in t he Re ac t io n e +c~ Z° -> hh,
P * • ’ ?
Using Inclusive El ectr ons j r
by
Paul R o b e rt S c h e n k
B .Se ., U n iv e r s it y o f W e stern O n tario , 1987 ” M .Sc., U n iv e r s it y o f V icto ria, 1989
i /
A D is s e rt a ti o n S u b m i t t e d In P artial F u lfillm e n t ol '.c R e q u i r e m e n t s for th e D e g r e e ot D O C T O R O F P H I L O S O P H Y
in th e D e p a r t m e n t o f P h y s ics and A s t r o n o m y
We accep t th is d is s e r ta t io n as c o n f o r m i n g to the r e q u ir e d sta n d a r d
Dr. A, A s tb u ry , S u p e r v i s o r (D e p a r tm e n t ^ f P h y s ic s a n d A s t r o n o m y ) Dr.R. K e e ler, D e p a rt m e n ta l M e m b e r ( D e p a r tm e n t o f P h y s i c s and A s t r o n o m y ) Dr.L. R o b e r t s o n , D e p a rt m e n ta l M e m b e r ( Q p p a rtn jc n t o f P h y s i c s a n d A s t r o n o m y ) Dr.T.W. D i n g l e , O p l s i d c M c m b o n D c p a r t m e n l o f C h e m i s t ry ) D r.D. H a r ri n g to n , O ^ p rid c M e m b e r ( D e p a r t m e n t o f C h e m i s t ry ) Dr.R. D i bois, E x te rn a l E x a m i n e r ( S ta n fo rd L in e a r A c c e l e r a t o r C e n te r) © Paul R o h c n S c h e n k , 1992 U n iv e rsity o f V ictoria
All rig h ts rcscrvi.il. D isse rtatio n m a y not he r e p r o d u c e d in w h o le o r in pari, by p h o to c o p y in g c o th e r m e ans, w ith o u t the p e rm issio n o f the author.
A B S T R A C T
T h e p ro c ess e + r ' > Z° -> 1)1) is studied using p r o m p t e lec tro n s. T h e partial w id th o f the Z" b o so n into b b pairs is fo und to be -100 ± .'l.r) ± 57 ± MeV, and die f o r w a rd - b a c k w a rd a s y m m e tr y in the re actio n <'+ o~ -> Z° —> b b is fo u n d to
be 0 .1 0 1 ± 0.0Jf) ± 0 .0 1 1 ± 0.0 0 0. E x a m i n e r s : Dr.A. A s tb u ry , S u p e r v i s o r ( D e p a r t m e n t o f P h y s i c s an d A s t r o n o m y ) Dr.R. Keeler, D e p a rt m e n ta l M e m b e r ( D e p a r t m e n t o f P h y s i c s and A s t r o n o m y ) Dr.L. R o b e r t s o n , D e p a rt m e n ta l M e m b e r ( D e p a r t m e n t o f P h y s i c s a n d A s t r o n o m y ) Dr.T.W. D in g le , O u t s i d ^ M e m b e r ^ p q i a r t m c n l o f C h e m i s t r y ) Dr.D. H a r ri n g to n , O u t s i d e lylcm bcr ( D e p a r t m e n t o f C h e m i s t r y ) Dr.R. D u b o i s . E k fc m a l E x a m i n e r ( S ta n fo r d L i n e a r A c c e l e r a t o r C e n te r)
Contents
Abstract Ei
Table o f C ontents iii
List of Tables v
List of Figures viii
A cknow ledgem ents xiii
1 Introduction 1 2 Theory 5 2.1 E le c tr o w e a k T h e o r y ... 5 2 .2 b -fla v u u re d H a d ro n D e c a y s ... 15 2 .3 b F r a g m e n t a t i o n ... 22 2 .4 S u m m a r y ...28 3 T he OPAL Detector 31 3.1 C e n tra l T ra c k in g S y s t e m ... 31 3.2 E le c tr o m a g n e tic C a l o r i m e t e r ... 35 3.3 M u o n S y s te m ... 38 3 .4 T h e O P A L T r ig g e r S y s t e m ... 38 3.5 E v e n t R e c o n s tru c tio n S y s t e m ... 39 4 Event Selection 40 4.1 H a d r o n ic E v e n t S e l e c t i o n ... . 4 0 4 .2 S in g l e E lec tro n S e le c tio n ... 42
4 .3 In c lu s iv e /luon S e l e c t i o n ... 4 2 4 .4 J e t D e f i n i t i o n ...44
5 Prompt Electron Selection 46 5.1 T ra ck S electio n ... 46 5 2 E lectron I d e n t i f i c a t i o n ...46 5.3 E n d c a p E lectron I d e n t i f i c a t i o n ...47 5.3.1 d E /d x ... 47 5.3.2 C a lo rim e tric C r i t e r i a ...52
5 .4 Barrel E lectron Selectio n ... ... 61
5.4.1 d E / d x ... 61
5.4.2 P re s a m p le r M u l t i p l i c i t y ... 65
5.4.3 E le c tr o m a g n e tic S h o w e r S h a p e ...65
5.5 P h o to n C o n v e rsio n R ejec tion ...6 6 6 Selection Efficiency and Background Fractions 70 6. 1 E fficiency D e te rm in a tio n ... 7 2 6.1.1 CJ E n d p o in t E fficiency ... 7 2 6.1.2 N„,r ,lp E f f i c i e n c y ...7 4 6.1.3 //-M atch E fficiency ...75 6.1.4 Nhikn E f f i c i e n c y ... 84 6.1.5 I f / p E f f i c i e n c y ... 87 6.1.6 /Vrr,||.;/r|x E fficiency ... 9 2 6. 1.7 Total S electio n E f f i c i e n c y ... 9 2 6 .2 M isidentification F rac tio n D e t e r m i n a t i o n ... 9 4 6.3 K in e m a tic and G e o m e tr ic E f f i c i e n c i e s ...97
7 I'z°->|j|>/ F|md 103 7.1 D a ta S a m p l e ... 104
7 .2 T h e I V . o ^ J l ' i . u d M e a s u r e m e n t ... 106
7.3 S y ste m a tic E rrors ... 108
7 .4 S u m m a r y ... I l l 8 T he b Quark Forward-Backward Asymmetry 113 8.1 T h e A s y m m e tr y M e a s u r e m e n t ... 113
8.2 S y s te m a tic E rrors ...125
8.3 IJ° m ix in g c o r r e c t i o n ...134
9 Conclusion 137
List of Tables
1.1 T h e in te g ra te d lu m in o s ity recorded, b y O P A L , at th e various beam
e n e rg ie s d u rin g the 1990 and 1991 ru n n in g p e r io d s ... 2
2.1 T h e ch arge ( Q ) and iso sp in p ro je c tio n ( 1 0 to t th e term io n s in the e le c tro w ea k theory. ... 8
2.2 T h e s e m ile p to n ic b ra n ch in g ratios m e a su re d by th e ( T J X ) c o l
labora tio n at th e T ( 1 .s’) reso n a n ce 130) in the c o n te s t o f three s e m ile p to n ic d e c a y m o d e ls ... 2 2
6. 1 T h e e ffic ie n c y fo r a p r o m p t elec tro n in th e angular range ().SI > •
| cos 0\ < 0 . 9 1 to s a tis fy the C J e n d p o in t r e q u ire m e n t... 72 6 .2 T h e e ffic ie n c y fo r the C J e n d p o in t r e q u ire m e n t fo r in c lu s iv e m u o n s,
in th e a n g u la r r a n g e d .tilb < | c o s 0 | < 0.91, w i t h p r > 1.0 ( ic V /c s e le c te d w ith \ < 2 .0 a n d < 1 . 6 ... 73 6.3 T h e e ffic ie n c y fo r the C J e n d p o in t req u irem en t fo r tracks, s e le c te d
as d e sc rib e d in the te s t, in th e an g u la r range 0.816 • | cos 01 • 0 . 9 1 ...73
6 .4 T h e e ffic ie n c y fo r a p r o m p t elec tro n to s a tisfy th e re q u ire
m e n ts m the an g u la r range 0.816 < | cos 0\ < 0 . 9 1 ... 74
6.5 T h e e ffic ie n c y fo r p r o m p t e le c tro n s w ith p r > 1 G e V /c to sa tisfy
th e N mmv re q u ir e m e n ts d e te rm in e d w ith p u rer in c lu s iv e m u o n s a m p le s ... 75 6 . 6 T h e e ffic ie n c y fo r a p r o m p t elec tro n to s a tis fy th e /V.,,,,,,,, re q u ire
m e n ts , in th e a ngular ranged.H ID ■' | c o s f l | < 0.91, after req u irin g C J e n d p o in t in fo rm a tio n in the track fit. T h e e ffic ie n c ie s w ere d e te r m in e d u s in g in c lu s iv e m u o n s as d e sc rib e d in th e te x t... 75
6.7 T h e e ffic ie n c y fo r a p r o m p t elec tro n in the r e g io n 1).^ I • |cos/V|
-0.91 to s a tis fy th e re q u ire m e n t k 8 m ra d a fte r all
o th e r e le c tro n se le c tio n criteria h a v e b e e n a p p lie d ...81 6 . 8 T h e e ffic ie n c y fo r a p r o m p t ele c tro n w ith p r 1.0 G e V fc to
6.9 T h e e ffic ie n c y fo r a p r o m p t electro n in the reg io n 0.815 < I cos 0 \ < 0.0! to s a tis fy th e re q u ire m e n t Nhika < Id a fte r till o th e r ele c tro n
se le c tio n criteria h a ve b een applied. T h is e ffic ie n c y is d e te r m in e d fro m th e l'1/p d istrib u tio n as d e sc rib e d in th e te x t... 87
6 .1 0 T he e ffic ie n c y fo r a p r o m p t elec tro n w ith p r > 1.0 G e V /c to satisfy th e < 16 re q u ire m e n t...8 8
6.11 A co m p a riso n o f the p ro d u c t o f th e a n d 0 -m a tc h e ffic ie n
