1—T----j---- 1---- 1----1— i—
1 '
1 1
AMY d a ta a t c e n te r of maS0 - 57.2 deV
I
1
—
In te g ra te d lu m in o sity « 33.3 pb” 1
'
*
—
----
e x tra c te d e^e” ------> fcfB
.
—
fit in |coS0|<O.6
S ta n d a rd m odel p re d ic tio n
-
"
i1
(►
^
—
—
i1
-
i
i
1
i
•
j
1 1
—0.5
__
1
1
0
•
— —
1----1----L.
,
0.5
CO 0$
F ig u r e 5 .9 : R e s u l t s o f f i t t i n g fo r A t a n d R b
1
1
121
1.0
—
-
-
0.5
—
-
<
O TPd
M
e
*
e
□ tpc J
M
+
X JADE
M
X MARK J M
X PLUTO M
• AMY
TA #0
•
TA #0
dELLO
M
«
MAd
V
8
■
HRd
e
L3
0.0
- 0 .5 -
-
1.0
—
60
cm energy (CfeV)
Figure 5.10: R esults for Ab
80
122
1.0
AMY m e a s u r e m e n t a t 5 7 .2 GeV
Int. lu m in o sity = 3 3 .3 pb-1
/
E lectrow eak + QCD
/
QED
/
0.8
0.6
0.4
0,2
0.0
40
SO
60
Center of mass energy (GeV)
Figure 5.11: Results for Rb
70
123
T h e standard m odel predictions are R b = 0.50 and A b = —0.56. Ab and R t) at
average y/s o f 60.3 GeV were
A b = - 1 .0 4 ± 0.62 ± 0.55 and Rb = 0.26 ± 0.15 ± 0.11.
T he standard m odel predictions are Rb = 0.64 and A b = —0.58.
5.4.2
Ab and Rb from form ulae
Rb can be calculated from the e +e" —► bb cross-section by integrating equa­
tion (2.55) over the angular acceptance,
f-o.G
I
J».g
^0-
7r<*2
fo.o.
/
g
\
j
3 = - 3— Rb I
(1 + cos29 + - A bc o s0 ) dcosd
dcos<?
2s
J - 0.6 V
3
/
(5.4)
giving
» I- 0.6 (Pb) = 1 . 3 4 4 ~ R b(G eV " 2).
(5.5)
Similarly, A b can be calculated from
_
1
°~B |c o n 6-"
= 0■. I
_
cn*e-
-
J"*
'
a
f - 0 .f i
,k,g. . <lcOS^ _ j 4 A
+ a * A d c o . * - 1-4 A t
<5 -6)
T he results for R b and A b obtained by hand calculation using equation (5.5)
and (5.6) is compared with that using the m inim um x 2 fitting m ethod in table 5.2.
The results for A b and R b as obtained by th e hand calculation and minimum
X2 fitting m ethods agree very well for the 52 to 57 G eV and 52 to 61.4 GeV data
sam ples.
This indicates that the m inim um x 2 fitting w ith tw o free parameters
is valid for these two sets of data sam ple.
R b as obtained by equation (5.5) is
reliable since it is obtained from a sim ple counting th e number o f e +e~ —» bb events
124
Rb
Ab
yfs (G eV )
Calculation
x 2 fit
55.2
0.58 ± 0.16 ± 0.12
0.57 ± 0 .1 6 ± 0 .1 0
57.2
0.50 ± 0.12 ± 0.12
0.47 ± 0.12 ± 0.12
60.3
0.40 ± 0 .1 7 ± 0 .1 3
0.26 ± 0 .1 5 ± 0 .1 1
55.2
- 0 .7 7 ± 0 .3 5 ± 0 .1 5
- 0 .7 2 ± 0.28 ± 0.14
57.2
- 0 .7 5 ± 0.32 ± 0.20
- 0 .8 2 ± 0.25 ± 0.14
60.3
- 0 .7 1 ± 0 .5 9 ± 0 .3 3
- 1 .0 4 ± 0 .6 2 ± 0 .5 5
Table 5.2: Comparison o f Rb and Ab using hand calculation and m inim um x 2 fitting
(obtained from unfolding th e background subtracted inclusive m uon even ts). T he
discrepancies in the values of Rb for the scan to 61.4 G eV d ata sam ple as obtained
by th e hand calculated and minimum x 2 fitting m ethods would therefore indicate
th e break down of th e m inim um x 2 m ethod for this data sam ple.
