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-- . iiii ii i1,1 iiii i i, , ,| J

This document and the material and data contained therein, w_ devel-oped under sponsorship of the United States Government, Neither theUnited States nor the Department of Energy, nor the Lel_d St_fordJunior University, nor their employees, nor their respective contractors,subcontractors, or their employees, makes any warranty, express or im-plied, or assumes any liability or responsibility for accuracy, complete- .hess or usefulness of any information, apparatus, product or processdisclosed, or represents that it_ use will not infringe privately-ownedrights. Mention of any product, its manufacturer, or suppliers shallnot, nor is it intended to, imply approval, disapproval, or fitness forany particular use. A royalty-free, nonexclusive right to use and dis-seminate same for any purpose whatsoever, is expressly reserved to theUnited States and the Univ_ersity.

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SLAC-I_-95-459TOHOKU-HEP-95-02

TO HOKU- HEP- NOTE- 95-07UC-414

A SEARCH FOR JET HANDEDNESS

IN HADRONIC Z ° DECAYS

Yoji Hasegawa

Stanford Linear Accelerator Center

Stanford University, Stanford, CA 94309

March 1995

Prepared for tim Department of Energy '"under contract number DE-AC03-76SF00515 '"

a

Printed in the United States of America. Available from tile National Technical [nif)r-

mation Service, U.S. Department of Cornrnerce, 5285 Port Royal Road, Springfield,Virginia 22161.

*Ph.D thesis, Tohoku University

BJlJOTC'fl

DISTRIBUTIONOF THIS DOCUMENTIS UNUMITED_

J

, ,_,,...... "' .Pl,r' pP=" r,=,_,, ,,r O, '_"' "1_ Irl...... l!_ ...... " ........ .i.,,1, ' ' 'l['lll ...... rl ..... I,_' r v,,_r ,'p,',_r,'lnl'",=l',r=p"' H, P==l]llll,.',rl,,T,,,,'pl, l_i=T 1lr ,=,,r,P''111I' ' '=i!llll_r ....... _=tlllr ',',l,q_l ...... =r,, ,l'l=ll ,_,=,1,, ,_,,r,lll,, _"""'_11 ......,, lllI= 1,1,1'='_II_P'_'I"

Abstract

Transport of polarizat:ion througll hadronization process is one of tile fundamen-tal interest iii Quantum Chrornodynarnics which is a theory of strong interactions. In

: the low energy region where the hadronization occurs, QCD calculations are dimcult,therefore at present the transi.)ort c_m be invest,igated experinmntally. Irl this study

we have searched for signatures of polarization of quarks and antiquarks in hadronicjets ft'ore Z ° --+ qq decays. The polarization of quarks and antiquark produced byZ ° decays are predicted by the Standard Model of elementary particle physics. Wedefined several quantities depending on "jet handedness" methods and studied the o

correlation between the predicted polarization and the quantities. The signal wasestinla, ted by analyzing power whicll represents degree of t,lle polarization t,ransportthrough the hadronization process. ,._

The Z ° decays were measured by SLC Large Detector and the polarized electronbeam pro_,ided by SLAC Linear Collider was useful for tllis study, The (late from the1993 run showed no signature of t,l_e transport of quark and antiquark polarization.

1 Upper limits on magnitude of tile a.nalyzing power were set in the range 0.05-0.15depending on the methods.

Acknowledgements

I would like to express my gratitude to Prof. H. Yuta for providing me with the" opportunity to take part in the SLD experilnent.

I would like to thank t'rof'. It. At)e, Dr. F, Suekane ailcl Di'. T. Nagatniile for

helpful s_lggestions and advises about this study. They also llelped my stay at SLACarid life il_ California. I want to thank Mr. Y. hvasaki who discussed various sllbjects

on physics and others witll file. I sllared a room with him during our stay at SLAC.

I would like to thaIlk the SLD collaborators. People in tt_e QCD working grouphave been very helpful. Especially, I would like to thank Dr. P. N. Burrows for llissuggestions. I learned a lot of tliings from his wit and leadership. ] t,tlank Dr. D.Muller for his suggestions. Steady discussions wit,h him were very useful for this study.I thank Dr, H. Masuda for discussions. His help extended not only physics researcllbut also my ordinary life. Tl_ese t,l_ree ge_ltlemen were interested in my progress andread my thesis carefully. 17ttlank Di'. T. Takal|ashi wllo was tlle illitiator of this studyat SLD. His proposal of tlm t,opic inade 1he write tllis thesis. I wmlt to tha_k Dr.

" T. Akagi for ills hell). I thailk Mr. Y. (.)llIlislli for collstructive discussiolls. I hadbelonged to t?ExperiineI_tal Group 13at SLAC. I would like tc) tl_anl,: Di'. I3. R.atcliff,

' tlm group leader, for his suggestions. I tAlank Ms. L. DePorcel for her llelp at SLAC.I thank Dr. H. Kawahara for advises and discussimls about detector s_udies. I wmlt

to thank the SLC people wllo lnade, efforts to deliver lligllly polarized electrons to' SLD and increase the SLC lu nlillosity.

I belong to experimental particle pllysics group at rc.l_oku Uiliversity. I wouldlike to thank people in the group. 1 thank Prof. T. Kitagaki, Prof. A. Suzuki, Prof.A. Yamaguchi, Dr. T. Hayashino mid Dr. T. Hasegawa for their suggestions andencouragenlellt. I also t,llallk Ms. K. Tagucl_i, Mr. T, Daigaku, Ms. Y. Suzuki an(tMr. H. Sugai wllo are oilice staffs for tlleir suPI)orts. I thailk Mr. T. Takaym)a, Mr.J Katayama, Mr. H. Hm_ada m_d Mr. . Naka,jima, who are technicians for theirsupports, I thank Ms. K. Tamae for her supports against computational problems.I thank physicists, graduate and undergraduate students: Dr. K. Neichi, Mr. M.Kuriki, Mr. 'I". Matsumoto, Mr. S. ttatakeyama, Mr. H. Kawasaki, Mr. M. I(oga,Mr. S. Narita, Mr. H. Araki, Mr. K. Fujita, Mr. A. hvasaki, Mr. M. Onoda, Mt'. O.

" Watanabe, Mr. J. Yashima, Mr. K. tlasuko, ,. M. Ishikawa, Mr. I(. Kawamorita,Mr. T. Maruyarna, Mr. G. Shisllido, Mr. Y. 'i_,. hashi a_d otlmrs for discussio|_s

, ,. about various topics.

, Finally, I would like to t;t_anl<_ny pare_ts for lmtie_ltly supl_orts for nly st;udy atthe university and continuous encouragement. I wish to dedicate this thesis to thern.

I,,

=1

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,q

Contents

1 Introduction 1

2 Polarization in tile Standard Model 5

2.1 Pol::rizat, i(u: ii: t,l:o, I5.;l(:,c,trow_.;al: '['l_(:ory . ................ 5

2.1.1 The EIect;roweak Cross S_ctioi: for Electroll-PosiLroll A_lllihila-,I

't tio:_s ................................ 5

I, 2.1.2 Polarizat, iol: ()I' out, goillg t'ermioIls ill c +c- --_ f/ ........ 8

ii 2.2 Polarizat, iol: ill Qtlallt.Um Ctlronlodynamics ............... 9d

I -,, 2.3 ,let Ha_dedn(:,ss .............................. 12

2.3.1. w polarizat, ioz: i1: w _ 7rTrlri,,.r................... 13

- 2.3.2 D(.;fillitio:: ............................. ld

2.3,;1 Jet l-laml(_(.ll:(!_s_i:: c+c, ' !\::ldhilatiol_s ............. 15

2.3.4 Selection of']'racks from a ,let .................. 18

3 Experimental AI)paratus 21

AC3,1 Tlm $I__ Lill(,ar C()llid(._r . ....................... 2]

3.1.1 I?olarizc(t _()llrc,(._.......................... 23

3,1.2 SI)i_ ']'ra_:Sl)()ri,at, i(_):_ ....................... 2d

' '263,] ,3 Polaril::(:!t,i'y............................

3.1.4 Energy _l:('asur(::n:(:::t........................ 28

3.2 The. SLC Large Detector , ........................ 28

_- 3.2.1 The T racl¢i::g Syst:em ....................... 30

- 3.2,2 The Particlelde::tif:icatio_:S_,steni, . . . . . , . . , , . . , , . , 3'o_'

iii

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CONTENTS CONTENTS

3.2,3 The Calorimeter Syst,em ....... .............. 37

4 Analysis 43

4.1 Introduction ................................ 43

4.2 Event Type and _'iggers ......................... 44

4,3 Event Selection 47

4,4 Flavor Tagging by Normalized hnpact Parameter , ........ , , , 54

4,5 Three Leading Particle Select,ion Method ................. 58

4.5,1 Application to w --+ 7rTrTrl/_.................... 60i

4,5,2 Applicatio!l to Hadronic Jets ................... 64

4.6 N Leading Particle Selectioll Method 80

4.7 Particle Selection Method based on I/,apidity and Momentum ..... 83

4 8 Systematic _'• Errors ............................. 89

5 Summary and Concblsion 95

5,1 Sumrnary ................................. 95.t

5.2 Conclusion ................................. 106

A Polarization for Analyses 107

B Detailed Helicity-based Analysis 111

C Systematic Errors 117

D ffh. SLD Collaboration 127

Bibliography 131

_, iv

i'ii .

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6,

List of Tables

2,1 The, axJ_flal_d vet,tor coupling const,ants ................. 7

3.1 The SLC paramct, ers for tlle :[993 run .................. 23

4,1 Sumnlary of statistics ........... ................ 57

'_ 4,2 Purities and constituent flavors of tile sax_lples.............. 58lt

4,3 Pch,i fox' the salr_ples............................ 60

4.4 Analyzing 1)owe,'s lhr tile 3-1eadillg-1)article selectioll lilet,llc)(l lo:' tileevents gellerat, ed I)y I(OI_,A[.Z....................... 64

" d.5 Analyzillg l_OW(-_I'sI'ov tile 3-1eadillg-l)article selec,tio1_Inet,hod ...... 70

4.6 Tl_e systemati(- erl'Ol'SOf t,l_eaaalyzing power for the 3-pax t,icle selectioz_method . ................................. 90

5,1 Results of tile a11alyzillg i,_owers fox' t,he 3-1eading-pavticle se,le(:t,iollirlethod ................................... 95

5,2 Upper limits o_lthe magI_itucle (:)I't,lle allalyzing power l'oi' tile 3-1eaclillg-particle selectioll metllod ............... 96

C,1 The sours:es i'o_'tl_e.s),st,emati(.', errors and _;a_nl.,lesfor estimate of tt_(-:systc;mat, ic:errors ] 19

C,2 The systerrtat, ic evr(._rsfol' t,!le,3-1(.'.ading-particle selection met;l_od, , , ]21

V

'ell," r'lr" .... rf' ..... r'l'll'II*' 'll"l"_l"lJ_ ..... t_" 0_I"' "ll_llr...... I,_I1,,_I'"101'11 '" III ...... i1,,, ,1']_1, ' _' r"qllrll'*"l ..... I_ ,H,illetillP, ',11................... irr 'Ill,gmr, ',lIItl, '

LIST OF TABLES LIST OF TABLES

!

viI

iiIii

T[ ,r,, ,, tpq' ,r_,p1rl_ ,l', I_' '111 ,r,,uq,,.......................... ' .... , q,ll,,T,jrlri, .......... I ..... , l UI'E_1' rRqrll...... _lp,qr I M_til Jl ,,,,B ,imlj,1 ...... i_ j........

List of Figures

2,1 Feynman diagrtuns of ¢:-_e- --+ f/ .................... 0

2,2 The interactions of' e_e_- _ "//Z ° -+ f/ ................. 8

2.3 The polarization of out,goillg ferlnions, 7)/, _ts _t fullctio_l Of 7', cosoand Ec,,, ............. 10

, ,t} 2.4 Schematic 1)icturc_of t,hest, rillg ntodel. 11)' !I 2,5 A dec_ty o[' T- --_ (ti-;.%_ 7r-Tr-TrtUr .................... ]3

e,

2,6 7,t_,t cts a t'u1_c.t,iol_ of P alia cos0 .................. , . , 17

2.7 Naive model.s of q -4 prrq' --+_q' 19

- 2.8 Schematic vie.:wof t,lle string model modified by Ryst(ill ......... 20

_1 3.1 The layout of the SLAC lirlear collider .................. 22

t 3,2 The schematic layout offtlle polarized elecl;ron source .......... 2,1

-! 3,3 The north darrlI)i_agring .......................... 25

3.4 The scllem_ttic layout of th(; Compton I)olarimeter. .......... 27-

3,5 The wire irn_tging syllc:llrotron r_t(tiatioll detector ............ 28=

3,6 A cut view of the SLD ........................... 29

- 3.7 A cross-sectior_al vi.ew of the SLD.. .................... 30

: 3,8 A cut view of the vertex det(::ctor, .................... 3]

3.9 Cell struc:tures il_ the cel_t,ral drift ch_trrll)er............... 32

o 3.10 Th(.: sut)erlt_b,(._rsiii t l_(:_C(:',_t,_'_tldt'it't ¢:l_t_tl)_',t'............... 33

3.11 The track reconstructio_ in the CDC ................... 35

3.12 The Cerenkov ri_lg irnaging detector(CRID) ............... 36

_ 3.13 The liquid argon calorimeter ....................... 397.

vii

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LIST OF FIGURES MST OF FIGUPtES

3,14 The warm iron calorimeter, ................... , ..... 40

3,15 The luminosity monitor ........................... 41

4,1 Examples of four categories oi' physical events .... .......... 45 .d

4,2 Distribution of transverse rnornentum of charged tracks with respectto the beam axis ..... , , , : ..................... 48i

4,3 Distribution of cosine of polar angle of charged tracks ......... 48

4,4 Distribution of distance of closest approach of charged tracks to thebeam axis ............... ................... 49

4,5 Distribution of distance of closest approach of charged tracks to theinteraction l)oint along the beam axis, 49

4.6 Distribution of number of good charged tracks in an events ...... 50

4,7 Disl_ribution of cosine of the thrust axis ................. 51

4,P Distribution of charged visible energy ................... 51

4.9 Electron beam polarizatioll of each event ................ 52

4,10 Jet rates as a function of yc,,,tvalue .......... .......... 54

''' 55 ",l,ll Definition of the signed illlpact paran_eter, .... ...........

4,12 Distribution of the normalized impac_ parameter ............ 56

4.13 Distribution of number of tt_e significant tracks in a event ....... 57

4,14 Distributions of invariant masses and the Dalitz plot of 3-7r system forthe events generated by I(ORALZ, , . . , , .............. 61

4,15 g_ distributiolls Ibr the eve21ts gelmrated by I(O1;t.ALZ.......... 62

4,16 Jet handedness as a function of coso for i:he events generated by KO-RALZ .................................... 63

4.17 Distribution of sum of ctlarges oi"fast,est 3 particles in a jet ....... 65

4,18 Distributions of invariant _nasses and the Dalitz plot of 3-7r system in

jets ..................................... 66

4,19 gZdistributions for the global sample ................... 67

4.20 f_ distributiolls for the ligtl_ flavor smnple ................ 68

4.21 f_ distributions for the heavy tlavor sample ................ 69

4,22 Jet handedness as a function of coso for the "_bal sample ....... 7],

4.23 Jet handedness as a function of cos 0 for the light-flavor sample .... 72

viii

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LIST OF FIGURES LIST OF FIGURES

i| 4.24 Jet ha,ndedness as a function of cos0 for the heavy-flavor sarnple. . . 73

I . 4.25 Masses of the 3-7_al_d 2-7r systems .................... 74_ 4,26 Dependence of tl'e _malyzing power on the inwu'iant mass cut ..... 76

- 4.27 Distribution of y_ut(3 _ 2) value for which an event changes from 3jets to 2 jets. 7_

4.28 Dependence of the analyzing power on Y_ut value. 78

4.29 Dependence of the _malyzing power on charged track multiplicity in ajet 79

4.30 Distribution of charged track rrmltiplicity in a .jet ............ 81

4.31 Depelldellce of tlle analyzillg power (:)i1Nl_,_,dfor the N-leading-particleselectioll nlethod ............................... 82

4.32 Distribution of rapidity of charged particles with respect to the .jet axis. 85

4.33 Distribution of transverse momentum of charged particles with respectto the jet axis ................................ 85

- 4.34 Dependence of tixe analyzing powers on n,_._, Art and Pm.in for theglobal sample ................................ 86

. 4.35 Deper, d'mce of the analyzing powers on nm,,z, An and Pmi,_for the lightflavor sample ................................ 87

4.36 Dependence o c the analyzing powers on n,,u_z, Art and P,,_.i,_for theheavy flavor samI)le ............................ 88

4.37 Dependence of the systematic errors on the analyzing power on Nz,:,./.. 91

4.38 Dependence of the systematic errors on the analyzing power on 'rtmax,An and Pmi.,_for the global sample .................... 92

4.39 Dependence of tile systematic errors on the analyzing power on nr,,_,.,Art and P.,i. for tbc ligllt flavor sample ................. 93

4.40 Dependence of tile systenmtic errors on the analyzing power on n._a_;,An and Pmi,, for tile tmavy flavor sa,nple ................. 94

" 5.1 The anaiy;;ing power as a function of NL,,ad for the N-leading-particlemetlmd ................................... 97

- 5.2 Upper limits on the magnitude of the analyzing power for tile N-leading-particle selection method ..................... 98

5.3 The analyz;ng power as a function of n._., An and P.,i,, for the globalsample. 100

' i

; ix

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LIST OF FIGURES LIST OF FIGURES

5.4 The analyzing power as a function of nmaz, An and Prninfor the lightflavor sample. 101

5.5 Tile analyzing power as a function of nma_, An and Pm/r,for tile heavyflavor sample ................................ 102

5.6 Upper limit on magnitude of the analyzing power for the particle se-lection method based on rapidity and momentum for the global sample. 103

5.7 Upper limit on magnitude of the analyzing power for the particle se-lection rnethod based on rapidity and rnomentum for the light flavorsample .................................... 104

5.8 Upper limit on magnitude of the analyzing power for the particle se-lection method based on rapidity and morrlentum for the heavy flavorsample. 105

A.1 Decws of partons irl the helicity-based analysis ............. 108

A.2 Decays of partons in the chirality-based analysis ............ 109

B.1 The Dalitz plots for sign-flip and no flip triples ............. 112

B.2 Dependence of jet handedness on invariant mass cuts ......... 113

B.3 Dependence of analyzing power on invariant mass cuts for 3-prong r• decays .................................... 114

B.4 Dependence of analyzing power on invariant mass cuts for the data . 115

C.1 Comparison of _ distributions for data i,o that for tile Monte Carlo.. 122

C.2 The systematic errors from the sources for the N-particle-selectionmethod ................................... 123

C.3 The systematic errors from the sources for tile particle selection methodbased on rapidity and mon_el_tu_n t'or tlle global sample ........ 124

" 0.4 The systematic errors from the sources for tlle particle selection lnethod" based on rapidity and mornenturn for the light flavor sarrlple ...... 125

|

C.5 The systematic errors from the sources for the particle selection method .based on rapidity and momentum for the heavy flavor sample ..... ]26

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Chapter 1

Introduction

Spin is an intrinsic nature of a particle and the spin state of a particle plays: ali important role in tile StandaM Model of electroweak iIlteractions. The inodel

i predicts that tlm coupling of a weak bosoll to a fermion depends on the spin st_,l,te ofthe fermion, which is called helicity. Parity violation in weak interactions is due to

- the asymmetry in the coupling between left- and right-handed fermions.

On the ottler lland, effects of t,lle spill state in strong i_lteractions have not be(::l_. fully underst, ood yet. Strong interactions are believed to be, described by Qualltum

: Chromodynamics(QCD). QCD describes well the nature of tile strong interactions inthe high energy lilnit where tlm coupling constant is small and perturbative calcula-

_- lions are applicable. The helicit,y of a quark or antiquark is conserved in this lilnit.However, it iu not obvious how QCD des(-ribe,s tile llelicity ill tile low energy regiol_where perturbative calculations are not reliable. One of tile typical t)tleIlome.na ill tllis

: region is hadronization ;the QCD mecllanism for hadron production. Several plle-nomenological hadronization models, which have been proposed to describe the stroug

- interactions iii the region, do llot take illl:,oaccount spin polarization. Therefore, tiletransport of quark or mltiquark l_elicit,y ii_ st.I'oI_ginteractions is of t'ulldalnental Jilter-est. It is at presellt a:l,_Ol)en question wlletlle.r the polarizatio|| of q_larks or a21tiquarks

: produced in hard collisions is observable via the final-stage fragmentation productsin the resulti_g jets.

Nacl_tma_n argued for a parity-odd correlation i_ quark fragme_tatio_[1]. Tl_e= correla, tioti was defined in .jets a,_d t,lxougl_t,to serve as a t,est of tl_(::l_(:_Iicit,yast, r_lcture: of quark-antiquark pair or a _neasureme_lt; of the, quark and a_ltiqua,rl¢ l)olarizat, io_ls.

2 . He pointed out that there was _o tl_eory to predict how large tl_e transport of tt_e po_la-ization through the hadroni_:ation process was. However, his optimistic expectation

- ',,'.ts that 5-10% of the polarizatio_ was transport, ed to final state ,jets.

- Dalitz et al, studied the tra_sport of charm quark I)ola,rizatio_ through decays=

_- 1==

,

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li....... ,ll_'_I"'"g,lI_l '""111',1".... H"',I,' '_,'"'"lIl,_,'lrI'!'_lll!'l'v"lll'l' _,,,,,,,,, _ _1,_irlI,,v,,,_ _,,,,,,_,,,_ _' ,,,,,,,lll_rl,l,!ll,,m........ _,, " ',lr' ,1, ""_",_ell' _1', l'lllll_,,qlV"l",',,"''_,.... " ',_," '"" .......... '_'l_'II,.... ,,,r,,,,,,_ , ,,,,,_,,............. ,, ,,', ......

introduction lntroduction

of c:--. D%r+hac!rons on the basis ofa rnodel calculation[2]. They concludecl that theexpected transport was small (_ 10-5),

Efremove _ al.[3] suggested a new concept "Jet handedness", which can be used: to determine the I)a,'ton polarization through its fi||al state jets, The idea was basecl

on an an::logy witha determination ot'r polarization using r --+ ai, t,,r -.-+rc rr 7r+t,,.rprocess[4]-[6] An observable which is defined from the momenta of hadrons in a jetmay reflect the helicity of the parent quark or mltiquark like the measurement of the

' r polarization. "Jet handedness" is defined as tl_e asvmrnetry of the numbers of,jetswiLh positive value of tlle observable and those with negative value. Jet handedness iswritten as a product of the quark and a11t,iquark polarizations and the analyzing power

, as Ctcoefficient. ,Jet handedness is different from t,tle 7' polarization xneasurement in thecontext of theory which describes the transport of the parton polarization throught,l_e l_adronization process. One of tt_e experin_ental interests is t,l_erefore wt_etherpolarization effects can be really observed in hadronic jets.

The z ° reso_a_ce is al_ ideal pla.ce to st.udy ttlis issue becalls(_ t,l_(::quarks iiiZ ° d :.c_.t},.,aret, " ,,' predicted tc) be highly longitudillally polarized by tile Sl,aildard Model

(SM)[7], If ,jet handedness is observed in ,jets by applying some method, tt_e a._a-15"zillgpowe,r for the inetliod can be derived l_y comparillg t:lle ,jet, llaild(?.dlless with

tlle expee/_ed polarization of the 1,az'toz2s. From tl2is point of view, tl_e study of jetlln.lldedness in e+e:- + q/i vi_t Z ° is suita.ble ['(_rtile deternlinatiol_ of tt_e m_alyzi_g]) OW(.:r, "

Recently F_,yski_suggested a 1)ossil)le origi_ oi'jet handed_ess[8] o_ the basis ofa_l ext.)erimel_tal result[0], t-It introduced ¢l_e color ",nag_etic" field as tl_e origi_ ina._lalogy to eiectro_nagnetis_, The idea l_a.sto I.)(_cl_ecked ext.)erin_ei_tally.

: At pre,sent, sign,ficant transport of t;l_e polarization has _ot, l)ee_ ol._serve.dex-: l._eriixxer_.taly.Howev_:!r if a. _nethod t,o observe such polarizat.io_l were developed, it

could be apt.flied to ,jets produc.e:l iri a variet,y of' liard processes iri order to elucidate: the spin dynarrlics of the underlying i_teract, io_s.

Motivated by this pl_ysics interest, we t_ave searct_(:'d for jet t_a_(.le(.lness i_l. Z ° -_ qq decays using a. sample of approxi_nately 50000 hadro_ic Z ° decays pro-

' 1ducecl at, the. SLAC Linear Col ider (SLC) i_ collisio_ of polarized elect:rotes with, unpolarized positrons. 'I'he SLC is the 46CleVx46GeV first c+e - linear collider suc-|ii cessfully operated in the world. The data used for tl_is study were (,olle('.t,ed i_ tt_e

1993 run of tlm SLC Large Detector (,.qI,D) wl_icl_is a general i)Url)(.)s(-_deu:,ct()r (.:o_-sisting of several subsystems with st_(:' of the art technology, '-171_eSLD ext)(-'rime_thas been carried out under an internatio_a,1 collaboration whi(-l_presently consists ofabout 150 physicists and graduate st.ude_ts from 32 institutes i_ Korea, It;als,, ,lapan,United Kingdom and the U_ited States. Tohoku U_iversity has been participati_g inthe construction and data analysis of the particle identitication systs,n_ (the Cere_kov

Introduction Introduction

ring imaging detector, Ol_ID).

- This study is an extension of the previous ones at SLD[9]-[ll], The thesispresents first experimelltal investigations on this subject, Tile outline of the thesis isthe following; irl this Cllapter, physics motivation and brief history oil tlm sub jet, t, are

" introduced. In Chapter 2, polarization of timnions is described withill the frameworkof the Standard Model and jet handedness is introduced. Tlle experimental apparatus

is described irl Ct_a.pter 3. Analyses of jet handedness are given in Chat)ter 4. Finallythe results fro,m tllis study are summarized in Chapter 5,

"2_

',Irl',, ' ',,",," 'rail' ',Irj,i ...... ,; ......... _1,,.......... , iqi,', ...... Ilqr ,'raa,,',N,,'v_p ,q" mWl_,_,,,,,,' lalll_ ',,IIRI,P'II 'rllgJ I_1 'vl'il_lqll II'IInNr ' ,nr'ip'rr....... _,_1,,,,,,,,,r_,,,, f_l,,aa,,qll ....... ,_Pl?,,lll..... _ilql"P"'l'"',ll ....... I_i"' el' _lll_,gll"rl_lll'l'l'IlP III]

Introduction hJtroduction

a

4iI

_ig,'_=,_........,',,,,_...... '......._,r,_,qrl',r_,N_,,,,iTli.... _rr,q'_',,Ir,,_q',''_q_'ll..... n_ir:_p,_,,,'_,_l,Wi_,_,,,rl,'_,,........ _rpr_'l_' ,,"'_,,l_Ipl,l_i",.... ,r_ "ilF''''_'I'_lIl_I'rl_"""r'_r"'m_ll_q_q',"_Irll"pl'r_..... 'FII"I_"_I'III]"H'P_llllmq'_w'="='"IP,m_rp'' 'P,_,IP'II_=TI"_I........,r',l'='_r_l_,r

Chapter 2

Polarization in the StandardModel

The St,al_dard Model of elementary particles consists of electroweak ttmory andquantum chromodyllarnics (QCD), Phenomena of ferrnion pola, rization are w(-_llun-

- derstood by the electrowea.k theory, but llot obviously in QCD due to tl_e coinplexityof the hadronizatio_l process, In this chapter, the roles of spill a lid l.)olarizatioll irl tlle

electroweak theory a:mdQCD will be described,

2.1 Polarization in the Electroweak Theory

2.1,1 The Electroweak Cross Section for Electron-Positron

AnnihilationsThe differenti_fl cross sectioll for ai: intera.ctiol:, A . B -, C+ D, in t,l:eir

center-of-mass syst(,,,_ l_as a gener_tl form (of':

d_(AB--_CD)I _ 1 _J/M_,(2,1)

where df_ is t,lle soli¢l ;u,gle eleInent around outgoil_g fi_al st,ate particle (.,[1.], ,_is t,l_esq_ared center-of-mass energy all'.l Pi a1_dp/are _no_nenta of l.t_e,illit,ial a.I_dfinal state

,. particle:s, respectively. M is the _natrix ele_nent. I_ tl_e process of' e+c - --->f./, _{is divided into two con_pone_ts a(.:cordi_g to two mediati_g bosom,s: (.)_e is a virl, t_al

photon which mediates the electro_nagnet, ic force and tt_e otll(:,r is the Z ° bos(.)_ wl_ict_mediates the weat( force. Figure 2.1 shows the Feyn_na_ diagranls for bott_ processes.

is a s_m of tlm two matrix elements, i.e. A4 = A,t_ + Adz_,. Accordi_g Io tt_e

5

I ........ III .... til ...... i1 ,lllqP................ llll')r_ _, _1_i_rl ..... lull , , i_ ''_I_11,_,1,,,' ,,rllll)l_l, la ,,1_'_ _llFil,llll_lllll ll'lll_l,II , I,,'i_1 ........ r(I,_,'1_,' ,,ll_lr' I,'IIl(I,,,, IlllIl,,n'lrmll,!,ir _l',,r, I_ '"""l!)llP<rl"l')li' 'lllltll_l'_llF_l_'lPItr'qlllll'lW_ltll I .... r'l"', ,Ir"_l ''lr'

2,1 Polarization in tile Electroweak Theory Polarization irJ tlle Sta,ndm'd Model

e"

_ ieQf 7/-z+," , i,y_

e

I_lV

q2

e )f

Z o

, g f.cA.f_,5 )

, - --_ a)_ "-_ 2 coi_Ow"_'/z(':ve + i(gpv-qpqv/M z ff

q2 _MZ 2 + iMZ 1-"Z

[i'igtlre, 2.1: Feynman diagrams of e+e- -_ "7-_ ff and e+e- -r Z° -> f f..q in cia,.:vertex fac.t,or ,is the electroweakcoupling constarlt;.Using charge of a pl'oi;one and tAaeWeinberg ro@c:0w, 9 iswri{;t,cn by 9 = e./sin Ow.

Feb'_lman rule, td_e,.seele,rne2_t,sare described in t:,erlns of t,l_epropagat, or and t,l_et,wovert;ex factors shown in Figure 2.1l'

-i9w, _.= ,a:( :)¢'w-7< .,,(-i,:)./",,,,, (2,2)

lr,,, Mz) -ic,7'

- 7 )'./ _.'_ iMz[ z ,_z,,--(@ - (,"-?)'.,,.Adz = 5/sin 20w ' q_ - + " sill 2Or,I; ..,I(2,3)

where ,),l,, Mz and F , ,z are 1;lie 7-matrix, mass and decay widtll oi' t;lle Z ° bosonrespect;ively, q is t,he rnonlellt;um 1;i'ansfer and qU_ s. Ow, eZ, 'and c:{taret,':l_,'Weinbergallgle, t,he vector couplillg mid tlle axial vector coupling ',:oIlst,mll;s, rcspect;ively. ']?tie

e.lectroweak coupling consl;ant 9 was substituted by ,<,;'_w' c{_and eft depend on the; third cornponent of the weak isospin, 7_, electric charge of a fermion f, Q/, and the ,

, 2Weinberg angle, sin 0w and are given by,

i

i 4 : r/

c_ = T/- 2Qfsin 20W. (2.4)

6

li=

lr,_.