cies a n d a d e te rm in a tio n o f th e c o m b in e d e ffic ie n c y fo r p T >
0.8 G e V /c . N o sig n ific a n t co rrela tio n is s u g g e s te d ...8 8
6 .1 2 T h e e l fic ie n c y fo r a p r o m p t ele c tro n in the re g io n 0.815 < | cos 0\ < 0.91 to s a tis fy the re q u ire m e n t 0.8 < 1C j p < 1.2, d e te r m in e d as
d e sc rib e d in th e te x t... 89
6.13 T h e e ffic ie n c y fo r a p se u d o -c a n a id a te to s a tis fy die r e q u ir e m e n t
0 . 8 < 1C/ p < 1.2, fo r p r > 1.0 G e V /c d e te r m in e d u s in g p u r e r
in c lu s iv e m u o n sa m p le s... 9 2
6 .14 T h e e ffic ie n c y o f the Ncr,n.;/,|X .e q u ir e m e n t, fo r p r > 1.0 G e V /c ,
as d e te r m in e d fro m th e N c r ^ iq ,^ d istrib u tio n as d e sc rib e d in the te x t... 93
6.15 T he e ffic ie n c y fo r a p r o m p t e lec tro n to s a tis fy the s e le c tio n criteria
in the an g u la r range 0.815 < | cos ()\ < 0.91 fo r tw o tra n sverse m o m e n tu m re g io n s...93
6 .16 T h e n u m b e r o f the p r o m p t ele c tro n ca n d id a tes e x p e c te d to be
h a d ro n s m is id e n tifie d as e lec tro n s fo r the e n d c a p s e le c tio n ... 9 4
6.17 T he n u m b e r o f the p r o m p t ele c tro n ca n d id a tes fo u n d fo r each
m o m e n tu m bin fo r the en d c a p s e le c tio n ... 9 4
6.18 T h e p e rc e n ta g e o f th e p r o m p t e le c tio n sig n a l that is e x p e c te d to
be h a d ro n s m is id e n tifie d as ele c tro n s fo r th e barrel se le c tio n . . . . 9 6
6 .1 9 T he g lo b a l hadron m isid e n tific a tio n rates fo r th e e n d c a p a n d barrel
elec tro n sele c tio n s, fo r p T > 0.8 G e V /c , d e te r m in e d in th ree d iffe r e n t w a y s... 9 6
6 .2 0 T h e variation o f the h a d ro n ic co n ta m in a tio n o f th e p r o m p t elec tro n
sig n a l w ith |coh < 7 , f o r p T > 0 . 8 G e V /c ... 97 6.21 The k in e m a tic and g e o m e t r ic efficiencies fo r (n u m b e r o f C J space
p o in ts g rea ter than !9 , p > 2 G e V /c , p r > 0 . 8 G e V /c , |cos(?jPt| < 0.9, a n d (0.815 < | c o s ( / | < 0 .9 1 ;, as p r e d ic te d b y th e J E T S E T
M o n te C arlo[ 3 2 1...98
6 .22 T he k in e m a tic and g e o m e tr ic e ffic ie n c ie s fo r (n u m b e r o f C J sp a ce
p o in ts g re a te r than 1 9 ,p > 2 G e V /c , p r > 0 . 8 G e V /c , |cos(?t|„.,lsl| < 0.9, |co s (Ijp, | < 0.9, a n d ((| cos flj < 0 .7 ; o r (0.815 < | c o s 0 j < 0.91;), v i p re d ic te d b y the J E T S E T M o n te C V / o / 3 2 / ... 99
7.1 T h e n u m b e t o f p r o m p t electro n ca n d id a tes w ith tra n sverse m o m e n tu m g re a te r than 0 .8 G e V /c , o b s e r v e d in the sa m p le o f 4 8 4 3 6 7 m u ltih a d r o n ic e v e n ts ...105
7 .2 T h e n u m b e r o f h a d ro n s e x p e c te d to h a v e b ee n m is id e n tifie d as e le c tro n s a n d the n u m b e r o f re m a in in g e le c tro n s fro m p h o to n c o n v e r s io n ... 106 7 .3 T h e n u m b e r o f o b s e r v e d p r o m p t electro n s (first c o lu m n ). T h e
s e c o n d c o lu m n s h o w s the e x p e c te d n u m b e r o f o b se rv a b le p ro m p t e le c tro n s p re se n t in the total sa m p le o f m u ltih a d io .tic e v e n ts. . . 106
7 .4 T h e so u rce s o f s y s te m a tic error in the d e te rm in a tio n o l T / v 'im,i
an d th eir c o n tr ib u tio n s to the total e r r o r . ... ! 12
8.1 T h e fra ctio n o f th e p ro m p t e le c tro n sa m p le that is e x p e c te d to be e le c tro n s fr o m p h o to n c o n v e rsio n s in three re g io n s o f (cos j. 118 8 .2 T h e ratio F , j l'}i,~>,.-) fo r each p ro m p t so u rc e ... 124
8.3 T h e a s y m m e tr y o b ta in e d b y p e r fo r m in g the lik e lih o o d lit in three b in s o f | ... 126 8 .4 A | ' h o b ta in e d fr o m the o b s e r v e d a s y m m e tr y in three b in s o f
|<’os Othrustl. w he n h \ m, w ) is taken fr o m T able 6 .2 0 ... 126 8.5 T h e c o n trib u tio n s to the s y s te m a tic error on A '}.■ H b efo re co rre ctin g
List of Figures
1.1 T h e cra ss se c tio n for<'+v~ in tera ctio n s s h o w n as a fu n c tio n o f the ce n tre o f m a ss e n e rg y [5}... 3
2 . 1 T h e cro ss se c tio n fo r th e p ro ce ss c +c " —> h a d r o n s m e a su re d b y O P A L 1 161... 7 2.2 D e fin itio n o f the a ngle 0 ... 9 2.3 T h e fo rw a rd -b a c k w a rd a s y m m e tr y fo r b q u a rks ( tria n g le s, so lid
lin e) a n d c q u a rks (squares, d a sh e d line) vs. the ce n tre o f m a ss e n e rg y ... 10
2.4 |\/ 0 „>hh vs. A|:.h at ^ = 9! .2 O e V and m y o = 9 1 . 1 7 5 G e V /c 1. . . 12
2.5 (a) P ' / o a,i - (b ) -+rr vs. th e m a ss o f the to p q u a rk (in ,) in
the the S ta n d a rd M o d e ! / / 7 / w ith </s = 91.2 G e V a n d Myo -•
91.175 G e V /c 2... 13
2.6 /V|'H vs. the m a ss o f th e to p q u a rk ( n i,) in th e the S ta n d a rd
M o d e l [171 w ith s f i = 9 1.2 G e V a n d Myo = 91.175 G e V /c 2. . . 14
2.7 T h e dec y sp e c ta to r d e c a y li°,i -> l ) ' v +ut,... 16
2.8 P o ssib le so u rc e s o f p r o m p t le p to n s fro m b q uark decay. ... 16
2.9 T h e three casca d e d ec a ys, (a) 1) —> r - » M (b ) l> c - » c~
(c) I) —> t <’~ ... 17
2 .1 0 (a) T h e e le c tro n m o m e n tu m s p e c tru m in th e rest fr a m e o f th e d e
c a y in g b -lla v o u re d hadron as p re d ic te d b y th e m o d e l o f A lta r e ll i et dl. ( A r M ) [ 3 1/, (b) T h e elec tro n m o m e n tu m sp e c tru m in th e rest fra m e o f th e d e c a y in g c -lh tv o u re d hadron as p r e d ic te d b y th e A C M m o d e l...2 0
2.11 T h e ratio o f th e elec tro n m o m e n tu m in th e p a re n t rest fra m e to
the p a ren t m a ss ( m u ) fo r h - 1- r (squares) and r - 4 <* (tria n g les)
as p r e d ic te d b y th e J E T S E T M o n te C arlo [32[... 21
2.12 T h e elec tro n sp e c tru m fr o m If m e so n d e c a y s as m e a su re d b y the
C L E O co lla b o ra tio n at th e T ( l . s ') reso n a n ce [301... 23
2.13 T h e elec tro n m o m e n tu m in the d e c a y in g b -fla v o u re d h a d ro n rest
m e n ts; m o m e n tu m g rea ter than 2 G e V /c and and transverse m o m e n tu m w ith resp ect to the j e t a x is g rea ter than 0 .3 G e V /c as d isc u sse d in S e c tio n 4.4, in the lab fra m e (d a sh ed lin e) and th o se that d o no t (d o tte d l in e ' ...25
2 .1 5 T h e a n g le b e tw e e n the re c o n stru c te d j e t ax is and the p a ren t hadron
d ire c tio n fo r s im u la te d e v e n ts c o n ta in in g a 1> > e d e c a y ... 27 2 .1 6 T h e d iffe r e n c e b e tw e e n the th ru st a xis a n d the initial in/ d irectio n
fo r s im u la te d e v e n ts c o n ta in in g a !> - > •• d e c a y ... 24
3.1 A vertica l se c tio n v ie w o f the O P A L d e te c to r w ith the m a jo r s y s te m s in d ic a te d ...12
3.2 T h e O P A L ce n tra l tra c k in g s y s te m (fro m j 3 5 / ) ... 33 3.3 T h e en d c a p c a lo rim e te r s h o w in g h o w the en d c a p p r e s h o w e r c o u n te r
is m o u n te d o n t h ' lead g la ss array (fro m 1331)...16
3 .4 A n e x a m p le o f a "c o a r s e ” clt ste r sp lit in to tw o " tin e " clusters,
u s in g the a lg o rith m d e sc rib e d in the te x t...37
4.1 A n e v e n t s e le c te d as a m u itih a d ro n ic Z" d e c a y as d e sc rib e d in the te x t... 41