T his can be
understood from th e fact the number o f events in each cos0 bin (figure 5.12) for
the scan to 61.4 GeV data sam ple is sm all, m aking th e differential cross-section
distribution sensitive to statistical fluctuations.
Indeed, th e d tr /d f l distribution
for this data sam ple (figure 5.13) has two negative bins which is unphysical. T he
effect o f the negative bins in th e forward region tend to increase th e asym m etry,
thereby giving an unphysical Ab = —1.04 m easured value. Ab by definition must
be JAb| < 1.
T he proper way to resolve the problem in th e scan - 61.4 G eV data sam ple is
125
to use the value o f Rb = 0.40 obtained by hand calculation from equation 5.5. Ab
is then obtained by th e minim um x 2 fit w ith one free param eter (ie. Ab). Doing
this gives
A,, = - 0 .8 6 ± 0.38 ± 0.06
(5.7)
w ith a x 2/d -o.f. of 0.98.
5 .4.3
F in al R esu lts
T he final results are summ arized in table 5.3.
average y/s (G eV )
Rb
Ab
55.2
0.57 ± 0 .1 6 ± 0 .1 5
- 0 .7 2 ± 0.28 ± 0.14
57.2
0.47 ± 0 .1 2 ± 0 .1 2
- 0 .8 2 ± 0.25 ± 0.14
60.3
0.40 ± 0 .1 7 ± 0 .1 3
- 0 .8 6 ± 0.38 ± 0.06
(calculated value)
Table 5.3: Final R esults for Rb and A|,
5 .5
L im it o n B° — B° m ix in g
Using equation (2.65) with a measured asym m etry of Abbs = —0.82 ± 0.29 (the
statistical and system atic errors are added in quaduture) and the standard model
126
-j
1----- 1-----1-----r
P t > 0 .7 G eV /c
°
AMY d a ta
15 —
No. of ev en ts
S ca n —
10
61.4 GeV
—
(i
(i
5 —
II
J
-1
1--------1_____ L
II
J i i i i 1 ■ ■ ■ i L
- 0 .5
0
J
I
0.5
cos 6
Figure 5.12: cos# distribution for scan - 61.4 G eV data
I
L.
127
T
1
r
1
---- 1----r
r~r
T
i
i i
AMY d a ta a t c e n te r of m a ^ = 60.3 deV
4 —
-i
In te g ra te d lu m in o sity = 14.7 p b
3 —
e x tr a c te d e+ e
> bb
-----------fit in jcoSd|<0.6
S ta n d a rd m odel p re d ic tio n
da/dQ
( p b /s t r )
°
CO $ 6
F ig u r e 5 .1 3 : M in i m u m
x2 f i t t i n g
fo r s c a n - 6 1 .4 G e V d a t a
128
prediction o f
Ab
=
— 0 .5 8 ,
the
B ° — B
X
m ixing param eter was deduced to be
= - 0 .2 1 ± 0.25.
(5.8)
Since 0 < x 5- 0.5, this result indicate that there is not enough d ata to see any
significant effect from
B °
— B
' m ixing.
However, a lim it o f x < 0.20 at 90%
confidence level can be set. Figure 5.14 compares the B ° — B° m ixing lim it set by
A M Y with other experim ents [54]. The plot for % ‘s determ ined using th e simple
assum ption for average x — 7 X1I + jx* as described in section 2 .6 .
129
0.5
0.4
0.3
A R dU g
0.2
CLEO
0.1
0.0
0
0.1
0.2
0.3
0.4
XS
F ig u r e 5 .1 4 : R e s u lt s o f B ° — 5 ° m i x in g p a r a m e t e r
0.5
Chapter 6
Future measurements
From the first day o f data taking in early 1987 until th e spring of 1989, T R ISTA N
was the highest energy e +e - collider in the world, and thus th e energy was increased
at every opportunity in the quest for the discovery o f new particles and physics.