, '_ II1 111!t1_' lt I'l tr' II1"".......... _P"'"""'"........V"'_l'"'t"''"'" '=_'n'".....'"'""'"'r',r,,'',,_,,..............._,,,,,,,,,;......,,,,nii''"llllllr'l'r'",nlt'l'tO"'" lilt' tVl, lrllr#r'""t'"_llr ','Ht' 1'It"tr'"'l'lrltt"_l_ Ilrlilllt'llH" Illlll[l_il' lltl t'tl 'lr'_l_tlllll'rllrlt!'tllt'l" 'IIi ..... _lll "WINI"

Polarization iiJ the Sta.ud_u'd Model 2,1 Polarization in tile Electwwea,k 'l'heory

,,<,,!:,,,,.,______1/2 0 .... 1/2 _ 1/2 1e-, It-, W-- -1/2 -1 -1/2 - 1/2 + 2Sin 20w--- 0,1,i,i8

. ,,_,<...,t _/2 2/3 1/2 1/2-4/3si,l20w 0,6605_l,,,_,.b -1/2 ..1la 1/_[--:1/2-i-2/asi,;_0_ _'", - (),D3o3

Table 2,1: Tlm third componont;of the weakisospin,oloctric charge.,the axM mid voclJorcotiplliig(.',Oi!stl:ll'ltS t,O t,ho wi),tlk bosoll for f'orllllons and lisyllll'llO[,i'y o[' [,hl), ,'.J'tl'(.!Ii_l;ll o[' h.,fi,-I.tiid riglit-lial_ded[Orl]!iOltS to th(J Z 0 , whoI't _.slI12 0|.. lt =-0,2318 ts used [9]

Table 2.1. gives tile vlllties of fttiese COul)liiig coiisfta,lit,s ['(_r lel.)t,()iis all(t ciliarks, li' i,lll.,initial elec.ftrolis are l_<llarized by ,pi, tile differelit, ial cross sec.l,ioli for ctc - --+ ,/,jr iswrii;t;en as

<m(c+c-->f)'),,.,,,, :v<,.<_Q}d'c_)s0 = 2,s' (1 -4-c.os_ 0)Q

" , ,e f ]-t- 2cAc_,1ccms0

i (: £'.,c 2 2CI,.,t,.A _D) I ,f2 ,f2+N<,i_,(d'__+ _ -- t<._....-i-_._)(i + c...<.>__0)

[' , ," 0},•+ 4 2c'.{',cA - (c7,, -t-"c<.;i c,os

with

O_2 s

k = 4 sin,120w (<s'--Aq_) 2 -F i 2<<_/lv'sz.,,, ..,, ,_.,,._, (2.(i)

where N<, is t,lie Illliril.>(.!r of colors ['or tile ['erIrliOll f, Ali fl:;riniolis iii t,lie r(.!a(.'.[ioli _tl'(:,

a,ssuiiied ft(.>b(! liii.iss (!ss, The first, aild t.llird ftorrris Iii'(.! (.'.olit,ril.)ul.,iolls ['r()ili i,lie 7' t.tll(.t

Z 0 exchaliges, rest>ec.t.ively. Tlio second Lerlll l'e.I)r(:;seliftS illl;orl'(.;rellc(:! bel,weeli l,lie 7

a,rld g 0 ex(.'.ll_-tIlg(_s, 7,(!. d_;d_z o -P .M*zoAd,),,

At the Z ° !-Jol(_, the i_t,orference ftorrn valiislies and t,l_c,coiiftrib_lt;ioii t'roni 7

exclituigo is lllucli slilaller (,---,10 -a) t;ha,li ilia.ft ft'ohi Z ° oxclltlligo, 'I'lleret'(w(,, ai. t,ll(,7'

- Z ° pole, the cross sec'.ftionin Equation (2,(1) is clorninated by t:lie Ctiird fterlli,

l'I'he, )olarlzatton o[' c:lc;(.t,rons is doflilod as: 'P = lz/t--_z_, wlioro 7iii' and 'n,t, are niliill_ers o[''li,17--I..7_,/,

right and le,fi;-.lialldod eloc',l;rons, rosl)ec,t,ively,

7

_i,,I ' ,Irl ,,1.... ,,ii,........ I_le',,"li,'' I' ........... '1........ _'" .11I, iii......... 1' ..... I_...... I1' ...... I_', ' ............................... Ill " Ill.'lllP'iH"'"lltV'"l''' r........ ,'ii " I lip''Ill" '151illlllr'l ......III........ pqll',lllllll..... il.... ''_I1...........II,r,

2,.1 Poh_riza.tion in the Electrowe_k Theory Polarization in the Sta,ndm'd Model

2.1.2 Polarization of outgoing fermions in e+e_- -+ f fi

w

• - ' " '_ tgoing fermions, Pf is defined by:The polailzatl(.zl of _lie ou <,

' dafR dafL

7:'I(P,cosO,.E_,)- .¢_s0 _zco_o, (2.7) "di_n_+ il_,Sr_'

d co,,_0 , d cos 0

where 0 is the scattering angle between the incicbmt electron mid tile filial statefermion. Figure 2.2 sllows four possible interactions of e+e- -+ 7/Z ° -_ fr. ai" ist,ll_ cross section lhr ctc- ---_,fu + ,f¢, and a/r' is t;hat for e+e- -4 f,., + fu, where tllesubil_dices/7, and L stalld for 'right-' and 'left-handed', respectively,

(a) -"& (b) ...v'./)_

ete __ ' --ea + e

'"_---J 0

.i.7 "y/ .,. "

(c ) ..__ 1" (d ) _'_I'L "'_,1z _;/_ o yl z '5"/

" __-z__*-_-¢ :z_-e e+ _ +

,i)-__ .i),,*__--'7°

1;igure 2,2: InU?.ractionsof (a)et)e_: ---}falL, (b) e))e+ -> ft, in, (c) eTc:)_-i.--_ ft, frf and (d)¢.:}_e_{--> frill,, Spin staw for om.:h particle,, is shown by zt batche, d arrow, The angle betwoen theout,golng fermion and the: dti'oct;l_m of tlm¢:!lectron travoling is de.flnod as O. 1)Ill'orc;nec;in I;ho crosssoctions for each evont typo givc:s net, outgoing formlon and anti fermion pohtrtzations, ']'hc dlffer(.;ncc:Is dllo I;() the dtfforoncc in tlm strength of the couplings of tho Z ° boson i:o right- and loft-handed['OI'IlllOilS.

By inm_ducil_g t,lle f'()llowing two coupling collstants, c{ealld c.:'f,,Ibr I,11_vigllt,-a.ild left-handed ferniiolis t,o l;lie Z °'

4 4 +4,

i

-li -=_.=.

'lll"_' '"' ..... ,,¥1' ,1_1,_,,,,,,,i,lll_,rl,l'_,,,,li,,,,"!llH.....' " I'111'..... " 'G'il'_',"'l'",','l'll"r_,'_ii'l_'r...._lllltl'll_l'l_'<_11r ' ' _f_rll,lil'_"_"rl'_'_illll_.... t_" 'GIi'_m#11'_IFlll'"_"'li,f""ll_l_lll_''_r_"l'llln_'_llU"lllI,'l_'_111_'' _'' ' II1,_,',',1_....._1_,_'|liq"l "iii' ,,,..... lilY' m_lr'lll_

Polm.iza_km in t_heS_mda.rd A4odel 2,2 Pohi.rlzat_ion h_ Quu.nt_u,J Chrolrlodynmnics

t;he ditt'erellt,inl cicss"_"s(:ct;ions, d(:,osO mid dcos0 ave obtain(-_dby substitut, illg c{,= 0" and c{e"---()ill t,ll0 dii:t'orelll;ialcross sectioll (2,6), respec,t,ively,

Figure 2,3 stiows th(-_polarization (2,8) as a function of c,.uiter'of-niass etlorgy" E,,,, for several values of electron polarization "P and cos 0, The polarization of tl_e

outgoing fermions 'Ps"strongly depends on .No,,,,and its absolute value reaches a rnaxi-rnum ai'oulld t,lle Z ° rllass region, The l)olarizatiol_, beconles s_aller as E<,,,,,goes awayfront the Z ° pol(:_, q'litls, allals'sis of e+c - allliillilations at t,l_e Z ° pole a.ll(m,s us t,osttldy rh(:',slzill i:[:t'(:_ct,s t_Ctile illl..i,xilrltlrrl quark polarization.

Using foliar,lolls (2.9), t,he ditferential cross section (2,6) at, tlle Z ° pole is writ,tenby tlSillg (-:1_all(l c/,:

"(_-'_i,o,,_<"--_::_<,,,,,- '<,,'_[_t--v-<:_,._+_'_+_-__<'_.')/<,;:+.(._(_,+_<,:0/( 1 -t- 'Poe :_ ] - 'P ' cosO] {J- t--7- '_< 2 <:7'_)(<''(:!- "{') ' (_)

']Tlie ctil['oreill, ial cross sections iii E(ltl_ri,t_ioli (2,8) are writl;ell:

dcr f r<oc (1 - AI)(1 + cos:_0 + 2Azc, osO)d ('os 0

- daj'_,rx (1-+. AI)(1 -t- c'.os_ 0 - 2Azc.osO) (2,10)d cos 0

where A I is writt, ell:

Cit -- :-'/, _--- ,

!_'f -_ ' f2 Cf.'2-lt" ("Ai c/__ + c:, s',' (2,11)

I and is lis_(:'(liii ']'aiJl_:'2.1 for \'_l,riotls t'erlrliolls, is til(:! (.)f'tile Z ° I.)osoliS,i_lZ polarizal;ioll

-- Irnlltil31i(:_dIO.... ]:A<,- 7:'

l Az :: 1--A_P' (2,12)

From Equat, io_s (2.11), (2,12) and (2.13), l;l_epolarization of the outgoi_g fermionsccmplecl t;o cii(-!Z ° (2.8) is giveli by:

. "Pi('P,c,osO) = - AS(1-t c°s:_0) + 2AzcosO1 -t-cos_ 0 -t- 2A z A: cos 0 ' (2.13)

" 2.2 Polarization in Quantum Chromodynamics

The polarizatioli of outgoing fermions is described asi the , s,cre.),,s ,.sect,loll as,yrnme-

try iri e+e - --_ ,fr as shown in tile previotls section, If the ferrrlions f, is a quark or

li''_lt'1 .... ' ........ I_lllil'"]'l ...... I' " _'"'"'l_f':lll_'''"'H_""linrqllV""llll'l'R'll,'nr_11,'_,....: 'm,'"""_'"'IIIl"""'IIIII''''r'......":'""lillll'"'"'"'1_''°'"""':"'rl'"V"_'"_:l""'_"#,'_,"'1_i,_I!111_1'I1_"'_!11_'@_I"'_1_'"_"'GI_IIII!_i,,_q,I_f":I'l__"'_"*'_....._.......I1_:'_l!lill'll_l[l_llll'i_:ll_i_l!_

r

2,2 Poh)rlzstlou iz_QumJIum G'hromc)dy,_mHcs' Polm',zst,o,_ i,J the S'_mJda,M Model

I_'igure 2,3' The poltu'iznLloI_ 'Pf as tt func.tlon of 'P, coso trod _c,,,. Solid, clt_shed trod doLLed

curves show Ltm "Pe,_(,r)'P,,c 8.1_d 'P(t,,,,,b, rOSl:}{.lctlvely, "Phe {.:l{.,,c.t|.'onb{.:,rm_l:}ol,tu'iztttI0n 'P t'm(.i c,os 0 fore,ttd| case t'u'e shown In tile [:iguPe.

10!

I -'11 ,', I)1_'_'_,,,vllO_l'll. ..... m ..... H,] _I,',_]m,"' ,,"' r_ ',l'",,' ' 'r_"I' ,',' I_1" "'" "....... q' " _t ' '"' _ ..... _ " '1)1'lllll ' '*II_ ' _1_ll,r-,l_......... _l_llI ,_,,,,I,_,r ,,,,_!1_, ,,.Hl i1_, ,_ Iii" '_r' ' "]llll _l,'_l'lll_lI_' II1'"'_"" '' '. 'IIl]lqll" _'_' I,) ..... II'" 1_' fill)If _l'"'_'l'l ]I'_"_ _l_l" ,2

Pol_triz_tion in t;l_e ,6't_md_rd Model 2,2 lJohtrization in Quantum Chromodynamics

(:' D (,,/.i.,()t !

" q q q q q q

Figure, 2,4: SchenmLlc l:)lcLuresof behaviors of quark and antiquark lind c,olor flux ttibos In thesLz'tngmodel,

ant, iquark, we only obserw', ha(trc)lls in fina,1 sl;_tt;e. Tllis process is called hadror_izatio_

or f,rety]'rrte'rtt_tt,'l;o'rz,alld is desc, ribe(I by Quallt, uiil Clhrorno(.ly|laIl|ics (QCJD) i|| l)rillcipl(-!.Floweret, it, is riot, ol._vh)us how t,he si)in or heli(.,,iLy of (.lt|_:l,rl¢ _l,llcI al_ti(.tuark is trails-

portecl Lc) _lle Iii|al st,a_e h_dl'on,s, since Llle haclronizatAon proc, ess is not; completely

ceflculable in QCID yet,

In tllis sect, iotl, a inodel of lladronizatioll is explained, Tlle hadronization niodel,

ttowever, does _ot, t,ake h_t,o acc_,,._nt;the process of the Lr_tnsI)ort, of quark or ant, iquark

spin,

" Hadronization Model

The Q(?I) (.lescril_es l)hencn_ena well it\ _t higl_ e._ergy regio_ wl_ere t,lm coul)li_g

constant; of t,lle st,ro_g ingert._(xt,io_, (_,, is s_nall e_ough to _-Zpl)lypert, urb_tt;io_ tlleors'.

However, pert:tlrl)at, ive QCD c_:t_ z_ot,be apl)lied to l)he_(.)m(:u|a i_ a low cu_ergy regioll

where the coui)littg (.t(.)ltSt,ttllt, becomes large. One of the typical l)henor.ne|_a whicl_

occ'ur in stlcl_ a low e_ergy regio_ is t.l_e ha.dr(.)_|iz_tt;io_|of quarks _t_(.la_t,i(tt_tzrks, 'l-'l_e

behavior of quarks a_<.l tu_l;iquarl<s t,hrough the hadro_izal;i<.)_ is difficult: tc) solve,

The, refore, o_ly l)he._oll_c,nological inodels are, prol)osed t;o clescribe what t_al)pens in

t,he process,

Typi(.',al l_adrol|izati(.m models are t;l_e i_clei)e,_de_t, t'rag_e_tat, io_ _nodel[1 di, tile

clust;er fYagrne_t, aClo_ _nodel[15] a_d tt_e st,ri_g _noclel[16]. Ali of' t,l_(:,_nclescril)e tl_ehadronizatio|_ ptm_lo_enologically.

" Arno_g t:he_, t,l_e Imm.I stri_g model[16] is a widely used model. In t,tie follow-

i_g, the basic: dy_anli(:.al 1)ict;ure of tl_is _noclel is ext)ltti_ecl wit,lI l_elp of Vigure 2.,1:

. When two colore(.l qtlarks are sel)arttt:ecl , a color flux tube is st,ret,c,l_ect beg\.vt-!e|| the_l,

This flux Lul)e is modelled by a relativist, lc massless (o_e (lin_e_lsional) stri_g wit,l_

a string co_st, a,_lt:oi' t_',_1 GeV/fin to siilmlated a linear c'.o_fi_erne_t force, I1_ t,lte

si;ring picture, (:)_e e_ld (.)f the st;ring Correspo_(.ls t,o a quark a_(.1 t,he other end to a_

antiqua, rk, wl_ile glu(.)_s are represented by excit_at_io_s (:)1'"ki_ll¢"s i_ t:txe st,ring. VVl_ile

11

2,3 Jet Handedness Pohtriz_tion in the S_mdard Model

the string evolves, it bi(._al,s' ' "' up into color q_]two singl(:,ts,'' , " this rate of break-up is cal-. t

•-',1 SS' ,1culated from a senllcla ....lcal model of ferrnion pair tunnelling from tile vac,uum, Tileenex'gy carried off 1),5,tlle daughter singlets at each break-up is well determined by _h.e

r'r_l __ . .'left-right' symmetry princi.ple, xm,: principle states that the final particle dit: _,,_ Itions should be blind tc.)tlm order in wtlich causally disconnected break-ups Ilk:.::,,.,

!

Assuming a parton, which means quark, antiquark or gluon, splitting A -+ B + tj, zi

t ",,is dethled as.

z =_.(E+ + (2.14)where E and p//are el_ergy and the longitudinal momentum along the parent partondirection, respectively, For the Lund string model, the fragmentation f'ullctioIl, whictlis the probability of tl_e splitting with z, is given by'

f(z)=N(1--Z , -z)"exp( bm_)z , (2,15)

where N is the normalization factor, and a and b are ttxe constants to be determined

from experiment, v_t is the transverse mass of the final state hadron with mass m andtransverse momentum, l)t: 't__ = m '_+ p'_, This iterative break-up of the string intohadrons stops whml tile mass of the string fragments reaches a hadronic scale, Tiletz'ai_sve,'se moment, tl,n (.list,ributions for hadrons can be t,at((:;llinto a('count by adding

anot,her parameter,

• . "t )Events gellerat,_::d by Monte Carlc: simulations ill whi('llt:llis _nodel is imple-.rne_ted reprodu('e real data such as mo_nentum rlistribution of tracks and number ofcharged tracks in an eye,lt well. However, this st,ri_g model does not take into accountt,tle effect of tile; Sl)il_or l_elicity of quarks and antiqua,'ks. Therefore, inf'or,nation o,_tlm spin and helieit,y of each particle is not obtainable from the Monte Carlo simu-lation. At present, we cm_ not predict the polarization of quarks and antiquarks infinal state jets from any of the Monte Carlo simulations.

2.3 Jet Handedness

A quantity related to the polarization of quarks and antiquarks underlying jets iwas first proposed i_ r(:;f, [1] in 1977 in which no prediction of tl_e magnitude waspres_.mted. _)

Irt 1988, Dalitz ct al.J2] calculated another quantity related to the polarization 1of charm quarks in c _ D+ _r+ hadrons and gave the value of order of 10-4, ttowever, .}the value depends on tlle model describing the decay of c quarks,

The experime_tal study of "iet handedness ''u in e+e - annihilatio_s was first

handcdn(.,,.swas ctcfinoclin [3],UThcterm of "jet , ,s'"

12

'12_"l,_la_....... t,l,t'_lnu,,_'_ II_l'lPtl_,,,,.... t,_,,'tit',_tI_'" ,,Itl,,t,,"lip I,IlllI_,t ,,_""'_ltli,_,,tl,,, "ll_tlr"" '_'n_1"_",'I,l,',,"1,_ r''ol',r_H',,__1!t_'I11III,11I_flINt'"IT'_a,t'a_...... _"_qll_"lll'r'"'lt_ll,"',,l"_l' __"rt'' 't,,_:,l,,,,"_ liltl',,"t_lIIii 'I_P'fI'' "'"_t'_

Polarization in the Standard Model 2.3 Jet Handedness

(a) LaboratoryFrame ___ (b) 3-7cRest FrameN

.r rc - l)a _ .._

/, Pal7/7+ tl ::I_:.'

- %. 0 •.... _i-_

e- ..._ +h Oal" _ "_ VT ;¢ -. __ll _ k3,,:/:.-- .,.:_iiii:!:, .-_

e'__ Decay Planey' Z

'

Figure 2.5' Schcn_at.ic view of "r- -_ a I vr -> rr 7r rr+vT shown bot,h in (a) laborat,ory frame and(b) 3-rr rest, frame.

suggested in 199213], because of high quark polarization at the Z ° predicted by the

standard m,)del. In the following, the concept of jet handedlless is discussed.,e

2.3.1 r polarization in r --_ rrrrrcv_

Tlle mlalysis nl('t,llod to find the quark spin transI)ort in ,jets is not know,l apriori.

One possible m(-',tllod[3] can be obtained from the hadronic 3-rr decay of a r lepto11'

L------_/.lo,/r-t.--___ Tr- 7/"+

for which s(._\'eral tl,eoretical works calculated the T polarization[all-[G], [17]. Tile- estimates usillg tli(.! properties of tt_e w(mk axial currellt m_d tt_e l_adronic current

gave reasonable agreem,mt witt_ the data [18], [1.9]. Therefore, we will discuss the r

polarizatioll accor_ling to ref. [6].

Figure 2.5 sllows coordinate systems of tlle 3-,pro,_gdecay of T- via. an al inesoll

, produced in e+c - a.llnihilation. Momenta of I)'1,_c-',2and k_.,tare assigned to two pions

with ne.g,'a.tive charge and a pion with positive cllarge, respectively, in the 3-_ restframe. /cl or/c2 is assigned to each of two negative pions at random. A vector normal z

13

i

"' ,_1_" "" "' ....... Itil'l_l,_rI_'......,, ,,_1_,1,1_,,_lz.... '_'llll'',.............,'_,,,...... ,='",........... tl_" '""_' '1_' llrr'Ill'"'..... t':.... r,, ,,,,,_l" I1''t" _1111_'li'"ll_

2,3 Jet, Handedness Polarization in the Sta,n&zrd Model

to the decay plane of al, ft is defined by:

• ^ kl × 2(2.16)

Using 7i, '.w polarization observable, cos @ is defined by:

cos@ = p%, . _, (2.17)

where p%_is a unit vector pointing to the direction of 3 7rs boosted, i.e the unit vectorof mornentum of al in tile laboratory frame, Asyrnmetric distribution gives the rpolarization as follows:

N(cose)(s_- su) > 0)- N(cos e)(s_-- s2) < 0) (2.18)"_ = N(cos e(,s,] - s_) > 0)+ N(cose(s] - s_) < 0)'

where N is the number of events observed with the criteria in the parenthesis, and

s_ = (k_ + ka) 2, s2 = (k2 + ka) 2 are squared invariant masses. According to [6], 7-/isproportional to the r polarization:

=_P_ (2.19)

where P_ is the polarization of T leptons and ct is an analyzing power for this method,

2.3.2 Definition

Handedness for the quark and antiquark polarization in a .jet was called ".jet

handedness" [3] and can be defined in analogy with the decay of v- --+7r_r'rrv_[6]. Sincequark and antiquark go to hadrons through strong interactions, tim decay amplitude

. must be invariant for parity operation. This requires one to choose an observable" which conserves parity. Taking the analogy with Equation (2.18), tile following ob-

servable, f_ is introduced as the simplest quantity which may carry l_elicit,y of quarkor antiquark:

where t_, k2 are the rriorrlenl_a,of two part.icles in a jet. t is the jet axis which representsa.unit vector of rno.mentuln of an underlying quark or antiquark. A selection of tracks

and ordering of momenta kl, k2 depend on analyses to be perforrned. In this study,tracks with higher momenturn are usually selected, because those tracks are expectedto carry information on l_elicity of quark and antiquark. A detailed explanation of theselection method and the ordering will be given in the following two sections and inC!:apter 4. _ is c').!culat(_d fear e_a.r'.hjet, individually. A .jet with a negative (positive)

I 1,l' |

........ ,, ,,Iq, l _l ' "lll_l __li " rl' _IH" " ""_ IIII ,I, _ ii illll ',_ _1'" l[i]l""""' _' "11111'i'l?lllII!'I?!11" "I ilr'" 'II'rll?'li_l'r _liI'"'ilfil_i'_ 'III" II_I" ,

Pobzriz_ztion in the St_mda,rd Model 2.3 Jet Ha,ndectness

value of g_is called a "left-tmnded" ("rigtlt-hancled") jet, Jet handedness H is defined&S:

" NI,- N/_.H=NL + Nt_ (2.21)

. where NI,, Nt_ are the numbers of left- and right-handed jets, respectively. ,let hand-edness is a statistical observable and is not to measure tlm helicity of an individualquark or ant, iquarl< ullderlying a jet.

A probabilit, y tllat a left- or right-hallded quark produces a left- or right.-tlande.djet is defined as:

1

P(qL _ Q < O) = F'(q/_ --_ ['_> 0) = [(1 - c_:) (2.22)

where a is the "alla.15,sillgpower" and takes a value between -1 t:uld 1. On tl_e otlmrhand, a prohabilit, y .for a le.ft- or right-ha.1_ded ,jet COlllillg from rigllt-, left-handedquark is also defined as'

1

The probabilities are considered for antiquarks independently, but in this study they-' " are assumed to be identical as those for quarks.

For a sa,:nple containing nL left- and n/_. right-handed quarks and antiquarks,_

_, jet handedn¢:_ss (2.22) is given ft'ore the probabilities by:

H = NI,- N/e=l N/, + Nu:i _ 1/2(1 - Ct)hL + 1/2(] + c.t)n,_ 1/2(1 + a)nL -- 1/2(1 --c_:)n,t

T_l¢._ Tfl,

2= 71'h', -_, T/,I,

. = (2.24)

- where 7_pis a, pola,riza,tion of quarks and ailtiqua, rks i_ the sample. The analyzing=

power will stro_gl3" del)e_d o_ tl_e selectio_ _nethod m_d ordering of the two particles.4 used in tile analysis procedure. Optimization to get a large value of the analyzing

power is import, m_t to observe the evidence for jet l_an,leclness.

2.3.3 Jet Handedness in e+e - Annihilations

_: As rnentio_ed i_ t,lle previous seetio_, the ordering of pa,rticles is important i_order to get a la.rge value of tile analyzing power. The polarization also depends on

"_: the ordering. II1 tl_e present study, we used three methods for the ordering of twomomenta, k_ m_d k._, in t,he Q definition (2.21)'

-

-- 15

i1,1_71_1,Ii111,qN'_llI,'.'l_ll'",llvll', ,,_1111'_1" II_l I,'IlI',ll" ITI'1,,_"_',, ,,1_,!11'_'1,1 ' II_[llll_l"" 'l,[_,_lll_',,'n_ e,, ,l!llll,,i,,i,,i,l[in ',',fill '_ ', ,,_ n,,'rl][l_[, ,.11 ........... Ill[_llm '"1" ".IIIl'l[_ " ' _l_ll_l"I,'ll_'q '_1,' ,lIl_l '"%llI'l_ .... I? "' " ...... ,I1_11.'" ', .... , [11_111'"H,, .... ,_ ._,, '

2.3 Jet Handedness Polarization in the Standard Model

• "Helicity-based" analysis, where the momenta are ordered according to theirthe magnitudes,

r t _ D• "Modified helicity-.)ased analysis, where the rrlornenturn ordering is arbitrary,but the sign of the vector product irl the f2 definition is defined by two invariantmasses, grid

• "Cilirality-based" allalysis, wlmre the momenta are ordered according to ttleparticle charge.s.

In this section, definitions of the polarization for these are described briefly. A detaileddescription of the polarization for both analyses is given in Appendix A.

Helicity-based Analysis

'Helicity-based' polarization is defined at a giveIl cos 0 by using tile differentialcross sections (2.11)'

v,,,:,- 4 +4_- _,_- _,__ -2 A__o,,..o (2.2_) "4 +4 +_:,,+,£ , +_o,+_0'

84 a_:where ,_, tri are abbreviations of dcosO' dcos0 in Equation (2.11), respectively.The helicity of the fet'rniotl a,tld antifermion in atl e+e - antlihilatiol_ event are alwaysof opposite sign, because t,lle antiferrnion ahvays goes in ghe opposite direction to til(._fermion. Therefore, t,lle replacements I_ -_ L, L --> /?, and coso --} cos(rr - 0) in the-

differential cross sectioxls (2.]1) give the following cross sections cr:_,ct:::..

4(_o.,,o)= J,,(_o,,,(_- o)),_:,.(_o_O)= _:_(_o,_(_-.o)).

. Figure 2.6 shows the polarization, 7"heras a function of cos 0 for 7' = 0 and +0.63 a." The polarization is independent of quark flavor, and reaches ---F0.72and _-k0.52 at

cos0 = +1 for bearn polarizatiotl of -0,63 and +0.03, respectively.

The fi correspondillg to tile definition (2.21) is t,aken to be:

i+

where the momenta, /_l, _c2,of two particles chosen from a .jet are ordered to be

k, 1> [/_2[and t is the jet axis. The methods for selection of tracks are described inSection 2.3.4.

aThe electron polarization of 0.63 is the averagevalue in the 1993SLD run[20].

16

iI[

_

_

5

Polariza, tion in the ,q_ta,ndard Model 2,3 Jet Ha,ndedness

. _ 1 ........................................................................................................._...............................................................................

0,5 +- ... ...........+......._.. •................................t_

_ .i./- _

"_ ". .. yff _

0

_+-+

,. . ++..-.

-0,5 ---

......... t_............ I ......... i ............. [ .................... l .......... l ........ I ............ L............ I ............ I ........ I ..............-I-" -0,75 -0.5 -0,25 0 0,25 0.5 0,75 1

COSO

Figure 2.6: 7)h_l as lt function of 'P and cos& Solid, dotted and dashed curve'_ show "Phe',for7) ---=-I-0.63,O tr:ld -.0.63, rospoctivcly.

Modified Helicity-based Analysis

{ ' ' I '_ }The modified lleltctty-:ms+.,d f_ is tlte same observ+d.fle used in EquaA;ion 2,1+)In this an_tlysis, t2 is defined for three part;icles with tol;al ch_tge equt_l to -t-1. When

one selects three particle a, b, which have tlm same charge, _md c, whose charge isopposite to t+,h_ttof a or b, t-2v+.od,het!s defined as:

= (K,,× (2.27)

where /_,,_t, are Life momenta of particles with same charge in the 3-particle rest

- fr++rne, and +',, =-- (t,:,,-t-/%)2, ,.%= (t_+-t-/c_:)?"at'(:: squ_.u'ed inv_tri+utt; rn_.+sses. [ is the .jet

++xis. The corresponding polarize+tion is the same as the helicity-b+tsed pola, rization'

a

"]7_rt_od,hel ---:- "Phcl

A z cos 0

= -21+ tosCO' (2.28)

17

,'l+l,,,+'," '" ...... ,r ' Iql"_l,1'+_';ll ,,,I ' tla,_',_ ,','lp¢#r .... ,'11II _1 'W" milli ,,_, 'lll'''lnn',p_l"_'',ll'"l'I"'lPrll"r'm ' ''_111 "mifi'pile+ _;+,'+sllll?llFlmlm'rpul_lltltr_PmpIIlll,'q_rl+_' ,, ,,'+,'++mll_

!

1I!

[ 2,3 Jet Handedness Polarization in the Sta.rJda,rd ModelI

[i ,,

Chirality-based Analysis

The chlrahty-)a.s_,d polariza, ion of underlying quarks and antiquarks is definedas: _ ..

%,,:_:4 - - + = "

p(.lm lzatxol_ is independent of cos 0 .where Af is given 1.)3'Equation (2,12), Thus, this _' "_' "but, depends on qua.rk flavor, The _ for t,his (:ase is given by:

"I

f/,#,i = {' (k+ x k_), (2.30)

where, t is the jet axis, and the momenta/_, h'_ for positive and negal;ive parl_ieles,respectively, are orde,red as giv(.;llin Equation (2.31), Methods for selection of trackstu'_.described in t,h(: followillg section, Tills form of tlm triple vector producl; is 1;aken:,;ueh t,hat a quark jet; gives t,he same sign of V_,,,mas an antiquark ,jet with opposite

, heliciLy, In general, t,l_-_clliraliW-based polarizat, ion is given by:

"p,,,,.,,= - (e.al.)| /i

where s/issign of cilarge of a (luarl,: ,f and R,: is t.he ft'action of ff events i1_a samplei of hadronic Z ° decays, Equation (2.32) will be used !.ater to obtain explicit values for "

7_.ch,igiven in Table 4,3 in Se,ction 4,,'1.

2.3.4 Selection of Tracks from a Jet

Two tracks tlsed ill tile d(:_fiilit,ion of f2 are selected i'rolll tracks iii a ,jet. The

selection of tracks depel_ds on assumptions of' the origin of,jet; l_ande(ltless.