4 .2 A n e v e n t s e le c te d to be a s in g le elec tro n u sin g the p ro c e d u re
d e sc rib e d in th e te x t...43
5.1 T h e m e a su re d d E /d x in m u itih a d ro n ic e v e n ts in O P A L (fro m 1 4 3 j). 48 5 .2 T h e m e a su re d d E /d x d istrib u tio n fo r sin g le elec tro n s in the reg io n
0 .8 1 5 < | .*os 0 1 < 0 . 0 1...40
5 .3 (a) (se e E q u a tio n 5 .3 ) fo r en d c a p sin g le electro n s, (h)
R e s o lu tio n a-(< lE/< l.r)/(< lE/d.r) vs n u m b e r o f s a m p le s fo r sin g le e le c tr o n s ... 51
j . 4 T h e m e a su re d f'E i„ J p d istrib u tio n s fo r (a) sin g le elec tro n s, (b ) p i
o u s and (c) m u o n s fr o m c N1 -> / / ' / / e v e n ts , in the reg io n
0 815 < ! cos 0\ < 0 . 0 1 . (d) s h o w s the three d istrib u tio n s o v e rla id
on a lo g a rith m ic scale. T h e v e ry sm a ll E / p ( ~ 0.000J fo r m u o n s is e v id e n t in ( d ) ...53
5 .5 T h e g e o m e tr y u sed fo r the co rre cted energy. ...55 5 .6 f h e c o rre c te d e n e rg y -m o m c n tu m ratio ( E / p ) c o m p a re d to the
ra tio o f the c lu s te r e n e rg y a n d m o m e n tu m ( E ,inJ p ) fo r p io n s fr o m
K° d e c a y s ... 56 5.7 T h e m e a su re d E / p vs. |c o h 0 | fo r sin g le e lec tro n s in lo u r m o
5 8 59 6 0 6 2 6 3 6 4 67 68 69 71 77 7 8 7 9 80 82 83 lin e s) in lea d g la ss... A s c h e m a tic v ie w o f die 0 re c o n stru c tio n in th e E E ... T h e d istrib u tio n o f \ 0 lrnrk - 0ciu« ir \ fo r sin g le e le c tro n s a n d p io n s fro m K° dec a ys. T h e elec tro n se le c tio n c u t is at 0 .0 0 8 rad. . . . T h e N,,ik.i d istrib u tio n fo r ra d ia tive bhabha e v e n ts in the region 0 . 8 15 <
j
cos 01 < 0 . 9 1 ...T h e Nbik* d istrib u tio n fo r sin g le electro n e v n ts in re g io n 0 .8 1 5 <
| ru.s ()\ < 0 . 9 1 ...
T h e E / p d istrib u tio n fo r d ie m u itih a d ro n ic d a ta ... (a) T h e ratio o f E ,,m, to the m e a su re d d u s t e r e n e rg y fo r e lec tro n s fr o m bhabha e v e n ts in the a ngular range | cos 0\ < 0.7. (L) T he ratio o f E ri„„ to E, , n i , 2 fo r th e sa m e tra cks...
T h e E ,,m, / p d istrib u tio n fo r th e m u itih a d ro n ic data... T w o tracks (th e m e a su re d sp a ce p o in ts are s h o w n b y x j, and th e d ista n ce (d j at th e p o in t w h ere th e ir ta n g en ts are parallel, d is n o r m a lise d in th e c o n v e rsio n fin d in g a lg o rith m to e n su re a co n sta n t e flic ie n c y o v e r the en tire v o lu m e ...
T h e e x p e c te d avera g e E / p reso lu tio n fo r p r o m p t e le c tro n s in the a n g u la r range 0.815 < | cos 01 < 0 .9 1 ... T h e E / p d is trib u tio n s fo r all ca n d id a tes w ith p r > 1.0 G e V /c
in th e en d c a p a ccep ta n ce w ith all th e ele c tro n se le c tio n criteria e x c e p t the E / p re q u ire m e n t a p p lie d ... T h e E / p d is trib u tio n s fo r all ca n d id a tes w ith p T > 0 . 8 G e V /c
in the en d c a p a ccep ta n ce w ith all th e ele c tro n se le c tio n criteria a p p lie d e x c e p t the E / p re q u ire m e n t... T h e E / p d istrib u tio n s fo t all elec tro n ca n d id a tes w ith p T >
1.0 G e V /c in the en d c a p a ccep ta n ce w ith all the ele c tro n s e le c tio n criteria a p p lie d e x c e p t th e E / p and 0 -m a tc h re q u ire m e n ts. T h e E / p d istrib u tio n s fo r all p r o m p t elec tro n ca n d id a tes w ith p r > 0 . 8 G e V /c in the en d c a p accep ta n ce w ith all the elec tro n s e
le c tio n criteria a p p lie d e x c e p t the E / p a n d 0 -m a tc h req u irem en ts. T h e .V(T,||./,|X d istrib u tio n s fo r all p r o m p t elec tro n ca n d id a tes w ith p r > 1.0 G e V /c in the en d c a p a cc ep ta n ce w ith all the elec tro n se le c tio n criteria a p p lie d e x c e p t the /Va.iii/.ix re q u ire m e n t. . . . T h e Ncr,\\.\/i\x d istrib u tio n s fo r all p r o m p t elec tro n ca n d id a tes w ith p T > 1.0 G e V /c in the en d c a p a cc ep ta n ce w ith all the electro n se le c tio n criteria a p p lie d e x c e p t the /Vit,//. /,/., a n d 0 -m a tc h re q u ire m e n ts ...
6 . 8 T h e E / p d istrib u tio n s fo i nil ca n d id a tes w ith p r • 1.0 G e V /c
in ih e en d c a p acceptance w ith nil (hr elec tro n se le c tio n criteria a p p lie d e x c e p t the E / p and req u irem en ts. ... 85 6.9 T h e E / p d istrib u tio n s fo r all ca n d id a tes w ith p , > O.s G e V A
in th e en d c a p a cc ep ta n ce w ith all the ele c tro n se le c tio n criteria a p p lie d e x c e p t the E / p and A'/,/*, r e q u ire m e n ts...8 6 6.10 T h e raw e n e rg y d ep o sit, in the in n e r n in e b lo c k s u se d fo r th e E / p
d e te rm in a tio n , fo r iso la te d m u o n s in the range 0.N1 r> * ] < us 0 | «, 0.91 s e le c te d as d e sc rib e d in th e text. T h e average raw en e rg y
d e p o s it is a p p r o x im a te ly 3 0 0 M eV . ... 9 0 6. 1 1 T h e E / p d istrib u tio n s fo r p se u d o -c a n d id a te s o b ta in e d fro m c o m
b in in g the s in g le elec tro n and m u o n data fo r the case o f />, •
0 . 8 G e V /c ...‘U 6.12 T h e b a c k g ro u n d n o rm a lisa tio n s u sed to esta b lish the fraction o f the
p r o m p t elec tro n sig n a l that is hadrons m is iu e n tilie d as electro n s fo r th e barrel se le c tio n , f o r p r .> 0 . 8 G e V /c ...9 5
6.13 T h e m o m e n tu m sp e c tru m o f th e d e c a y elec tro n in the rest fra m e
o f th e d e c a y in g B m e so n , as p re d ic te d b y the A C M m o d e l /.?//, fo r i) —> a ~V\. (squ a res) h -> tic P„ (tria n g le s)...101 8.1 T h e d istrib u tio n o f Q ei js 0t i,nl„, fo r all p r o m p t elec tro n candid a tes
w ith P i > 0 . 8 G e V /c a n d p • 2 G e V /c ...115
8.2 T h e n u m b e r o f id e n tifie d e lec tro n s fro m p h o to n c o n v e r s io n s as a fu n c tio n o f |ro.s | ...117 8.3 T h e ratio o f th e n u m b e i o f elec tro n s id e n tifie d in sim u la te d data
fo r ea ch p r o m p t s o u rc e to the n u m b e r o f e le c tro n s id e n tifie d fro m d ire c t b d e c a y . ...119
8.4 (a )T h e d istrib u tio n o f the n u m b e r o f CJ sa m p le s u sed in the tra ck fit, fo r all m o m e n ta , fo r n e g a tiv e (so lid Une) and p o s itiv e (d a sh e d iin e) charges. T h e d iffe r e n c e s in the d istrib u tio n s arise fr o m L o r e n tz a n g le e ffe c ts in CJ. (b) s h o w s the sa m e d istrib u tio n , e x c e p t w ith a m in im u m m o m e n tu m re q u ire m e n t o f 2 G c V /r on th e tracks. T h e d istrib u tio n s arc sim ilar, e x c e p t at largo n u m b e rs o f s a m p le s ...121
8.5 T h e o b s e r v e d n u m b e r o f ev e n ts in a fo rw a rd (.r \.r\) bin m in u s th e n u m b e r o f e v e n ts in the co rre sp o n d in g b a c k w a rd (,r I r\)
bin d iv id e d b y the su m (.r ~ - Q.-os 0 ,|llllsl)...123 8 . 6 T h e ra w c lu s te r en e rg y fo r iso la te d p a rticles in m u itih a d ro n ic
e v e n ts ... 132
8.7 T h e p a rticle flo w in three j e t e v e n ts \(i7\. T h e data (p o in ts) ate fr o m [68], the M o n te C urio (h isto g ra m ) is J E T S E T 7.2 122]. . . . 133
8.K A p ro c e ss th a t g iv e s B a B° m ix in g . T h e virtual t q u a rk m a y also be an u o r c q u a r k ...135