N ow that the battle for th e highest energy has clearly been lost to SLC and
LEP, T R IST A N can concentrate on achieving th e highest possible lum inosity by
using m icro-beta insertations [55]. T he resulting increase in data will improve on
all the m easurem ents m ade by A M Y . In the run period from February 1990 to July
1990, A M Y ex p ects to accum ulate another 30 pb-1 o f d ata at 60 GeV.
W ith th e exp ected high statistics from th e future runs, it will be possible to
m easure the relative cross-section and asym m etry for e +e “ —* bb , Rb and Ah , and
for th e e +e “ —» cc , Rc and A c , using the m atrix transform ation m ethod described
in this chapter.
131
6.1
M a tr ix tr a n s fo r m a tio n m e th o d
In this m ethod, the angular distribution o f the inclusive muon events is fitted to an
expected distribution w ith five free param eters and m atrix elem ents which contain
the inform ation about th e transform ation betw een th e ratio o f th e observed inclu­
sive muons and the actual quarks which produced them . T he five free param eters
used are R|, , A|, , Rc , A c and th e yield o f the hadron fakes, Rh, from all the five
flavors; u, d, s, c and b.
The observed number of events in th e i-th cos# bin, N(cos#j) can be expressed
as follows:
N (cos0,) = £ [ M c(ij)R t N c(j) + Mb(ij)R bN b(j) + MhftJRhNhO)]
(6.1)
j
where Nr = ^
(1 + cos2#j 4- -AfCos#j) is the number o f events in th e j-th cos# bin
from th e orginal quark, expressed in term s o f a cross-section o f one unit of R. cos#}
on the left hand side is defined by th e thrust axis direction and cos#j on the right
hand side is defined by the quark direction. T he m atrix elem ent M (ij) is the ratio
o f th e number o f observed m uons in th e cos#} bin that com e from the quark that
was produced in the cos#j bin in the e +e “ —» qq process. T he m atrix M therefore
determ ines the transform ation betw een the number of observed muons and the
num ber o f quarks that produced them . M (ij) can be calculated using the LUND
6.3 M onte Carlo and it contains information regarding the effects of:
1. Smearing in # due to th e different definition of #.
132
2. Efficiency for detecting b and c quarks by requiring a muon.
3. Cascade decay of b —+ c —►(i.
4. Muon detection efficiency.
5. Hadron fakes (non prom pt m uons).
M |,(ij) and M c(ij) are the transform ation m atrix elem ents for the prom pt muon
sources b and c respectively. M |,(ij) is for the hadron fakes from all five flavors.
As a first approxim ation, we can assum e Ah to be zero since hadron fakes do not
retain the charge inform ation o f the original quarks.
This m atrix transform ation m ethod was used on the data collected between
center of mass energies o f 52 G eV and 57 G eV. We used 12 data points in the
M inuit chi square fit. Six o f these d ata points cam e from d ata w ith P t < 0.7 G e V /c
and |cos#| < 0.6 and th e other six from data with P t > 0.7 and |cos#| < 0.6.
T he results were
A c = - 0 .6 8 ± 0.33
Rc = 1.64 ± 0.61
A b = - 1 .1 0 ± 0.64
R b = 0.68 ± 0.23
measured at an average energy of y/s = 55.2 G eV. T he x 2 f° r this m easurem ent
was 0.82. The yield o f the hadron fakes, R b, was 0.01 ± 5,26. O nly the statistical
errors are shown here. Figure 6.1 shows th e dtr/dcos# versus cos9 distribution for
the data and th e fit.
These values are consistent w ith the standard m odel expection of
A c = - 0 .4 0
K = 1.51
133
At, = —0.56
Rb = 0.50
An estim ated lum inosity of around 180 p b -1 is required, however, to reduce
the error for Ab to around ± 0 .2 — a value com parable with th e errors obtained in
chapter 5.