This study is lnotlval;ed by two models. O_e (of the assumptions ascrib,,s theorigin of jet, handedness to si_nilar phenome_a l;o _l_e r polarizatio|_. The ot,i_erassumes that jet bandedness is caused by fragment, ation phenomena,

Selection Based on the Analogy with r Polarization

In the analogy with the r polarization, we assume that a ligllt flavor qu,M< qsuch ns u or d, goes t;o 3 res (i)lus a,nol;her quark, q') as a result of tl_e lladronizat;io_,i,e. q -_ r_rrrrq', The rnosl; plausible decw of the quark (i is to pass through the aland p resona, nces, There are l;wo decay modes for al meson whicl_ interfere wid_ eachother like 3-prong decays of r leptons as shown in Figure 2.7. If the helicity of thequark or a,r_,iquark in Z ° -+' qq is _;ransported to _he al meson, we can ot)serve ,jet

18

1 lt

, _1111i._ll,llI ........ Irl..l'u. 'l,m',"lllt_ ' ._ ',_'lllI' _I" ..... "li.......... " 'VV','_II " .m"" "U_'qrl_l ' "_ n" '" "._rll'" ,rr' u'rr's,. , m r_.... ..r.l¢_,ll_l.ly.._.l_llIillU.,,,u._..I__,.Ii..t.lr_,. Iir._l,iI_r_"l'_lI"_l II'IRt "rllUl_t'"" '_l_rI'[_lrllI _'_'1_1_'"" IIIIl' Ul[ll"'l_lm__11r' '111

Pola,rizatio_ ii_ the St;andard Model 2,3 ,let Hai_dedness

q

...._ql

p

-...._q

[Pigure 217: Nalw_modelsof q --_[nrq'-._7rTrTrq',

handedI_essil_a silllilaranalysis'asfortiler polarizatioll.One c'.allexpectalsothat' i

' the leading pargtcles ill a jet carry helicity ix_fox'nlatiollof a quark or antiquark in: Z ° -+ qq, From tlm above view points, wt select a set of three highest momentum: tracks from a jet and require that three tracks have a total charge equal to +1 or -1i

. - and invarim_t mass iI_ a region of al mass. hl addition, we require ttlat at least one, of the two pa,rticle illvariant masses with zero charge is in the, region of tile p°-inass,2 where ali particle, s are assuIIled to be rr, ']'.}leInolneI_t,a il_ tl_e 3-selected-part;icle rest,

" fra_ne are used t,(, ('alculate f_s frown (2,27) a_d (2,371)

=

Selection based oz_ Fl'agmentation Phenomena

12,ysl,:in[8]introduced "color ,' ", lnagne, tm field H as well as "color electric" field- which is ordinary color field. This assumption is an analogy with electromagnetism,

Figure 2.8 shows a. schematic view of the string rnodel modified by 1],ysl<in, Heassulned t,llal; l) was ge_erated by the spi_ of t,l_e quark c7 m_(I was l)ara.llel to c7,

;- /:t" oY,\,Vl_el_a color string becon_es lo_g e_lol.lgh duri_g tl_e fragnw,_tation process,th_:,string is brokel_ and a _ew quark-a_Ciquark pair is l)roduced at botl_ e_lds, At

_i _lle beginni_lg, tr_tllsverse n_onie_t,a of new quark a.nd mlt;iquarl¢'wil;t_ respect t,o theinitial stril_g are ballap,ted, However, movi_g i_ t,he color-_nag_et, ic field tl_ey get, ail

-' . additional _no_l_e_l,llll_ (Skt a_¢.l -Skt sl_ow_l in the figure). Tills _ome_l:un_ l_ick is of=-4 -,_

the order oi'a. few t,e_lMeV/c[8] and tl_ese _no_ellt, a, d.tc¢,a_d .-dtc_ c'o_lt,aill i_t'or_atiol_: on l;he helicit,y o1'l_lieini_;ial quark or m_t;iquark,

,I ' -,.+

Wt can oIlly observe tlm hadron mome_ta, .not the additio_al momentum 5/ct,'1 Therefore, based on this assumption, we look for angular correlation of two particles

from the sa_ne st,ri_g break up in order to get; nonzero ,jet t_aI_dedness. Tl_e mo_nenta= of two t,racl<s il_ t,l_elaboratory frame are used to get _'_sh'o_ (2,27) and (2,31). [ in=

1 9

..... .¢,,i",,v',, i',Ip, 'l_ u,',¢,,' I11........ _,i_,, ..... ¢llr,l,ll ,',l,lll,ltl .,,ri ,, l_i lliillll..... i,,l' ,,,, , li,pill,,,l,,i 'N Irlli_iiqlP_'"' 'ilO"l'iil'_ilil't.... qlll'_i_"II1 ' ''lil1_['li.... 'lliilr

2,3 ,let Ha,ndedness t_oh_,rtz__,tion in the St;m_da,rd Model

_ F------_-"_Color E._ k'. k_,

8 kt A _' -->

ii/+T /" -- -- Color HI

-k 't

F'igure 2,8: Sc,homatlc.: viow of tlm string model rnodtliod by R,yskln, Ite added "color rnagn+_t;tcfield" In _tdcltt;low I;o color flux tube, Due to this fie]el, q'c]' imlr g_et, ncldlt;iotl_tl lllonl(?nl;tllrl kick

,

(') ') c.l (2,31) sllould be a ullit \:ect, or of' t_llc-_qU_trl,: or ant, icluarl,:t,hc.,,£-2definit, iot_s ,,,-,.-7) _l_

moment, uln, T.his sc.,,ettls t,o bc:: represented by the jet; axis,

, 2O

.... Pill...... _r , iii+ mr',,,_r +I'_" +I+_"qll '111l_p 'il" ,pip4lr lalnllll_'l+lp'+niml"'_n p_" ,q'rl!'"qrlI Iii' ,,,,

p

Chapter 3

Experimental Apparatus

Tile SLAC linear collider (SLC) is located at the Stanford Linear Accelm'atorCenter (SLAC) in Stanford, California, SLC consists of a 3 kln long linear acceleratorand two arcs which bring the electron mid positron beams around to the interac.tioI_point (IP), The linear accelerator is tlm world's longest and accelerates both electrollsand positrons ill the stone straigl_t li_le tlp to til(:!energy of 5(1GeV,

Due to _he single path collidm' scheIne, the SLC c.an have only one IP, The SLCLarge Detector (SLD) is placed at that position, The SLD was desigll_d for g¢:',ll_:_ralpurpose to study, for example, precision tests of the, dectroweak theory, QCD al_dheavy flavor ph3sms, el;c, Ill order to acconipllsh this purpose., t,he SLD was built t-rodequipped with a sl;ate-oSl;he-art, t,ecllrlology for tracking, particle idmltificatioll andcalorimetry s3,st,e,ms, IIi tills chapt,(:u', characteristics of SLC aIld SLD are de_.wribed,

3.1. The SLAC Linear Collider

The SLC _"' 'ccnslslas of' _.t3 km long linear accelerator, wllicll accelerates bottl_- electrons and positrons up tc) the ellergy of 50 G,eV, mid the two arcs, which t:n'illg

') atm view of (,l_t!_the beams tr) tile iIlt,eractl___l point, lP, Tile schem' " SLC, is showl_ iiiFigure 3,1, In this section, l;he delivery of tlle electron and positron beams froma,,electron sourc(_ t,o tile [P is described,

. The l:)eam collisioll cycle of' tile SLC is 120 Hz, In each cycle, two bun(.:llesof electrons are producect at, ml electroll source 1' C)lle_Of t:tlem is delivered t,o tl_e

" lP through tile linac and tlle a,'c, alld anoglier s(!u'vesfor l_oSit,rotl produ(:t,ioll al, two-

1There ttro D,vo sourco,.q for eloctoroll producttoa; a thormtonlc SOtlrc(.i and a polarizod sourco,a

Tho pohu'lzodsourco was used in the 1993run, A dotallod description of the source,will al)l)oltriiiSection 3,1,1,

21

2 1' :

I' I'1_ .... qIH ']' li'"' '" "' llp III 'i_ I'II ' "l_li_"_[! "' 'li .... i,IIll , _l,iFl,I..... ra, ,'fell, ,,, ,m, iI_lll , , sll,,_,, _', ,_1,,1111,rl,,' Illll_lWl'",_, _ 11_Fr ' _ li "VI' 'll'PllI ' '" _lWq'r, ,,_' ' ,lr,,, Ip_ ' " li..... i I,i..... lr, dE.... ii,, inI N_I,i ep, i,l_ ..... pit

3,1 '1'he SLAC Linear Collider EXl:>erhr_en_a,lApl:mr_us

Compton\_ P.o!arlmeter EleotronSpin

+ D " r-- Dlreotlon ..\ f" _ColllderAros _Existing e Return _ amplng_ \\ / '_ / Llnao Line '7 Ring ] \Polarized e"

\.L /\ / _ rf _Souroe/ ZI' -z / //" / \ Sp r,Rot.tlon 1k__, / Jr" / \ Solenoids- /V

'_-%",_, J//,_/ LlnaoMoiler _+ oi ..... _/e" Sp'In Thermlonlo_._oa__ Polarlmeter u. ouuluu Vertloal Souroe

I;'igure 3,1: The layout of t,ho SI.,AClim.uu'collider,

t,llirds down t,lle liIlac, Posit;roils are collect;ed fi'olll elect;romagn(:'t;ic sllo',vers prod uced

by ill,ject,ing 30 @eV elect;ro_ls ont;o a t,arget;, '.['lloso posit;tons are ret,urlled to t,tle

begllliling of t;he accelerat;or mid deliv(._red t,o t,lle IP via t;he s()ut,}l arc ill t;lle stone

wa,y as elect;rort bunches,

AI; an energy of 1.2 Ce\f, both elect, ton a_l(.l l)osil;ron bullclms are lead to t;lle

llort;l_ a,nd sout, h daml)ing rinks, resl3ec, t;iv(:_ly,wl_(ir(:!the emit:rance u of t,lle buxlchos isred tl(.',_(.[,

Art,er t;he damping rings , t:llose bunclles are ret;urned to t;he accelerat;or andaccelera,ted t;o 4G,7 GeV, At; tile end of' t:ll(.: accelera,t,or, t,hey are separated by t;he

bendillg magnet; t;o be lead illt;() t;ll(::arcs, Durillg t;raxlsport;al;ion in llorCh and sout4_

arcs, t;he bemn lose t:l_eir (:u_ergy by about; 1 Cle\" due to synchrot, ron radtat, ion,

13efore reacl_ing t,l_e i_t,eract, i(,_ regio_, clue b(.,mns go t;l_rougl_ a series of n_agnel:,s,

called t;he final foctls, in order t:o cOnll)ress hr.)rizo_t,a] and vert;ical l:)ea_n sizes down

I;o 2,0 and 0,8 l._rn, r(.,,spect;ively, 'l"l_e elect;ro_ and 1.)osit;ron bea_s collide wit, h eacll

ot;l_er at, t,he IP every 8,3 ms(be_m_, crossiTu,l t,ime),

Aft;or passi_g t,l_rough l;lle i_t;eract, ion regio_, tl_(:_l.)olarizatio_ of t,he elect;ton

1)cam is measured by t;lm Co_nI)t;on polari_net;er, El_ergies of both bea_ns are _neasured

by t,l_e wire imaging sy_cl_rot;t'on radiat:io_ det:(._cCor(\'VISIt,D), before the beams are

dUml)r"d,

In general, the lumi_losit;y of a collider is given by:

N + N-

E = J"l_.X _-|'Tro_,,a:_ (3.1) •

where N + and N- are t;he number of posit.rons and elect:.rm_sper bunc}_, f/_ is t;he

Ulgmtt:t_ancots doftnod as mo_ spread x spat,h4 spread of'a bunch.

22

Experiment_l Appar_ltus 8,1 The SLAC Linear Collider

repet, ition rat;e, cT.vand c_j_u'ot,llc-_vc_rt;tc_,tlarid l_orizont_l spot sizr_s, Ttlose paranlotersof the SLC for [he 1993 ruI_ are sllown ill Table 3,1, The lumillosity of the SLC for

" the 1993 run had tlm peak value of 2; = 5 x 10_em-_see -1 equivalent; to a r_te of_bout, g0 Z ° events per hour for t;l_eobservable (neut;rtno production excluded) cross

. seetton of cr(_,+_- --_ fr) = 32 nb al; the c.enter of mass energy of 91,26 GEV[21], Tile, performance of t;he SLC ill cim ,1993 run was summt.trized in T_tble 3,1 together wit;li

tile design wtlues,

, Pttralneter Design Value The 1993 R,un, Intensit;y (x_ _ A'+(_,4') 7 3

' [ N- (c,'-) 7 3i l:t,ept_Lit;ionR,t_,t_e,,]',,t(Hz) 180 120

I Betml Size (/til'l) I t-Iorizontal, c_a, 1,6 2,6, ] Vert;ic_:_l,o'y 0,8

Lurrliliosity(Z°s/l._r) 650 50(pe_tk)c',- t_olariz_tt,io_l N/A 63%Up "I.'illl(.: N/A 70%]n[egrt_ed Z_s :_ N/A 50000

Table 3,1: Comp_rlson of t,h(_¢',.,LCpar_m_otorsfor the 1993run to the doslgnv_tluos,

3.1.1 Polarized source

Figure 3,2 stlows t,lle sc',llema._;iclt_5,ou_of t,he polarized electron sourc.e loc_ttedat: tl_e beginlli_lg oft,hc._ac.c.o.lert_t,or, rFt_epol_rized source co_lstst;s of' glirc:!eI-)'al'ts" _;wo' ' :S_.tl_l)l_ir(:_l,tsc:.ls, tt sr!ties of' } ' "NAC4-purni)c:!dTi ,',,' c l)t,_c,_tlelem_ul_;st:c.,cotlt,rol Lhr, int,r:l_sit,y,

| pulse length and circular polarization _md an electron source with the photocathodei made', by strt_i_lecl-lat,t,ice_galliu_ll i:tl's(._li(l(._(Cl_fs),:'.rs, s_t.tl (_h(:,pol_trized gun), ':l_li(_,: _;wo YAG l_.-tsersproduce _;wol)uls(:_ss_::lmrttt;c,dI)y 60 _ls ill order be produc.r! t:wo

bui_cl_es of elect;tons: else {'orcollisio_ tt_ld glib:!other fo.t' positro_l produc_iot_, .t_lo,.'¢lasers produce,, pl_ot;o_lswigh wt_velongth oi' 865 _m' 'I'l_e,,pulses are randomly left;- or

. right-circularly l_ol_trizc,,dby a circul_r I)oletrizer iii order to l'eduee systern_tties, andl;hey are guic.l_d t,o _lle pho_;ocat,l_od¢_i_l t:lle pol_trized gun by tile Ol_t;i¢.'._lelement, s,Finally _chepulses _.trei_ljected t,o t,ll(:_pl_otocat, llode wi_tl -1201(V pot,en_;ial,

When c.:ircul_xrl_c.)larizedl._l_ot,c__ls,..rrc:il_,jc:_c:l:edt,o C]_-_.fs,I.)olarized c::lc:_c.:Lrollsitl'(_enxit,_c:_cl[22],Tl_e Lt.xc:!orc:_cic.alIll,ILLof the I)oL_.triz_.tt:ionwit;li _.tlior_llal tryst;tri is 50¢/0,The ¢,xpe,I'ime,nl;_l lJrc_al,:t;llrougl_ ,,_,,tsbrought; by the us_:,of tAle strtuxiecl..l_lA;l;1cec,_3st,_l.I.heoret;Ic_illy, Llle st,r_tiliod-latt,ice l)liotocat, l_ode ca,n produce I()()cX)I._olttl'iz_xtioll,lt_

23

t..... P_llqq" _' ....... ' _ 'III' ....... I1' I Y I' Ill Ill "" I*PI_q''till _P tlP' ,rl'eP,l_ nt'll '11 III ....... M 'P ,'lpI ' lie .... IlrlIql_' le'li It"llIl" ..... m,,lll_[I "III I till

3,i TIio SLAC Lmem' Colhder _ 'Expermwnt_l Apparatus

YAG-pumped.,..B.,,,.,h,..,,,,_.,,,'_//Tl:SapphlreLasers(3ns)

'-" _,,. 750-870nrn ,-- Lefl._or,Rlghtr_,,,.,,.,ho /.'2___ ., BunchntensltV /Olrculany HotarlzeaLight

,.,_._/ ......_:::,,BP'7_".>._ / Oontrol

/:!:i:::: :!":!;_'%_!':" " •

'%!:_!_:':ttili_i_P_,., . ""/.x,_ ./ ThermionicGun/" 2''_''':_._._ ,,"# \_'¢' ' iiJnpolarlzed)/ / .... ..? , .....,,'" . .....,

PolLll_rl[l"ht / [,4;_,.., ,.,_.iul/aCr_,i,.,(.,.,,,,../ (preM:_orBOrXcuiar_. u / / Polarizer "%../ polarization)

LaserPulse /' ' Ga As _'_.,.,,, ._:_:/i:i_:.....,/-Ohopper2 ns Oombner Oathode !':_! .::.::.:_: i::'_1

....:.:.,:..::..,.,.:.;,,.;:r.:.......,,..... t,,'_"_:'' ""............' ....e I .,_ _"_........__('¢_!,_'............__.:;'"_;II __:_ _!.............., ................................._!i{_! _._"t : _ ,

11._.-.1,- _.:,_,_,_;.,,:..,:: ._,:_,::.::_i_&::::: :':,';'_!_ !ii_:!!!iii!;ii__.._.......Shroud ../ ,,.'_.... ',...'_ ""

, , ,'" , /-" Subharmonlc _v_...._LoaaLOCKo,,_-.;'---, Buncher(100ps) - "_'"hJ_,.. ' ,.,_

Gun S-Band ///' P"_Bunoher(20ps) /

/4 .g3,:_^_ AcceleratorSection

[;'ig'ure 3,2' The schematic Jayoul;oi t.}x._polarl:/,od elccl,ron source al, the SLC tnJecl;or, The sourcoconsists of rho [asor_rho optical eh.:rrmnt,s and IJm polartxod gun,

pracl_ice, _llepolarizal_ion reac'l_ed about; 90% o1_ I:,l_etext; bench[23], I_ the 1993plO'Sics run, t,t_isst:rai_ed-lattic:e crystal was used ns t.lle pl_otocathode, Tl_e _;trainedlatt;ice crystal consists oi ClaAs__:,:I:_;,:(z = 0,24) substrate of tl_icl<_ess2,5 t._,_nwith ancpt:axial layer of Oa.As of l:l_ir.,,kll(:;ss(),1-0,3/m_, ,,\l_d approximat, ely (:)_eal:omic layero1'c.e,siu_n and [luori_e applied t.o the sur[ace i_ ()t'der Lo de,cre,ase the work [u_ctiondov,,_ to zero ornega.t,ive all(l i_crease (.lll,ttllt, l.llll (:_l:liciel_cy(5%-1,5(_),

3.1.2 Spin Transportation

The electron polariza[io_ l_as t:o I._(:_i_ai_l,ai_-,d during l:l_e,accelera.tioI_ a_d,delivery tot;he IP, Tl_ere are t,wo _:_ai:_sources of' (.lepola.rizat;ion of t,h:-_elect;:'o_ beamfronl its source tot, he IP; il_ t,l_edalnpillg ring mid 1;l_earc,

Energy spread in _he elect',ron bunch leads I;o in(_'oherent Tl_omas precessionwitl_in t,he bu_mh in l;he elect,romagnet;ic field ii' the spin of electrons in the bunch

24

=

M'''tr_'_IIr ,_, til , il,i ,'nif, . ,, ' rl Irl'lllJ" " '" ,,,i, _111.... _,ir ",irr _lt_ ',. tl .... ,lt tilt" _' ' _' '' " " lip ,, rl., ,,i _ ,iqll!f,,, ,;111_,,,,,, _11_, , rl

ii

Experimental Apparatus 3,1 The SLAC Linear Collicler

---, Solonold _ _ _' P

' \_q9 4 _k\\ t_.____v _ . ,, ._.lt:._,,,' _i • up

?' J'_dJ" 2. .,-.%- t ,

On mi, I a

I " ,axa'_,"",_:_ ._ I/a," ii.",°.....,>...........,,,,,o............ -- -- .-;_

ll_ ItamSotllh Ring O 7

I RI'L SolenoldOn _

I I LInaoSolonoldO,,RTLSolorioldOil _) t_) LlnaoSolenoidOI1Itt

Figure 3.3: Tile sclierrlal_ic view of' tile norf.h darll.ping ring, Spin vector at. each pc)hit

is shown by ali arrow,

_L

direcl;s along i_lieil' lnolrlelita, ']?his incohei'eiit precession causes depoiarizatioll ofthe elect, tons, This effect is '," -'sc.ilous in the damping ring where 'ciae electron l)tlllCh

spends about; 8 ms and liinkes t,elis of l;tiotisail(.ls of revolutions, Figure 3,3 sliowsl;tle, scherrlatic view of Lhc nort, h darrlphlg rirllr Vlllere, errlifot,allce (.)felecl;roll buciies isre.duced,

In order to avoid depolarizal, ion of the elect, rort beam in the danipilig ring,' Sthe elect,roll spill,.' are rotated t,o t,l_evert,ical direct, ion before being ilijecl;ed ilii:o i_tie

dampil_g rilig, so l;}lal: t,liere is I1Oliorizc)lil_a] c',orrlpolieil{, ii1 t;tle da, rlli,_iligj rillg, '-fills

ro{;a,l;ioli is ci:l.rried gills I)y Olle s'tllJl:_r(;olldtl(.:l;illgsolenoid called a SiJill i'ot,tl,i;or located

at; l;he liliac-t:o-riIlg lille, kfl;(-,r (:!llet'gy spread iri the beam is reduced iii tile dairipilig

ring, the spin vector Ctl, ll [)(2 c)riented to l:lll arbil;rary direction by two spin rolaators at =

. tlm ring-to-linac line and the lhlac,_

Tr_tnsport, lrti;iOlio[' lr,lie elec',l,roll be_tiri iii {,lie arc is coilt, rolled by a series of iliag-ll(Jl0s,Therefore, incohere,nt spill precession due. t,o energy spread ca,rises depolarizat, iolim

Of t;he elecl;roil beaarl, Ii1 t;he 1993 l'Uil, elecLrolls were kept I)olarize.cl vertic, ally iii tile

linac and their spill were rot;at;ed longit;uditially at the exii; of tlm arc, The estimat, e c

of the depolarizatioli was about, 1,4 % for a gaussian energy spreact of a0,1,5 % iii

the beam[24],

2<5

=

,i, llllllllllllll_l_ , _ ih_l I1' ' ' II til Iii .... Illl'il _I_ Ifr ] Ill' III ,' rl I'I' .... II 11I"11' 11_' ' 1 1_''IIM

,, i,_, , e,,llI ','r_il,ll,i II{" '11I_....."r' _'"_{lllilpllli'l' II!" 'II i" II' '"''" I,," i, _ ,'l........... ,, " ii', ..... ,1'1_........ IIl_......... ii' ,, _ ,_........_ll,III<',_

3,1 The SLAC Ltnea,r Collider Expex'imental Apl_U'atus I

3.1.a Polarimetry

There are two devices to rneasure the electron polarization: The linac M_filer po,-la,rimeter and tlm Compton polartlne[er just after t;he lP, In this section, po]arilnegryby the two devices and sp_n transport; iz_SLC are d_.sclibed,

Linac MOiler Polarimeter

'; The linac M_ller polarimeter based on Mcdler sc'at[ering (e-e- -4 e-e-) isset at; tl_e end of tl_e linac irl t,lle PEP extract:ion llne,%his is used for diagnostic

' measurements of the polarization before the beam enters the ilorth arc, Tlm device, section for polarlze:,d bemn elecCronsIlle[tSl.lres the polarizat;ion asynlmetry ix_tile cross ' '" " ' " ,

scatt;ered by the electrons in atom of _.t_lillsertaable lnagnetized iron 1;arget,, By varyingtl_e beam and t;arget polarization, the longitudillal beam polarization is extracted:

4

where A'''_:"'_is Che measured M¢011erasymmetry pt,,..,j_,tis the longitudinal l;arget "") i ,_ 0 .p(.lallzatlon, and A_ is t,lle lo_gitu(.linal M_ller asymmetry at the selected mo_en_urn,

Due _o the location and t,lle met;t_od, nl(-2asurenlel_tsby this device need a special .i .i

run in which the elec_;ron bean_ can not be delivered to the. lP, The average of several i!

_neasuremm_ts by _l_epolarimeter was (65.8-_t=2,7)%[24],

The dominant systematic errors co_ne t'rol_ l_l_et;heoretica.1 u_c(-'rt,ainW in the !' ' , , _,s the po.est,_rnat_on of the polarization of the target electron since atomic _,ff(..ct,,.on

larization are not comI)letely u_dersCood[25],

The Compton Polarimeter

The schematic layout of t,lm compton polarin_et, er is shown i_ F'igure 3,4, 'l"hecompton polarimeter is placed at 33_n down stremn of the SLD and consists of threeCOml)onents: a YAG-,pun_ped Nd laser, a series of optical elements to cont:rol in-te_sity, pulse lengtl_ m_d circular polarization m_d a gas 0erenkov cou_ter to det:ec.tscattered electrons, .The polarizat:ion measure_ent of the device is based on the "cross sect;ion asymmetry in Cornpt;o_ scattering between a polarized electro_ and acircularly polarized photon (e:-7 -4 e:-7). After tl_(:',electron bemn leaves the IP, ,.it interacts with tl_e circularly polarized pl_ot;o_. '1"lie photoll is tin,crated by thelaser and circularly-polarized by opt,ical elemm_ts,t_he_guided to the "Compton" IP,The scattered electron is _neasuredby tl_e 0ere_l,:ov det_ectorafter being bent by theanalysing magnet,,..

| 26

iii o

'"' ', ',_,............ _lll...... _,..... r_ _m,, _ ' '_' ' '_" '_',1_""..... I1_' ' '"' '"_" " " '"_'ml_" ' U_r_'l_'e " "' n,,,_,.... _'_, '111'_,_ml I!ll illlI_ ,11,,,r_,m ,,, _I_'1,1II' 'fill 'IllI' _1[Ii'1' '1_' _l,',,_m

ExperimentM Apparatus 3.1 The SLAC Linear Collider

Compton Polarimeter 532nm" FrequencyDoubled

YAG Laser

Mirror- Box --_

Pockels CellLeftor RightCircularly

PolarizedPhotons

FocusingSLD ,/- and

"_ SteeringLense

MirrorBox(preservescircular

polarization)Laser Beam

AnalyzerandDump ComptonBack Scatterede-

"ComptonlP" -- CerenkovAnalyzingBend Maqnet Detector

" _ Proportional1.93 Tube Detector7268A1

Figure 3.4: The schematic layout of tile compton polarimeter. The Compton polarimeter is locatedat 33 m down stream of the SLD. It consists of the laser, a series of optical elements and a (_erenkovcletector.

!

, The cross section for scattering depends on the polarizations of electron andI

photon as follows:

dcr---A- da---2-u[].+ P,y[_A(E,)] (3.3)dE_ dEs

where E_, is the energy of the scattered electron, au is the unpoiarized compton

scattering cross-section, P_ is the photon spin polarization, Pe. is the longitudinal. polarization of the electron and A(E,_) is the Compton asyrrlrnetry function define.d

as

i

; (k--k')'_/kk'+ 1 + cos00 _ (3.4)t

...+

'i with k and k5 being the momentum vectors of the incident and scattered photol_s,

_l_ l_l.)_L, bl_,'_l), CI, IItA o' 0 bll_ l)llObUll bt3i:Lbbel'lllg _:tll e. III ¢Ile'' i_Jd run_ [,he average elect, rort

-' polarization measured by the Compton polarimeter was 63.0 :k 1.0%[20].

_-_,

N=

nl,q_ I, ,, ,llr lr ,. mu,,i, _), , ,,nim, ',, iii, lily, NrelIii nll_llp ii iiiii I " _I ,,,i .... ' _I'," ,. itlp_llfllll ,1.iI ,i_i ,,11 _ Ii I, i,iiF mrI i,,i, 11 'IF..... , ' " lll',_lll'l, " " I_I) '_ ll'l_l" ii .r ,, ,, ,, u ,, , ll]ilrlllll ,

3.2 The SLC Large Detector Experimental Apparatus

3.1.4 Energy measurementi

Ii .

[ Speotrometeri

i Quadrupole MagnetI Doublet Vertical

, ---_.v '%,,lxv _Ji _ Horl_] ....' _SynchrotronRadiationXJ _""_ , Bump'i _ Synchrotron

LightMonitore + 5771A1

[ 2-90

It,

[ Figure '3.,5: Schemat, ic of the wire imaging synchrotron radiation det, ecl:or for the SLC enorgy

i measurement. There arc one si)ectromet, er in each of two arcs.

The beam energies are measured by a wire imaging synchrotron radiation de-

tector (WISR,D), shown in Figure 3.5,located at ,just before the beam dump. TheWISRD is essentially a deflection spectrometer. Before reaching the WISR,D, eachbeam goes through a series of three dipole magnets in a split-beam configuration.The first magnet induces a horizontal spray of synchrotron radiation that provides areference pedestal for t,he l)endillg down stream. The second magnet is a preciselycalibrated analyzing dipole wllicll bends the l)earn 15 meters upstream of the WISRD.The third magnet provided another horizontal stripe of synchrotron radiation. Theposition of this last stripe is compared to the position of the first one to measure adeflection. The beam energy is then calculated a,s,

C.

where 0 is the measured beam deflection, B is the magnetic field in the &nab,sis mat-

. net, and d/'is the path length along the beam. The synchrotron radiations detectedo by Compton scattering of tl_e electrons in two screens of copper wires. The ineasured

rnear_ center-of-mass eller'gy for the 1993 run was 91.26 GeV.|

3.2 The SLC Large Detector

The SLC Large Detector (SLD) is a general purpose detector to study physicsat tlm Z ° mass scale, Figures 3.6, 3,7 show tim cut and cross sectional views of theSLD.

The construction of tlle SLD was carried out from 1.986 to 1991. The SLD islocated in a 1.5rn deep pit inside the collider hall built on the interaction region of

28

............. Illlql ........... I,I ..... ill'lr ''ill ............ PlI'I'" ', ..... '1' ..... _1' 'rH'IIi........ I,II,,WI,,, ,'ii ....... I'_'1' a!r,,_lllr i .... ,'pl,'",tl_I,' Hv .......,'" r'l",'u,,I,'r",'ll'[lllill _r_,,,_,it,_,rr!ll,,,',,','l',.....!ll,_!l,I_,"'i"lIl"l_l'r'"_l_'rlttllt'r,"l'_r'""'V'

Experimen_a,l, Appara, tus 3.2 The SLC Large Detector

" SLDSupportArches

. Magnet Coil

aMnadgnet IronWarm Iron Liquid ArgonCalorimeter Calorimeter

Moveable Door

C_,erenkovRingImaging Detector

i!

e +

Drift ---'Charnbers Vertex

" Detector 9._a5731A2

- Figure 3,6' A cut view of the SLD, The endcap in the positron arc side is not shown for clarity.The luminosity monitor is also not shown,

the SLC. All detector coinponents are contained irl _ 9 rn diameter octagonal steel

structure. The SLD consists of three rnajor subsystems: tracking systern, particle

identification system and Calorimeter system.

A silicon vertex detector (VXD), a precision central drift chamber (CDC) anda set of endcap drift charnbers (EDC) for low angle tracks serve for charged particle

tracking, hientification of' charged particles is done by a set of (_erenkov ring irnaging

detectors (CRID). Calorimetry is provided by three parts: Liquid Argon Calorirneter

(LAC), measuring the electromagnetic part of the energy and the hadronic energy,

a Warm Iron Calorimeter (WIC), instrumented with strearner tubes and being also

" capable t.o track escaping muons, and a Luminosity Monitor (LUM) which measuresenergies deposited in the extreme forward and backward directions. All the com-

. ponents, except for tl_e WIC are placed inside a norrnal magnet coil producing a

0.6 Tesla magnetic field. By measuring tile curvature of the charged particle in the

magnetic field one can determine its momentum. Platforms all around the detector

support tlm power supplies for each component. A small building on top of SLD,

nr.enmmorlt_l.(_q t.ho f'nqt.h_,_ ,'_",dr_t #!oofrr_n{oe (t;'n) for ,h,_ ,t_,,_ ,_r.... _o_,;,,,_

_-- 29-

, ,,i, 'rMIIrlr.'lrpFI liT i'l_ll_i 'H qill ' i?llil ..... ,,'"l,llI,IIli_ ,,,, 'II .... qlrrli'iil ''.' I'H '" _I" ""_Filff' ,r ,q, ,T_rl ii l'IIm'' " ,H,,,,,,, Irq'l:'_'"',r:'ri' 'Ill" 'i',, _I_ 'qll: ..... i_ q'lllfrlll l'ql U,l : rIIlii i,ll'il: _ rlT_ " , ]_ ..... _flPimliilqIraqi $111_lllllmIll,_lq['I,'F II u11q_llTlp111r" r.... II 'lllllllillpll_ll ..... ,_iiiiliIII_i,_I

3.2 The SLC Large Detector ExperimentM Apparatus

q

4 Warm IronCalorimeter --

3 Magnet Coli IIE

I I I I I I / / / 1[ I I I I I / ,' / ,' / zI _ J _ , Llquld Argon ," ,."" .,,,"

o J,_ __,_, Calorimeterr.: III//'"" ........ "'IIIIIit111t1111/// ///" _ 2

£3Cerenkov

Ring ImagingDetector

1

Drlft --Chamber

0 En 1 I I I

0 '_ ",_,Distance (m)Vertex -_ Lumln0sity --_ SLC

Detector Monitor Beamllne10.92

7282A2

Figure 3,7: A cross-sectional view of the SLD.

' 3.2.1. The Tracking System

- The tracldng system COllSisl;s Of tlle vertex detector and the clrift chambers which_: measure curvatures of charged tracks going through the magnetic field of 0.6 Tesla: ibr the cletermination of their mc)mellta.

4

i

i The Vertex Detector

Figure 3,8 shows the Vertex Detector (VXD) which is placed around the beampipe of 2.5 cm radius surrounding tlm IP to precisely measure 3-D si)ace points wherecharged tracks pass t,hrough. It provides good reconstruction of secondary vertices.The VXD has 480 silicon cllarged couples devices (CCDs). Bach CCD contains 375 x

578 22#rh square pixels and each pixel works independently to detect the space points.The CCDs and their driver electronics comprise a ladder. 4 CCDs are mounted on

30 __, le:

_

t '' '' ........ II[I IIi If I ............. Ifrl' I'1' Illl _1_1_' ' I)"J' "] ..... ' .... 'J ,, ,1',..... ,l"'r_'...... J_.... ,,.......II" '_lt' '1'"'p_" " _1...... flu'1' I!" liar's,,.... '"'rV III.......... "III"''111I'_'"I'II'F'III...... fill..... I111tl,' ,l]I',[rl,',r'r,t,,q,I,'I'"' i' I_..... I'l't,,I,']yl,rlJlJl'N,''II",,111-

Experimental Appar_ttus 3,2 The SLC Large Detector

S!rlpllne" ,-"'Clamp

Survey ......',_'"" ;...... .o.Apertures ............ /__,._\ _.\ \ __,,,<.,.//f]

' o o o -..