9.1 I'y/t-tU vs. A[’b at y /s = 91.2 G e V a n d m Zo = 91.175 G e V /c 2.
T h e tria n g les co rre sp o n d to th e S ta n d a rd M o d e l p re d ic tio n [ 17] w ith a H ig g s m a ss o f 3 0 0 G e V /c 2 a n d various va lu es o f the top q u a rk m a ss fr o m 80 G e V /c 1 to 2 0 0 G e V /c 2. T h e u p p e r c u rv e is fo r a H ig g s m a s s o f 6 0 C 7c2 and th e lo w e r c u rv e is fo r a H ig g s m a s s o f 1000 G e V /c 2. T h e square is th is m e a su r e m e n t o f th ese tw o q u a n titie s and the d o tte d ellip se d e n o te s the 6 0 % c o n fid e n c e reg io n o f the tw o m e a su re m e n ts c o m b in e d ...138
T h e r e is a g r e a t n u m b e r o f p e o p le to w h o m I o w e d e e p g ra titu d e fo r th eir help and s u p p o r t d u r i n g the long jo u r n e y th a t led to this d issertation. First and fo r e m o s t I e x p r e s s m y d e e p thanks to the e n tire O P A L c o lla b o r a tio n fo r c r e a tin g a w o rk in g e n v i r o n m e n t w h ic h is so p le a sa n t an d pro d u c tiv e .
W h i l e e v e r y b o d y in O P A L has c o n trib u te d in s o m e w a y to this w ork, 1 must e x p r e s s spec ia l thanks to: R. S h y p it, from w h o m 1 hav e learned a great deal; J. Kroll fo r h is help in the u n d e r s ta n d in g o f the C L E O b ra n c h in g ratio m e a su re m e n ts; S. T a r e m fo r h e r c o lla b o r a tio n in the a s y m m e tr y m e a s u r e m e n t and, a lo n g with R. V an K o o te n , fo r d e v e lo p in g th e c o n v e rs io n finder used in this w ork.
F inally, R. d ’E n tr e m o n t has lived th ro u g h the h ig h s and low s o f this w o rk and h e r u n fa ilin g s u p p o rt and c o m p a n y have m a d e it all that m u c h e a s ie r
Introduction
T h e p h y sic s o f e le m e n ta r y particles has a d v a n c e d fro m try in g to u n d e r s ta n d the p ro p e rtie s o f a large c o llec tio n o f particles, to d e a lin g w ith only tw e lv e fe rm io n s (the q u a r k s an d leptons), o n e spin ze ro b o so n , and tw e lv e spin on e b o s o n s
that m e d ia te the po ssib le in tera ctions T h e s e intera ctio n s arc th e s tro n g force,
re sp o n sib le fo r the n u c le a r binding; the w eak intera ctio n , re s p o n sib le for n u c le a r beta d ec ay ; and e le c tro m a g n e tis m , re sp o n sib le fo r ato m ic b in ding. T h e r e ex ists a th eo ry that p re d ic ts the b e h a v io u r o f the w eak and e le c tr o m a g n e tic in te ra c tio n s as on e e n s e m b le . It is this theory th at will be tested in this thesis.
C e rta in c o n d itio n s m u s t be satisfied fo r the th e o ry to m a k e m e a n in g f u l (i.e. finite) p re d ic tio n s for all e ne rgies. T h e r e m u s t be three tim e s as m a n y q u a r k s as le ptons, e n s u r in g th at the sum o f the c h a rg e s o f the fe r m io n s is zero. T h is is a c h ie v e d by the inclusion o f a q u a n tu m n u m b e r called “ c o l o u r ” . E a c h q u a r k m a y h av e o n e o f th ree p o ssib le v alu es o f the c o lo u r q u a n tu m nu m b er. T h e in te ra c tio n in v o lv in g this q u a n tu m n u m b e r is the stro n g force. T h e w e a k and e l e c tr o m a g n e tic in tera ctio n s are blind to colour. A scalar p a r t i c l e ’s in tro d u c e d to in c o rp o r a te m a ss into the theory. Finally, in a d d itio n to the w e a k intera ctio n w h ic h tra n sfe rs c h a rg e , there m u s t be a w e ak intera ctio n that d o e s not in v o lv e the tra n sfe r o f charge.
T h e Z° b o so n w as p re d ic te d to be the m e d ia to r o f the w eak in tera ctio n th a t d o es n o t in v o lv e a tra n s f e r o f cha rge. S u ch “ n eutra l c u r r e n t” in tera ctio n s w e re first seen in n e u trin o s c a tte rin g e x p e rim e n ts in 1973 [2] and the Z° b o so n was o b s e r v e d d ire c tly in p ro to n -a n tip r o to n co llisio n s in 1983 [3], T h e L E P a c c e le r a to r [4] at C E R N w as d e s ig n e d to study in detail the p ro p e rtie s o f the Z° b o so n u sin g the clea n e n v i r o n m e n t o f c +v~ collisions.
F ig u r e 1.1 s h o w s s o m e cross sections f o r o + o~ co llisio n s as a fu n c tio n o f c e n tr e o f m a ss energy. In p ro c e sse s w h e re a Z° can be p ro d u c e d a large e n h a n c e m e n t is
1 A lth o u g h (tie m e a s u r e m e n t o f the m a ss o f the Z° at L E P has b e c o m e the first particle p h y s ic s m e a s u r e m e n t to h e sig n ific an tly affected by till the k n o w n forces o f n a tu re 11 ], th e force o f g r a v ity w ill b e ig n o red here.
e v i d e n t w hen the c e n tr e o f m a ss e n e rg y is equa l to the m ass o f the Z". E x p e r im e n tally this large e n h a n c e m e n t y ie ld s high rates, m a k in g possib le the d e te r m in a tio n o f th e c o u p lin g s o f th e f e rm io n s to the Z}\ In particular, final states w ith q u a r k - an tiq u a r k p a irs p ro v id e a p ra ctical o p p o rtu n ity to s tu d y in d etail the p ro p e rtie s o f the q u ark s.
T h e L E P a c c e le r a to r [41 is h o u se d in a 27 km c ir c u m f e r e n c e ring tit an ave rage d e p th o f a p p r o x im a te ly 50m . P o s itro n s and e le c tro n s circ u late in o p p o site d i r e c tio n s, c o llid in g in e ig h t p o ssib le p o ints a r o u n d the ring. T h e d e s i g n lu m in o sity o f t h e m a c h in e is 1.6 x I031 c m- ^ -1 w ith a ce ntre o f m ass en e rg y o f 100 GeV. T h e r e are d e te c to rs in four o f the e ig h t c o llisio n points, A L E P H [6|, D E L P H I [ 7 |, L3 [8[ and O P A L [9]. T h e w o r k in this thesis uses d a ta co lle c te d w ith the O P A L detector.
T h e first p h y sic s run o f L E P w a s in S e p te m b e r 1989 am. a p p r o x im a te ly 20 pl> 1
o f in te g ra te d lu m in o s ity was d e liv e r e d to e a c h e x p e r im e n t d u rin g the period o f 1989 to 1991. O n ly the d a ta co lle c te d d u r in g the 1990 a n d 1991 L E P ru n n in g p e r io d s are u sed here. D u rin g those runs, L E P w a s o p e r a te d at a p p r o x im a te ly s e v e n d iffe re n t ce n tre o f m ass e ne rgies. T ab le 1.1 s h o w s 'h e integ ra te d lu m in o sitie s re c o rd e d at e a c h e n e r g y p o in t b y the O P A L detector. c e n tr e o f m a s s e n e rg y (G e V ) ( n l . - 1) (1 9 9 0 ) (nl. ') (1 9 9 1 ) 8 8 485 90 89 627 114 90 393 159 91 3432 5763 92 457 161 93 563 277 94 562
T a b le 1.1: T h e in teg ra ted lu m in o s ity recorded, b y O P A L , at the va rio u s b ea m
e n e rg ie s d u r in g the 1990 and 1991 ru n n in g p erio d s. T h e p e a k o f the cro ss se c tio n is at a p p r o x im a te ly 91.26 G e V , the e n e rg ie s g iv e n in the table are ro u n d e d to th e netu'est integer. T h e lu m in o s ity v a lu es c o rre sp o n d to th e d e te c to r c o n d itio n s d e m a n d e d f o r the fo r w a r d -b a c k w a r d a s y m m e tr y m e a su re m e n t.
D u e to t h e p o ssib ility o f g o o d statistical p re cision, it is possib le to test the c u r r e n t th e o ry o f the in te ra c tio n s o f the Z°. T h is thesis reports o n two m e a s u r e m e n ts o f th e c o u p l i n g o f the Z u to the b q u a rk ; the partial d e c a y w idth o f the Z" into b q u a r k s (the fractio n o f the total n u m b e r o f Z () d e c a y s that are bb p a i r s7 and the f o r w a r d - b a c k w a r d c h a rg e a s y m m e t r y in the re actio n r +c~ - Z" —> bb. T o g e th e r th e s e m e a s u r e m e n ts test the s tre n g th an d fo rm o f the c o u p lin g o f the Z ” to b q uarks.
C ro ss -S e c ti o n (p b
LEP
CESR DORIS e V —> h a d r o n s P E P PETRA TRISTAN e*e~ —> g*/jT 10 120 100 20 40 60 8 0 0 (GeV) C e n t e r - o f - M a s s EnergyF ig u re 1.1: T h e cross se c tio n f o r c +v in tera ctio n s s h o w n as a fu n c tio n o f the ce n tre o f m a ss e n e rg y /5/.