134
ie
10
da/dO (pb/etr)
a
i— i— i— i
■ |— i
i
Rfc R. -
0.68 ± 0.83
1.64 ± 0.61
X• -
6,51
overall fit
• ■
t — > 44
i
i— |— i— i
i
i
|
A» - -1 .1 0 A 0.64
A, - 0.66 ± 0.S3
i
i
i
i"
J
~I
*
c — > ft
a
4
e
o
r ■ j * ■ t 1 1 1 1 i * * 1» ‘ 1
t
0.0
0
0.0
■ • *—
1
ooa 9
Figure 6.1: d<r/dcosd versus cos0 distribution for matrix transformation fit to the
52GeV - 57GeV data
Chapter 7
Conclusion
T he results for th e e +e~ —♦ bb cross section and forward-backward charge asym ­
m etry using an integrated lum inosity of 33.3 p b -1 at an average center o f mass
energy o f 57.2 G eV are Rb = 0.47 ± 0.12 ± 0.12 and Ab = —0.82 ± 0.25 ± 0.14.
T hese results are consistent w ith the standard m odel predictions o f 0.56 and —0.58.
T h e m easurem ents of Ab are in fact consistent w ith the standard m odel prediction
throughout the energy region explored so far. Thus th e axial-vector coupling o f the
bb to th e Z° is consistent with being g \ = —1 /2 . This in turn is consistent w ith
the weak isospin asignm ents T 3l = —1 /2 and T 3R. = 0 for the b quark. T h e simple
topless m odel discussed in section 2.5 predicts Ab = 0.0, hence the m easurem ent
rules out this m odel at greater than the 99% confidence level.
T he m ain assum ption for the analysis is that th e yield and asym m etry for
e +e" —> cc is correctly given by th e standard m odel. W ith more d ata, it is possible
136
to measure Ab and Rb using th e m atrix elem ent m ethod described in chapter 6
w ithout having to make such assum ptions.
Ab and Rb m easurem ents can also be obtained by using m ultihadronic inclusive
electrons events, and this is now being done at A M Y.
Using th e m easurem ent value of At,, a lim it on B° — B° was set of x < 0-20 at
90% confidence level. This result is consistent with th e 90% CL lim its found by
M ARK I I [56] ( x < 0.12) and by JA D E [57] ( x < 0.13) but has poor agreement
with the 95% CL lim it found by MAC [58] ( x > 0.21).
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Appendix A:
T he AM Y Collaboration
J . Lim,® K. l m l a y / I*. K irk,* R .R . M cNeil,* W . Metcalf,® S.S. Myung,® C .P , C h e n g ,b P . G u ,b J , L l,b-« Y .K . L i,b
M .it. Y e,b Y .C . Z h u ,b A . A h a s h ia n ,' K. G o t cm-,' K .P . l lu ,c E .H . L o w ,' M .E . M a t t s o n / L. P ii lo n e n / K .L , S le r n e r ,'
S. L o s i ii / C. R o s e n f e ld / A .T .M . W an g ,d S. W il s o n / M. Frautschi,® H . Kagan,® R. Kass,® C .G . T rahrrn,®
R .E . B rc c d o m /'* G .N . K i r n / W in s to n K o ,f R .L . L a n d e r / K. M a e s h iin a / R .L . M a lc h o w / J . R o w e / J .R . S m i t h /
D . S t u a r t / K . Abe,® Y . Fujii,® Y . Higashi,® S.K . Kim,® Y . K urihara,® A. Maki,® T . N uzaki, ® T , O m ori,*
H. Sagatva,® Y . Sakai,® Y. Sugim oto,® Y. Takaiwa,® S. Terada,® R. W alker,®,n F . K a jin o ,1 R. P oling.i T . T h o m as,'’
V . I s h i / K . M iy a n o / It. M i v a t a / T . S a s a k i / Y. Y a m a s h ita ,1 A . B a c a la ,min J, L iu ,1,1 F . S a n n e s,m S, S c lin c tze r,1"
It. S lo n e ," 1 J . V in so n ,"1 P. Auchincloss,® D, Blanis.® A. Bodek,® H. B u d d ,° S. F,no,° C .A . Fry,®1® l i, llarada,®
Y .II. Ho,° B .J . Kim,® Y .K . Kim,® T . Kum ita,® S.L . Olsen,®'h N .M . Shaw,® A. Sill,® E .H . T horndike,® K . Ueno,®
V ellsarris,0 II. W . Zheng,® S. K o b ay aslii,p A. M u ra k a m i,p J.S . Kang,® II.J . K im ,q M .ll. L e e / D .ll. M a n /
E .J . K i m / D. S o n / T . K o jim a / S. M a ts u m o to / R. T a n a k a / Y. Yamagishi,® T . Y a s u d a / T . l s h i z u k a / a n d K . O h ta u
* L o u isia n a S la te U niversity, B a to n R ouge, LA 708U3