__'_ _,"_C /j Annulus

.. '<._: Outer Shell

'__ _... i.i; __ (BerYII[Um' '"

-: "Beanlplpea.so (25 mm rad) _._,

,t,

a Figure 3,8' A cut view of the vertex detector (VXD),p

a

! " 'CI_-s on top and bottom sides arc slightly overlappingeach side of tlle ladder. The C, '_3: each other tc)ensure full coverage, 60 ladders are arranged in four concentric layersi

_1 ius1; outside the beam pipe at radii between 29 and 41 mm.

The VXD is built in a low mass structure (,,o 1.1% of a radiation length parlayer) to minimize multiple scattering.

Information ft'ore t,he VXD is useful to distinguist_ secondary vertices from theprimary vertex where electron and positron interacted. The secondary vertices areproduced by deca.y in fligllt of ll(:avy flavor hadrons with short lifetime and T Icl)Cons.Therefore, t,l_eVXD is a powerfl_l tool for st;udy of those particles.

The Drift Chamber system

The barrel and (mdca.p drift chambers provide the position arid momentummeasurement for charged part;icles, A set of t_igh voltage wires provides a uniform

. electric field in a gas filled volume, A chargedparticle traversing this volume ionizesthe gas atoms and the electrol_s drift with a constant velocity towards the anode. Inthe high gradient field near the anode wires the electrons avalanche, amplifying thesignal. Measuring tl_e (trifC time and using the klmwn drift velocity, the drift distancecan be determined to an accuracy of about 100pm. A track fit_ting program then

31

3,2 The SLC La,rKe Detector Experimental Apparatus

s6o ..... +-_-]+.... 1W--"-F---'_+_r -_o 4' ¢' •

+ o + x o ++ -t. _ + + '

o o.F + _ "t" +

_4" ' , +u _ ",' :.: _ ,( x _ x × x, Ni y,

520 -- "-

x x x _ x ,K x x _ K K x x ×

,,, + + + xo

x + + ×o --

..500 -- x + "F ,H °x + + x

,_ "i"+ ×o>, × -I' + ×

u

,l 'El0 -" k + + xo

x + -I' ×o ,,x + + x+

. _.. ,__ "K :,< x ,4 × x x × x x x × xq bU

,140 -- --x K x _ "|' x

i" +a x -t"+ .I..+ + oo _ ' "f -I"4 -t. , o.............l..................I...........L..............L..........

,120-4 -20 0 20 40 60

x (_)

" Figllre 3.9: Cell scruct.tzres il_ (:he.c:(.:z_Lz'_ldrill chamber, Showl_ are the sena; wit'es (circles), fieldwires (c',ros:._syml):.fl_._)and guarcl wires (plus symbols),

recoIlstruct, s Llle tu'a,,jec'.l;oryo[' the trac',k ('rom tl._esl)ace points provicled by t,he driftrr'_l (1c'.]larlll:_er,.LJ_:.(:urvat,ureofLIi(-:trackillLl_ema_l_et,i(.:fielddet,ernlillest,llepa.rtic]e

Ill01I I(:!IIt,Llill,

ExperimentM Appa,ratus 3.2 The SLC L_rge Det,ecWr

_r:.,-_.ff--:_._-_.'--_?-_. -_v,W,-_,. .,w--UU. ...-O.-,-.-,-C--._r_ - . , _I.-.--U,_- . -

* ..,_LL..,:.:.',,",.:P...."....:.:.:"..:."::.,../."'..'........:.."_'"".'...",f..:..:!"....."...,,_,,_'...:':.:....,

...... ......",, .L:.:.:_.L.':,":.........: . • ..

. ,':_':"':,..,x .... ,:,.. :; ":::,:,,hV.;,,:',:.'• . ... . : .... :,,':

... .>'"_ _ 'i.'.. '....... i"".........,....:.',i .....i._:':":':":",........!

• ":',:,:,.,:_ .... .'.,:,:v:• " v ..v..;.' .....: .,,,...'v'

......! .... ,.,',.v..:v:&".., : : z

• "......... ,,:".';'.":v:" _';'" " ',":':':':'2v

":!!/!i "........ " . .. " " %: - .,.

• " ' " .. .''"',!_" .'......... " " "

' . _..'.., • .. .i.,,'....:.', ., , .. _ '..,,,..,,., ......". v. , ", ' •.... 'J::" , ",,. "h, .'4:' .. , ',,:: .. , ...."

.: ii"..._.,'_" .,"...::::....:.'..'"'..'..:.'.'"_!!_:..,'.,.......,'.::i,_......'.:.'", :_,....'..".........::':_......, ., '"::'.."...';"...:.".:.'.."'.,":"'"..:."._!I_:.,'2..':.,":.'.'"n'.'.i,::.'...'"._.:_._:,_....:.. ".'

,I "i; , ,'.:'.,.I.'.Y....: ". ':.:'.".."'"..:..:' .":'..,"":'!'._i,_.v . ..........i..." .":...'".:. '

Figure 3,10: The struc, ture of the SUl)erlayc:rs in the c{:ntral drift c,hamber, From inside to outside,: (loft, to right tn t,lm figure), the; SUlx:rlayors wero arranged in order of AUVAUVAUVA, where A," U and El rc:l)re,sent for the, axial la,yew and two stereo layers with -_t:_41mracl st,ereo angles,

-

-: ing up to 80 space points per t,rack, Since Llie drift, cell is syrr_lnetric about the sense: wires, it is not known, which side of the sense wire the electron came from, To resolve_ the left-right ambiguity, the cells are staggerecl in each superlayer, An axial layer is_ set at every third layer wi_h tl_e wire are strung parallel to the beam axis, The rests- are small angle stereo layers wlmre the wires were strung at'a :t:41 mrad stereo angle

with respect to the b_-_amaxis, From inside to outside, the superlayers are arranged- in order oi' AUVAUI"AUI,"A, wl_ere A, U mid V are represe_ted for the axial layer

and two st,c.lc.(."•, •, _ layers witl_ -_t:4]_rad stereo m_gles shown in Figure 3,1[), The stereosuperlayers are a,lso used for determinaticm of a coordinate alo_g the wire togetherwith charge division technique, Ea.eh sense wire has identical readout electronics ont)oth sides of the cl_m_ber, tl_en a hit poi_t is determined by comparing the outputsin both sides, The charge division determines the coordinate of the hits along thewire to an accura.cy of _ 6 eta, Tl_e position along the beam axis (z axis in the SLD

: coordinate sys_mn) is better cleter_it_ed by hits in stereo layers,

:: Endcap Drift Clmmber ']"l_et,rack momentum,resolution (:)fthe CDC drol)S ()Ii'at angle_._ot"less t,l_a_ 30° wil:,l_resl)ect to the beam axis, since t,l_enumber of hits onsense wires decreases iii t,l_isregi___l,To improve t,l_eresolution il_ t,l_is regio_l, two sets

-. of drift chaml:_ers, tlxe E_dcal.) l)rif't Cliambers (EDC) were set at (-,ach of el_dc'.aI.),

=

OOO O

.

_-=

r........ ,'" ,I " [11'a ..... _r'l,' i, ........ i,,r ........ Ilrp,,, m Irr' ' ,a_l_l ' _,,lrl II'111 ' ' '_ ..... I' _ ........ ,Ii,It_l,rl =_1_,I rtr'l '", IIr rl,llll IIl'r I''llPlll 'lrllrll_ I', "_ I'll 'H' i,a ,,,IlnllIllI " '_'l,llll 'r'll'iq llllr_[,,r"I,,""_llr IIl_

3,2 2."heSLC Large Detector Expelmmn_ttl Appa, ra,t,us

The EDC of' etmh sicle consists of two drift chambers, imler and outer, located at 1,2m and 2,0 m away from tlm IP and covers the region between 12° and 40°, Each ofthe four drift chambers has threesuperlayers with a relative rotation of 60°,

The Magnet

The magne( _ iu a 5,9 m diamet,_'_r__tll(.l6,4 m long coil situated between ,tile LACand the WIC, A cul'l'(._ll_oi 6600 A tllrough 508 turns provides a InagIletic field of

, 0,6 ".[.'_-_slaili _he center of the coil, Tl_e iron strt|cture of' the WIC on the doors and

the barrel serves au tlux tct,urn 4, The Poisson-.parametrization of the magnet, it fieldin the coil:

0 ?'ZF3 F _ - _

Br 'Q)Zo

Bz =-" B° -I-0,51317'/'_-- 2z'27'0z0

where 13_) O,()21,:IT, .13o 0,601"I:",•--= = ro = 1,2m and z0 = 1 5m agrees v/it,li etde mea-sured field to witllill 0,05% inside tile volume of the CDC aild to withiil (1,4% for the

EIDC, The uilif'orlrlit;y of til(?,field is lllor(:: thall adequate for til(:,,trackixlg nl(!:asure-lnellts aud the radial COml.)OllellLoi' clle field is sir|all enough for ttlr:_re,quirelnents ofthe CI_,ID,

Tracking Performance

The raw hits from tlle VXD _uldthe drift: chaml_ers are used for the track

'.,. recotlstruct;ion divided illt;OtWOStel)S: pattern r(::coguition in tile drift chatnbers and,

\ linkil_g of the l_it,s in tile VXD and the track fc)ulid in tlm drift chamber.

",. Figure 3,1.1.sliows a scherrtati(: illustratioI_ of tlxe reco_xst;ruct;io_lof tr track in

[!@,CDC, A_ first, two trac.k seglnetlts for eat li cell are r(-_co_lst;ructedby Xu tiLt:ing of' '_ s_ cell5t,l_o_esegments to 8 lilts of the s(._,.(:,wires in a , Ttiose segments are called vector

, \ w'l

/nts, \.[hen the vector litts are fitted to a track, Charge division is used for pattern

recog_\[!ion, howeve.r, final t:rack t]ttint. uses only Lhc i_fOrlnation ft'ore re,tier hits,\

Th_..hits i_l t,l_cVXD are clus(:("",-,¢lby pattern re.cog_litio_lwitl_ a loose constraint'\

on t,he prir'aary verW.x irl advance of the extrapolation of the track fou_ld ii1 Lhc driftchaml)ers_, 'i'hose tracks are extral)olatcd into the VXD and linked to clusters in the

aTlm magne, t was mtmttf'acturecl by Mitsublshi Heavy Industry Company,,I"_ l.[h( magtmt;yoke was manufacttu'edby l(awasakl Heavy l)_dust:ryCompany,6The two segment,s arc due, to left-rlght ambiguity of the position where a track really passed

through,

34

',,ii' )i_ " tr_,r,it ,,'it, 'ric .... )i 'U l'i"=rill ' .,t,l rill r, ,r ..... ill" lr ' lli,i 'II_,I'"""_"" t_tl]'i )_Itll ...... ,',Ii",",tl',_,tlt,',"" ','iqilltlq '", l'Ipll , 'ill,l ',)i,,il ,iii,!IiI ,.,, llrll,,pl

Experimental Appar_us 3,2 '/"he SLC La'ge De_ec_or

" r---_j._'_-- \-5_ -J _l.od'r,',,,:,k----_._._._,..,

/

Figure 3,11', 'I..]_osc,honmttc tllust, ratlon wf rho re(lonstructton of a trtu:k In the CD(?, Soltd arrowsiii thc_lol't_tlguro show t_liodrift pabhs of oloci:rons from IonizeD,Ion of ii charged track, dashed ro'rowsare nlli'i:or images of l;hctroaI drift paths,

VXD, Eacti clusDer is allowed to be associated with one extrapolated track, Then a

combined track fit is performed using the Billotr method[26] taking into account the" track multiple scattering in Dhe detector material,

The CDC with a maglletic field of 0,6 Tesla has a the momentum resolution

. of[27],,

<'__s,::__/0,oogs_:+(o,oo49p(Ga,lc))".p

where 7) is til{-! lliOiIit:llt, ill.ll {.)f tl, t,ra{'k in (_-leV/c, For the; combilied CDC and VXDtI't_Cl<, til{-.',IllOlllelllLUlll rosolu{,ioll is[27]',

<_'-'= v/7i,oo95_+ (o,oo2Gp(c,a,l_))_,P

The combination of' DileCD(] and VXD improves the resolution significantly,

3.2.2 The Particle Identification Systern

The Cerenkov Ring Imaging Detector

Tlie dJerenkov R,ing Imagillg Deteet:or(CI_,ID) shown iii Figure 3,12 is used fc)rpartirle identlhc_mon and flavor tagging, When a charged particle pass(:,s through amedium, exceeding the speed of ligtit in the medium, the atoms get polarized andemit photons (Cerel-ikov radiation), Ttie opelling angle of the light cone with respect

35

=

......... ' ",,,," ' 'lllr' ,, ....... ,_r , ",' ,,'"'11' ' ,"_rrl..... ,,,,,,,, ,,,l!l,,,,,,,,,,,f_i,,,ll rlf, pl, ,,' ,_,,li .... ,,'Ii ,,ll,,i_il ,, ,,H ,i_ll li'l,,i, ,,, i,, ,'Ii, ilii,i,lli',ll_l"",,l"lll, .... I'l'rlli iii i,,,in ii i_1' ii,Ii"' ""'l_,_,llli_'"l[l"_'l'l"iti,_ll'

q

3,2 The SLC Lm'ge De_ec_or Experimental Apparatus

Gas nadlator(01_FI2/N 2 MIx)

Mlclplane lyllrror ',i Array

External Drift Box

Field Oage--_ e" Deteetor

-_ If

Liquid Radiator O21q°+ TMAE

(O8 F14) __.--.._

e+ 0"

7757Ao g-g2 *

L;"tgure3,12: Twocross,.secelonalviowsof'tlm ba.rrd 0orcmkovringh'nag[ngdotec'tor(barrel CRIB),Wavy lines showLhc'traces of (Jerenkovphotons, Tho l_hotonsare converted to electronsIn the dz'tf_box by 3.MAl.,

to t:he inciclent track, 0c is related t,o tile velocity and an index of .refracLioll of thel_lediuln, 'r_as follows: cos@- 1/(/':/'/_(,\)), where fl is t;he ratio of the wdocigy Cothespeed of light,. The illclex of refract, ion ¢tepends on tlle wavelength of a picot;on, A, Ift,he al_gle Oc, is measured, oI_e can ¢.let,errnine tt_e velocity ot" the particle, Togetherwit,Ix a momentum measurement, of Ltle I)arLtele,. t:he ma,.ss, and hence the type of Lhe

parLicle can be del:ermined: 7n --=pV/('zzcos 0c,)u -- 1,

T.he Cll,ID coz|sist;s of Lllree lllttill part;s: liquid radial;or, t,ime projec:t;icu_cllazn-r'"_ t ' )bets (1PCs) t;o del;ect; phot;oils alld gas radtaLor and spheric, al mtrrcrs £o reflect, the

lfl_ot:c)llsLc)t;hetopr, 's" C.,erc.mkov._,,, l!'igure 3,12 shows t;l_ebarrel @RID, the emL.slo,_ of t:llel.)tlO(x)liSand how Lodelete cllezn, At; first:, ghe imrt;iclc_ft'ore t;he IP passes Lhrougl_a t,hi_ layer(10 mm) of liquid radia, t,or which is Freon (F(;C_4) wit;h an index of re.,fraction __= 1,277, For/J 1, Lhc Cerenkov angle of the phoCoz_sis 672 mrad, The

photons are mainly e_niCt:edat frequencies in the near ult:raviolet (UV) regicm (170-220nra), therefore the outer side of the radiator vessel is xnade of quartz glass, which is_ransparent, to the UV light, Typically about, 12-15 photoelectrons, which will be de-lined below, are expected for apart, iele of [3= 1, AfLer being refracted at; the quaz'_z

36

.....................................,i...........iilll.............ii_ ' ' Imlrl',1_ ,e ,, ,UnI?I_, "_1_11"=ll'lllq'll.... liT'Irl'" li....... pl'l'NplIIIII'IllI'IH'I" '111lm' '11..... _ ql Iipi ,r e_"'"ll" "'_

Expertment, M Al._p_,r_tus 3,2 Tt_e SLC Large De_ector

window by 236 mrad, t,he photons pass _mross the 13 crn gap to the TPC at an angleoi 52 mrad with respect to the incident particle trajectory_ forming tt circle of 17 cm

' radius _md about 1,5 cm width,

The outer side of the 'FPC ts filled with 76 % of F_CI_ as gas radiator and. 24 % of nitrogen, Tile gas r_dtator has a 10w index of refraction of n = 1,0017

and is transparent to UV light, The gas radiator thickness of ,,o 45 cm expects %9photoelectrons, Those photons are emitted at an angle Oc of ,.o 53 mr_ld for a trackwith _J = 1, Tlie photmm tu'e reflected and focused bad( onto the outer side of theTPC by a seL of spherical mirrors mounted on the outer wall of the CPdD vessel,

A time projection ch_unber (TPC) is used to detect the (Jerenkov llgh:t, Thedrift volume is filled wit,het, hane saturated with TMAE(Tetrakts Dimethyl AminoEthtum), whic,h converts the _erenkov photon to an electron with a very high quantumefficiency in tlm wave length range of 170 to 220 nra, The photons enter the driftbox .from the top and t;he bottom through a quartz window and are absorbed by tileorganic TMAE molecules and knock out an electron, called a photoelectron, Tileelectron drifts to the sense wires in tlm uniform drift field of 400 V/cm est',ablished bya set of equally spaced wires around the box, The sense wires and readout electronics

. are located tt_ the mldc,ap side of' the TPC, Negative high voltage is applied on themidplane side of t,he "PI:-'C,Over a m,:xximurn drift distance of 126 cm this amoullts tct apotenLtal difference of G0kV between the HV side and the readout side, The electrons

, drift, parallel Lo t;lle rnagllet;ic, l]eld produced by the magnetic, coil in the detector, Tlmi

anode of eacll drift box is made of 93 carbon f]ber wires of 7t.ml diameter, strung in tiler_._dtaldirection with _tspacing or 3,2 mm, Each wire has identical readout electronicson both ends for charge division, 'rbe z-coordinate oi' the electron conversion, alongthe beam axis, is obtailled from _he measurements of the drift time and the azimuthalcoordinate is determined by the anode wire address, The depth of tile conversion inthe drift box is measured by charge division on the sense wires, The detector is

optilnized for single electron detection, typically a dozen electrons from ea('h circlemake it ttl[ tlm way to tile anode, However, it will also detect the l_trge dE/dx signalof ionization loss :from t,he charged ptu'ticle passing through the drift box,

Tlle barrel CR,ID consists of dO'rpC!s...._,.,d() liquid radiator trays, and d00 sphericalmirrors, Each endeap por(;ion or the (2RID has 5 TPC]s, 1 liquid radiator and 60mirrors,

.i

3.2.3 The Calorimeter System

q.7'hetask of the c_dorimetry is tctme_tsure accurately the frac.tion of electromag-) _ 4net,it ,rod haclrc nlc enerDes frmn til(:; dec.ay of the Z °, ccrvertng t-_smuch of the solid

, t

tingle aroux_d tl_(-:;IP ,:tspossi.bie, This large solid angle is very ]_pctl_tmt, b(-;cause of

37

lP'"" rl , ,, " Irllll ' ' .... _11' ii 'lh ,11 ',,' ir_ Irll ',lr , [111' ' n,' " _ ". ..... ' '_111ql lr 11'[_1 ,11 I1' r_,' '11 "' III1' .... "" III " 'lI_ ' ,", ',rll

3,2 The SLC Large Detector Experimental Apparatus

cleanly separating events with missing energy, The SLD calorimeter consists of threeparts:

, a lead-liquid argon calorimeter (LAC), which absorbs most_ of the electromag-neticand hadronic energy in order to rneasure them,

. a warm iron calorimeter (WIC) which contatns tlm tails of hadron showers andt;'acks penetra'_tng particles tllrough the LAC, such as muons and

. a Luminosity Monitor (LUM) which measures tlm energy deposit of the Bhabha' ewmts at very small angles to tlm beam and determines the luminosity of the

SLC,

The electromagnetic part of t,tie LAC has 22 radiation lengths Xe, and the LAC andt;he WIC togeLher have 8 interaction lengths _ to absorb most hadrons completely,Elect,rons and gammas form electromagnetic showers which can be distinguished frornhadronic showers by the profile of the energy deposit, Electromagnetic showers de-posit most of their energy within the first section of the LAC while hadronic showersextend nmctl further into the detector since the hadronic interaction length is greater_han the electromagnetic radiation lengfil, The forrn of the showers can thus be usedto separate electro.ns frorn pions and/or protons, An EM shower rrlatctled to a trad(in the CDC will be identified as an electron and can thus be separated ft'ore a showerinduced by a gamma,

The Liquid Argon Calorimeter

The LAC is placed inside the magnet coil, to avoid degrading the performanceof the calorimeter due to energy absorption in the material of the coil, The LACworks as an ionization chamber and consists of stacks of lead tiles interspaced by

gaps filled with purified liquid argon hS a sensitive material, The tiles at groundand negative high potential are mutually placed, Tiles at tlm same potential areconnected togeflmr like a daisy chaill t,o form projective towers pointing to the lP,The signals are induced on the anode when the electrons from primary ionizationdrift to the electrode, Since no secondary ionization occurs in argon, the signal m,ustbe amplified by charge amplifiers,

The towers have lateral dimensions between 6 and 12 cre, somewhat larger than

the average lateral size of an electromagnetic shower, Tlm towers are further splitinto four parts in the radial direction, making tlp two electromagnetic parts of the

°1 -- e-1 of ali charged particles Interact doctromagncttcally in one radiation leagth and 1 - e-'lof all hadrons interact strongly with matter of one Interaction length ttmy are passing through,

38

I1.....,.... .,, ,_, .v . ,,, 'v ,r,,, ,,,, ..... _, rl,....... r_,fly,'' ,, .... ,.'"'"" "*lr' ',i ' ,r,_'r',, ,, _1n...... ,.... ,_i,rll,,llii,,r,,,41, 'ii Iqll]!l"".',"_l

Experimental Apparatus 3,2 The SLC Large Detector.r -%_ , .........

Strapping_ E_rel I.AO

. _v ,y, _: :__.,_,_,, , • _ _s,,. _._'_ _."<"'

, _\/../..-,r ,_ EMTopplate# EndPlate_,

NotohodforMountingRail 0-_filial

Figure 3.13', The barrel liquid argon calorimeter (LAC).Shown are three o£the 288modules thatmake tlt) the barrel LAC.

calorime'_er, E1 and E2, and two hadronic parts, H1 and H2 as shown in Figure 3.13,The geometry of tlm electromagnetic section was chosen to provide the best possibleefficiency for isolating electrons from semileptonic decays within jets, lowest possible_r/7 overlap background, and good position resolution. The LAC is placed inside avacuum vessel and surrounded by a cryos_at which is cooled by liquid Nitrogen, TheLAC's endcap is a. continuation of the barrel in the forward and backward direction

with a similar internal tower geometry, The endcaps fit like plugs inside the barrel.Together they cover al.'_out 98% of the solid angle for electromagnetm' showers,

Since a liquid argon calorimeter has no gain in the sensitive medium and there-

fore produces very small signals, low noise amplifiers must be provided, The approx-imately 44,000 electronics channels require a fast pre-processing of the event to formreliable trigger information and to reduce the data volume passed to tlm computer.

The Warm Iron Calorimeter

The hadronic energy which escapes the LAC "_s measured by the Warm IronCalorimeter (WIC) which also serves as a muon tracking device and as a flux return

39

=

[I,, ,_lr'rll[I........ 'f_ll!.... q_,,'_l.......... I',_I" _fI_"r]l"lalllll .... HaH,,Ill ,I.......... Illl,,,,,l_l,'......... '1'f11" 'rr]l""MIl '"111r'.......... 9' ..... r,rl ....... _ " 1" ..... tl ........ ' .... ''rl I ......... ' rl..... I_ I' ' ' kI_l '1............... III .....

3,2 The SLC Large Detector Expertn_entM Apparatus

DetailofSingle_Layer ,,

Double for MuonTracking /

Layer

LI _ 2 --'-J / "O •

........ - --- [,[ I I I--I_ " _ Plastice4ubeContalner

, ',"--:- ",' - . - :t! L -- :_-':'"_" " \ TransverseStripsI _ -..-C e '_'_'_ LongitudinalStrips

Detailof DoubleLayer4.947028AB0 i tO0om ,J , ,,,

l_igure 3,14: ".['huwormh'oncalorlrnet_er(WlC),

' yoke ibr Lhe magnel;ic field, The iron sl_rucLure is segmented inLo 18 layers, 50 turnmstrume, nLed wtth stre,amer tubes(Iarocci gas Ltfbes) shown tnthick with 32 mm gaps'

Figure 3,14, At 90° _:heiron makes up 4 inte,raction lengths; togethe, r with the LACand t,lle coil, t,he SLD has at least 8 interac, ttoll leIigths in any direct:ion, The "vVIOc',onslsl_sof eighl_ barrel se('Llon surroundll_g Lhc coil in au oct;age nal faslllon mlcl /:weenclcaps, covering almost, Lhcentire solid angle arc)und Lhc IP,

In Lhc center of t,he slighLly c(.)nclucLivographite coated plas¢ic 9 mm × 9tonis(,reamer Lubes, Lhc,re is tt 10()/.ml wire of BeOu held at 4.5 kV in a gas inixLure of25% argon and 75% isobutane, O_l the top and bottom of the tubes is stripes of

* G10 material plated wi_h copper pat,terns in the form of strips arid pacls, A chargecli_" pa.rtiele passing through the gas mixture forms so-called sLre,amers, small discharges .

from t,he high volLage wire to the surfac',e, inducing c,harge in the copper circuitsproportional to t;he energy of _he particle, typically 1.2 pC per streamer and al)out

7-8 streamer per Ge.V of ea_ergy;

In Lhc eigh_ c'.cII]ns of Lhc barrel se(;Lion t:l_ereare 17 layers of tubes, Tlm st,ripsrun parallel t,o ghe t,ubes, ex('ept in layer 8 and 17 where they are perpendicular Lol;hem They are reacl ou_ cligi_ally provicling an exact t,racking of the particles in 'r-¢

4O

_ ......... i'_r ,,,,ill ,_1 el,' ,,1', ,,I ,11r ii,ill...... ,¢,, ii_,lrll,,lallffq,,,, ....... i,, f_,v pl' _ .i,

Experiment_l Appm'_tus 3.2 The SLC L_rg'e Detector

CDCm

Beampipe

v×o M Sk•

10cm

3.9, MASC LMSAT 782B,,,8

Figure 3.15: The luminosity monitor.

and two poit_ts in z determining tile angle of tile muons to better than 10 mrad.

- The geometry of the pads is a continuation of tlie hadronic tower structure of

LAC. The readout is analog, proportional to the energy deposited. They are squares

of 265 mm x 216 mm on the inner most layer, increasing in size to 295mm x 316mm

" in tile outer plane. The first eight layers are connected together to measure the energyflux in tile "front tower", tile remaining 7 layers form the "back tower".

The endcap region consists (of eight horizontal and eight vertical layers of tubes

read out in a similar fashion as the barrel with strips along eact', tube and pads in

a tower structure. To cover the gaps between the endcaps and the barrel, so called

45 chambers have been installed on tile support arches. Along each section of the

octagon there are two of these chambers, staggered by half a cell, 120 cm x 375 cm in

size, with strips parallel and vertical to the tubes. Tlm WIC contains a total 101,488

strips and 8640 towers covering 97% of the solid angle.

The Luminosity Monitor

. The Luminosity Monitor (LUM) [28] in tile SLD consists of' Small Angle Tagger

(LMSAT) and the medium angle silicon calorirneter(MASiC) shown irl Figure 3.15,The LUM provides SLD's small angle electromagnetic coverage, measuring photons

" and electrons in the 23-200 mrad region. The main function is to measure the lumi-

nosity by tagging of electrons in Bhabha events. With a total of 23 radiation lengths

The LMSAT and MASiC are cones c[ silicon detector centered around the beam

41

3.2 The SLC Large Detector Experimental Apparatus

pipe with a projective tower structure very rnuch like tile LAC, Tim LMSAT coversthe angle,s from 23 to 65 mrad and is about l_m frorn tile IP, right iii front of tile finalfocus magnets. 'The MASi.C covers the angle of 05 to 200 mrad and is right next to °the VXD at z = 4-200 mm. On both devices each of the 23 layers of silicon detectoris interspaced with tungsten plates of l radiation length. Like the electromagneticpart of the LAC the monitor is split up into EMl and EM2, two sets of towers infront, of each other.

i42

',I, ........ ,,I'l,_'lll........ ,....... ,.... _, '_ ',_',_,lll'r'"_r,_,ll!l!l...... lrl_ ,iq,l_T_l_"_H , 'lr,qlll, ,,,_,r_llp,,rl,,liI_,_,rnlnnil_,,,........i_

Chapter 4

Analysis

4.1 Introduction

The data taken by the SLD in the 1993 run and the events generated by a, Mm,Ce Carlo simulation are used for this study, The brief' sumrnary of the production

of Z ° bosons by the SLC and data taking by the SLD is described, followed by thedescription of event generation by the Monte Carlo simulation.

b

Z ° Production by the SLC and SLD Data Taking SLC produced the firstZ ° in April, 1989, Z°s were measured by the Mark II detector which was located atthe IP of the SLC prior to the SLD. The Mark II detector was replaced by the SLDafter it collected about 700 Z ° decays in 1989 and 1990. Tile SLD was rolled in tothe IP in the sl)riIlg of 1991. '.File SLD collected about 400 Z ° decays in the 1991engineering rul_ without the electro_ beam polarization. In the 1992 rull, electronbeam was polarized with magllit;ude of 23% and the SLD collected about 10000 Z °decays. In the 1!)93 run, the electron beam polarization was increased to 63% due tothe replacement of the photoc, athode by the strained gallium arsenide crystal..Tl_eluminosity of the SLC was also improved and at the end of the 1993 run about 50000Z ° decays had been accumulated by the SLD.

I The SLD Monte Carlo Each events are reconstructed by using the data fromindividual detector elements, Tlle reconstructed events may get biased due to the de-l ,

] tector effects such as tlm limited coverage and detector resolutions. Those effects givei bias tc) sorne results. Therefore, we t_ave to esti_nate the magnitude of the effects mid'

' correct such results by using events produced by event generators and the SLD detec-I

---, JSTSST[9] [5]._, tor simulation. There are several event generators, such as 2 , HER,WIG 1 _

43 =

:lll '1' ,,IRI_"'I_..... Irrll'_'"'11....... ii],, ,111],I ',,, ,],"',1 ......... r, "mr"'" _'ltl'r"ll '] ........ vll[''""' ']f '1"'111'11' "r"rlN'_r'lrl'r '_ ..... ""_ql0' '""qlqil_ I....... ,V,I"'llf'In'P'"H'_' '1 .... ,,,I1,1, H,,,i,,,'llllr,, ,,rpl_ .... _,,,,lllr .... ,,' IIIr,l" ,li' _,r,e, ,, ..... _ ....... ,,'

4.2 Event Type a,nd 7Hgg'ers Ana, lysis

i for ¢+e - -+ qq, KOR,ALZ[30] for c+e - -+ T+T-, BHLUMI[31] for e+e - --_ c+e - and' . lSI MCTWOG[32] for 27 events. It depends on the aim of tile study whicll generator "i used The generated particles are fed to the program calle.d GEANT[33] which sire- "I

ulates particle decays, nuclear and electrornagnetic interactions, multiple scattering,! ere GEANT Was tuned to the SLD so as to reproduce well the response of the SLD.

i ,]ETSET version 6.3[29] and GEANT version 3.14133] were used for the hadronic 'i event generation and the SLD detector simulation, respectively. Generated events_' have the same inforrnation, c,g, hits in the CDC, output from each of the LAC tower,

etc,, as that contained in the real data, Those generated events are fed to the SLDreconstruction prograrn whicl_ rec(:,nstructs cl_a.rged tracks iz_ the tracking sysLem,ldetermirles tille energy deposit in t,lle calorimeter system and identifies the charged

! particles. This procedure is the same as that for the real data,

This study ibcused on the transport of parton polarization through thehadronization process. As mentioned in Section 2.2, none of the hadronization modelsimplements the spin transport through the hadrollization to event generators. There-fore, events generated by the programs are expected to have no signal in terms of thepolarization and we can not estimate how large the signal can be. However, thesegenerated events are useful to estimate systematic errors or biases introduced by theanalysis methods,

4.2 Event Type and Triggers

Events produced by decays of the Z ° are divided into the following four cate-gories:

II

® ttadronic events,

i • I:iLlectron-positron events,

• lt+tl,- events and

O 'r+r - events.