S u ch tests are im p o rta n t, as it is w id ely b elieved that the c u rre n t theo'-y is only a low e n e rg y a p p r o x im a tio n o f s o m e dee pei u n d e rly in g truth. D e v ia tio n s from the p re d ic tio n s o f the c u r re n t th e o ry m a y p oint the w ay to u n c o v e rin g any hidden aspe cts o f the n a tu re o f e le m e n ta r y p artic le interactions.
Chapter 2
Theory
2.1
Electroweak Theory
T h e unified th e o ry o f the e le c tro m a g n e tic and w e ak in te ra c tio n s results fr o m w o rk b y G la sh o w , W e in b e rg and S alam ( G S W ) [ 10, 11, 12|. A l o n g w ith Q u a n tu m C h r o m o d y n a m i c s (Q C D ) , a g a u g e th e o ry o f the s tro n g intera ctio n , it fo r m s the basis o f the S ta n d a rd M o d e l o f the intera ctio n s o f q u a r k s and leptons. T h e g a u g e s tru c tu re o f the S ta n d a rd M o d el is S U ( 2 ) x U ( l ) x S U ( 3 ) , and the in te ra c tio n s are m e d ia te d by tw e lv e v e c to r g a u g e b osons; e ig h t c o lo u re d g lu o n s o f th e s tro n g in teraction, W + and W ~ o f the c h a rg ed c u r re n t w e a k in tera ctio n , Z° o f th e neutral c u r r e n t w eak in tera ctio n , and the p h o to n o f the e l e c tr o m a g n e tic intera ctio n . O n ly the “ e le c tr o w e a k ” se c to r o f S U ( 2 ) x l J ( l ) will be d iscu ssed here.
T h e G S W th eo ry has m a n y free p a ra m e te rs; tw o c o u p lin g c o n s ta n ts (g\ an d
<h) fo r the U ( l ) and S U (2 ) g ro u p s, the m a sse s and m ix in g s o f the fe r m io n s , a
v a c u u m e x p e c ta tio n valu e o f a sca la r field (the H ig g s fieid), and the m a ss o f a s c a la r particle (the H ig g s bo so n ). T h e th eo ry re d u c e s to th e F erm i th e o ry o f c h a rg e d c u r re n t w eak intera ctio n s (13) an d Q E D 114] at low e ne rgies. T h u s, by c o n s tru c tio n , the th eo ry e x p la in s all e x p e rim e n ta l d a ta o f c h a rg e d c u r r e n t w e a k in tera ctio n s at e n e rg ie s m u c h b e lo w 100 G e V an d in c o rp o r a te s Q E D . T b is th e o ry a lso pre d ic ted the e x is te n c e o f neutral c u r r e n t w e a k in tera ctio n s, w h ic h w e re first o b s e r v e d in 1973 | 2 | . It is these n eutral c u r re n t w e a k in tera ctio n s th a t are the s u b je c t o f this thesis.
D u e to the re n o rm a lis a b ility o f the G S W theory, o n ly a finite n u m b e r o f e x p e r im e n ta l inputs are n ee d ed to fix the p re d ic tio n s o f the th e o ry at all o rd e rs o f p e r tu r b a tio n theory. S in c e the c o u p lin g s <j\ and g-i, a lo n g w ith the v a c u u m e x p e c ta tion value (v) o f the s ca la r field are not m e a s u r a b le directly, a set o f e x p e r im e n ta l o b se r v a b le s m u s t be c h o se n to fix the theory. T h e c h o ic e is c o m p le te ly arbitrary, an d all c h o ic e s are e q u iv a le n t in the lim it o f infinite e x p e rim e n ta l p re c isio n an d infinite orders o f p e rtu rb a tio n theory. O n e set o f in p u t p a r a m e te rs , base d on p h y s
ically m e a n in g f u l inputs, has b e c o m e p r e d o m in a n t in the literature. T h ese inputs are n = c 2 /A ir m e a s u r e d in T h o m p s o n sca tte rin g (//J ~ 0){< is tlie ch a rg e o f the e le c tro n ), the m a s s e s o f the W * a n d Z° g a u g e b o s o n s (m \v and m y o ), the m a s s o f
the H ig g s sca la r an d the m a sse s o f the fe rm io n s in the th eo ry ; n f. S o m e o f
th ese in p u t p a r a m e te r s are not k n o w n or are k n o w n to a fairly low precision. T h e r e are m e th o d s to o v e r c o m e these u n ce rtain tie s and w ith o u r p re sen t k n o w le d g e the th e o ry is w e ll c o n stra in e d . It is im p o rta n t to m e a s u r e as m a n y in d e p e n d e n t o b s e r v a b le s as p o s s ib le to e x p o s e a n y in co n sisten cies in the p re d ic tio n s, as eve n o n e m e a s u r e m e n t w h ic h is in c o n siste n t w ith the p re d ic tio n s will d e m a n d m o d ificatio n s to th e theory.
In the S ta n d a rd M o d el, the lo w e s t o rd e r c ro ss section for the p ro c e ss e ' c > ff
( 7 a n d Z° e x c h a n g e ) is g iv en by {151
r t f. « r H c [ \ i > ( . s ) ] 4 ■/i / v u ' r m | \ i > ( * ) l ‘!
-T h e f a c to r N c is 1 fo r lep to n s an d 3 for q u a r k final states, f d e n o te s the final stale f e r m io n an d /if = w h e re * is the c e n tr e o f m ass en e rg y sq u ared . Q1 is the c h a r g e o f the f e rm io n , a n d 17 an d «r are the v ec to r and axial v e c to r c o u p lin g s o f th e f e r m io n to the TP. T h e fa c to r \ (J(.s) is g iven by
w ith niyo, t h e m a ss, and Vyo, the w id th , o f the Z° boson. F igure 2.1 sh o w s the cross
s e c tio n fo r the p ro c e ss o + <,_ -» h a d r o n s as a function o f the ce n tre o f m ass e n e rg y as m e a s u r e d by O P A L 1 16|. T h e h a d r o n ic cross section is pSO.Hti i ().(>‘2) nb 1 lb) a t th e Z° peak. B y i n tr o d u c in g the notation da dii £ y V , V 1 -: ' l / 7 r [ L ,i(.‘0 ( ! f c o s *0) W h e r e (7i(.s) = Q ’f - 2 QjI', I 7 h c [ \ i , (•''■)) I -I' « r ) L 'r + tlr — '1/tfUf ) | \ | | ( . s ) | J (V2(.s) = Q'f - 2 ( 1) r K 0 7 H c [ \ n(.s)] + ( i P u 2) i ' f \ \ {)(*)\'i .S - Ill y0 “f i I ilyo I '■/}) (2.2) C\Y - (2.3) m y a a n d (2.4)
OPAL
3020
10 0 X x 9 4 Vs (GeV)F ig u r e 2 . 1: T h e cro ss se c tio n fo r the p ro c e ss (*+ c>~ - * h a d r o n s m e a su r e d b y
G P A L 1161. T h e o p en p o in ts are fo r th e data c o lle c te d d u rin g th e 1989 L E P r u n n in g p e rio d a n d the s o lid p o in ts are fo r the 1990 ru n n in g p erio d . T h e c u r v e is the p re d ic tio n o f the S ta n d a rd M o d e l.
the fa cto rs \>r anti </f are g iven by i'r = - , - J L ~ ~ (2.5) 2's i r O r / ‘
«r =
C2.6)
i . s w f i i ’T a b le 2.1 s h o w s the c h a rg e (Q ) an d isospin pro jec tio n {/,<) a s s ig n m e n ts for the k n o w n fe rm io n s, a lo n g with the postu lated to p quark.
fe rm io n Q (units o f 0 !■, I'r 0 1/2 (' -1 -1/2 0 1/2 A -1 -1/2 I'r 0 1/2 I -1 -1/2 U 2/3 1/2 d -1/3 -1/2 c 2/3 1/2 s -1/3 •1/2 t 2/3 1/2 -1/3 -1/2
T a b le 2.1: T h e ch arge (Q ) a n d iso:,pin p ro je c tio n ( l :i) fo r th e fe r m io n s in the
e le c tr o w e a k theory.
T h e f o r w a r d - b a c k w a r d a s y m m e tr y (A |.h) is defin e d as
a - <7^ ' oh() > ()) ~ fT(('os 0j"_ ()) n 7
1 H r r ( r o s
0 >
0 ) + rr(,-os()
()) ’the d if f e r e n c e b e tw e e n the n u m b e r o f ev e n ts with the o u tg o in g fe rm io n scattered in th e fo r w a rd (cohO > 0) d irec tio n (/V/,') and the n u m b e r in the b a c k w a rd d irec tio n ( Nb) d iv id e d by the total n u m b e r o f events. 0 is the an g le o f the o u tg o in g fe rm io n w ith re s p e c t to the in c o m in g ele c tro n d irec tio n ( F ig u re 2.2). A t c e n tr e o f m ass e n e rg ie s n e a r to the mar.s o f the %°, m ass term s for the k n o w n fe rm io n s in the cro ss se c tio n f o r m u la ( E q u a tio n 2.1) m a y be n eglec ted and E q u atio n 2.7 b e c o m e s,
{v'i + + « r ) '
F ig u r e 2.2: D e fin itio n o f th e a ngle 0 . N o te th a t 0 is th e angle b e tw e e n th e in c o m in g
ele c tro n m o m e n tu m v e c to r a n d the o u tg o in g fe r m io n m o m e n tu m vector.
for the pro c ess u hc~ Z° —> ff. T h is also im p lies that, for x /s « m y o , the cross
section for this process, n e g le c tin g the p h o to n (Q j ) term , m a y be w ritten as
d a ((
tl cos 0 B
8 r
-f- COS 0 T ^ ^ ^ (2.9)
w ith B a n o rm a lisa tio n c o nstant. T h e S ta n d a rd M o d e l p re d ic tio n fo r A p B at \J& = !) 1.2 GeV, is 0.085 117 i. 1 T h is is c o n siste n t w ith the p re v io u s L E P m e a s u r e m e n ts :
AjjH = 0.097 ± 0.057 ± 0.014 O P A L [18]
A'ph = 0.126 ± 0.028 ± 0 .0 1 2 A L E P H [ 19]
A',Jh = 0.101 ± 0.000 ± 0.021 D E L H I [20]
A ' ^ = 0 .i:U ) tg :° « L3 [21],
D u e to the .s d e p e n d e n c e oi \ (), the fo r w a r d - b a c k w a r d a s y m m e tr y v arie s w ith the c e n tr e o f m a ss energy, F ig u re 2 3 s h o w s the p re d ic ted c e n tr e o f m a ss e n e rg y d e p e n d e n c e o f the f o r w a r d - b a c k w a r d a s y m m e tr y f o r b and c quarks.