b i n s titu te for H igh E n erg y P h y sic s, B eijing
r V irg in ia P o ly te c h n ic In s titu te a n d S ta te U niversity, B lac k sb u rg , VA 24061
d U niversity o f S o u th C a ro lin a , C o lu m b ia , SC 29208
® O hio S ta te U niversity, C o lu m b u s, O H 43210
f U niversity o f C a lifo rn ia, D avis, CA 95616
* K E K , N a tio n a l L a b o ra to ry for H igh E n e rg y P h y sic s, Ib a ra k i 305
h T s u k u b a U niversity, Ib a ra k i 305; ' K o n a n U n iv e rsity ,K o b e 658
3
U niversity o f M in n e so ta, M in n eap o lis, MN 55455
k N iig a ta U niversity, N iig a ta 950-21
1 N ihon D e n tal C ollege, N iig a ta 951
m R u tg e rs U niversity, P iscataw ay , N J 08854
" U n iv ersity of th e P h ilip p in e s, Q u e zo n C ity, 3004
° U n iv ersity o f R o c h este r, R o c h este r, N Y 14627
p S ag a U niversity, S ag a 840; q K o rea U niversity, Seoul 132
1
K y u n g p o o k N a tio n a l U niversity, T aegu 635; 1 C h u o U niversity, T okyo 112
1 T okyo I n s titu te o f T echnology, T okyo 152
u Saitam B U niversity, U ratva 338
Appendix B
M onitoring the perform ance o f th e M UO
TR IST A N “physics runs” occur three or four tim es each year, w ith each running
period lasting for a few m onths. Cosmic ray data are collected before the beginning
of a running period to determ ine th e efficiency of the muon chamber. D ead or noisy
channels are repaired whenever feasible.
During the run, physicists aTe on shift 24 hourB a day to m onitor the performance
of the detector. T he M UO gas system and power supplies are checked three tim es
a day. T he online VAX com puter m onitors fluctuations in the M UO high volatge
(H V ) and autom atically ramps th e IIV up to th e operating voltage of 3,100 volts
at th e beginning o f a “fill” and lowers it to 2,000 volts at th e end o f the fill. A fill
refers to the injection o f the e + and e~ beam s into th e Main Ring, and subsequent
acceleration o f the beam s to the targeted center-of-m ass energy. The beams are
dum ped at the end of th e fill when their currents becom e to o low. Each fill typically
last fromo one to three hours. An audible alarm is set off whenever the HV current
exceeds a predeterm ined level and the HV is turned off autom atically to prevent
dam age. This m ay happen if a drift chamber wire is broken causing a short-circuit
or by less catastrophic occurrences such as accelerator noise bursts. A t the end
o f a fill, th e online system gives an end-of-run summary. T he M UO efficiency is
m onitored by using cosm ic rays obtained during th e cosm ic ray gate betw een beam
crossing. This efficiency is reported in the end-of- run summary. Any abnormalities
are reported to th e person-in-charge o f the M U O . A m ore thorough diagnostic of the
M UO.is done off-line by running a program which plots the wire and counter hits in
th e M UO. Figure B .l shows a diagnostic plot o f th e M UO using this program. The
plot is used to m onitor the performance o f individual channels and dead or noisy
channels axe fixed whenever possible. For exam ple, th e plot shows that channel 63
in sextant 3 layer 1 is dead.
146
D ia g n o s t ic P lo t s f o r r u n 7 6 9 9 t o 7 7 0 6
S e x ta n t 3 Layer 2
S e x ta n t 3 L ayer 1
120
120
100
100
00
BO
I
a
a
"
00
40
40
20
0
20
40
20
B0
S e x ta n t 3 L ayer 4
S e x ta n t 3 Layer 3
£
B0
40
ebum el number
choanal num ber
120
120
too
100
so
B0
B0
m
40
20
20
10
10
20
SO
channel num ber
S e x ta n t 3 C o u n ters
1200
1000
a
BOO
a ooo
400
0
10
20
20
channel num ber
so
F ig u r e B . l : D ia g n o s t ic p lo t o f M U O
BO
147
Appendix C
W here was I in the schem e o f things?