Examples of typical ew_.nts in these categories are shown in Figure 4,1. Hadronicevellts are characterized by a burst, of t,racks observed ill t,l_edrift challlber and t,lleyform jet-structure. For c+e- and ll,+t.t- production, two back-to-back charged t,racksare reconstructed in the drift chamt_er. These two types of events are distinguished

7either by deposit of electron la,gne.t;ice_lergie.s in tlle [,AC or trackilig by tl_e \_ It, Bothcharged tracks in tl_e electroll-positro_l pair productioll llave large a,lnOUllt; o[' e11ergydel)usit in the electfoIna.gn'.',tic t;a','t,(.._ftlle LAC. due t.o t,l_, (,l(-,('.t,ro_ag_etic sl_owers.

44

....... _]_ ..... ]] '_l' 'li _ ..... _ 0' I_l ..... Hill .......... Ill _]_' .... '11 ']_][_]_ '_' 11" 'l' Illl,r]lnJ_,_,JIMlrrlI'l,lllll'l,,r..... Ill_'"l"" _JIl" I]lI 'r l'll1' ''''' I]''l''llll Irl'l_[[lll , I_llIIIr,,,%lllllllllll,l_lil,,ip,l,, ,, "t11"'"'_"1[ -

Ana, lysis 4,2 Event Type a,nd Ti'ig'gers

)\........o/. &...../ .

(d)

Figure 4.1' Examplos of t'ouz' categories oi phs'sical events. Shown are (a) _t hadronic evont with

2 .icr,s, (b) an c+e - l)_th' production, (c) a lt+tr - pair production and (d) _ candidate of a r+r -pah' production, wirer(.,, a r- altd "r+ decay(.:d into three charged parttcles(_t "_-prong docay) and onecharged l)_U'{,icl(: (a 1-prong; d_'ca3'), lgac.h *;t'ap(.:zoid indi(.tatos an energy &!posit in a t.owor of tll_LAC und its ar(.:a is l:U'Ol_Ol't.l(uutl t.() the _tnlount o[' the dolJOSil,,

On the otll(-_r llnlld, (.:llul'g_:_dI,_'acl<sill t,ll(-_/i,+t,,- pair 1)mdUct, ioll lose e.ll(-_rgies o1113;I.,3'

io.niz_¢ic)n so l:,l_-tt,I;1_(_3, del)osit, s_all I'_'a(_tt,i(:)_ (.)1'tlleir (_,_ergi(::s(about, et f'ew l_u_(lred

MeV) in tl_e LAC. 1_ ad(titio_l, tt_e t,ra.:_(s are observed by tl_e WIC surrou_di_lgthe LAC, 'I'l_e r+r - l.)_tit'l._roduct:io,_ eve_._t;s,_xhibit tile cl_u'acteristics different fron_

hadronic events or or,her lepton-a_tilepl;o_ pair production events due ¢o the v_trietyof decay modes of r leptons, The event, i_ general, l_as t;wo or more tr_mks, but does

_ot l_ave so l_lal_y I,_'acl<s_ls a ]_a{l_'(_l_ic(::\.'el_l;s.T decays it_l,o c., t_.or }_at.l_'o_sso I,llal.

I "

Event Triggers Tile t._l.l_'l.)Os_-_of t,l_eevellt, trigger iu t{_reduce t,lle baclCgrou_d _we_lt,s

_ts much as possil)le witt_out, loss of plvsic, ttl events. Tl_e following f-ire trigger typeswere used to select, l;he event:s:

Z 45

_

=

, .... ,,_lI_,,_ _'_ _I .... '"1_' '_'n',"_ _r_,,_..... "I'll'r,_,_qll"'_ll ' '_'"'111'1111'"_'_ ......... II"_"'_l"'IIl_ll"'"ll"_' _1_'1' "11_' r_lll_ _'ll'[_lI"I.... '_I_'_I'_,I'_I"'_'""RH_I'II1 " I1_"........... 'If'llnl' ..... n,.... ," vIIIIl_"'"l','nl'u_,"_,,l" "1,' _!_'"1111' 7'1

4,2 Event _i_po _nd _'ig'g'ers Ane_lj,sis

• The energy trigger, which is the most irnportant trigger described below,

, The luminosit, y trigger, wlli(:t_ requires a minimum deposit energy of 10 GeV ineach of two haole-to-haole to\ver_ in the LUM,

® The tracking trigger, which requires two or more tracks detected irl the CDCwith an opening angle > 20°,

,, The hadron t;rigg(:r, wllicll is a c0rnbillatioll of the energy trigger alld t,lle rra,ck-ing trigger witll at, leetst ollc:_t;rac.l<iH the CDC, and

i• The random trigger, which records events at the time of a beam crossing at a

, fixed rate of 1/20 Hz for tl_e purpose of ba,ckground studies.

rr'l! (_ -._.n... t,rigger r_tt,e ctel)ellds oll tile l_ea.mc.onctiLiolls, The h_t(tron trigger is often usedto reduce the trigger r_te when the. beam conclitiolls a.re noisy. Among these _riggers,the energy trigger is most, irnporl_-mt,, The energy trigger[3d] uses information defiiledby the following t,l_reeLAC clu_.tl_t,it,ic:_s:

® NEMI-II, whicll is tile llul_l.)er of I.,AC l{i;N'It,owe::rst,l_a.I,t_:tve sig_a.ls abox,c:_60: ADC (:oun_s,

. EHI, Lthigl_-gl_resl_old energy such, wl_icl_is t:he sum of energy recorded in aliINM tower wigJl sig_:_.ls _:tl._c)v¢.,G0 ADC c.:oul_gsa.nd HA.lD gc)wc_rswigl_ sigt_):tls_bove 120 ADC cou_t,s _,_d

_, ELO,> a low-threshold energy sum, whict_ is the sum of energy recorded in allt)3Mt,OWC_I'S_tbovo.8 ADO _._,_1(.1nii I-Iii) t;owers _.tbov¢::1.2ADC,

'" l lgl_¢:!I.,,\C energy sca.le is b_-tsc_d(_11t,l_c!¢:_nergyd(:!posit,of a minirrmm io_izi_g (_l_i_-

i I) 1)a.rCicl(.'.,sucl_ as inuon, gl_e /\IDC c(.)u_t,s for t,h¢:_1BM t,owers a_d I-lAD towers1_ c:orr(:_spoi_dto the following e_ergies i_ tl_e t;owers:

E;M t,owers '1 ADC cou_t,_2,8 MeV rnin-I,HAD towers' 1 ADC cou_t,_?,,5 MeV n_i_l-l,

Tt_es(_const_.mts were detc::rlni_ed I._y(:orr_pariso_ of tt_e ADC counts for _mons within

their expected energy deposit, in ea.cl_tow(:!r, Tl_e c-mergyt,rigger requirements are:

1, NIBMHI >_.1(1,

2, IBI--II> 15 GeV mi_-l,

,3, 1_[,O < 1"10GeV rain-I,

,_n=_,,,_prl ....... lr,......... ,m ........ , ,,, ,i ipl ,,pl 17, ,r, nr,,v, 'rf=' '==lr llll = " _=..... ,,"' It'=1," ,,m,'_ql ',1_' ,,r_ ,.... =',_lp_,,,, ...... ,ll',,e ,llllq, ',li_ .......... _lmllr' I!1=11...... _'_1I¢..... ,,,',,rrll,Hnr_,,,'",e'_'_'"en,ll_""lP' I_lI' ''_

Analysis 4,3 Event Selection

4. EHI > 1,5 x (ELO. 70)and

. 5, Each north/south side of tlle detector must llave NEMHI > 0,

E,equiremellt, s 1 all(.:l2 ide_tif'y large, ellergy deposit, s ill the LAC c,aused by llaclroilic

• events, The bad(groupie.Is due t,o beam-wall mid bea._r>gas illtert.wtions are re|||oved

by 3 and 5, SbC rnuon backgrou_lds 1 are relnoved by 1, 2 alld 4,

; 4.3 Event SelectioniI, Events sat, isfyillg tlle trigger criteria still c.ontain background events besides tlle.

! Z ° events, Sillce olllv tile, lladroI_ic evellt, s of Z ° decays were used in t,l_is stll(Iv,D

J bac,l(grollll(l (._\,ezJ(;s_ _lll_.ll(,[.}t,otlic. (_vezlt_sl_tisl be relr|o\,ed t'ro_n tile evellt sa_lll)les, ]liI

t,l_e study, o_lly c,l_a,'ged t,rar'ks _n_-_a.s_lre(lby tl_e ce_tra.l drift, cl_alllber alld tlm vertex

' detector were _lse(l, 'I'l_erel'ore, t,l_e l_adr(.n_ic e,ve_t select,io_ del)e_ds (.n_c.t|arged track

measurer||el_ts m_d II(_)ill['()l'lll_"tt, iOll O[' t;}l(:_ C[I,]OI'i|II(![,Fy \VtI,.%.' HSf:K], It, _,ts perfor_ned i_

two steps: good track selecl, io_ a_d l_adro_ic eve_t selectio_ usi_g t,l_ose tracks,

' In the first: step, the good track selection was performed by requiring tl_e fol-

lowing four criteria for charged tracks:

• the tra(:l< l_ad transverse _non_entun_ of p_t. > 0,15 GeV/c with re,specl; t,o t,llebea.ril axis,

| • cosine, i.}['l_olar a_lgle O wil, ll respect. I_ogt_¢.:I.}ean_ axis was ii_ _t ra_lge of'-0,8 t,o0,8,

| ® dista_ce o[' tile l racl_ s closest aI)l)roacl_ to t,l_e bet.un a,×is was le,ss tl_a_ 5 c_n&ll d

® distance of t,l_e,l;rack's closest; api)rottch to tile int,eractio|| poii_l_ along t,tle betu_axis wa.s less tha_ 10 c_n,

Figures d,2, ,1,3, ,:l,d a_ld ,1,5 sinew dist, ribtll, io_s of t;ra_lsx'erse _noll_el_t,tl_l_\\'it;li respect,

to l_he heals| axis, Pl, c_si_,':, of polar a.l_gle O, cosO, distDm_ce of closest al._pr_ac.ll to

" gl_e bean_ axis, ro alld disl,;lll(:e of closest; atl_p|'oach Lo t;lle i_lteractio|| l>oi_lt, nlo_g tl_e

t.)(:_tl,lll a,xis, zo,

- _The SLC produce,s muons who_ stray ole,ctrons and positrons collide with collimators, Someof these muons are t,ranslmrted to by the accelerator and st,riko the SLD at a nearly horizontaldirection,

:_Background me,ans events _._uchas int,e,racttons of the beam with the beam pipe or gas inside thebeam pipe,

,17 --

.......... ,_ ' ,',,,_,',, ,, ,,,lr,,, ' ' ,' " .... 'I.... _l'l' "" ..... '_1' "".... ,'"" _lr""l?l!l"" ' ....... '_'1_"""'_" 'l_ll_Y"" " ...... ,,,',,'1", 'II,,,,,,,,"rr', _,_.... _l'Ir"l'l'" "'1"..... ""',,,I',,U_"" rills,'qll, ,,, 'r,' II,,Ill' ' 'II'1" ...."#" "''' '" [lllll'l'rll'

4,3Event Sdection AnalysLs'

,,_" 2 7_-"q'_-%-_:7 ,;'_._ -c_! "1............................................................................................................................................................... ,i

: , " ",b,:

\\ ""e_,::'+I te to t

""l "t 1_'\"_ t"t-"'°t\ ", ,. • "t 0+_ il I ...... I

,\ \ \ ",1'. ", ", ', I

_"-"-\ • ota,0.t+.,- ._• , \ • I+X.4 t • I •

"..., ,. . g _.• ,.U _. li.

0,5 ,'-",,',]., '. (

+'I:;i[!iii i0 = i:: :Ll;:"lt:i.+,,l,.+lJl,.+,+ I J.j+ I J,J.,l..lll._lL,_ l.ll.l._._ I I lll0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Pt (GeV/c)

F'igtlre 4,2: Dlst, rlbut, lon of I;ransverso nio_nonl;um of cha+rgc,d l,racks wit,h respc, c,l; I;o t,ho beamaxis, Potnt;s ropresont, dalm, at+d htst,ogrmn sho',vs cfu, Moltt, e Carlo shfinial;ion, Charged l,ra,cks In t;ho

hatchod region were not us(._d in t;hls sttt(-ly

:.,_,,. . °0 .... . • • ._.

o 0.6 ::,5:,..:::,:,: ,, 0+,.,__.- t.+

. • :._ • o'"'' .... I.'] ' l_'_, • _•,,,,1'

' >2""/-0,4 t:l"r- ' i /2

7 1

1 ,l:i-, x',. ......

-1 -0.8 -0,6 -0,4 -0,2 0 0,2 0,4 0,6 0,8 1It,

COSOtraok

Figure 4.3: Distribution of cosine of polar angle of charged tracks, Shown aro data (points) and +the Monte Carlo shnulatton (histogram), Chargod t,racks tn the hatched roglon were not, used in this

study,

i I AO.

"t_J

t

' HIll " ' _' " '"' "l*_J " .... H,r r, .,, _,lll,_ ,,. lJJ ' " III r,, H' '_U' " _'1_1_r,, ,, ....... , , q,,,_lljl '"11"_" ' _lllll,l_llr_l_l'',,,, i,,'Ullll'lr,, lilt ,,. H,,_ ,_ ,,_ ,,., ,,_,_, .11 rlmr_i,,p,Pl,,.

.... ,, _L . ,_ ,_ ,_ ill , _t, , _i, ,dl ,,i¢,, , 41,I, ,II ,,Jill

e"[_["_.'_.,,,...... , .

"1

10

ii'ii,._ ,.t,t.O!Oell•2 .o,..... ' .I0

" _.,,e..J,'¢}_O IO(

,:II lIill il,.,._.l.:...l_ll.....J..l.IL.Lt..l..It..:..LL.._..i.i..:..l_i..i._[.,.:,._0 0,5 1 1,5 2 2,5 3 8,5 4 4,5 5

ro(cm)

].:'i_ure 4,4: I)l;._l,rlbttl,tol: or dist,:u_c_._o{'clos<._sCapproachof chargedtracl<sl_ot,ho beam axl,u,Showl_at'ech_;a(points) tu_dtht_Monto Carlo sl_mllat;ion(iflsl,o_ram), 'Fl_orot,ua ctlsct'ol)ancybel,woondat,a_u:dMonte Carlo in l:horo,_lor:or }at,g:.:clls_;ar:c',o,Tho cllscrepancytsascrlboc{t_obac.l<Kn._undtvacl<s

' and l,racl<ing l'aiJ_l_'e, 'l.'ll_: Mul_l,_: Carlo (Ioos l:o_c(mq)h.:_.,ly simul:_t,_.__,l_ureal _.wel_t,sin rho r_t_,'ion,

No i,l .....................................................................................................

•u 1Z'I""

-1 "}°_,,10

le_o . •

._ t _ o 5J • •

10 _ O • o • 40 • _ • • • • • o • o ID • • • • 0 g • • @ • •

' , ,

10 .._-_,l..l _._,_.,.l_l, .1._ 1_, ,._ i. ,._.l.l._.:_ 1._._.l..1 _._._...10 1 2 3 4 5 6 7 8 9 10

e

z0(cm)

,!9

IIII"_1'_'I_1"1_1}1_"1_'IIII....,_" '"fl_ll_'_ ' "_l'_'lqlI'_......_1....... iF"n,'"'rl_"r',_u"r"'""ll' 'lt ' ,,Iq,_,...... 111t ....... I,r" ,,Ir_',ri,llr" li" ',"etll,_=' _r,'"........... _,r,.... ,,........ lr ,.......

! o,1 ........ ,,....... 10

[ 0,06.--..... ;i;i.; I

} 0,04 ' I"1 tI ....i 0,02 I._:._'.q,?,..'. .j*l ' "t I-;.__TLI w 1 , , .

: 5 10 "15 20 25 30 35 40i

i Numberof chargedtracksI!

i

, ' " (poilll, s)];'ifftlr(._4 6: l.)lst,ril:,uqor_oi"nul_fl.,_:ror t_;c..,Ic.'llm'Kc._d(,l'ac.',k,.'4111Cttl eV(.',III.,S, Sh(n_, li artl d,hLl.I.

_nd t,h(_,Mu_a.,C_u'losl_h_.l,h..,_(l_lst,u,__;r_u_),lt;vc:l_t,sir_t,l,._hat,ch_._drc.!_;ior_,,v_.,,ronoc,usedIn t:hehlli/,[ysl,s', [.,II,L'K(._Iltlllll)of o[' OI1LI'[(:,'4Jll dlll,,_t I1[ I.W(_[rltc',l,tSiS (.',(_)I/LrII.)ULi()I'_['t'orn c:t_:',- _ltttl -" and T'tT -

pair l)roducLh.ms,

1 _ _.*_'_x:.\\l.............................................................................................................................._-:,m_,-X'v',

_0.75 <-.:',',,

-' ..0.8 -0,6 -0.4 -0.2 0 0,2 0,4 0.6 0.8 1

COSOlhrust

}°igt.lr(:;.,1,7: l)lst.rlblltll_ll of c.OSll_eul' I,Ii(_l,hrlu4t,nxis. ,.£1_owH_u'edat_ (l:_ldnl,:{)_mdt:lle [VItriol,(:Carloslnml_d:lon (hlsl_c,gralu), l!',vu_ll,s11__,1_._I_tl.c,l_udrc_gh:H_were not, used In I,he _u_dysis,

oo3i iEL] '

Z..o,o2 i'I' ';_.lIii_/'i!!i)!)!:ii!_ii_i

0,01 ' ''i 0

, ,.i °i, /_ ,..'_

. 0 10 20 30 40 50 60 70 80 90 100

Evls (GEV)

Figure 4,8: ])[Sl;l'il)tll_iolloi' c,Llttrgud ','lsiblo euergy, ShOWI1 ii,r(.1 da,ttt (pol_l,s) _UKIl,hc_Monl,o C_u'loshnuhd;ton (hl,,._ogrmn), Events in th(._h_l;choclrc_glonwc:r(_no_ usocl in fl_o m_dysts,

51

,E

r

,, ...... ,_' , ..... I1_11, '_,, ,,_, 'I_ I_, ...... ,_ _,,............ II _ '11ifp '" _11_IIp " ' " _P, _l]r

4,3 IEve,n_ Select;Ion Ana,lysis

_ [=-o,70,_::!L-........................................................................................................, ,"i'lltlttIIt!I[" ,1tt_!_11!i_!1t1!1!1!t!!l!j!ll+',,,",t ' ..... ii'' '!_[l[tl"iiittil!i_......,,i, IIIitlt_lllllt ,, _!t':'!1! ", ,llftt0,5 . , +

0,4

0,3 --

0,2 _-

0,1

0 ....]--++"'+ .l_.+..J..++_.I.._.+++.__.+I. ++J...J..+l__.l._++.,+.+._+...l+u_._+.i.._L__.l_.+.,_+i._..t.+_t+....[...l...__t.._.i.20000 20500 21000 21500 22000 22500 23000 23500

Run

Figttt'c++d,9; l_3h::ct,rc:mbc.:antl:_olartzat,lc.mslu+wrlas a ftlrtc+t,turtof run nurnbur, Eac'.hlJolt_t,rc.'l:_rus.uttt,sl+hob¢.'mn polttrtzrd, tc.mm<.+£tsurudby t,hu C<.mtl:_t,c.+rtl:mlarttilut_c.:rrmtu'art event,,

41

"" , , +:,,ect;rozlbeartl _t,t_c+lt;}_c+;(+,c+'_Z_l.:>-.l+Itc:,SLC providc++_st:Ite lotlg'it,tlditl+tlly l._ularized '_ " ,I

[,cul l.+olarimI?,t;ernteasurus t,ltc.+l:+<_>lrtrizat,iot+ <+£t;llu buatn dowtt;+t;re,rt,ttt o[' t,ltu SLD asclea:ril.+ed itr Sect.,iult 3,1,3, 'it;tris st,udy t,uol++,advattt,ages of t;lte longit;udiltaI c:+lect,t'otlbt:+a,nt polarizat;ion, so t;ttat, t.;ttc.:ttnal yzittg power for ,jet;hmtdeclness is det,ermitted at,lligll ,_/,c.(.+tlracyill t;ll(:+tlulicit:5'-l+use¢lattalysis, 'l-'ltu heath pularizat:iott ts tnc:,asur(:+dc:+v-.¢:,+t'3+'3 tttinttt:es by t,llu Corrtl:)t+,ot_l.,oI++iriltlut,ur, rl'lt<:',l.+t.+larizat;iotlPor (:+r_cltc.+vc:,.ttt,is t,hol)ularizat, tott tttet:'_st.tr¢:+tn¢::tlt, clusc::st,itr l;illl(:+ t,O L}I¢.!(:\:(::lit, Figure ,1,9 sltows t,lte I.)(:+ttttt

l.+c>larimat,i+.++lof (:'l'+_r'l(:}l()\;(:!IIIwl+ic.'.I+s_ll+isfi<+tlt,ll¢++tI++_X'C+Itadt'otltc.c++,,'u_t,s¢:+lc:+ct.iottct'it.c,+t'i+.t,Tit+:+++_\'(:+t'+tg(:',el(::ct,rolt l.+¢:++tt_l.+Ol+triz+tt.iolt {',PI I'i.+rtil<-+]993 t'Utt was ¢:+St,iltlat¢:+d tj+' usiltgt,ttc-.+ttltttittosit,y ,,vc.;igttU:+dav(+rag¢:,'

] -.,

('p)= (t + 4)_VE., 'P+, (,I,',.+>)(!tlCll1.3

" _ ) ,,,wl_c:_rc:_N is t;l_eLot;al l:_Ut_l:_urut' c._v_:,,_t,sPi is polariza, Liot__nc:_asuredby t:,l_eCoital. t;ul_

l_c.+laritttet;c:;rnear t,llu it,ll uvc:+tlt,,++t,tc.l,.c =. 0,017 is t;ltc:_cltrutttat;ic,it;y corrc:+ct:io,iforl+)olut,izat,iott biases due.+t+c:+t,ails it+ t,tt<:,,I>c:+atlt¢:+ti¢.+rgydist:t'ibut, iott, 'l'Ite avc.+t'agc:;vitltlt:+

was[+O]:

Select,ed event:shad t,lte,trt_gtlit,u<:leoi' eloct,rot_I)_atn polarizat_ion in _ rm_ge"be.t,wuet_0,2 attd 0,8, If tltu l_olat'izat,ioll was tleg_t;ivl:_,-(/,6,3 was used for t,llc,.ll_licit,y-basc:_d

52

........ III_ , 'q_q.... "'I'..... ,P_'_',, ,_............... m,,,_,e,, ,H',., , ,'r '_i_'"III_1'_'' el............ I_,Pil+P.... rr ,'."fn_q....... _II[l"TI "'Pll"'I_'',',+,,'I' "Irl......... " ,,,, ,,,i_

Analysis 4,3 E_.'o_$S'oh:>ctio_

t" -ianalAsls as llominal polarlzat_loll, IIi tllccase tbr blle posit,lye polarizat, ton, +0,63 was' tlS(:id,

The m.mlbe_rsof evemt,s wii;ll right;- and Ioft,-l_anded bemn pola,l 'lzat,ic' • _nwere 13515and 16519, respect;ivoly a,

lm,

2-jet ovent_s were select;cd in order t,o avoid conl;arnlnation from hard gluonemission, shlce we can not; pre,diet tlle polarization of such gluons, There are severalalgorithms t,o i:lnd jet:s[36]-[38], Ali algorithms basically ccnstsI;"_' " ot' two processes:ca,Lcula,l_ing inwtrianl; t;he lnass or it similm' quant;lt_y for each pair of l;rac,l:s in anevent,, and ('olnbil_ing t,he t,rac.ks, 'I'lle, JA1-)E algorit,llm[36] was used in t;llis stucly, Iiitlm.{'ollowing, t;ll_:_procedurl:_ ill I;l_e,lADE algoritllln is explained as tul example:

1,. Tilt, scaled "il_v_l'ial_t,l_lass" Y.ijof ev(:_rypair of parbiclc:_sis calculat, e¢l, asstll_li_lgali l_adro_s go I:,(._n_ssless:

2t_,'.,:5'._(:1- cosO.,.,i):_/_._-- _, (,t,4)

'lrl.,'.l

where I-'2i,L;'j arid c.¢_sOi,._are l;ll(_parl;icle energies and the tu_gle bet_ween {;l_e,_," Evi,_ is tl_e,total e_c::rgy in t}_eevmlt,

'_ ' pseudO-l)art,_c.le2, The pair wit,Ix t,lm smallc_st,itxvarialxt,mass Y,i_is c_.x_t._x_c::(.lint;o a" or c:.lust,_.:rlc I_y l_d¢li|lgt,l_c:_ir,t-_no_l_(._llCa._,:

1_,= t_,_-I- 'lJj (4,5)

As a restllt, of t,llis prc.)cec.lure,,I;l_elll.llrll.)er (.)f l;racks iii f;lle eye,lt, decreases by

OI1(_,

3, The abovc:_procure.lure is rc:!pc._al_edullbil t,l_es_nallesl_ i_wariant; mass Yo bc:_covneslarger t;l_m_a c.',ut;c_ffvalue 'Y,,.,,t,?),,utdei:inc:,,st_heresolut;m_ oi"two ,lets, ,_clect,lo_of t;he y_,,t val_c:_dc:_pc.,lldsoll t.ll(:!l_mrl.)Osc::c._fst,udic::s, "-I"}lc:_re_llaining l_Setldo-part, jolt:isarc.!(_lc::l:i_(:_£las ,i_.!t,s,

'i'l_e,dc::[i_it,io_l of t,I_c,,'-;c.:aic,_li_vt._l'ilt_lI,lllt_s,_I_l_.lt,ll(:_c:_,v_xbill_tt.i(_,lc.'.rit_c.,riacl,.,pc,llcl (_1t,l_e,algorit, lllti _lsc:_(.l{'c,r,ic._t,-lilldi_lg,

O

l?igure ,t,i()slac_fwsl:llc_h'act;io_lsoi' 2-,jet;c:wcnt,s alic_lc:_,,e_ll;sc.:ol_t:ai_i_lg3 or _l_c._n.,,}c-_l;sas a t'tl_ct,io_ ot' :t/,,,,_value f'c_rt,l_el_ac.lro_lice',,e_lt:si_ t;llc case of l;l_c._JADE

- algoriflin_, /ks ?],,,t value::i_lc:.reases,2-,jet,eve_lt,s iIlcrc_a,'.._e_t_lc.1muir,i-jt:it;(3 or inc.)rc:_)cvent;s dc:_c;ret.tsc._,'i'I_c,_y,,.,,,value lias t;o be s_nall enougl_ t,o avoid t,l_eco_lt,mlli_lat,io.iiof 3-,jet;evevlt.s, i,c, clc -- --> qi]9, It' a :}-jc_t,cycler, is c_at,c._gorizedas a ,.,9-j(,t,.,.evc.,_lt,I._y

:_'l"horower,._only 2 ovc._nt;swl_,l_no polarlzat, ion ITlOtl.,b'UY.'c'rll(!Ill..,'.['ho.y v,'c._r(:discarded,

53

,,,,,, ,.le,,,,...... ,,_r, qllr,,,q _"""'11_' Iqlq, ,',p,v_e",," n'n'_llln ,_l,'r,_=='"P!"_LM'", ,lllr'llr ' ,,IH,,p,,II,_1,' rl'l_p_,,,,,l'le,l,,,.... r,.._ ,,, i,,11_ ...... p_,ll,,; rh, ,,lr rH ..... I[I'll 'rl'lr' .... el"LI II' "It IlI'l ........ It ......... II,t , t,

.l'4 F'!avol,' Tag'gtng' b.v Normalized h:nl2_ct Pm'atnete_' A,nMysi,_

l'-'ig_li'c:!,_l,I(): ,l(__tr_._.t,(_e;s_.['un(.',lAonc,r;(A,,tv_duot'(__rt,lm l'm.drcJnic_(._,,,(._l_ts,Sl,)wl_m'ot'r_w,tlormof2-,ltir,c.,vc.;nl_s(l)olnt,s) _vlclc,,vc,nt,s wltll 3,l_.'l.,s.'or mc.Jr(._(SCltlt_rc.'s),y,,,, = 0,03wasusc_clIi_t,hlsantdysls(slum'uby m'ro,,v),

some Yc_tvalue, it,s t:l_rusl; axis doc.,snot, rel)resc:,,lit; quark mid aut;iqum'k _no_x_en_umvec',t,ors correctly. Tl_e c:o_lt,a_ui_at;ic:m _ay dilute _ signal mc:msurecl in t,his st,uc:ly,However, a. small vMue of Y_,.t res_it_s i_ decrease o[' 2-,iet, eve_t:s tu_d znak(_s l;l_esLa-t;ist,icM flucl_ua_ion iu :'esult;sincret:se, The Y,,,,tv_:_luc:,,used t,hroughoul; this study wt_s0,03 (l?igUre 4,10), A.I:, !l¢,.,,t.=: 0,03, 2-jet, e,\,elll; rat;e was t'ou_c.lt,o be about, 65% ofl_adronic eveHl;s, II_ c.):r(l(.!r t,o gel:, (t()rrc:!c:t, l)_u't,c)ll ¢liv'ec:l:io_,t,l_e_-u.lclit:io_l reqllir(.!m¢:!_ll;

o[' t,llc-_acollinearil# a._igic-:'_ I,o be less i,llt_l 20" Ici'l; _tl)out,9(3%o[' t,l_(-_2-jet, evc:!_it;,s,']'l_erc-_reiHzd_ed[)9,12,819C}2-,ic-._t;c_vei_tswil,l_ Ici't,-,z'it_'l_/,-l_zz_cl(2c.]elec_'.t,z'()v_l)C)larizal,i()va,reSl)eC'_ively,

4.4 Flavor Tagging by Normalized Impact Pa-rameter

$

A 1._anctecl_esssig_al _ay I.)edilut,ecl i_ llcmx,y (lUm'k c2vc::ul:s(Z ° --_ c/.!,biJ), siI_c'en_al_5't:racks come c)tlg fi'o_n cl(:,,(_'.aysc:)['Sl.)ix_lc::sslxc,avy _esc.)lis, l)_flit,z c/,, (_l llav(:_ ii' ,

. repc.)rt,ecIa,st;ucly of t,lle (.:xl:mc:t,c:;dl_.l_l(lc._cl_:_sssig;_lalfor c_:l_m'mClum'l,:smlc.lcc:)l_c:,luc.lc:_dt;liat; any ,spin effect; result;ling ['rc)_xiD* or i)'* c.t(-:c_,yswas very sm_,fll[2], "l.l_c2rc:_l'c.)rc-_,

'_Tl-macolllnearLWz_nglois dc.fflnc._clt_,sclLf.rorc_rw,c_I.-)ot;w(.,,¢.m7randan auglc._I)ol;wc.mn_w¢.)Jot;s,

54

_I ...... ,, , ,i ,' li,__111,It,i .... ,, , , ,rllln till!lp ,,ii ,,,, ,i,_ ',, "_,q.'"'"" '_ ', ...... 'I,l_' ' 'llr " " '_ , ,r,,ppillli_ ,il_' ,_nlr_l q,ie,'lip_ 'm, ,

Analysis 4,4 Fhwor Tagging by Norma,lized Impa,ct Pa,ra,meter

yy,lD

Extrapolated Jet Axis. Track

Extrapolated:

Track

fX

- Figure 4.11[: Definit, ion of th(_ signed impact, paramct;cr, 5, The sign of the lmpac, t parameter" del)ends on lab(.; loc, at;h)n o[' ali itlt:(:u'S(:',c',tiOtlbeLwe(.',n a extral)Olatc'd track _tllc.t the ,jet; _txis i tl xvhi(.',}l

l;he tr_tc:k are contained.

=h.