At an y v a lu e o f | cos 0\, the f o r w a r d - b a c k w a r d a s y m m e t r y m a y be m e a s u r e d as
JV( + | c o s 0 | ) - /V( —|co - 0 \) A p B| cos 0\
V ( + | cos 0\) + N ( - \ c o s 0 \ ) 3 1 + cos2 0 ’ (2.10)
'Throughout this thesis, unless stated otherwise, all Standard Model values arc derived using m Zn = ill. 1 7 5 G eV /c2, nil = 132 GeV /c2 and jn| 1irb, = 3 0 0 G c V / r 2.
03 b.
^
0.12 0.08 0.04 -0.04 -0.08 -0.12F ig u r e 2.3: T h e fo rw a rd -b a c k w a rd a s y m m e tr y f o r b q u a rks (triangles, s o lid lin e)
a n d c q u a rk s (sq uares, d a sh ed line) vs. the c e n tre o f m a ss energy. T h e se cu rv e s are th e S ta n d a rd M o d e l [17] p r e d ic tio n fo r a to p m a ss o f 132 G e V /c 2 and a H ig g s m a s s o f 3 0 0 G e V /c 2. m 7n = 91.175 G e V /c 2 is indicated.
w ith /V( + | r o s 0 | ) (y V ( ~ |n > H 0 |)) the n u m b e r o f fe rm io n s scattered at positiv e (ne gative) cos 0. T he e x p e r i m e n t . ! sensitivity to the fo r w a r d - b a c k w a r d a r y m m e tr y thus varies as | r o s0| / ( l + c o s2 0), and th e re fo re it is im p o rta n t to e x te n d the a c c e p ta n c e to as large values o f I cos 0 | as possible.
T h e partial width o f the Z° fo r each fe rm io n is specified by the S ta n d a rd M o d el. In low est o r d e r o f p e rtu rb a tio n th e o ry the partial w idth into fe rm io n p airs is g iven,
fo r ene rgies .s « m Zo, by [ 15]
—>rr = { u ’f + rtf) . (2.1 1) has been m e a s u r e d to be I li.nl = 0 . 2 2 0 ± 0.008 ± 0.018 I h a d
I
= 0. | <)8 ± 0.000
±
0.011 ± 0.021
1 h a d = :i8.r) ± 7 ± 11 M e V = 0.215 ± 0.017 ± 0.024 I h a dAll these re su lts are c o n s is te n t w ith the S ta n d a rd M o d e l p re d ic tio n o f Fzo-un, = 870 M e V [ 1 7 1. Pj,,,,! has been n ie a s u r s d to be 1.740 ± 0.012 G e V [25].
It is im p o rta n t to n o te at this p o in t that the a b o v e e q u a tio n s will be m od ified w h e n hig h er o rd e rs o f p e r tu r b a tio n th e o ry are c o n sid e re d . H o w e v e r no m o r e d e g r e e s o f fre e d o m e n t e r the th e o ry in h ig h e r orde rs. T h e G S W th e o ry m a k e s o n ly on e p re d ic tio n fo r an y o b se r v a b le , an y v a ria tio n o f these p re d ic tio n s arises p u re ly from u n c e rta in tie s in the ca lc u la tio n s ^finite o rd e rs, a p p r o x im a tio n s ) o r in the input p a r a m e te rs . F o r the f o r w a r d - b a c k w a r d a s y m m e tr y an d partial w id th to b q u a rk s, F ig u r e 2.4 s h o w s the a llo w ed re g io n o f v a lu e s at the Z° p e a k d u e to these u n ce rtaintie s. T h e r e m a in in g freed o m o f the v a lu e s c o m e s m a in ly from the u n k n o w n m a s s o f the to p q u a r k and the m ass o f the H ig g s boson. Abb is m u c h
m o r e sen sitiv e to the to p q u a r k m a ss than is the q u a n tity r Zo T h is arises from
the c a n c e lla tio n o f s o m e o f the to p q u a r k m ass d e p e n d e n c e in d ia g r a m s that e n te r the c a lc u la tio n o f r Zo->i>i>. F ig u r e 2.5 sh o w s the v a ria tio n o f Fzo_>bb a n d Pz°->rc w ith the m a ss o f the to p quark. S in c e P Zo->iii> is m u c h less sen sitiv e to the m ass o f the top q u a r k ( m t), a m e a s u r e m e n t o f r z°->bi> m a y test the S ta n d a rd M o d e l m o r e p re cisely eve n w h e n the m a s s o f the top q u a r k is u n k n o w n . In c o n tr a s t A |j B is sensitive to the m a s s e s o f th e top q u a rk and H ig g s b o so n (F ig u re 2.6). T h is d e p e n d e n c e m a k e s A |)b a less re lia b le test o f the m o d e l w h e n these m a s s e s are not k n o w n , but a m e a s u r e m e n t o f Abb could p ro v id e an in d icatio n o f p o ssib le valu es o f the H iggs m a s s o n c e the top m ass in k n o w n .
O P A L [22)
O P A L [18] L 3 [23] A L E P H [24].
>
(D 379 378 'X X I N 377 376 375 374 373 372 1 0.072 i i i > I . i i i I i i i i I i i 0.076 0.08 0.084 i i i i i i I i i i i I i i i i I i i i i I h 0.088 0.092 0.096 0.1 0.104 a !;,, F ig u r e 2.4: Fy/1->!>!) vs. A | ’h at \ / s = 9 1-2 G e V a n d m y » !> I . ITA G e V /e 2. T he tria n g le s c o rre sp o n d to a H ig g s m a ss o f 3 0 0 G e V / K T h e u p p er c u rv e is fo r a H ig g s m a ss o f 6 0 G e V /c 2 a n d the lo w e r c u rv e is fo r a H ig g s m a ss o f 1000 G e V /c 1. T h e to p m a ss varies b e tw e e n 8 0 G e V /c 1 (to p lef t ) to 2 0 0 G c V /e 1 (b o tto m right). T h e u n e v e n n e s s o f the lin e s re fle c ts the ca lcu lu tio n a l uncertainties.378 IU <§. 377 I 376 1' t ? 375 374 373 372 371 . .L ...i I I I I I ___1 _ i - i i I -> L _ i i I i I I -I I ■ L 80 100 120 140 160 180 200 ith ( G e V / c 2) 300 O 299 298 297 296 295 294 293 120 140 160 180 200 80 100 Vh ( G e V / c 2)
Figu>"* 2.5: (a) I'z0->i»i. iinc^ (b ) F / o v s . the m a ss o f the to p q u a rk (?/> J in the
the S ta n d a rd M o d e l I1 7 j w ith y /s = 9 1.2 G e V a n d My_,o = 9 1 .175 G e V /c 2. T h e
tria n g les co rre sp o n d to a H ig g s m a ss o f 3 0 0 G e V /c 2, w h ile the u p p e r c u rv e s are fo r a H ig g s m a ss o f 6 0 G e V /c 2 and the lo w e r c u rv e s are fo r a H ig g s m a ss o f 10 0 0 G e V /c 2.
0.104 0.1 0.096 0.092 0.088 0.084 0.08 0.076 0.072 80 100 120 140 160 180 F ig u r e 2.6: A p B vs. the m u ss o f th e to p q u a rk ( m j in the th e S ta n d a rd M o d e l / 17/
w ith v/s = 91.2 G e V a n d M v« = fJ1.175 G e V /c 2. T he tria n g les c o rre sp o n d to a
H ig g s m a ss o f 3 0 0 G e V /c 2, w h ile the u p p e r cu rv e is fo r a H ig g s m a ss o f 6 0 G e V /c 2 a n d th e lo w e r c u r v e is fo r a H ig g s m a ss o f 1000 G e V /c 2.
2.2 b-flavoured Hadron Decays
T h e a v e ra g e b h ad ro n lifetim e has been m e a s u r e d by O P A L to be [ 2 6 J
I ..'57 ± 0 . 0 7 ( s t a t ) ± O.OG(sys) ps. (2 . 12)
W ith this a v e r a g e lifetim e b -fla voured h a d ro n s p ro d u c e d at the Z° travel a p p r o x im ately 2 m m b e fo re d e c a y in g , and th e re fo re d ire c t o b s e r v a tio n o f b -fla v o u re d h u d ro n s in the d e te c to r is p ra ctically im possible. Identification o f h a d r o n ic ev e n ts that o rig in a te fro m bl> q u a r k p airs thus re q u ires the identification o f the b -fla v o u re d h a d ro n from its d e c a y p ro d u c ts in the detector.