T h e A M Y detector cost in excess o f $12 million and took tw o and a half year
to design, construct and assem be. It involves th e effort o f more than 100 physicists
and graduate students from 20 institutions, [see appendix A].
A successful collaboration of such a scale necessitates the distribution of responsibilitites for funding, construction, m aintenance and data analysis. Table C .l
shows the institutions responsible for fabrication and funding of th e major com po­
nents [59].
M any o f the com ponents were built in the U nited States and shipped to KEK
for assem bly and installation.
For instance, during the construction phase, the
LSU group set up a laboratory in the basem ent o f Nicholson Hall at LSU for the
m anufacture of th e electronic end-boards for the m uon chambers.
I arrived at KEK during the data taking phase and m y hardware responsibilities
was m ainly in th e m aintenance and repair o f the m uon drift cham bers. I was th e on­
site person from LSU who was responsible for th e muon drift cham bers, including
the muon gas system and electronics. I repaired and replaced broken electronic
end-boards, broken drift chamber anode wires, restored dead channels and repaired
noisy ones. I have also performed repairs on the muon scintillation counters. During
d ata taking runs, I was “on call” 24 hours a day to fix any problem s related to the
muon drift cham bers. In addition, like all on-site personnel, I took th e normal twice
Item
1.
G ro u p R e sp o n sib le
F u n d in g In stitu tio n
B eam P ip e
a) B ack g ro u n d Calc u latio n
O n -S ite G ro u p
b ) R a d ia tio n M asks
O n -S ite G ro u p
KEK
c) V acuum I'u m p s
O n -S ite G ro u p
KEK
d ) B e ry lliu m T ube
R o c iie ster
H o c h ester
e) D e tailed D esign
O n -S ite G ro u p
2.
L u m in o sity M o n ito r
Saga U niversity
K EK
3.
V eto C h a m b e rs
O n -S ite
KEK
*1.
C e n tra l D rift C h a m b e r
a ) H a rd w a re C o n stru c tio n
R o c h este r
R o c h e ste r
b) E le ctro n ics & C ab lin g
R o c h este r
R o c h este r
S.
T rig g e r S c in tilla to rs
O n -S itc r
KEK
6.
X -ray D e te c to r
N iig a ta /O n -S ile
KEK
7.
S how er C o u n te r
a ) P b P a n e l F a b ric a tio n
VPI
VPI
b ) C a th o d e E tc h in g
U C (D avis)
UC (D a v is)
c) A ssem bly
R u tg e rs
R u tg e rs
d ) C a b lin g & E lectro n ics
R u tg e rs
R u tg e rs
c o n tin u e n e x t p ag e
l(em
8.
9.
G ro u p R e sp o n sib le
F u n d in g In s titu tio n
M agnet
a) C ull Sc C ry o sta l
O n -S ite
KEK
b) Iro n
O n -S ite
KEK
c) C ryogenic S y ste m
O n -S ite
KEK
<i) I’m vrr S u p p ly
O n-S ite
KEK
a ) P u rc h a s e E x tru s io n s
LSU
LSU
l>) A ssem bly a n d T est
L S U /T IT
L S U /T IT
c) S c in tila tio n C o u n te rs
LSU
LSU
d ) E le c tro n ic s
LSU
LSU
O n-S ite
KEK
R o c h e ste r
R ochester
O n -S ite
R o c h este r
M uon D e te c to r
1(1.
Low-/) Q u a d ra p o lc s
11.
D a ta A cq u isitio n
a) O n L ine C o m p u te r
b) CAM AC
Sc
FA STBLtS in te rfa c e s
c ) R ack c o o lin g schem e
O n -S ite
d ) T rig g e r E le ctro n ics
OSU
OSU
12.
E x p e rim e n ta l H all
O n -S ite
KEK
I.').