=

we should use o',,'v light Ilztvor ('u,'a,&Z,,._;.q)evetlts in order Co observe the possible

h_uidedness si_.....,..,+n this study, tile data is divided into two samples whicll origin_tted

: h'orn _t light or ,e_t\,y fl_-wor qq,

g ' 1' ,1._ The sep_u'_tl:io_ of l_gl_,, flavor (.',ve]lt;sfrom hef.try fl_:tvor evcllt;s uses _.t[]avor

-" t_gging tecllxli(lue '5. Fle_tvy t l_wor taggizlg often Inakes. use of tlle illI'c.)rtnatioll c.)tl t,llc,

decay length of heavy flavor l_leSOtlS, e,q, D, B, etc, As the decay lengt,}l is sllort=.1_1

(typically _t few htzt_dred l_,n_.), t:i_ey are detectable o_ly by placiI_g a very prc:_cise- position detector _ear tl_e lP. _]'t_is tneatis tt_at the (:;fl]cient i:l_wor tagging strongly

depends on tl_e l)erfort_a_ce, oi l:}_edel;ect, or _t_r.] it;s loc:atio]_, The VXD il_ l:}_eSLDsatisfies tl_e requirernet_ts arid, in practice, achieves t_igl_ efficiet_cy for }_eavy t:l_tv(_r

tagging. Light flavor (:,,v(.mt:s are _._ti-taggc:.,d a.gai_st t}_e l_eavy t]_wor taggit_g,

- , Event fl_-tvor t;aggit_g used t,}_esigt_ed x-y i_l)aCt, lJa.ra_t_{-,t,(._,r,rS, Tl_e p_ra_llet, c._reis defined a,'.+l;l_e dista_ce ()t' closest a.pl)r(mcl_ of' a cl_at'ged t,racl< to tl_e IP i_l x-y

--- pl_me 6. Figure 4.11 sl_ows t,}_(+,,def:i_lit,ioil of the sig_le,d iml)act l.)a.ranlet:er, tS, Ii' atl--£ , 1 * . .1 +- ...... l.

" ex_r_tl.>O_e_beu_,_,.,, cro:.4:.4'.::.;tl:" i"t "";_ b{:_['orei_-__,le_._,sr,a,_r_rcmct_ to t,l_e IP, it,s 5 is

= set to be posit, ire, On t,l_e oi;her }_a,nd, if tl_ere is an i_t,ersection betwee_ a track a_d

SThc flavor tagging method was often used t.o me_sure lifetime of B hadrons[30]-_ C;The x-y plalm is de[itmd as a plane perpendic.:ular t;o t;he beam t-txis,

-

=

-- 55

......................... ,,............. ,_,............... ,"'_'_..... '"' ',IV'"rlf.'",,'+l,_Iff,,..... ,e++',I+,','.... ,_+.......#PI+*"'"J,''"'elJlI[+Ps'JPq"l"'lJIlI_'IJI!!'"""I@I_'P"l"'llll""PJ'J_lJ",_"lll',+_qgJlllilll_"Ifnl'rll'lJl'lll'lJlq'l_llllqli'"%l_Jrlq'"11

4,4 Flavor Tagging by Norma,liz(.id Iml:)a.ct, Pa.ra.meter Analysis!

!

iI

] ,,_ 10 4 , data "" - ,o:_:_:t_ [.....] uu,dd,_sevents

1 _ 10 3 _. , [_;_ [s_]:...t .:/..-_,bb events "

i >-;I' 1o2 .I;+J " '""" .,. ,..

,, _l-,k,:.ii.:,:,.+:_,t::j:::[_,'.:t.,' ' )+.J t :.,+__,.L :''.

-,0 -8 -6 -4 -2 0 2 4 6 8 0

6/_5

.Pigur(-! z[,].2. Dist_ribu(_ionof (.h(.:iI(.)rn_,liz(.:din_l:)act,p_ramet(.:r, Shown are da,t,a(l)oint,s) and t;h(:Monk(.,Carlo simulation (hist,ogra_ns), l"2a('.l_of t,w(.)kinds of hatch(.',dm'(.._asshows cia(.:c(.)ntxribuLi(.)nfr(.m_oi','and bbevents t,o (.:t_Lri(.',sin d.:i M(.)r_t(._(,at lo simt_lation,

i

t;t_(-_jet; axis aft,(::r (:l_e t,ra(:k passes it,s (',l()s(.,,st;at)l.)roac}_, i(;s 6"is _leg'al:iv(._.

I_ addit, ion t,o (-,he sl:andm'd go(.)(.t t,ra(:l,: s(._lecl;i(.)ncrit, eria, (;he f(.)llowi_g re.st;ric-

(:i(:)_sare imI:)os(::d i_ (.)r(.l(:wt,(.)(._s_r(.' g(.)()(I lr_(:_as_,_r(:_)._(:',l_flso[' t,l!e i]l_l.)a.(.'.L l)ara]_(.;t,er'

!• Lro.cks mus(; l_ave a(: l(:m.st,2 (.:lust,(.:rs(.)fl_it,s i_a(tifI'er(::_t;CCD layers of' t,l_e V'XD,III

i ,2 5,()• t,racks rous(; l_av(.',X / NI-)I;'7< il_ a t:racl( fit Lo (:lie CDC l)i(:s a)_d

• t,racks rous(; _(.>t,(.:(.)_t(._t'r(.)_,_1''() 1.)_trt.i(.:les(ii' a._xi_varia_t, _;_,_._s(.)t't,w(.)Cracks falls

i_Co in a range of I( o (.)r A() l_ass, t_l_(.)set,r_ml<sare r(.,,_nove(.t).

The signed _or_la.lized i_nlm(.:L l)ara_(_',t;(:r, (5/cr,_, was d(:_fi_._(::das signed i_l.)a('t_

l.)a,ramet:er divided l:)y its measuri_g error, ?igur(._ 4.12 shows t,he signed normalized

impac(; parameter distribut;ion for dat;a and t,l_e Mont, e Carlo si_rmla(;io_, Tt_e slm-

'" '('" of' 1)osi(_ive in,pa.(-(; l_a.ra]_(:'t(.:r,'s:s(:_(:_ni_ oulat, i(.)_ we,li rel)roduc(-_s t,he dat, a, '-l?ll(:_(..xc.,ss

]:,'igure 4,12 is ascribe, d t,o Ll_ese,col_(.lary v(.:rt,i(:(._st)roduced by d(_(.',a,ys i)_flight, o[' t_eavy

flavor mesons, The heavy tlavor _nesons are only produced in c(_?or bb (_ve_t,s,Tl_is

(lum_t,ity was us(:,,dfor fla,vor t,a.ggi_g. Tile flavor t,a.ggi_g purit, y and efl](::i(::l_cycl(::l)e_d

o_ t,lm cut value of _;l_enor_nalized irnpacg I.mran_eLe,r(/,/_e 'no'rm_,lized 'impa,ct p_r(m_e-

t,er significartce). This value must, b(:: Ol._t;imiT,ed in terms of t,he l-)uritoy m_d <..,.Ificie_cy.

7Number of degrees of freedom.

56

......................... ' ...... lr' ............ _rl'll' )'11' " '" ........ q)_"''" '" "..... "_ "1)'1__t.... I_r'lll'll' '))' _':_.... " irll " ' 111.... _,,,i,'1_ .... 'l!t" 'ql_lllllllIII" I_lrl _...... I_',),,,,) _,1qf' II' !11.,

Analysis 4,4Fire,or 'lh,gging by Normalized Impact Parameter

J

_ 20000 * data

_1 __.J uu,dd,ss events

" 15000 ._ _.,',_' cc events.:<; bb events

10000 ....-_

- [7"_ 7.i-i5000 ..... 14-4_,'.4:_-;'1_ t','=2":,_b_,x./

F,z,@zR,-'-<zl-,.7 t; ',,;;I = ,

0 1 2 3 4 5 6 7 8 9N of tracks with 8/¢r8 > 3

Figure 4.13' bistribtltion of the l_umber of tlm significant tracks in an event, Shown arcdata(poitll;s) arid tlm Monte Car!o silnulatioll (histogranl). Two different hatched areas sllow thecontributions from c(?and bbeyelets to _,ntrics in the Monte Carlo simulation.

, In this study, ii' 6/a5 of a track is more tllan three, that track is called a 'significant

track', The number of significant tracks in a heavy flavor event is expected to bemore

than that in light flavor events. Figure 4.13 shows the distribution of. the number of

significant tracks in ali event. Each event was classified as being of light (u, d or s) or

heavy (c or b) quark origil_ according to tl_e number of significant tracks in the event.Events containing no significant track were assigned to the light flavor sample and ali

ottler events were assigl_ed t,o t,lle lleavy tlavor sample. ?l:lle 1lumbers of evellts iI1 tll_

light atld heavy favor saillt)les are givell in Table 4.1. The global sample iu detined

as the sum of tt_e ligl_t and heavy flavor samples. The purities and components of

SanlI._le I{,igl_t-handed "P Le.ft-handed T'Hadronic events 13515 16519

. Ligl_t flavor 4608 5547

2..jet events Heavy [layer 3588 4395Glol_al 8196 99,12

al,

Table 4.1: Sun_nary of statistics. 2-jet events are a subset of hadronic, events, and arc classified

into tlm light and heavy fhwor samples according to the number of significant tracks in a event, Theglobal sample is the sum of the light and hcavy flavor samples.

57

................. ,.......... _,1,.... ,,,'...... _,I_......' " "I_'............_...... ,,........_, ,,'lr"' ',,,'",!r'_'_',_1_',',"",_,,,','_,_,............ _l_l_...._,,r,, ,,,',r_ilt[ll"r,,p,,,_...._'"_"'""P'I_"'"_"'" _lllr' "...... _'_"_l'I_......It,"_'_""_lrr"_r_'_ ,,_lllll_l!lp_-

4.5 Three Leading Particle Selection Method Analysis

L

- - Fraction of events from flavor: (%)Sample Purity(H) uf_ dd sg c_ ..... bb

I

Light Flavor 84,04-0,2 23,610.2 30,6:J:0,2 29,9=I=.0.2 12.8±0.2 3.i4-0,1Heavy Fiavor 70.3+0,2 8.3=t=0,2 10.3=t=0,2 11.1_-t=0.2 2216=1=0.2 47,;_±0.3.............

Table 4,2: Purities of the light and heavy flavor samples and constituent flavor of these samples,estimated by the Monte Carlo simulation.

flavors irl ttle samples estimated from the simulation are given iri Table 4.2, The lightflavor sample contained about 56% of all events and its purity was about 84%,

4.5 Three Leading Particle Selection Method

Tliis method was based on the analogy to the measurement of the 9-polarization

for 3-prong decays of 9-leptons[3]. In particular, since all charged tracks were assumedto be pions, this method was focused on the decay of the al meson into 3 charged_s via p meson and Tr, The initial parton in Z ° _ qq may be contained in such anal, The method measures the polarization of the al sirnilar to the 9-polarization onthe assumption that the parton polarization is transported to the al. As shown inSection 2.3.1, the measurement of tlm polarization is based on the theoretical modelof the 3-prong decay of tlm T via the al. Therefore, it is essential to select pairs ortriplets of particles which produce an invariant mass in the region of the p or al mass,respectively.

In order to fultill tills r_._quirelncnt, the mlalysis was perforrned in line with thefbllowing procedures:

i

1. The three highest momentum particles in each jet are selected if they had atotal charge of -_t=1.

2. One of the invariant masses for the two oppositely charged pion pairs is required

to be in the range (/,62 < 7rt_ < 0.92 GeV/c u (p-mass region), and the invariantrnass of the 3-7r system is ill the range 0.86 < m_Tr_ < 1.66 GeV/c u (al..mass *region).

4111

"- 3, The particles forming the higher mass pair are used to calculate "lm

|

ah, = (L x L), (4.6)=

58

...... ' ......,............... _,....,,, ' tl..... ,,,,,,'.... r_........ ,',' ' ................. ,'1_,q, '.......,i,',, 'III ,,v',, ' ..... _11.... IIIlll,I ...... _'!ll'"'_ll_I_lll[H_"_T,_,,,,,",,,,,r',,,,",V_"P__"!r_',_,_,_" ,llli,,l![_,,ri,pl_"i'_',,,_Ir,_l,,iI_,',

AnMysis 4,5 Three Leading P_trticle Selection Method

where the rnorrlenta of' tile. particles are defined in the 3-particle rest frame and. fill[> /_2[, t is the thrust axis signed so its to point along the jet direction, k+

and k_ are rnomenta of particles with positive and negative charge, respectively.For the modified helicity-based analysis, f_rno,t.hclis calculated by:

..s

= × -s0) (4.7)

where k., kb are momenta of tlm tracks with the same charge in the 3-particlerest frame, and s,, = (k. +k_,)", sl, (1%+ k,,) '2are the squared invariant nlassesof the two pairs of positive and negative particles.

4. For all cases, tlle ,jet tla.lldedness H is defined as the asymmetry irl tile numberof jets xvitll positive mid _legative f2. Tile helicity-based and modified llelicity-based Hs (lepeIld c)ll tlle mlgle defillillg the ,jet directiml cos 0 and tlm electrollbeam polarizatiol_ "P. Therefore, .jets are divided into several subsets ac,c,ordingto coso and P, mid jet tlandedness H(P, cosO) is calculated for each subset.The ellirality-based H does llot del)end c)I1coso and P, but the handedness isalso calculated for l;he subset, s.

5. The analyzing powers tbr tlle helicity-, modified helicity- and chirality-basedanalyses are determined ill the following ways. The helicity- and modifiedhelicity-based analysis fits tile following Hh_l(P, cosO) and H,,,,od.h,:Z('P,cosO) tothe measured handedlless:

cos0)= cosO) (al.S)

I-I,,,,,l.l,,l(7-),cos 0) = C_.,.,,,,t.h,,l7:',,od.h_l('P,COS0) (4.9)

wit,li

A z ('P) cos O"Ph_,l(P,cos 0) = "P,,o,t.h_l('P,cos 0) = --2 1 + cosu0

(,1,10)

where (_ is the analyzing, l:)ower to vary and Az(7 9) -- _._;_'ae-'P_il_e analyzingpower takes a dif:t'ere_ll,value I'or eacl_ analysis. The analyzi_g power for t.l_echirality-based allalysis is det,errni_ed by tlgti_g the me,ast|red t_a_lde(.l_(_ssto

" the followi_g H('P, cos 0) tbr eac,l_s_ml.)le:

H(r-,..:,,.,.o)=

Pc._i does _ot depe_d o_ "P and cos 0. Therefore, the handedness is fitted toa consta_lt value. According to the ft'actions gix;e_ in Table. 4..2, T'd,i for eachsample is calculate(t anti givm_ i_ q"alfl¢-;4,._.

,_1"' ,r, ..... _llvl* ..... til, il[l_' q, _ ,,,r_r[lI_,,,, ....... _l_,[_" '_]l_,,'r_l,,Nl' II ,' ,__', _,,' i,r, ,_ _11_, _'" ' ' '_ _1_ vlrlrl' '"' III '_ll']' ,Ii " '"l'_ '"_N',l_l"l ' _I ' u',, '.... _'_ ' "Vll"_' ,,,,H _,,, 'ql'_ll' " II m_' '"_' _ "'n' F, _[*1 "_1'_.... ,'"_11_,_" lp' _[I III' ,lil'lr

4,5 Three .Let_ding Pm'title Selection A4e_hod Analysis

Global Light HeavyPct_i 0,391-_t:0.003 0,354:t:0.003 0.442i0.004

Table 4.3: The polarization for the chirality-based analysis, Poht, for the global, light and heavyflavor Samples. "

4.5.1 Application to T--_ '_TrTcu_

Before this metllod was applied to the real data, we tried to study events ofiT -+ ?r?r?ru,by.the methocl, Tim events were generated by the Monte Carlo prograrnKORALZ[30] whicll simulates c+c - --_ 7"+7-. Decays of -r leptons into, for example,pu,r, alum, followed by decays of p or al generated by the Monte Carlo programTAUOLA[40]. The Monte Carlo programs take into account ther polarization andgive good agreemez_t; witl_ the pr(._dic.tio_smade by tt_e electroweak tlmory[18],[19],

About 1241( (,,+c--_ T+T .... (:!Vc:!lltSW(:!r(:!gellm'ated usillg t:lle progralns. Eac}l r-alld r + in Clueevents was seJect,iw:ly fbr(:ed to dec_y illto a.i14, arid aiJ-P_,respect:ively.The event generation was _na(.lewithout tile SLD detector simulaI:ioi_.

Figure 4.11.4shows distributioxls of tl_e invariant masses of two ?r+Tr- pairs wlliel_give the Dalitz plot; for t.he 3-?r system (Tr+?r+?r-' or _r ?r ?r+), The invariant mass ofthe 3-7r system is also shown in the figure, p-mass peaks in the two distributions ofrn_r_rare clearly seen due to al decaying into 3-?rs via ptr, f_t,_l, _,,,od.h,,_and 12_hiwere

| defined for each triplet satisfyil_g tlle COll(.litio_sfor invariant masses of 2 ?rs and 3 7rs- given in the previous section, These triplets entered the hatched histogrmn show_ in

tl_e bottom-left of Figure 4.14,

,Jet ha_dedness would be visible as a no_z(:;ro _netu_ f2. II_ particular, ,jet, l_an(.t-edness for the helicity- and modified l:elicity-based analyses is of' opposite sign forevents produced with left- and right-ha_ded beam polarizations. It also l_as oppo-site sign for jets witl_ positive and tmgative coso = t._.,the z-comi)on(2nt of t, 1?'ortl_e chirality-based analysis, ,jet handed_ess does not depend on the beam polariza-tion and the jet direction. Figure 4.15 shows tlie distributions of f_h_,_,f_,,,o,u,_,land_o_i, For the helicity-based analysis, each f_ distribution looks symmetric about zero,implying that any jet handedness is small, There is a difference between the _'t distri-butions for forward jet:s a,_(:tbackward .iet,s for tlle modified lmlic',ity-]netl_od. For t,llecl_irality-based analysis, it se(_s t,lla_ tl_(._r(:_is ali e×cess it_ t,l_(:_p(._siciv¢___clliregio_.

The jet handedness for ali tl_ree mlalh'ses was calculated for each bi_ ofj(:!t direc-tion coso according to Equatio_ (2.21) separately for eyelets produced wit,l_ positiveor negative elec .... _...... D,,,,,,I_...... ,, ,,1_,,,,,,,in Fi,,',,,', -I labl.U_uem_l polarization. ,,,u,._....................... o ..........

I

60

:z

........" ""'_"'""....'........'""'_'" ''_-_'" _'r......_,'È_'__'_._1_'`_i_____._r_,.-._-_-_'_._ ,,.:.,,..,,,,.,_....,,..........,,,.................._,_-.._-

Analysis 4,5 Three LemMing Particle Selection Me_hod

/I ,./

¼

C.9

1.4 /' //. '

E / /

l . ///

fl- / r/'j-, y. ,:.<

1.0 -_.---<...."-,--_--",-.... .....-:......,:.......,_.-........_1-4--_ ......... <-_¢:-X- :_n tl'h _ . _ . ' ' " ' ' ""

1-ii . _.

-i.I -

0,2 ........ [..... J...... l ..t...... ' I !20000 15000 10000 5000

.¢ .. : 5000

,

0000 • , ,'r I: 5000 •

E, ,0,5 1 1,5 2 0,2 0,6 1.0 1,4 1,8

m,r_. (GeV/c 2) m.,_(GeV/c 2)

Figure 4.14: Dlstributions of Invari_mt m_ssos _md the D_tlttz plot of the 3-7r system, The top-leftanti bottom-rl,_ht figures show (,v,,oinvariant rnassos of _r+_r- pairs, m_r_., p-mll, SS penks in both

• the top-loft and bottom-rtght_ figures m'o seen al; ,--.,0,77 GoV/c _'. Ilatc.h(.,cl rc,glens in these, twofigures re,l)rosont crtterht (in text) rot' the, invariant r|msses of rr+_ "-,Tho bottom-left Iigurc, showsthe distribution of tlm invlt|'htnl; nl_tss for t}lo 3-7r system, v_t_r,r_-,The hatch(._d l_tstogrmn in tlm

, bottom-l(.,,ft tlguru rol)rOsollL thu tripluts lyilqz; i1_tl_(._(_)vi:trl_tl:)I'()_L_iC)IIiii LllO, l)aditz ph.,t (t,up rigl_t) tLlld

s_ttisfying the col_ditions (in lext) for rh(.: tnvarlnrll: _nnss or th(_ 3-_r sysl;(.,n_.

61 -:

=_i

.... " _IIP ...... I_lq"#' ""1 HII" ,',, ,Iq_ll"'" ' "_lrr ',_H,, .......... i_,Pllill,,i,,, ,,,,, , lit' ,,',,, ,lit' _,1r, ............ I, "qll" .... r'r"' "lllrl, " " .... " "rl]lI"" _'" ' ' ' ' _ll'_, " tl, II1" '_1_" .....

4,5 Three Leading P_wtlcle Selection Method Analysis

¥

5000 ................................................................................................................

- P, = -0,63 r'-I Hel, P,_ = +0,63cq Nel,_4000 t,eam I ' -- _eam /I

1

=ooo f {ii i frl"-lLc_ooo ,I r I -- I" l

-0,4 -0,2 0 0,2 0,4 -0,4 -0,2 0 0.2 0,4_hel _2hel

5000 .................................................................................................................................................................................

° r l Mo<l.Hol. Pi,o,,,,=+o.631_I Uoa.Hei.4000 7__.Pbeam = -0,63 t: .....'ctd3000

ooo. i :l !, ,ii_ ff"/1, ,._" , _L,. ,

:i1000:

0 ::i_..i._L...l....l_...i._L-:i.'...1....1..l._.l..i.7.l,,.L_l., i...i_..I ..l ........i. i ..1....1._.i._L.<_.l..:J....i..J ...i__1..._.t.:,-/...I...._i.....i..._i.__.l...-0,4 -0,2 0 0,2 0,4 -0,4 -0,2 0 0,2 0,4

"Qmod,t'iel _'mod, hel5000 ...........................................................................................................................................................................................

40003000- Pbeam--0.63[_.1,_ "_ "...._hc,m i..t"_l:l

: _2oo0. 1" /l rr Ii1000 I j I '/lo::i,IlI..,I.,.I,.l_:./,I,.I I,II,!:<,,_,,, I.,......, I ,, I,_L,I ._,l ,I,:,<J,,I, III,-0,4 -0.2 0 0,2 0,4 -0,4 -0,2 0 0,2 0,4.

_2chl _"_cht

l.i'igure 4,15: fl dlstributlol_s for i;ll(.,,I,.:ll(.',lty-(u_p), lrioclifi(._d holtc, tl;y- (lniddh.,,) mid c,hiraltty-I)ase, d

(bol;,l;on]) il,lilllyses, The left, iuld right figtu'os show rho dlstrilJutions for ,jot in loft- and rtght-hi,a_dod(.;l(.!ct,ron boll.Iii ovont.s, Solid lind eh.tslled liist.Ogl'lUl]S snow Lho dtsl;rU)uth)ns of _lhet for jet;s l)Otlrbhlg

forwtu'd (cos 19> [],) a.nd ba,ckwtu'd (cos 0 < (],), rospoctlv(?,ly,!1

i '62 -

_

'r"ll' ...... _11'"'" , ,in,, ,rl, _li rl,,, , .... I'r " lip'. i,i,,,.',',' if,i, "'II .... ,,,,,,1,11,_,, ,,u ...... Irl I, ill,i, lt ..... ,',,.'Hiilll,ql',u, " ri[,,,I,illlllr , iii ..... irl'Ii" ,....

AnMysis 4,5Three Leading' Particle Select, ion Method

,,+

..... 0,2 Hdi£_it_y_.............................................

.,.U,.

Pbcl,n= -0.63 Pbo,m = +0.6309

0 ....... =.-i:_----O-_o.....9_..._....o_=-iD=.--.=.i.......... _e=o_-=-_o.-..-m__o._w_e....=_.......m ml

I

I, -3

-o,2 .........................I...........................I...........................I........................................I.........................._I......................I...................! -0,5 0 0,5 -0,5 0 0,5 1' Modified Helicity

"r" 0,2 .......................................................................................................................................................................................................09 Pbeam = -0,63 Pbcam= +0,6309(DG

" ¢d-r e-.t....m-

, -0,2 .....................[..............................I..........................L.......................................I...................I..........................I......................-0,5 0 0.5 1 -0,5 0 0,5 1

ChiralityC% e"l

.. :I:: u.-,...............................................................................................................................................

= -0,6309 I be_,n Pt,e,ar.= +0,6309

I °C-o= o ............L.L.il.aL,i.L,._..i.,...i.__Lii,L.5,.......... _.®........, ........®.......®......w......".....®....."-

g

-0.2 ...........................1........................1...........................I...................................................1.....................I.........................1.................-0.5 0 0,5 I -0,5 0 0,5 I

coso coso

[Pigure 4,1.6' ,lot I_andc:dne,ss as a runc,t;lon oi' jet dh'oct;ton coso and the beam polarlzatkm 'P forthe, hdlctl_y- (top), modified hcllc l_y- (middle) and chlraltty-basecl (bottom) analyses for the, ¢:wml,s

' generaeecl by KORALZ. Events were clh,lcled into left- (left) ancl rtght-tmndect (right) events. Soliclcurves are the result of the best fit of l_quattons (4.8), (4.9) and (4.10) to clara and the reduced XUSof the fits are 1.25, 1.30 and 1,02 for the helicity- ancl mocllfled helicity- ancl chirality-based analyses,

, respecttvdy, Data wore limited to the region of --0,71 < cos 0 < 0.71 by the detector lmc,eptance.

(33

,...... l,fl_ll',,, ,,...... ,I I,W ,irl mlll"'I,,_,III, r,l IIMI'II lllqU...... _P'Ill''U'_.... ,r. ,'i'I'' m ii n,lp rmlF"'lll',l'llpI'",'I'IIU_'III[,'"I)I,l,"ll1'llmmr'll','"'"'li"l_llirll_,,,l,,,vlFm,".,,ill"'III_

4,5 Three Leading' Particle Select;fen Met;hod A.t_alysts

I-Iellcil;y 2I -0,C318=1:0,007Modified Helicity 0,113-_t:0,007

Cl_ir_llit;y -0,250±0,C)20

Table 4,4: Analyzing powers of tam hol M tS'-, modified helMty- and chh'alll_y-based analyses for theevents generated by KORALZ.

The harlcledness ill eacll bil_ for l;lle ''helwlls,-based analysis in Figure 4,16 isl.q_lalland small angular mid 'P dependence call be seen, This fact; means l;hat; I;hecorrespondhlg analyzillg power is small, For t;he modified helicilS,-based analysis, onec.tulclearly seethe angular and _ depenclellces of the handechmss, 'l_he chiralil_y-basedllall(ledlless in eactl bin is _egat, ive alld nii the values are allnosl; equally away fromzero.

'I"he obtained handedness was fit;t;ed to .H('P, cosO) in Equation (4,8), (4,9) or(,1,11) for l;he helicit;y-, modified llelicib,- or clliralit;y-based analysis, respect;ively,allowiIlg tlle analyzillg l_ower _r t.o vary, In t,he fil;t;ing procedure, "P/.,I and _,,..,,t,/.,twere averaged over ea',ll cos 0 I)ill O['0,1775 and 'Pc,hi=: A.r (Equation 2,29) was 0,14,:18as gi\,eil in Table 2.1, The fit,tillg was perl'orrned ibr evm_t,sproduced wit;l_posil;ive or

' _egai;ive bemn polarizat;io_ si lnult;al_e:_ously,Tl_e result;s of the ttt;t;ing are sl_own as t.hesolid curves in Figure 4,16 for ali a_a.lys(.,.s,and t;he fil;t;ed analyzing power is list;cdin Table 4.4, SigniticanI; _onzer(.) sig_als were found for the _mdified helicity- m_dctliralit;y-based mlalysis, iXsmall _lr)_lzerosignal was als() found for t:l_elielicit,y-basedanalysis, TI_o chiralit, y-based a_lalysis gives l;l_elargos_ _nagnit;ude of t;l_e an_lyzingpower, However, _l_emaxi_ntl_n sig_iit:icaI_cea/&a is given by t;t_emodified helicii:y-based analysis, The result;s suggest, l;l_at;_,,,o,_,h,,land t2_,hireflect; the helmlty of t;he 7"lept:o_l,

4.5.2 Application to Hadronic Jets

In the pre,ceding sect,ion, signitlc',m_t,signals of tam polarization o[' r leI)t(,_s wereobserved in evelfl;s generated by K()I_.ALZ using t;he modit-ied helicity-and ctliralit, y-based analyses, However, t,l_ehelicit,y-l.msed mlalysis did hog slimy a signillctult sigllalof,jet l_andedness, S_nce tl_e nieclla.nisrl_ of t_an,.porl; of t;he part, o_ polarizat;ioll _laynot be the same as t,hat fort let)l;ons, we t;ried /;o apply both ghe analyses for tt_e

., 3-leading-particle select;ion _net_l_c.)dto jets i_ the data, The procedure of the a_lal,'_s_s

I was idm:t,ical to tl_al; pe,rformed for t;lle r events,,I (34 _=

........ li ........ r ,,, ill_l I , I_a.... v:_a,, II,',ll .... III_ '_'_'_1'1"'' lr II'1' _ .... I,_a ,_,' ",_'_1"' v', ""'l_ .... _'l','l!_'llPr_ ,,, III, ...... ,,l_'rl,q',',,I ""ll,,"w qi _"_1 "',l'r'" II'l,' II_,l_l_l','.... I1 "Ill..... i_rl,_r ,_l_,,Iq]r_qll_,,irlllle,,1_...... rl_,_.......

i

Anulysis 4,5 Three Leading Particle Selection Me_hod

Figure 4,17: Distribution of sum o[' charges of fastost 3 par6c.les In a jet, Jots falling into hatchodbins woro usod In this analysis,

., l;'igtlre ,t,17 sllo,,vs l.lll._(listril_ut,iotl of tile s_llll of t.lle (.'.llargesof t.he 3 lea(.li21gcharged l.mrt.icl¢:_s,k.bol.lt, ]0% of jel:,s llave a Stll_l of c.llarges of -3 or +3, [[' tl_e3 t;ra,c.l,:stake posit,ive or llega,I;i',;ecl_arge at randon_, 2,5%of jets would ha,vo suchcharges, The distribut;ioz_ seen_sto reflect; the transport of the charge of a partonthrough tl_e fragmentation process, ,Jets witt_ the sum of charges of -lot +1 wereused iii the mlal3s_s,

Figure 4,18 shows dist,ributions of l_l_etwo invariant masses of rr+rr- witll tl_eDalit,z plot of the 3-_r sysl;etn (rr+rr+rr- or/r rr rrt"), The distribution of d_e invaria_tmass of the 3-rr syst,en_ is also sl_own in tl_e ligure, Air,hough clear resonances were_ot seen, f2h,,t _t_¢.t_'Zc/,.iwere ¢1¢::I]_¢-.',_.tfbr each jet: _lsing t,l_e3 leading particles w}lic}lsat,isl'y tl_ocrit,eria rort, lle illvnrial_t, mass¢,sof' tile 2-rr a_ld 3-rr systei_ls, Sud_.jetlsarC:'indk'.at,ed by t:lle lla.tx.:l_edllisl:,ogra_t_in bot,t,o_n-M'to[' Figure 4,18,

Distribut:io_s of _h_,l, fZ,,,o,_.h,,land _;_,/,iare sllow_l for t/he global, light flavor' and t_eavy flavor samples il_ Figure 4,19, Figure 4,21 and F'igure 4,20, respectively,

The calculations of' t:lie ineasured liandedl_ess mid t,l_eprocedure for extracting tileanalyzing power _._:were oxact:ly t;l_esarrm as l;hose performed for the r events, Forthe chtraliLy-based mialysis, t,l_ocalculation and procedure were ahnos_ the same asthose for the r credits, excepl; for the poln.rization of quark and antiquark, "P,,h.i,"P,,/,i(Equa,tion (2.29)) was averaged over the flavor composition of each sample, estimatedfrom the simulat, iolls n_ld weighted by t,l_e sign of the quark elmax'ge, "Pchifor eacl_

(35=

_-_=

--Z

,..... r_.............. ,l_ ..... _,,_......... 'llIl'"''""'' '_'_'' , ,',l' ,r.... ,," ' _' ",",'_...... ','_[t_''" ........ _1,,",,,,.... 'Irl" ', ", ' _,I,........¢,r"',',"_,'

I

I m ev Lea,drag Pa.rt_cle Solect;lo_ h4e:,t;t_od Az_rl,_,s_s

iI!i ' ,

1 4 - rr - ' ......., ,q , ii. , ii , t , .

E if ' .... ' .............,,,,Ill ,I , _,-_, ,/,I i,, . , , ,, . ,

i _ o_ 4 • ,... 4 ,.(I . til, i,,, , , , , i ,, _ i ,_ ,, , q,i ...., , p ,i ,J , ,_, , ,t, ....... , .