T h e d e c a y s o f h a d ro n s c o n ta in in g h ea v y (b and c) q u a r k s are m o s t easily u n d e r sto o d in the c o n te x t o f the so ca lle d “ S p e c ta to r M o d e l” [27]. T h is m odel m a k e s the a ss u m p tio n th at the d e c a y o f a h adron c o n ta in in g a h e a v y q u a r k is the in d e p e n d e n t d e c a y o f the heavy q u a r k v ia virtual W em issio n , w ith the o t h e r q u a rk s in the h adron h a v in g no influence. A fte r the h e a v y q u a rk d e c a y s, all the r e m a in in g
q u a r k s form h ad ro n s. F igure 2.7 s h o w s the sp e c ta to r d e c a y B°,i —>
D e c a y s or h a d r o n s c o n ta in in g h e a v y q u a r k s thus pro c eed via a chain o f virtual W em issio n . W h e n lep to n s are p re sen t in the d e c a y p ro d u c ts o f the h a d r o n , the d e c a y is term e d se m ile p to n ic ( i f the lepton is an elec tro n the d e c a y will b e term e d s e m ie le c tr o n ic ). A ny lepton th a t orig in ates d ire c tly fro m b e r e q u a r k dec ay s o r from any o f the th re e c a s c a d e pro c e sse s will be term e d a “ p r o m p t ” lepton. F ig u r e 2.8 s h o w s that th e d e c a y chain o f a b -fla v o u red h a d r o n m a y re s u lt in tw o p r o m p t leptons, w hile c h a d ro n s m ay o n ly p r o d u c e o n e p r o m p t lepton. T h e d ec a y c h a in s b —> c —> <,+, b 4 r - > c~ an d b - 4 r - 4 o~ are k n o w n as “ ca sc a d e p ro c e s s e s ” an d are s h o w n in F ig u r e 2.9. 2
T h e b ra n c h in g ratio o f a h a d r o n (h i) into ele c tro n s B ( h \ —> i'V7.X) is g iven by
the ra tio o f the partial w id th into ele c tro n s d iv id ed by the total w idth. T h e lifetim e o f a h ad ro n is j u s t the inverse o f the total width an d th e re fo re
T h e re la tions in E q u a tio n s 2.13 an d 2.14 m a k e no a ss u m p tio n o n the ac tu a l d e c a y m e c h a n is m s . S in c e s p e c ta to r d e c a y s o f th e sort s h o w n in F ig u r e 2.7 are e x p e c te d to be the d o m i n a n t p ro c ess in se m ile p to n ic d e c a y s o f h ea v y q u a r k s , the se m ie le c tr o n ic
I1(h\ —> (■/'<..V) = — (2.13)
■Throughout this thesis, the charge conjugate processes arc implied, e.g.: I) -> <• - 4 e + implies also h —> c —> i’_ . When no distinction is to lie made between b - t r 4 e+ and b - 4 c - 4 p“ the symbol h -4 c —> <■ will denote both processes.
W +
B °
D ‘
F ig u r e 2.7: T h e d e c a y sp e c ta to r d e c a y W \\ ■ -> I)
F ig u r e 2.8: P o ssib le .sources o f p r o m p t le p to n s fro m b q uark decay. N o te that b
F ig u r e 2.9: T he th ree cascade decays, (a) l> c c + (b) 1> —> c -> t~
d e c a y rates fo r tw o h a d ro n s (h i an d h „.) c o n ta in in g the sa m e heavy q u a r k should be
e q u a l; r / l | _+l.^A' 52 U s in g this e x p e c ta tio n and E q u atio n s 2.13 and 2.14
the s e m ie le c tr o n ic b ra n c h in g ratios and lifetim es o f tw o h a d ro n s c o n ta in in g the s a m e h ea v y q u a r k sh o u ld be re la te d by
T!± = !1± !L L Z L ^ pi <5 )
Th,
11(1,2 - > < • ) ’r e g a rd le s s o f w h e th e r th e total d e c a y w id th o f the h ad ro n s are equa l o r not. F or the D system , the b ra n c h in g ratios and lifetim es are m e a s u r e d to be | 2 8 | ,
r|)o = (4.21 ± 0.10) x 1 0 - ,:i s (2.16)
r o t - - (10.02 ± 0 . 2 8 ) x 10“ l:! s (2.17)
H (l)° -> c+.V) - (7.7 ± 1.2)% (2.18)
B ( D ± - M ' . V ) = (10.21-J;')% . (2.19)
s e m ile p to n ic d e c a y s o f these m eso n s.
T h e v irtual W e m itte d in b q u a r k d e c a y m a y m a te ria lise as any o f the pairs: e - E£, n +V fn sc, d r , d u o r su. Q u i g g and R o s n e r [ 2 9 1 h a v e ca lc ulated the rates for th ese virtual W b ra n c h in g s, a s s u m in g th a t only l> -> c W " o cc u rs anti 1> > uVV
d o e s not, to be: r ( i > c( ~k ) = s i ’ » t e ) 5 ( 2 . 2 0 ) P ( l ) — > c / U P , , ) -
I '
- ( “ ) V ( - r / . « . , ) ( 2 . 2 1 ) F ( b —> c tV t ) ■= I 1'., f e ) '
. ' / O ' " ,i
( 2 . 2 2 ) r ( b - > ( c ( d u ) ± c ( s u ) ) ) =( s t ) r7 ( ' " . / " ' i . )
( 2 . 2 3 ) F ( b - >(c(dr)
+e(sc)))
=jo n. ( s ) ” " 1'1" ' ' /
< > ■ ( 2 . 2 4 )T h e m , are m a s s e s o f th e fe rm io n s and F„ is a n o rm a lisa tio n factor. T h e phase s p a c e fa c to rs f { y ) and </(/;) are given by:
f ( v ) = ( 1 — . ( / ' ) ( ! ~
-V ±
/ / ')
-I‘V I"
Ul(2.25)
an d
g ( v ) = (I
- 7.V/2 - //V8 - , VVI0) ( l
~ u ) ' ri± . V ( 1 - ; / / 7 10) In ( 1±^ p ) •
If the m a ss o f the b q u a r k is taken to be mi, -- .TO G e V / c 2 , the c q u a rk m ass is ta k e n to be rn c = 1.5 G e V / o2 and u sin g the r m ass o f m , - | .7fSd I G e V / r2
then
T h is p re d ic tio n has n o t been tested directly, h o w e v e r it c a n be s h o w n to be p la u sible. T h e h a d ro n fo rm e d by the ch a rm q u a r k fro m the d e c a y b - » <• W ~ , will be a s s u m e d to d e c a y to e le c tro n s with the b ra n c h in g ratio 11 (c -> c>+ ) = 0.079 [28], w h ic h is an a v e ra g e o f low e n e rg y m e a s u r e m e n ts with u n k n o w n m ix e s o f c h a r m e d h ad ro n s. T h e virtual W ~ is p re d ic ted to branch into a c q u a r k and a d - ty p e q u a r k 15% o f the tim e. D u e to the m a g n itu d e s o f the qu ark m i x in g an g le s [28], cs is e x p e c te d to d o m in a te , henc e it will be a ssu m e d that 15% o f the tim e the virtual W ~ :'orms a 1)~. H e n c e I1(\> -> r - » v) m a y be w ritten as
l i ( U - > c - > c) « H ( r - > o + ) + 0 . 1 5 / ^ ( D ~ - > ( - ) .
U s in g B ( I) " —> ('_ ) = 1.00/ i ( D ° - » <'“ ) (fro m E q u a tio n 2.15 u sin g r D~ = 4. i5 x 10“ 1:1 s 128]), the p re dic tion is I1(\> -> c - » c>) « 0.09, w h ic h is in g o o d a g r e e m e n t w ith the m e a su re d v a lu e o f (0.097 ± 0.010) [30].
A n ex p e c ta tio n fo r the lep to n m o m e n tu m sp e c tru m is n e e d e d to p re d ic t th e efficien cy fo r leptons from h e a v y q u a rk d e c a y s to satisfy a n y k in e m a tic r e q u ir e m en ts. F ig u re 2 .1 0(a) s h o w s the m o m e n tu m o f th e electron in the d e c a y i n g h a d ro n •rest fr a m e f o r the d e c a y b c ~ 7 v '. T h is sh o u ld be c o m p a r e d to the sp e c tr u m in F ig u r e 2 .1 0 (b ) for the d ec a y c e + //(.s. T h e large b - c q u a r k m a ss d iff e r e n c e re sults in a larg e r ele c tro n m o m e n tu m e n d p o in t. A n g u la r m o m e n t u m c o n s i d e r a tions also s u g g e s t that the e le c tro n takes a large r fraction o f the a v a ila b le e n e r g y in b d e c a y th an in the c o r r e s p o n d in g c h a rm d e c a y (F ig u re 2.11). T h e ele c tro n in b d e c a y will h a v e the h ighest e n e rg y w h e n it recoils a g a in st the a n ti-n e u tr in o a n d the c h a r m e d q u ark . In the c o r r e s p o n d in g c d e c a y this to p o lo g y is n o t a llo w e d f o r m a ssle ss final state particles, d u e to the lefth a n d ed nature o f the c h a rg e d c u r r e n t w e a k interaction. In th e case o f m a s s iv e final state particles h elicity c o n s id e r a tio n s d e te r m in e the elec tro n m o m e n tu m sp ec tra s h o w n in F ig u r e 2 . 1 1.