E le ctro n ics H u t
O n -S ite
KEK
II.
A n alysis
a ) M o n te C a rlo
O n -S ite
b ) D a ta L ogging S y ste m
O n -S ite
c) O ff line a n a ly sis
O n -S ite
d ) D isplay S y stem
O n -S ite
Table C .l: R esponsibilities for fabrication and funding o f A M Y
150
a week eight-hour shift to m onitor and operate the detector. T h e shifts consists of
two people who stay in the electronics hut to begin and end d ata taking for each
fill, calibrate the pedestals for the electrom agetic shower counters and check the
end o f run sum m ary generated by the com puterized detector m onitoring system for
any m alfunctions or inefficiencies. Shift personnel also scan th e events collected to
look for possible interesting physics events and detector problem s.
T he physics topics that are o f interest at A M Y include:
1. The test of the standard m odel.
2. Tests for substructure o f photons and leptons.
3. Searches for new particles.
Various off-line analysis groups were organized to concentrate on the different
aspects o f these physics goals. I was active in the m ulti-hadronic inclusive lepton
group. T his is one o f the principal groups since A M Y was optim ized for lepton
identification.
One of my tasks was to stud y th e efficiencies for inclusive muon
detection and m aintain the software for muon selection. T he hadronic eventB were
scanned one at a tim e to be sure that the software was doing its job in selecting
muon events as designed.
The scanning also noted for im proper reconstruction
of tracks and the inform ation was fed back to the person in charge o f th e track
reconstruction program.
The A M Y collaboration, up to May 1990, has published 15 papers in professional
151
journals such as Physical Review Letters, Physical Review D and Physics Letters.
In addition another tw enty papers were contributed to international conferences.
In order to m aintain a high standard in the results, drafts o f papers intended
for publication in professional journals are m ade available to all collaborators for
com m ent and queries.
Presentations are also given by the people who did the
main analysis during the weekly and m onthly group m eetings. T hese presentations
include detailed explanations of the m ethod used in the analysis and the results
obtained.
In addition th e proposed paper has to be approved by two internal
referees before it can be subm itted for publication.
R epresentatives of the A M Y collaboration have also been active in giving nu­
merous talks at local and international conferences, sym posium s, sum m er schools,
and annual m eetings of the Japan Physical Society, Korean Physical Society and
American Physical Society. T he results have to be given at one o f the A M Y group
m eetings before presentation to outside m eetings. All these m easures are designed
to m aintain a high standard for results from AM Y.
As a representative o f this collaboration I have presented th e results of the
m easurem ent o f Ab and Rb at various A M Y m eetings while I was in Japan and th e
U nited States and at the Japan Physical Society Spring m eeting in 1989.
T h e results for the m easurem ent of the e +e “ —> bb cross-section and forwardbackward charge asym m etry from th e 52 G eV to 57 GeV d ata sam ple were pub­
lished in Physical Review Letters 63(1989)2341. I updated the results to include
152
data up to 61.4 GeV as described in this dissertation and for the 25th International
Conference for High Energy Physics to be held in Singapore starting A ugust 2,
1990.
V ita
T he author, Jit Ning Lim, was bora in 1960 in Singapore, a first generation
Singaporean w hose parents em igrated from Hainan Island off m ainland China. He
received his B .S. degree from th e N ational U niversity of Singapore in 1984 and
B .S.(w ith Honors) the following year. He attended graduate school at Louisiana
S tate U niversity in 1985 and received his M .S. in 1986. He began working on the
A M Y experim ent at KEK in T sukuba, Japan, in 1988. In 1990 he returned to the
U nited States where he received his PhD degree in Physics.
153
DOCTORAL EXAMINATION AND DISSERTATION R EPO RT
C andidate:
J i t Ning Lim
M ajor Field:
P h y s ic s
Title o f Dissertation:
Measurement o f e +e
— > bb Forward-Backward Charge Asymmetry
Approved:
M a jo r P ro fe s s o r a n d C h a irm a n
D e a n o f th e G ra d u a te S ch o o l
EX A M IN IN G C O M M IT T E E :
r\,
D ate of E xam ination:
10 J u l y 1990
ji
C\ ( <
^