/",''U iI_ ":"'° ''_:I' _7;,.,,.,/':;'::::........... :'::"',, , ,,i ' o i i , , ,

"._ . .'_Itll}'f4.l[)_tJ,{-Jll ¢_'u'_| ,'_'.* , _'._ , ,'., , ".t , ,'t., ,',

0,6 =::......:.........iiti Illl()L:|{ji:lt|(]llit:l_,lt3tll, l'(I (l/u o . _ . , (i _* , , ..........' lillE)El ;.I[ll[)[3Elll pD, III" ,' , , ' . ' " ..........

u[.,X3EJEl{]l:]ii(ll|mpn u 9{q..... , , , .... , ...._,[I'_TJ_EIrJ(_'JI/1H_- rl u,_, _q,, , ,, , ...............

[1[ .......... I - ::I(.JtIEI[-[._.j[:)IHUEI()O...(_ I _. , , , . , , ..... , .......

' :)(TE)L.Li]LICI{]lgltjt]_I3u _1 . , _ , , , , , ° .........

UllCTE)(:)(JElu _ Cit)t* . (I,_ _/ * ' _ ' ' ' ' ' ..................... k................... r,rlr,.t')..c,_ 'H'" °'_ * o/ .............

I I I I,"/ / / I

2000 1500 1000 500 ,, •

500- IL'i /_ ../

_, .I ioo / -I,, ooo.....

0,5 1 1,5 2 0,2 0,6 1,0 1,4 1,8m_,,,_(GeV/c 2) m_ (GeV/C)

F'igure 4,.18: Distribudorxs or Im'arlnnt_ __t_,_.,_and the Dalit;z plot; of 3-'n syst;errx, The top-left;and bottom-rigl_t figures show two lm'arlant masses of _r-t_r- pairs, m,_,r, tIatched regions in thesetwo figures rept'osollt tl'lO criterll.t (tll text) for rho Invariant mass of _rta -. The bottom-loft figureshows the dlstrlbutlon of the tnvarhu_t nmss for l;ho 3-_r sysl_em, m,r_r. The hatchocl histogram Inthe boL_om-lort figure represents the triplets lying In the overlap rogton tn the Dalll;z plot (top right,)and sat, tsfytng tlm criteria (in text,) for tile lm,arlanl; mass or the 3-rr syst,(:un, "

66

.......... ,i ........ " '"'Irl" rll .... "I' _,"Ill'q,, 'lr,, '_,llm,...... ,l"li_l'r',,',IrrlI""Itp ..... IHt' 'r i_'W,lluir'",i,_q_l,,,_', ,i_,'_I,", ....... " " ,'"' " " 'm' '_.... ',"'"'' "II ""I'I' _...... I'lllll.... tilt' ,llillrr_ "'" _Ii ',l'ti

An_l,y,s,is 4,5 Titre OLeading Pmi_icle Selec¢ion Me_hod

' "_ 500 .............................................................................................................................................................................

' 400- Pbmun='0'63 Nel, - Pbmml= +0,63 t-Icl,

aoo:-- .r+!l.i: -_oo I ii - ,rlJ&"i,

.... ii i '1O0 11 ..... r_J:' iiii I '"i_ 'I 0 .._e...[.._t___L.l-:}'.?J_+l..,I. 1 ..l .1...i:,.L.L.l._a...J...l........L_.[__L.L.L,Lz'__[.J.._.L__L..L..L]it:_L+.L_-L_L__.[_i....

-0,4 -0,2 0 0,2 0,4 -0,'4 -0,2 0 0,2 0,4_'_hel _'-_hel

_o500...............................................................................................................................................................................................

_ooi..._,+,,,,,=-o._3!i_._od.._,....._,+,,.,,=+0.63_of.e,.

2oo ,iii !:1-i / !,_,IO0[i _1: [,: r "l t / _..I'J' -i-i'.l_I

0 [::.L..I..........l_..+.l--J:._'l....l ...... l ...... t...J.:'_Lt...LL,I.........t l I. l i ,.JA:L [ I t L I--I.'L-.L.,,.L--L.L__L_..L_- -0,4 -0,2 0 0,2 0,4 -0,4 -0,2 0 0,2 0,4

_"_n'locl,hel _"_mod,hel

. _ 500 ..................400 Pheam= .-0,63 Chi .... Pl_emn= +0,63 Chi, '

I ,,:/, :ii" _2oo ]Ii " ,I _t_._.,_,i100 . ii: .1.1, ,._ ,, l:l.!!

0:2. I_ [ ..I .l... t,.+,:i_ .'tI ['l l.. I.. t_ +_t...t: .':{_ l__..l....L._l+.-.l........ l--.l ._.._l__..l...l ...Ll:.['i__L..._l..+..[.._I..._+I._+.'[._L....... t......... I .....-0,4 -0,2 0 0,2 0,4 -0,4 -0,2 0 0,2 0,4

_ohl _ohl

l?igure 4,19:t2 distributions for t:huhelMW- (top), modii"ludhollo,try- (middle)trod chlrallW-basod, (bottom) analysos for rhoglobal Sal+ttplo, Tho loft, tuld right flgurosshow rho distributions for jet in

loft-and righL-handodolocLronbu£mt(.we,nLs,Solidanclclashedhistograms showrho distributions of[_helfor jots l.+otnLlngforward (coso > 0,) and backward (++:(.3sO< 0,), rospocttv(:@,

IL

67

,,llPr ......... 'rts ...... '11....... plll ,lilPqll, " "" .... " q" " .... tl+ ,irl,_1,,_Ptpl ,r,' '-'ffl _ rtlhl," ,,lll,'ll Ii ''_ '"II ,mlP llllr,,,,,,, H,pi 'llrpi'i

, t"( _1 I) . i,'1,5 Three Lead.h_g Pm'_Jclo ,_¢-i+:,(:t,_ot)Met;hc)d Atla.ly,s'ls

d

250 ..............................................................................................................................................................................................

o :: :' = -0,63 ,-, Hel ...... Pbe,lm)= 4-0,63 Hel,

o 200 I_,o,,,,, .>/L..

Ii,ii!: ., -k,.i

m lOO j.] i

' 50 " I_ .if I i i.t0 L+.I...+L+.L.1...,b::i[i__,-.t__L_L.,.Y+'.,'.++'.L._,__t.__.,..%.t......L I..+,L._.t__lu---....._+._hl_.+LL..,:.._.L_L_'+.,.__LL__L+

, -0,4 -0,2 0 0,2 0,4 -0,4 -0,2 0 0,2 0,4Qhol _}'hol

e,) 250 .................................................................................................................................................................................................0 +,

c::; 200 Pbe.tul_= -0,63 Mod, Hel .....Pl)cmn= +0,63 Mod, I-Iel

Jl i

u..I 100i )jI "50 .... j-_ "t.,'0 I._..L.L+.I...I,-:l,.!:?+.+.t..t..I.........i2:'i",.[-,...+,+....i.I._+.......L_I.._LLI..L£-I.._LL..I__.L.L.-..L.',.L.L..J...L+I._.L

-0,4 -0,2 0 0,2 0,4 -0,4 -0,2 0 0,2 0,4£,.,o+,,.,,,250..............................................................................t:_..tQg.>_!.....................................................................................

o ' :_ 3 '£ 200 !- Pb,.mm= -0,63 C.ht.... I i_,,,,_= +0,6+ Cht,

'=.,ff150 / ..... I+ _ 11 0 0 I + -- _

5o ii_ 'II , .rl_ _,._.,' 0 :: i .I+.i t I.-,1,_'i t I .I I +'i'".I_I .I.i.l... t.... t .I..t.....l_..L_:!t'.. i. i.__l._.L..l..'.t:tJ.._l.,t...l..l..L +.. .,0,4 -0,2 0 0,2 0,4 -0,4 -0,2 0 0,2 0,4

Qctd _ohl

I;'igt.lre 4,20; +1dtst;rll)ut>lc)nsfc)r t,ho holtctb'- (top), modlfiod holtctty- (rntddlo) rind chtrrdtW..l:)t_sod(boLL(mt) armlys(.is for t'ho light tl£wor sarnl)le, '.['lto loft attd right [Iguros show rho distributions rot,jut,

=an

-.e-. ht loft- £md rigttt-llatt(l(.+(:loluct,t,ort l:Ju,tmtm,,onts, Solid arid drtshod hlsLograms show t,ho distt'lbutkJr|sI Of ['_heI for Jots potnttrk_t; fC.)l'Wtu'd ((',OS 0 .b., (},) llll{l bad,:ward (cus0 < 0,), rusl_OCl;lvoly,

II

G8 ¸

,,?l,r , _1'11 ....... Ip_ , ,li Ps II1,' m,'' '_li' If'trill ,w H,t.... P[I' u'+ ,I) i'+ i+)pI .... _lI.... I1' P II_ _ll)l_ r_)l )_, '"m"" _I H+irfll" rl' ll"UHql _ llr'_ qll' '),,Ti ,llqr+l ,rllq,,)_.... ,,pp,

Analysis 4,5 Three Leading," Particle Selection Method

O4o250__.

' 200 Pbeam ='0'63 Nel. Pbeam = +0.63 Nel.-

'.S= 150-

w 100

50 - ' i {:_. ' '" .. .

-0.4 -0.2 0 0,2 0,4 -0.4 -0.2 0 0,2 0,4"Qhel _'2hel

e4 250 ............................................................ i.......................................................... tI 0

/,::5 200 -- Pr,cam= -0,63 Mod, Hel ......Pbcam= +0.63 Mod. Hel,

i "_

, m looL ] :ll _ .;,i50- _ _, ' -

0 --.L_I__J__J..._I_ ........_t....L_L_J.... 23;.'1-__._L......................... -_ .............." -0.4 -0.2 0 0.2 0.4 -0.4 -0.2 0 0.2 0.4

_"2mod.heI &r"_mod.heI04 250 : ..........................................................................i....................................................................................

o 200 i{_....Pbc,,,,)= -0.63 Chi. t- Pbc,',m= +0.63 Chi.

i 150 }}- l ..... ,1

t-- .:

m 100}!:-- iI' _.

50?_-- ,S [- /0 __j.__j_.,_..j_.,_._h:£._4_.L.[._.._..._..L.__.._b:L_LA__L.L..L_L.J.__J_.._...L_,_.,.L=.a__.LLL___.L_I_.L__..L._J_.L

-0,4 -0,2 0 0,2 0.4 -0,4 -0.2 0 0.2 0.4

)chi Qctd

Figure 4.21' _ distributions for _b(:llelicity- (top), modified heli('ity- (middle) and (.'hirality-ba._(,(t" (bottom) analyses for the l",eavyria" ,' ._:ample.The l(,fl;and right, figures show the distributions for ,jot

in left- and right-handed electro:_b'" a (.wents. Solid and dashed histograms show the distributiol_sof [_hd for jets pointing forward ((::,.),sO> 0.) and backward (coso < 0.), respectively.

.)

_

69 --=

I

., u, ', , . . , p,,.nll i. .. _1 It ,,,.Hl _,r.r,......,.............I,,'"'"......"'"'_'.....r'l,t,_'" )r,l_q',,,l_l,tll_',_'""_'"'_,.....ir',_p_,,r)'r:ll,,,,,,_llll_ll,_lI,',ffl_'l_lr_111_')rlg¢''""llllllFllr"lV$'II1"'111111_1'",,t,_1.'illiI, irr.i,ii,..,',l,....1,,ll,l,.,lllrq,.,,_i,,..',,11,,11,,.rI,i1_,]!1t!......,i ,, iiir',_l'Nlfrl_D'['ll['_,_li,B!,l',',,!ll,lll'fll'"III_"

4.5 Three Leading Particle Sele('tim_ Met,hod Analysis

Analyzing PowerAnalysis Global Light fla,,/or Heavy flavor

--Helicity -0,029+(),024.... '0,057±0.'031 0,007±0.03dModified Helicity 0.055+0.024 0,056+01032 0.0554-0.036

Chirality -0.C)0i+0,026 ....0,052+0,038 -0,058:t:6,035

Table, 4.5: Analyzing powers for the IMicit,y-, modifiedhelicity- and chirallty-basedanalyses.

sample is given in Table 4.3,

Tlm rnemsured handediless and the results of the fitting are shown as a functionof cos 0 in Figure 4,22, 4.23 mid 4.24, for the global, light- and heavy-flavor samples.

Since the light- mid heavy-ttavor san_t)les are independent of each other, there isno correlation ill result, s fronl tllosc two samples. However, the global one is sum oft,tlese two samples, therefor,.',, rcslllt.s froln the sa.inple is correlated with those from

-_ tile light- and heavy-flavor Smnl.)lcs.

Most of the nleasured llall¢lcdIlCss (shown as points) is consistent with zerowittlin 2a. Angular del)endorsee is llc)tseel_ ill tile helicity-based lmndedness. However,the Inodified ]_elicity-based tlmltle(llless t',.._rtile tl_ree sanlples seems to slightly del)endon coso and 7'. 'I't_e cllirality-l:)as(xl t_aI_(ledness is scattered randomly ill ali cosoregion. The fitted al_.alyzix_gp(m,ers for all three analyses with the three samples arelisted in Table 4.5.

The small angular d(.'pendelmc of tl_e modified helicity-based handedness givessligtltly large analyziilg p()wers for clue ll_ree smnI.)les. The analyzing power for theglobal saIIlple is inost sigIliticmlt a_ollg ott_ers and is away from zero by 2.3(7. Tlmot,t_er analyzi_g poxx',cts,are (:(:)t_sisCc_Cwit)_ zero witl_in 2ct.

Dependence on Invariant Mass (]tit Tile 3-1mrticle selection metliod uses in-terference pl_enome_a in a_ --+ ptr --+ _rTrrrto measure the polarization of quark andantiquark. Therefore, it is useful to estimate the amounts of a_ and p mesons included

i in the smnples. Tl_e amounts d .perot on tlm invariant mass cut applied to the 3-_r and ,

(_

2-_r system. We expect tl_e l_anded_ess signal to decrease as the amounts decrease.

Figure 4.25 shows i_variant _m_ssdistributions of the 3-_r system and the 2-_rsystem. The p resonance of can be see_ around 0.73GeV/c _. The resonance is fittedto a Gaussian plus quadratic and the tit gives 0.73 as the peak value and 0.05 as ti_ewidtl_ of tl_e Gaussia_ (list.ribut:i(.)_. Itowc'ver, a_ (_.l-.n_eso_resonm_r.:eca_ _:,t, be see_in the figure. This may imply Cigart:l_el_andedness signal will be small.

70

'eq'tl_l" "' " _"'"' ' _ ......... '" " ..... " _' lt ,Iq ',lr'_r .... _ 'qll .... _ "_" _=llqlel_'l"_ "_' IP'I'PI_"_'' 'l,n" '"" _ _fl_' ',rl ..... I_li" ,r'l,_,,_l'_ ,_n'll,_11n ,_!e',, H' ,, _flqv,'_li_ll'HIr i_ ',',_I_ ' _" _TIIIIII_,I""' 'll_l' I_i_'r''"""_111"_'l'l_ '_,,l'r

Analysis 4,5 Three Leading Particle Selection Me_hod

. Helicityi 0.2 .....................................................................................................................................................................................

Pbeam = -0.63 Pbeam = +0.63ffi(li

• +."3

-0.2 ........................J........................'.:.I........................I...............................................I........................1...................I......................-0.5 0 0.5 1 -0.5 0 0.5 1

Modified Helicity

-r" 0.2, ...... :_.......................................................................................................................3..................................................

= I...................1........................1.....................1......................................L..................L .................L................., -0,2-0.5 0 0.5 1 -0.5 0 0.5 1

ChiralityI 0,2 ..........................................................................................................................................................

PI;<,a,n= -0.63 Pbcam = +0.63(,o

,,, I

T

"3...................... i.......................................................0.2 l.........................J.....................1.......................1.................. l 1 .............

-0.5 0 0.5 -0.5 0 0.5 1coso coso

Figure 4,22: Jet handodnc'ss as a func,tion of the jet direc.tion cos0 for the helicity- (top), modifiedhelicity- (middle;) alid chirality-based (bottom) analyses for the global sample. Events were divide,d

LcpIa-• int,o left- (h_',fi;)ltlld riglit-llaiide<l (riglll,) events. Solid curves aro the results of tlw best fit, of pt,ions (,1.8),(,19) alid (,1.1{))t.¢_data aii(I the redllc',e.d,k'eso[ t,hc;fit.sarc:0.95, 0.73 and 0.,tl for tl_c'helicity-, inoditied }lelic,ity- alid c',liirality-basodanalyses,respec,tive,ly. The data wore limited tr.)the

, region -0,71 < cosO < 0,71 by t.lie detect,or aCCel)tanco,

! 71 '

,,...... ,, _','r_lq, ',',rra......i_,,illp..........,l_,",*' rrql rlqtr'iIlilll IIil.....r'l'l'"' '_pIi' _,' 1_1'1_1III" ',l"l" ' "" _r_lll'"" tlit11'11"1''"' _tlrII'l'_lllMlllli"'"i":lI' ,,,u,,,,,11tl_ i,r 'i'lr,,,,lllI,l,_l_ll',llr'l,,_lI'lllrl,',,Ull,',,,,_1_i, l_l_llGIl',r,vl_lilr......il'rl'fP.... I',r'll_IIl'I_'_ll'qll'r'"'fll"

4,5 Three Leading Particle Selectiion Method Analysis

Helicity "::I::

Pbcam= -0,63 Pbcam= +0,63

.....

.'22

{1} I"3

-0,2 .......................I...............................l..........................I..........................................I................1.................................1...........................-0.5 0 0.5 1 -0.5 0 0,5 1

Modified Helicity0.2 ......................................................................................................................................................................................

-r- [ p 9 beam= +,beam=- ,63 P 0,63

23

021 .......... L ................... i/. ........ I...... I ....-0,5 0 0,5 1 -0,5 0 0,5 1

ChiralityI 0,2 .............................................................................................................................................................co Pbeam= -1_'63 Pbcam= +0.63 /

"0

m .. -.:.,--_--:: .

i / ......- :.-2- -:- T :.- -- -:: :_--. _.......

0 ........... "2 :: :: ": ' ......

:l::

"3

-0.2' ................1.....................1....................1...........................................I.......................1...................1........................-0.5 0 0.5 1 -0.5 0 0.5 1

coso cos{}

i;'igure 4.23: ,Jet l_m_dedl_ess as a t'll_ction of the jet direction cos 0 for the. helMty- (top), modifiedhe,licity- (nficldle) and chirality-based (l:}{}{;t{ml) analyses fbr the light-flavor sample. Events we.re

divided into left- (left) a]ld right-Iron{led (rigllt) {2vents, Solid curves are tile results of the Ix:st fit

of Equations (,1.8 _ (4.9) and (,1.10) to data and the reduc, ed XuS of the fits are 1.19, 1,01 and 1.1{}lhr the helicity-, n,xlified l_elicity- and cl_irality-based analyses, re,spectively. The data were limited

to the region -0.71 < cos 0 < 0.71 I)y the dete{'.tor acceptance,

E

72

IIIi',I",,','i,_lllQ,",",'_,' qr " ,' "Plllffi'li_11Fl'P''I'l "'" l'['li'""_ill"_Ir"'"III" lllllF'_li_'fill" ,_i'i,,....il"p,"'_' ""r'",'_',,_Vllllr,ll' u'I,,' '"'"l_"q_IPll'_ll_,t'llr'lli"_i_Pr 'Hlilj_"'"""llllr i!,,' _I" rll' 'ilr 111'_" ' q*_P,"e_'q"" " i"r_p_llll......... ,_I_,'_.... ,,',,." ' n ,.,i..n 'I"' " .r_,'t.

AnMysis 4.5 Tflree Leading P_rticle Selection Method

• Helicity:1:: 0,2 ......................................................................................................................................................................................................to ' Pbeam ='0'63 Ph_am= +0,63to(D

° +-o 0 ......... - ........ - - -,...........................

i I

i -,: -o.2 -.....t.............................i.......................l.......i...............................................................................................................

-0,5 0 0,5 1 -0,5 0 0,5 1Modified Helicity

..........-r'ziii=:o:6!i......................................................I.......PZm ;0:63............................................"O

........ 7 i- ':-:- i ......... .:..:.:....... -::.-. ii-21

- -0.2 I I 1-0,5 0 0,5 1 -0,5 0 0.5 1

Chirality

(1)-o 0

I

-0.2 ............. I .............. 1............. 1..........................................1............ I........... I...........-0.5 0 0.5 1 -0.5 0 0.5

coso coso

Figure 4,24: ,let, hancledne.ssas a func,t,ionof t,he jet direct,ion coso for the helieit,y.. (top), moctifiedhelicity- (midclle) and chirality-based (bottom) antdyses for the, he_wy-flt-worsa.mple, Event;s were,

" divicled int,o left,- (left,) Imcl right,-handed (right,) events, Solict curves are the result,s of the best, [-it,of Equat;ions (,-1,8),(4,9) and (,1,I0) to data and t,he reducecl XuS for dm ft,s are 0,27, 1,05 and 1,09for l;l_ehelicity-, mocllfied he,licit,y- arid (:hiralit,y-base.clanalyses, respectively. The ctat_!,were limib;d

, t(_the rc:tgion.....(),71 < c(_s0 < 0,71 by t,ll(.,,detector aCCel)tailce.

_1

=_ 73

"'I'! 'J_I' IIl"l I '_q'" qql'qPl'"".......... I1"1 'm,,," ' ,Hr,I'I" "ll.r ,lllll , ,,," i_ . ...... _,lll, p1,,i,,,, ,," "n',," lll,,,.l"JI_ ', Ifll,", ,mr'_rl,', ,,1_' ,¢1,, ' ,'," "'1II1,' ,_,,rll,,,.'rill "lI_m ,,llNl' ,11 .... ,,lllll,,"1_.... lll'lOl'q_'"'_l'lr_"rlIUIll'"lllllt xll_

, " , d,5 Three Lea, ding P_rtiele S'elect, io_] MeLhod As_zlys'is/

(/....

/ 't /' ,

=

74

,, ' ii_l, '1_..... lp ............ i1,'1'1ill _llt....... :Z,l_ _,, III"el' _,, ....... _II .... ii, IIl"_....... ., q,lPrll' ,_ ,n GIll"_" ' ...... V i ,FillI .......iii, ..... Iiir ",lill,,"','z,] ,_il ,,IIIIIF,,,,'II1']i'11iqp ' ' _,_.... r:l:', ro'it ..... I1_' "11 irl,il'll[lllll' '',_ '.,i'll' n "li'li' '_ p

An_.flysis 4,5 Three Le_tding Pa,r_icle Select, ion MeShod

To investigate tile ctc.,,pendence of jet tlmlctedness on the applied invm'iar_t masscut, three cuts were coIlsidered in addition to the standard invariant mass cut (cut

" 1) shown in Section 4,5',

no cut no invariant mass cut applied,

cut 1 0,82GeV/c u < m_,.,_ < 1,62GeV/c for the 3-7r system and 0,62@eV/c _ <'n_, < 0,92GeV/c, _ for o11_:,,of the two 2-7r syste.ms,

' ,42@eV/c for the 3-7r system and 0,69oGe,V/c <Ctlt 2 1,02GeV/c u < 't_z._,,,_< 1 ' u _,-,, ,_m..Tr< 0,8456:IeV/cu for olle of the two 2-7r systems, allcl

CUt 3 0,82GeV/c u < 'ri_.,r,r,r < 1,62GeV/c"' for tl_e a-zr system and 0.62@eV/c 2 <'rr_r < 0,92(;IcV/c u Ibr BOTH of t;h_-_two 2-7r systenls (1'1 cut),

l?igure 4,26 sllows dependence of t;lle mlalyzing power on the invariant masscuts. Ali pollers in ea.cl_t:igure _.tre,correlate, d wit,ii eacll ot,her. "rl_e no invariant masscut tellds t;ogive slnall ana lyzillg 1.)owc.wsfor all analyses with eacll sarnIgle, IExcept,il_g

Dependence on Yc_t _t\s _1_(_Yc.t, value increases, gt_econta_ninatio_ of 3-or-_nore-,i(._t. events in tt_e Saml_les increases, q.?l_etl_rust; axis for these events does not represent

• , . , " , '< 'Yl_is meanstl_e quatl(-m_t_quml axis, tt_at; the handedness signal may be dilute., astt_e conl;aminatio_ i_(.reases, Tlmrefore, the dependence of analyzi_g power o_ tl_e

?.lc,tavalue was also clleck¢.!d',Pigure 4,27 sl_ows dist;rib_tion of y,_ut,(3-+ 2) \,l_lue forwl_ich a_ event, ct_a._ges i'rorr_ 3 j_._tst,o 2 jets, Evm_ts wit}_ large y,ut(3 --_ 2) value.are multi-jet, cv(_t,s, a_d l;}_oscwitl_ slnall _._ are _lgencil-lik(_' 2-jet _v_:_,t,s, Tl_et_a_decl_ess signal _ay 1_¢_larger for tile ¢._ve_at,switl_ mnall y_,ut.(3-+ 2) value.

I_'igurc :1,28sl_._\vsd¢:!t_l!l_de.ilccof tl_¢.:al_alyzil_g power on Y,,t. value, [);ac}_l].ll_t-

15'zi_g pow¢:r{'orc:acl_'t/,,,t \,;_lll¢,is (let¢._r_li_l_._¢lxx.'it,t_ev_:Ilt,s wit.li t,la¢:_y,,,t(3 -_ 2) < Y.,,t,Lherefore, poi_lt,s i_ _:_aclifigure, are also corrc:_lau._dwitli ea¢.:liotil¢:r, Tile m_alyzi_g

s¢:.c,_i_,._ot to d¢:I)e_ld¢._ltla¢.,.Y,,,t value a_ld all a_als, zi_g powers are the samepOW(:;r '_s

witl_in t:lleir statistical errors for ali alia lysis wil,l_cacl_ sa_nple,

" Dependence on Charged track multiplicity in a Jet The del:_e,_denceof tl_(-.',m_alyzing powe.r o_ c'.llarg¢:dtrack _mllt.il.flicityi_ a jet was also checked, q'lle a_tlyzing

. powers were determin(.,,_l for tl_c,following samples:

,jet samples 1 jet:s co_t:ail_illg A: c'l_arge_l t,racks a_d '

_'-_-......_' 2 ,j,'__ cor:taining AJ(317 r,l.:..qq.l,._rg.d t:ra('ks

75

"1', 'FIq'"'FII'"II'_n""_IglgI_rI"II_I"T'II'":'"'III I'_'_'''''''' ...... ,,,,,, ,, _e....... ,,v'Ilrr,'lll','ll'_:' ]lr,_: ,til, ,, ,1',,,_,' I_ I "w_'[ ''''r, ""'"'111 ,prr, ,_l,l,[_,rll,IlIIl_r,, .... I1''11'11,_, TI'' ,linrll,,,'ml_,,,_,,Im_ll'k_:l,I,iiIllll,_,n';_,IFIt_.... _, ,'q:,,_'lv

q

4,5 Throe Le_ding Particle Selectlon Method An_@sis

i wI

i

i|

1 Global

- t-tel, Mocl, Hel, Chi,

, .... ,++ ..... +i _ 0......., .....i......; .......i _ _._

i '_ -0,1 "" ' -.....I c_I rf2g < -0,2 ........1.........1..............1............1.....................1......... l_..........1..............1..........................1................1............1..............

no I 2 ,3 no 1 2 3 no 1 2 3

! Light Flavori

[,,i_ 0 ....., ......................... -- .................................. _._.--..........._ -0.1 .....

_ i<4:-0,2 ........t.........1.......1.............1............. 1........1.............1...........1....................1......l........1............1......no 1 2 3 no 1 2 3 no 1 2 3

_ t-tcavy Flavor_ 0,2 .................................

I! _ l.-lel lX,4od, t--1ol, Ctli,I _ 0,1 '

o + !'| o-

-o,2t(. i........i .....i .....i......... _ l ..... i. i i ino 1 2 3 no 1 2 3 rio 1 2 3

Invariant mass cut

];'i_tlrc!4.2G: I)c'!_eild_Ilc_oft,llc'...:mlyzillgpcw,'eroi_tl_c,im,ariazltma._ cllt;.Each o{'rJmf_urcilt._ '_(rio, 1, 2 tl.IM 2,) is cle|in_,_liii text. Ali l'_silll;s iii __;l.'lc'lltigtlrc, are eorroh.l,ted with cuicll ol:ller.

7O

.......... ,r, ,u ,",',,,'1,,........ ,I........ fill, ,lr..... I',,?...... ,,llr'l m .... _i,,lllPIIl,...... _I' '" ,'ii' ' _'_....._,,l'_l''""","_l'l"_;'l'il"rii..... ,, ,, _,l,lilrlrr............ iii,i,,lii,,,IiI,'111'11_',li,li,,lll_l[llt' ,i........IlIGI_IlI'_II[l'_r_...._'l

Analysis d,5 Three LemMingParticle Selection Method

"104 _L

: -LI

loa _- \L

10 2_-_ \-LrL_- L-, 't---i_

10 ---- Lm.-1__ -L_

;L,._LLI_L_,_L_LLUd_.I_.J_Ld_LIJ_J._LLL_LL0 0.05 0,1 0.15 0.2 0,25 0,3

Youtt...

[_'igure 4,27: l)istril_:ltton oi' !1c.t(3 --_ 2) vtdue for which tu_ ovent clmn_._esft'ore 3 jets to 2 juts,

i,

where 1V is a_llUllfl:}erill t;ll_::ra.I_ge3 < N < 13, 'therefore, ali ,jets are divMed iIlt,o _Lset of 11 ,jet s_u_lples for bol, ll cases, A set of,jet salnples 1 consists of 11 s_unples whicl,is ill(tel._eIldellt,of'e_tcllolller so t,ll_tt t,lll:,r(_,'.;llll,illg_tll_._13'zillgpuWersare illdeI)e,zlde_t,.However, 13 s_,_ples _[' tile ,jet sa_lpl(:_s'2 _re c(_rrel_t,e(lwil,l_e_(:l_ot:l_erso t,l_tt tl_eresulting _mnl3,zi,_gpower is c,orr(:l_tted,

Figure ,1,29 sl,ows _lel_e,_d('llceof l,l_e,a.:l_13,zi,_gpower o_i t;t_(.',vl_u'ged-tr_tck-_,_ultil._licityi,_ _t,j,:_t,Becztuse of poor statistics, we cn_ _ot see _t dependence of the

, a._tlyzi_g l_uwer for tile ,jet,s_llll._les 1 o_ t,l_e_ult, iplicit,y, but; t,l_em_.dyzi_,g power i,_

i' tl_e low ,nult, il)licity r(::gio_ls(.m_nst,o l_we _tsligtfl;ly l_u'ger value for the cl_irality-b_s(.Klanttlysis. Stnt, ist,ics ot" t,l_e,jet s;ulll._l(.:s2 iu also poor i_ file low _lultil.)lici W regioI_,l_owever, _11a,_a.lyzing l)ow(_rs nrc consistent with (!_ch other witt_in tl_eir statistical

,.. (II'I'(.)l'S,

77

l'' ,m,,,I 'fill=,,"II'l}I '" I_'1111''I' ', III'r'''t'''.... '!Fl"llmr,,,,,I ...... I,, ,,I,ll111,1,_' '....w']_ ....... "' "I' ' ,'I,,,,, ',ll_:'II,,,,_,l{l I'I"_l '"lf]"l''*"IFn'II".....'"'"'llt" 11_F_IWTIl''''" '"" .....{I1rl'll,llr,_'li ','"''l, " "}"'_ I_{'III'II

4,5 Three Leading Pa,rt,icle Selec_km Mot;hod Ana, lysis

p

Global

os o _, ,,,, ,'_ -0,1

10,3 10 -2 10.1 10.3 10-2 10.1 10.3 10.2 10.1Light Flavor

l!................................................................i .........i:t+++ii,................_'_-o,1(o

< -0,2 ,l _.J...L..La.l.,,l.....,.._,.Lll,,_l.....l...__ ,,,t ...l_._,L_.l,l.......l:L..Itillil._.I_.LI i.il,I.....L._a_t.i.Ulii......L._.i..ltiUd_., r__L.l.

10 -3 10 -.2 10 -1 10 ..3 10:2 10.1 10 -3 10 ..2 10 -1Heavy Flavor

$ ' H,oo..c_ 0E

< .0.21 J.._ J.l_J,_ .t.I . l,J _ ll,l _ liz,llLI I _LL,I..L.L_-3 -2 -1 -3 -2 -1 :3 -2 -1

' 10 10 10 10 10 10 10 10 10

Ycut

F'i_ure 4,28: Dc.,4)ond(.:lw,(, (.)f tl_e analyzing l)ower ()x_ Y,,ut value,, Ali points lI_ (',a(',h figure arucorrelated with olmh ()tl_c:r,

_ 78" '"........ _11........ ' .............. _ll'r,_i:_p...........

' 7!)

,t,,, , II .......... ,t, ......... )_+', ' ,',,....... +I',,_,_II, v ,, llm' "' II+II I, li "' rllr ' '_'lll ' Pl ,l+'Ig!',_'I+ ",I'[INIP '. ' ' ' 1111.... fill_I _"P#lr'''''' "" _" 1111'II ":' ......