T h e C L E O c o lla b o ra tio n has re p o rte d m e a s u r e m e n ts o f the s e m ile p to n ic b r a n c h ing ratios l l { I) -> <\Y), l i (b -» <• -> o.Y), at the T (4,S') r e s o n a n c e u sin g v a rio u s d e c a y m o d e ls [30|. T h e C L E O c o lla b o ra tio n c o n s id e r e d the free q u a r k m o d e l o f A ltarelli et a l. (A C M ) [31] (a s p e c ta to r m o d e l) an d two fo r m s o f the d e c a y m o d e l o f I s g u r c / r / / . 133]. T h e original m o d el o f Isgur e t al. ( I S G W ) has, in prin cip le, n o free p a r a m e te rs and p re dic ts th a t the d e c a y s B - » D c + ^ . Y , B —>■ l ) V + /x..Y a n d B -> l ) * V + /',..Y, o c c u r at the rates 2 7 % , 6 2 % an d 11% resp ectiv ely . C L E O a lso c o n s id e r e d a m o d ified version o f the I S G W m o d el (I S G W * * ) in w h ic h th e re la tiv e rates to D a n d 1)* w e re held co n sta n t, bu t the b ra n c h in g ra tio to I)** w as in c re a se d to 3 2 % o f the total. T h is c h a n g e in the B -> L** b ra n c h in g ra tio im p ro v e d th e a g r e e m e n t w ith the C L E O d a ta [ 30].
T h e C L E O c o lla b o r a tio n ’s m e a s u r e m e n ts o f the b ra n c h in g ra tio s B { b - » I X ) and B {b •-> o I X ) w e re o b ta in e d by fitting the o b se rv e d lepton sp e c tr u m [30].
F ig u r e 2.12 sh o w s the m e a s u r e d elec tro n sp e c tru m , w ith the fit to th e A C M m o d e l s u p e rim p o se d . T h e m o d e llin g o f the se m ile p to n ic d e c a y is im p o r ta n t f o r
C/> o <u T5 <U X ) a e 70 60 50 40 30 20 10 0 0.4 0 0.8 1.2 1.6 2
(a)
2.4 2.0 p ( G e V /r ) 175 150 C/i >> 125 ■g 100 75 50 25 * i -J «1 * V 4 -2.4 2.8 0 0 0.4 0.8 1.2 1.6 2 p ( G e V /r )F ig u r e 2 .1 0 : (a) T h e ele c tro n m o m e n tu m sp e c tru m in the rest fra m e o f the d e c a y in g
b -fla v o u r e d h a d ro n as p r e d ic te d b y the m o d e l o f A lta re lli et al. ( A C M ) j 3 l j . (b) T h e e le c tro n m o m e n tu m s p e c tru m in th e rest fra m e o f th e d e c a y in g c -lla v o u rc d h a d ro n as p r e d ic te d b y th e A C M m o d e l. T h e large b~ c m a ss d iffe r e n c e resu lts in a la rg er p o s s ib le ele c tro n m o m e n tu m .
- T "
- f
p j m u
F ig u r e 2.11: T h e ratio o f th e elec tro n m o m e n tu m /v in th e p a ren t r e st fra m e to the
p a re n t m a ss ( m u ) fo r l> -> c (squares) and c v (tria n g les) as p r e d ic te d b y the J H T S E T M o n te C arlo 1321. T he d iffe r e n t sh a p es o f th e tw o d is trib u tio n s can be
e x tra p o la tio n to re g io n s o f low electron m o m e n tu m , w h ich are not e x p e rim e n ta lly a c c e ssib le an d to sep a ra te d ire c t b d e c a y s 1'ioin c a scad e decays. D ifferen c es in the e x tr a p o la tio n s re su lt in d iffe re n t b r a n c h in g ratios. F ig u re 2.13 c o m p a r e s the m o m e n tu m s p e c tru m for s e m ile p to n ic d e c a y s o f B m e so n s in the B rest fram e from the A C M and th e IS G W * * m o d e l. T able 2.2 s h o w s the b ra n c h in g ratios o b ta in e d by C L E O in the c o n te x t o f th ese m o d e ls 130].
ISGW model ACM model ISGW** model
B {b -> lviq)% 9 . 9 ± 0 . 1 ± 0 . 4 1 0 . 5 ± 0 . 2 ± 0 . 4 1 1 . 2 i 0 . 4 I 0 , 1 Ok .
I
I 1 1 1 . 3 ± 0 . 7 ± 0 . 0 9 . 7 ± 0 . 8 ± 0 . 0 9 . 0 1 0 . 8 1 O.ti B { b -> lu,u)% 0 . 0 0 ± 0 . 0 8 ± 0 . 0 4 0 . 2 8 ± 0 . 1 2 ± 0 . 0 4 0 . 2 r 1 0 . 1 0 I 0 . 9 2T ab le 2.2: T h e s e m ile p to n ic b ra n ch in g ratios m e a su re d b y the C lJ iO co lla b o ra tio n
at th e T ( 4 S ) re so n a n c e [301 in the c o n te x t o f three se m ile p to n ic o e c a y m o d e ls. T h e b ra n c h in g ratio B {b —> //>/q) in c lu d e s the 1> > li'/n co n trib u tio n .
A t >/s ss oiya, the efficien cy for p r o m p t ele c tro n s from b d ec a y to satisfy any k in e m a tic r e q u ir e m e n ts is d o m in a te d by the en e rg y sp e c tru m o f the parent b -fla v o u re d h a d r o n s ( f ra g m e n ta tio n ), as s h o w n in F igure 2.14. T h is is in c o n trast to m e a s u r e m e n ts at the T ( 4 S ) re so n a n c e w h e re the B m eso n s are p ro d u c ed n ea rly ,t rest an d thus the lepton m o m e n tu m s p e c tru m is d o m in a te d by the tlecay sp e c tr u m . S in c e it is n e c e s s a ry to use s e m ile p to n ic b r a n c h in g ratios d e te r m in e d at the T ( 4 S ) r e s o n a n c e and these b ra n c h in g ratios vary with the m odel o f the lepton m o m e n t u m s p e c tr u m used, it is n e c e ssa ry to tak e into ac co u n t these c o r re la tio n s w h e n c a lc u la tin g p r o m p t e le c tro n k in e m a tic efficiencies.
2.3
b Fragmentation
T h e p ro c e s s by w h ic h a qq p a ir e v o lv e s into a system o f c o lo u rle ss h ad ro n s is k n o w n as fr a g m e n ta tio n , w h ic h is d o m in a te d by n o n p e r tu r b a tiv e processes. A o im plistic p ic tu re o f the fra g m e n ta tio n process is that the c o lo u r lines o r force b e tw e e n the tw o q u a r k s are stretched an d p ro d u c e qq pairs that also m o v e apart. T h is p ro c e ss c a n c o n tin u e until no m o re en e rg y is a v a ila b le to m a te ria lise qq pairs. T h e q u a r k s p r o d u c e d in this m a n n e r then g ro u p into c o lo u rle ss states, w h ich are the o b s e r v e d h ad ro n s.
In this p ic tu re o f fr a g m e n ta tio n , q u a r k s are m o s t likely to g ro u p into h a d ro n s if th eir v e lo c itie s are eq u a l. A h e a v y q u a rk m u st lose very little e n e rg y to m ateria lise a light q u a r k w ith the s a m e velocity. T h e r e fo r e it is e x p e c te d that h a d ro n s c o n ta in in g a p rim o rd ia l h e a v y q u a r k sh o u ld carry m o re o f the initial q u a rk e n e rg y on a v e rag e ,
0 1 4 0 6 9 0 - 0 0 7 0 . 4 0
*
E l e c t r o n s
0 . 3 0 -o 0 . 1 0 r D - r U l i / 3 . 0 01.0
2.0
0 4 . 0 M o m e n t u m ( G e V / c )F ig u r e 2.12: T h e elec tro n sp e c tr u m fr o m B m e so n d e c a y s as m e a su re d b y the
C L E O co lla b o ra tio n at the T ( 4 S ) reso n a n c e [30]. T h e d ire c t a n d casca d e c o m p o n en ts, as p r e d ic te d b y th e A C M m o d e l [31], are sh o w n .
r a m b e r of B — >■ e.Y d e c a y s 35 30 -25 20 15 10 -5 - 0 • ACM m odel ▼ ISGW** m odel ® _y y T T * ® Y ▼ V _ # I Y Y < « -Y- i « Y-Y-* Y « a Y to V -Y-» •Yto V® Y® Y* t
l I i ...i— i - i — I - l j — L - i— i— j - . i I. _ i i. —i— i _ L j _ l . I * . * « 0 b > b t o « « s « «
0.4 0.8 1.2 1.6 2 2.4 2.8
p ( G e V /r )
F ig u r e 2.13: T h e e le c tro n m o m e n tu m in the d e c a y in g b -fla v o u re d h adron rest
140 120 80 X) 20 2.4 /; (G e V /c ) 0.4 0.8 1.6 2.8
F ig u re 2.14: T h e ele c tro n e n e rg y in the rest fra m e o f the d e c a y in g B m e s o n (s o lid
lin e) sep a ra ted in to th e e le c tro n s that s a tis fy the req u irem en ts; m o m e n tu m g rea ter than 2 G e V /c and a n d tra n sverse m o m e n tu m w ith re sp e c t to th e j e t a x is g rea ter than 0 .S G e V /c as d is c u s s e d in S e c tio n 4.4, in the lab fra m e (d a sh e d line) a n d th o se that d o n o t ( d o tte d lin e). T he flu c tu a tio n s ir< th e B m e so n m o m e n tu m in the lab fra m e d o m in a te the p ro b a b ility that an ele c tro n w ill s a tis fy a n y k in e m a tic re q u ire m e n t im p o s e d in the la b fram e.