'.1,5N Le_d_ng' Particle Select_o_J Metfiod Azja,lysts

4.6 N Leading Particle Selection Methodm

us metl_od Is o_e of' thc:_ge_lc-_ral_:_×tellslol_sof the 3.1eadlng-part_lcles_flectlo_Ine_hod,

'Ylxeprocedure of l;}iis lnethod wtts tlle t'ollowi,xg',

1., NI,,,,L(k 3) c,i_:_rgedptlvtic,le,_werc._se,lc_ct;edfrom eacll jet ill orde,r of tl_e lnag-_litudo,of tl_oir mon-lel_t.a..Ali ze,ro-cllargc.,,paLrsi,j among these NI,,,,_particles

' " .... _ " iterttt uwe,re c,c_)_s_de,red t_s sal_ll.)les witllout applyixlg tlie IlIV_U'II.I, III; II I.IS,.N CI' s(.!d

in _he i)recc:dillg lnetllod.

t?'_,,dand t-_ wc._rcc:.alc.'.ul_-ttc_lfor c.!aclllmir',

_' :/_ -_t "-'%i,_--- i:,(_,._;,-x _.F)..4'

wllorc-: l,',i, l_:j wc._rc_l_lc_l_l_:,lli,_tc._t't._,,,,(_Imt"t,ic.tlesc,,liosc.!_lt'rc.)_lt,l_o NI,:,,_Il)m't,ictles-d ,.-,t

boosted to t;lxc.,Nt,,,,,rl)_rl:ic'.lc:'rost, t'ra_x_c-_,_._¢.1It,',_1> II01,Tl_c:,t._airof particles,

k;,t,'._; " "', were iclc:,,_tic,._lto I,Ii, IC cxc.,,el)tt,llat, k, was one o[' ki, k.,i with l)oS_t,_ve,

c,lim'g¢_,a_d t,'.:);w_t,s.'tile otlic._rwit,li _eV,at;ivecllargc:_,If a jet did _tot l_a,,,eNt,,,,Il)art,ic.'.lc.:s,l;l_ejc._twas (_xc'll_clc.:dl'rc.)n_t,l_ea_lt_lysis,

3, "L"t_c._ave,rage::c.wc._rt_"J, (t-_o} (_t'a.:'_'agt:_c:_tl_c.)c.l),m_d t,l_e_'_0v,,itl_ largest _ag_i-t:ude, _-Y"":'"('_.a_:'i_,'lr,i,_c_t,l_c_cl)wc,r_ _sc.,c.libr tt_c._a_l,tl_sls,

Npu ir,,,' E,,,_I_'"l

) '_',,tl{_rc__N_,,,i,,,_wa,'; tl_e i_ll_lll_r c)t' tl_c.',c.',o_llbiuatiollsc_rI os_t,ive mid _lc_gativec.:liarg¢:_d1)ttrt,ic.tlcsi_i t.llc.!NI,,,,_l._rl.ic:lc!s, sip;ll (_2i:i) is stg_l of ,9.ij wllic:li is l,lic.!

; lltt"g¢:st,011(:! ill l_lagllit, tldC!, '1'11¢,11¢)I,1tl,i¢,)11,_i.i I,(.!['(._I,S1,0{!it,lier tl_,,,l or_- lleltcity., or clliralil,v-I_ased _tI_tls'sis rt_sl_,::ct,ively,

| ,1, ,let l_t_c.lc:duc_ssfor t,l_c:I_;lc)l.)txl,lib;tit alld l_c!ax,y flavor s_Unl)leswas c'alc:ulat,ed for

_atl_ler as tile, 3-1e_tcli_l_-l_trl.i_.tlellietllod.

There tta:,, t wc_dill'er_,llcc._sI)_l,_x'_c_t,l_:,sIlletl_od _lcl tile 3-1eadill_;_,l.mVt,i_,l¢:_nethod; I_ tlm presc.,,x_t_xtet,llod, llI(.)l'{_ tl_a_l 3 l._u'ticles are used ror the calculati,_J

I...... I]' " III 'll_ _qr ii ,'1II ...... , ,, ,_' ......... _l_lqll "'ii II'r i_rHtll II I'111t ,_ 'l_III ' _l'lllllI '11 II ' "lip _',

,_5000 ::'-:':'":...................................................................................................................................................................

_4000 ,':_:i:::: ,. o_

-,,,,,[ i

1000 --'" , .... [_,L "- ,

' 0 :::1_.,;I.:]: ' . I . 1. I I I I I ' I " I _ .... I ...... I

5 10 15 20 25, ' Number of tracks in a jet

,,

:} l;'[_tlr(:! 4,3()' l)lst, rll._tlLh._llul' ('.l_m'l._cdt,rt_c'.k nlull;lplic, il_y In _.I,,I(._L,Shown are clal;a (poinlm) and t,hu' MonL(._ Carlo simulat,lvn (hisLogran_), '.l:hu li,vot'tigo mu.lLlpllclt, y ts about, 8,5, Since Nlec,_l was 3 or

" inor(.:, ,lots (.%:ml,ldlllllg 2 or less I,rl_.('l.,:s(l:dnncd hl hatched r(._¢lon)wore removed l)et'oroh_md, I)tl(_ Lo

poor sta.i, istic.s o[' l_i_._;hmtllLilflic, lt,y j(.:Ls, Llm Nl_,acl va.lUO v,'a,s set III a l'o_;lon o['3 <_ NI_,_,I < 17,

of ,Q, Furl;ll(;r, t:hls zllet,llod cl(:m>..;not, require, iIlv_tritrllL _t_,sscrit,eri,t'_for __1)a,ir _:_,_:1_.

ticie_lt,ly scO(_l_(_dl'ro_ _lor_' t:l_al_3 l)_trt,ic.les, ']-'l_entel/tlocl, llowever, l_ts a, risk t;omake t,he il_['or_ta,l_iol_sllleared out: be.oa.usel:mrt,icles wit:h _o ini'orma,t:io_ oi' i)a,rtx_)_

l.)ol_u'izat,io_ _1_._'I_eused, ".l'lleOl._l.il_u_l_u_l)er of' I)arl,icles rx.)1)eselect,ed inlay exist,,

Figur(_!,1,3()sl_(_ws1,11_,_list,ribtlt, io_ of l_u_l.,berof cl_argedt.r,!tcl,:sii_ a ,let:(ct_ut'flalI.'t'_tck_w_tltil_l'ic,itll il_ _ jet,), 'l'l_c a,,,erag(_o1'I;1_(.'.(_'l_m'gcdt,racl,: l_llt.il)li(.Ail,y i_ tt ,i(_t:was _tl:_o_lt,S,5 '1'1_: ' _ _ ,, A'l,.,,,t,,'alue v,,asset, i_ a,r(_#;i(._of :_ < Nt,_,,t< [7 I_(_ca.u.,4(_I,l_c

st,at,isr,its gol l_oor iii t,ll(_l_igl_lllult,il_li(',it,yregio_,

• Figure .1,3] Hl_mvst,l_e,a_alyzi_lg power (_l)t.ail_(,.(lfor cac:'l_NI,,,,_valu(._lhr t,l_c_;l(_l.ml,ligl_l, tl_\'{_r _11{1ll(,_vv ll_w(_rs_l_ll)l(-'.s,No lt_lnly:,',il_gl_,.)wl_ris plot.fed t'_r t,l_(,

= c.l_iralit,y-l_ls(,(Ia_lysis wil.l_ NI,,,,,_-:--:3, sil_('.(_file (,.l_iralil.y-b_s(,d_t_alysisalway:; _;iv(,.'-;" zero 9,,,,t,ircs_llt,illg il_ z(:_n.),ic,t, l_al_dedl_(._s,':ldu(._ t,o t,lle (icli_it,io_, Smile kind sy_l_bol,'-;

: i_ eacl_fi_tll'(_ at(, c¢_rrcla.t.(_(lwit,l_ea(:l_ol,l_er, 'Til(, m_alyzi_g powers of t,t_(',nrel'age,_u_d_na,xi_ml_ _el_l_od llavc Ol.fl_osit:cslg_ i_ t,lle n:'.gic,_of s_all .NI,,,,,_for t,l_(.,,t,llr(m

s_m_l)le,s for l:l_ecl_ir_tlil,_,'-b_s(;dn_'tlysis, 13oI:1_n_nl,yzi_g powers are at, _tbotll, 2o ¢)f

. 81

p' " 'I'I...... 1.......... ,IIIIIII rl,,_l.... II ll',,'r, ,, ,_l,"_,?l![llI[ll,' ', ,, lqrlt ',, ,I ,,,qnm,',,,, II ...... II"',r,, ,, ...... II _lllltll_ ' ...... _I" qHllllr¢l'll'rp ....... I .... q#lll, r" i_I ...... _,', , II_........ II _,ml,,

4,(3N _oadhig' Pa r_iclo ,S'do('_lo_ Mol;hocl Al_al,y,_.'is

Global

_o,2 ::.---.-l-iEi-,.di.i_,.-.-,--iN_,-_-!....................i :..................(:fl,ii:,ii[t)J-giNv_I......................................./1""'t_

i!........... ::..... t+_.:ma,+<..i....... /_"':+ )""; . ............ i..,..t:J.',Max i......... '..-i-'-:-:/_0,1 ..:....

5 10 15 5 10 15, NLoa¢I

l_,ight Flavor .......

0.2 l:l_.;lldtty• '.Avg ]I' :/- I chir,ility ,,.Avg --,+""l+.lA

O / _ +r'lm'_l'['t''' [ ' '

cu ,:!.2:.i [ ++,-'+,.....-, ....,_:.:r..... _.......+o 1+ !i:;++&?L'I i +_.o,i : ..............

i i i i I .... i.... I+ i, L

5 10 15 5 10 "15NLoad

Heavy F_lltvor

_o,a H_i_i_tv.iA,;_,.... /I I: [ (::_ii",ii_t+";+':A"_........... :+)i,o,-1 : " ,.,,M,-,,_ ,},/'I' ,1," 1.... +,-.,:M+,x ,, , /_

........ {IH......"14 L'_,.o,1 .... ......i'Xl+I.........+;...........' "+ : _1!T/'

< -0,25 10 15 5 10 15

Nt.m..i

[_'igl.lt'_:;,1,3:1' l)(+;l_(mch_rtc(+_of t:l_{;+maly;,,illgl:.:_',v(.,rurrNt,,.,I l'(+,t'tlu_gl(Jlmi(tUl0, ll,u;llt(_n(_ddlu)lu.:lI_otvvyflavorsarttlJlus(IJ(_I,Qllll), '1'1+(_h.+l'tal_dt'if,;l_cllgt.trossl_mvt.hu£malyzlngpowurfor rho Itc+ll_..ILy..t_(l (.!l_Irallty-l:Jl+,s(.l(:larmlys(._s, rt.':;l:_(_(+',l+tv(.4y,SI'K_WIIat'(+_t,l_(.ltW(:_raI_(+linul,h,)d (l_(_lnts) tttl(:l ntt+,xlmtltnrrmtl_c.+cl(UlJC.+nS(ltlari.!s).

,1

82

' "pl,+,,1,1 m,l',.... ' '" ,lip......,[" '"qf ,_r , ' ' ,,...... _l+q'+lr'[Pe,m'r -_,,r, '_,,+IIPlllr'_31_'l"t""mill.... l'l"+'_"",'++,...... +, ""_ III_Ir+'_+r",' +,,'r'+_,,...... r, _B_II,+, ," '_I'!IP#I_' "" "IP"_IIP'' IIll_+T,,,'llli+,,'ill rlr .... H, '

• t

!_1 ,,,,i,, rll,,_','_' ' ,,_,,,"_l,",",,,,',',,_......_r,_ .....,',_r,' ',",_," _l,,plplil_I',,_'_'_.........i,_,,"rfl'_..... _,_,l;r,,r"I_17'"'_P.......F_'""" "_P'_'""11'rillr Tl'["trl_' r,

Analysis 4.7 Pa,rticle Selection Method based on Rapidity and Momentum

their statistical errors away from zero, but there is no apparent dependence on Nl_.d.

It seems that the analyzing power is independent of Nl¢,ad and has a value within 2ai

away from zero for ali Nl_,.d values. We found no optinmln nunfl:)er for enhancing the

analyzing power through ali Nl¢,.d values from Figure 4.31.

4.7 Particle Selection Method based on Rapidityand Momen.tum

This method is based on the assumption that jet handedness is ascribed to

fragmentatioll phenomena [8] as stlown in Section 2.8. According to the model, tile

polarization effects Inay appear i_l angular distribution of hadrons produced from acs,sc_t_a_ to select pairs of particles likely to besame string break up, Ttlerefore, it, is _, ' '

produced by such a st.rillg 1)re,ale up.

Studies usiilg JETSET 6.3[29] showed that it is useful to select a pair of t,racks

according to the difference in the rapidity with respect to the jet axis of the particles

in the pair[41], Requiring zero charge of a pair is not needed for the selectiou of

particles from the sarne stri_lg break up, but the condition was used in the chirality-

based analysis. ']:.'he proce.dure is the following.

1. Charged particles in each ,!ct were ordered in their rapidity'

Yi = _ lnEi

+ Plli

Ei - Plli

where Ei alld Plli were (:!ll(.;rg3, alld l(.nlgit,udillal tlIorneIltUlIl (of particle i witll

respect to tlm thrust axis, signed so as to point along the jet axis. Each track i

was assigned a nurnber 1 < ni _ ntr,,.c_,,, where rti = 1 for the particle with the

highest rapidity.

2. A pair of charged particles i, j was required to have max(n/, nj) _< n,_,a._and

: [ni- nj[ < An.

3. Since the signal was expected to increase with transverse momentum Pt with

"- . respect to the thrust axis as mentioned in Section 2.8, Ip,. l+ I>..i[> >,,,,,_ wasrequired for pairs of tracks, where P,,,,,i,,_is a paralneter to be tried to vary.

_" i'j'. 4. ,Qi_Jeland S2_hi were calculated in the laboratory frame for each pair satisfying

these criteria:

= (k',+,×83

ii""1 .... _,,. ,, ,,,,,, ,,,, ,,,r,[l"' r,,',, l,,,r' 'll,'lll ",l?l,, ...... I,,',, ....... ,,.... lll" 'III'" .......... I'" .... ',' ,r,,,r, '":"'I""_!,_'_,,"'""',",_1,"'"","" ,'"l,,IV' ',_',,,_l,,,Irl_..... '11,,....... _,,.i_ 'llil_r, ' r,,,l_,, '.1_Ii!1,,,11, ',,,,'l[lill ,,H,111IIIIl_'llll'llllllll,",,"rml"IIIIIIl" I ..... III lllll I'II ' flr_"N

4,7 Particle Selection Method bas'ed on l_.apidit3, and Momentum Ailal3,sis

where fv/, kj were rnornent, a of two particles in the laboratory frame chosen from•-4 "--_

Nt_.d of the h.,adi,,g partic.l(:,s a,,d ]k,i[> /_;y].Tlm tracks, k_, f_;; were identical

to ki, k5 and t_,i+ was one of/_i, ]_jwith positive charge, and h-'j.was the other withnegative Charge. Both the average, {,Qia'}(average method), and the maximum,flij with largest magnitude, _2"""*(maximum method) were considered:

- E fi;I(_"_'i.'j} __ 5_ )rrirs I'i-'nJl.<- An

a"'",': =

where N.pair is t;he lll.lllll.)er of COllll.)illal;iolls of l;wo particles which satist'y t,lle

criteria on nr,,a:,,,An and P,,,.i,,. sigll (fiij) iS sign of f_.ijwhich is the largest one

in magnitude. The not,ation f2'*jwas used to refer to ali's:' or Qf.;,{.;for the t,elicity-or chirality-based mlalysis, rest.)ect,ive!y.

5, In ali eases, the ,jet handedness was calculated for tile global, light and heavyflavor samples in the same rna_|ner as the 3.-leading-particle selection met;hod.

Figure 4.32 and Figure 4.33 show the distributions of tile rapidity, y and transverseII1Oll'lellt;1.1ITl, /)t wit,li respect t;o the t;l_rust axis pointing momelll;um of the .jet, wllicllis used as tlm jet axis. Figure 4.34, Figure 4.35 and Figure 4.36 show dependenceof analyzing powers on n,,,,:,;, An and P.,,_.i.,_in the global, light flavor and heavy flavorsamples, respectively. Sanle kind symbols in each figures are correlated with eachother. On tile assumptioll tllat, particles witll l_igl_ermomenta carry more iI_forrnationon the underlying part.o_s, 'r_,,,,,:,:az_d A'_,.were varied in tl_e region,s 2 _ 'r_.,,,,,:,,_- 3and 1 _<A'u < 'u,,,,,,- 1, resl)(.!ctiv(,_13', ]),,,i, v/;.lsvaried i_ t.ll(:_ra_ge 0 _- l).,,ci,,.<_ 3.5GeV/c. However, t.l_e stat.ist,ics of t,l_(,l_rese_t dat:a l:)eca_ne poor in tl_e t_igl_ 'l).,,,.i,_region where the t_a_dedness sig_al nlay be pote_t, ially large. In tlm case of lahecriteria n_,,,._:= 2 and Art = 1, t,he averaged mett|od (shown as points in the figures)produced the exactly smrle results as t.l_at,for tl_e _naximum _nett_od (sl_ow_ as ope_squares). Even t,hougt_ n,,,,,._:is _l_(.)ret:t_m_2, it. seems that tl_e difl'ere_|ce bet:weenthose two results is quite srnall.

In the high p,,.,.i,_region, the analyzing power gets negative for tl_e helicity-basedmethod and it tends _o be large m_d posit,iv(-:for tl_e chirality-based analysis. However,in general, the analyzing I)ower is (:o_siste_t, with zero wit,l_i_ '2cr of it,s statistical errorin ali Pruinregions.

84

'"1_ ...... ,.... _1'_' ,.,r,.,,, , ,,,,..... ',rl,_....... II'IPIr'I," _"" "S' '" IF'r'_'"l' " 'l'i" "illl .... ,li, mr_ ."' f,".lll'_r '_P ..... ,lr' 'r "'l, ,_lp ,'li ,r ' I_ '_"plll_l' II_" .... iu'lt '' II'""IIP 'l_l'l'l'lll_ll'ttl" '1_111 " 'l,,rl'l_ll'l I1_1'""" llnl' "ni H,,, =,_ll,l,ll_lll,_r .,11,.11IiIl,iltll,qll,I IP,.'l, I -

Analysis 4.7 Pa,rt,icle Selection Method based on R,apidity a,nd Momentum

" m25000 ....................................................................................................................................................

-_20000 - ._.r_°%_

15000 -- • ,

oooo .i.l.L I't.l.5000 .j I,.i,

, io.;°l+j, [oL%o ,0 -J-L--L-J'=I-osO-_L-L-_l._..I.......:.._.L.L_I__I_._L_._L..L.J..--L...L..L_.--L..L-I-._.L..i..__-J-A.-._--_..-'-I-°J=_==_-J....-2 -1 0 1 2 3 4 5 6

Y

tPigtlre 4.32: Distribution of rapicliw of charged l)tu'ticles with respect tr) the ,jet, axis. Shown are- clara (points) nnd the. Monte Carlo simuhttion (histogram).

.,..10 5 ...................................................................................................................................................................................r®--O_ O.

t / tOI. 0

4 /Ol@l@lO10 -

L_J I@ l oi ° lo i @1.o1 @l.01 @_ O10 3 -

1..(1l_0

- t.@ LqD.t®t •

10 2 _ "°'e'°,o., e •

_-@JO) • •

10 ' ' _0"*_®[

/I __.L._I._t.__t_...l.....+hL_L.._.t__L..l....t.....t__.,_._l..._J.._.J_._t_.t_..Lu_..LL.L_I_.,_u__L.._..t_L_LJ..+U._.t_I.._+L..L.,+_t..__,

0 0.5 1 1.5 2 2.5 3 3.5 4Pt (GeV/c)

Figure 4.33: Dist,ribution of transverse momentum of charged particles with respect Lo l;he jetaxis. Shown are clara (point, s) and the, Monte Carlo simulat,ion (hist, ogram).

85

di

)

4.7 Particle Selection Method based on Rapidity and Momentum Ana, lysis

n = 2, An= 1l_aK ................................................................................___-....................................

0,2 L--H-;-[[ciW-;:_iXvg-.......::.............. Chirality ®i'Avg , .:-.-_.....::......... L-Ji..:Max.... [ ...... ;.......... ::......... t-J[;Max. i ......... ::............

0_O ....i-_ o ..... 21 i .......... 2 ....c-

_-0.1 2--"! ............. ::-............ :,............ {................ ::............. i ............ :,............ i....... .....C" ' ' ....

<-0.2 3._u_L_,._u_J_.I_I_L_,__.t_.J_LLL_..._.+_L.I_L_LL++.._L_I_*_i+_LtJ_LI_.A_Lt_J._I_LLLA_I_LL,0 1 2 3 Z 0 1 2 3 4

Pmin(GeV/c)n = 3, An= 1

lllllX ........... " ..................................................................................................................

0,2 .....iq-_i[ci-i-3S----.-TiXv-g.......!............ Chirality , :Avg,.--

(1.)

o_= 0.1 _-.............. si:..:Max .................... t:J.:Max..............:.......-_---"1;.......+__,"

.-- _ , ,

,

,r- 71.__LL_L_L_L_L.L.L__..L_t._L-J._+L_LJ.._._L-J+_L.+Lh.J_.... L..J_..[__L_L_..L..L_L_J_J._.L._, ....... L.L.I._ _.h_ I..._h_.[.+J._...[_< -0.20 1 2 3 4 0 1 2 3 4

Pmin(GeV/c)

....... llm+.tx = 3, An = 2

¢; 0' 2 [--Hei-ici[y "" :Av,"-........ Chir',tlity • 'Avg

X,.. • _ -

_°0'1¢ , t ............, L_..:Max...... i ....... ... tj:!.:Max...........,...................ii_i......._o.. ii: -........--+- . ....._.....---_-+............ ,+, ...i-i',+r+++..............c- )- b

"< +0.2 __t.... J._._J++_L.L_ J__t...LJ..... Lh__t___LU_Lu....LLL_L_LL,_LLLLLL.L._LLJ_U+0 1 2 3 ,_ 0 1 2 3 4

Pmin(GeV/c)

Figure 4.34: Deponderme of the analyzitlg power on p,.,,i, for combinations of (frm,x, A?z) = (2, 1)(tof)), (3, 1) (micldh.',)and (3, 2) (l,(_ttorrl) for t ll+._global samph.;. The left and rigt_t figures show theanalyzing power for tile helicity- ;ttlcl cllirality-l,as(.,d atlalyses, resl:_ectively. Shown are the average(1)oirtt,s) ancl maxirrturn (open squares) itl+<ltods. For p,,,,,, > 2.5 (-_(.!V/c,th(_armlyzing p+nversareshown multil)lied by 1/,:1,because tam nnalyzing l)OV,,(.;rsin the high P,,i,, region have quite largevalues and errors cornl:mred to t,ltose in t.lte low l_,,+i,+ region.

86

=

' .....,....... ,1,,,,,,,",rp#,",' ,I ......,,,. P,,,,,,'li ,,, 1p!ll,,qtll',1'. .... I1"" '," flip''II""PI_'I'I[II''"l"',lill+'r]ll_'llll",',ri," 'llrl.........is,,,,,frf,,,,,+,,,,,,,,,,,""tl)_'"'li'lP'Iii .....ql',''"ti+'_#,"'""ll"'"_il'.'"r" ''' '"'"1!1'_'''""P''" ql_'PImll'rll+'',1,'P,,,r,,hlF, ,l,l,_lP,r'.' _ptl'_m"" II'll'l#t_'"_' 'Vim')

r

Analysis 4.7 Pa,rticle Selection Method based on Rapidity and Mon]entum

n_ =2, An= 10.2 _--H-e-i-ic-iiy-i;i-)-Av_ : Chirality ,i :Avg

O.] :................... ui..:Max ............ !................... i .......... c-Ji.:Max...................... i.......

z_-..... ....... , ...........: •..... .... ///_-o.1 _-.--!..............!-............i............;...................!.............;............,............i...........I:::< -0.2 :-.l__.J/.._.Li_.l..J_l_.L._.l_.l....,.i...l.._L,...J...l....Ll_.l..,......,_1._1...L,..L..._..L..Lt....t.,....1.,.._.,._..!.1...l._l..1

0 1 2 3 4 0 1 2 3 L' Pmin(GeV/c)

nina x -" 3, Arl = 10.2 .....t4 c:i{_;. Xv_ .....:................._.............................Cf_i-i:g{ii-0;;7TX-vg.....:................::.....................

'. , : .; , : _..

} o.1 ......... ,: .Max : .... :............. . .... i.J).,.Ma×..: ..... :i_........1. "a. • .? -7-,,E

_.-.0.1 .................... ............. ............ ................ ............. ".......--:>"--.......... ..........

_-l:'('l,gv,_ i 1.1 I. i ..1 1. I i. I i .i i.t.l t0 1 2 3 4 0 1 2 3 4

P,,_i,_(GeV/c)

...... limax = 3, Ari = 20.2 _.Helicity ,::Avg ' " ....................C_[-liraiityo::Avg : ........ :............

i,m ... , llll. . .q_]: ,:Max ......... i . . _-_j . ._o0.1 v_!..:Max. : i .-2 . .

(1:I .- . : ;

i/ / I / I I

< -0.2 _q_...i_l__L__i.__i.._k.l__l_i_.i_..l. I_i _l....1...L_h.i...L..I..J.....L...l...L..I...L...i i........L. i...I., i..... 1 i _1...l...i..i ...L...I...I.0 1 2 3 4 0 1 2 3 z

Pmin(GeV/c)

Figure 4,35: Del)On(:lorico of t:,ll{.; nlmlyzing power on ]),,,i,_ fljr coml:)ilial;ions of 01,,,.,<,;,,A'_) :-: (2,1) (top), (3, 1) (middle,)and (3, 2) (bol,i.om) for tl_<.;lit_t_tfl_worsample,,Ttte, loft, and ril_ht [igt.lr(is

" show the ttnalyzin<n;powe,r for i,he l-ic_lic',il,y- and ('hirality-basc;dItn_lyse,s, re,specLivoly, Shown arot,taetworago(point;s) _tndinltxirlltlnl (Ol:)ori squa, ros) methods, For P,r_i,,I_ 2,5 C;e,V/c.,ciaeitna.lyzin{_;

l)owors i.u'oshown muli;ipliod I:O, ]/4, bec.l.iusc;l:he _tna.lyzingpowers in t,ho tiigh Pmi. rogion haroquite large valuestriiclorrors conlI)aredLo f,hoso iii Li'le,lowProf. region,

87

:! --I '' Iii.... _ I IIi ,,r _i', '111..... _'" ' _ TM _rlll'l,rilf'lII7"' ' "lilt I'll_''r " ' "'" ltll_,_r ' hill, ql,l,,'"'Hit"' '"_'"' '1,""I'[I " 'l[I,[Pll'_111,1w, _l_i",m ' Ii'_I1_'qlr_'lli ',lll',l_,_,q',e III',"II1_'.... ,_11_,_,1,1,111__ ,ill!r,,,,111, r, _'ml_'"'ii" Hi II _'illii'' _H'_V" _"Hi lr H_'lllrl_' ql_l' i_ ..... Ipl'_llllH_ir_'_' I'll

d.7 Particle Selection Methud based o_ f_.apidity and Moment, un_ AnaJysis

.._ __,__nm,_72"An= 10,2 [z Helicity oi............:Avg ! i Chirality ei :Avg _, ! ..,1

i.., -' 1 ', / / ; ', ', . "/ :\ : "/"' tj ' \ '/ .[-_.... '........... cr-M.ax...I'X ...... : .......... ,.................... ,..M_x......... ...... ,-r..... _-.

<_o .....,---.--.::::>.-.-- ":_ .........--. : ..:.:. ......_-0._-_ _............................... i";:;...............................i......................

_.1__i__l_...t..L_.I._1...Z._l..........L.;......... ........ .... ...................<-0.2_.__L__,.,_,__J_..L.,_,__,_L0 1 2 3 4 0 1 2 3 4

Pmin(GeV/c)•,-"i A_ !

0,2 }.-i;ieiiciiyii iXvg.... nm_,=.-_'/-m.=..'...........................................................................Chirality *i ',Avg .

-_.......::....... _:,::.:Max, 1 ................. rJT.:Ma.x,-<r:l':.-,.... . .....-i":'7_1O ........

_.n,1 --.

<-0.2 :LLL_L_L_I.._L._.[_L.L..LI_.._I_._.l_hl_..l_[_h.l....L.._.L.J.LL_I_..L_L..L_LI__LL.t._.I....]_Lt_.L.Ll__l._..l_..l_..i..0 1 2 3 4 0 1 2 3 z

Pmln(GeV/c)

.. i!,_,_,_..................................................

0.2 .....i-i{_licity ,,7 :Avg ., Chirality ,,i :Avg : :......!........... c:j!.',.Mt[_:]:{:[l_,3,......... :................... :........... t:::.:Max._..4. ........ !........50,1

o_ i _;65__.t-__._ _;; .i, -__-..............i_.....,o, 0 : 74"7;:..........:.......___ -:_-0.1

I

< "0,2 iL..L.[._.I._-L._ t...I.__L__I.._ 1_..1....l..._i._ J_..l__l.._1 _._L .I_....t._L.. i......... Lh.f._ t._A.._l_., i._-l_....l.._d....I_._..L_i ...1...L_ l... i....... L..i. _1.._

0 1 2 3 4 0 1 2 3 4Pmin(GeV/c)

Figure 4.36: Dc,pertdei_cc;of th_,analyziilg power on P,,,i, for c.ombiriationsof (,z,,_<,,,A_z) = (2,l) (i.op), (3, 1) (nlidcllc) aiid (3, 2) (})ot, l:oill) for the hc;a\'yflavor SamlJle.'rlw left and rigllt tig/iresshow the analyzing power for rho helic,ity- and c,llirality-based analyses,resp_,cdvel;y.Shown m'otl_e avorago (points) arid lllll, Xlllltll]l (o[)ull squaros) methods, For Pmi,l _>. 2,,..rl GoV/c, I the rtrialyzing

powers are shown multiplied by 1/4, be,cause tlm ana.lyzing powers in tlm high P,,,i. rogion hav(_

quite large values and oI'roI's cOnll)arc,d to those in the low p,,,i,, t'C.:giOIl.

88

I[........i,' '1,.,In.... Iii.,,1,, "',......,,...... ,,I,,,,,i,,,'.'' i?",' ,,,I,,u,..........,' ,i, ',,........... ,_'1"ill,ii ,, ' illll''li i ,iri,,,, ,,',ii,,,'1......In,r'l£l ....r,.... Irlll,,'lil,llIlllIriII1r," 'rr]i, ,I,l,,ir,,",',"'it",,ii,,'"l"i','tl!'li _1.........,llll"l,lllP_""ll"!"l"lllrl,,i,....,',ii',',",,,.,rl,,li',ll

Ana, lysis 4,8 System_tic Errors

4.8 Systematic Errors

If ali particles produced in an event are detected wittl precise measurementsof t,lleir energies and mor_(:;l_t.a;_1_(.1an ideal analysis can be performed, any t)l_,ysicalresults coming from sucl_ daCtt would not contain any uncertaii_ties except for st:atist, i-cal fluctuation, Suclt an ideal detector, howeve:', does not exist, The acceptance andresolutions of energy and mo_nenturn measurements ark limited for any real detectors,Therefore, ii; is n(:_cessary to estitnate the correction or systematic error from theselirnitations to obtain the correct r¢:_sultsor the reliability of the results,

The results presented it_ the preceding sections might be also affected by theevent selection with lirnited ¢leCector ttccel_tmice arid motneni_ultl resolution, etc,']?herefore, exactly i;lle same mlalysis _xsill the preceding three section,S were per.-forlrled to estimate t,he systematic errors ft'ore tlte followillg ttlree sources,

1., Track and event sc;lection, wllere by al)plying several sets of tt_e track andevent se,lectio_t (.:riteria, tl_e wtriation of the results is calculated in order toestimate Cluesyst,e_natic (._rrorsdue to tl_e selection.

2. Jet finding, where tlle systematic errors due to jet fitiditlg algorithm aIl(.l Y¢,.,tvalue ark estimated, a_d

3, Analysis, wl_ere by usillg tile fact. t,llat jet l_andedness stlould be zero for tile,. "t )e.vents gellcrat(._d I)v tl_e Mo_t.e (,arl(. simulatio_t, the bias due to a._a.lysis xnett_od

is esti_at;e(.I,

The at_als,zi_g power _'_rS calculated witl_ Cluecriteria wl_ich were ain_ed forthe systematic study o[' eac]l error source, ".['lie syste_natic error t'ro_ eacl_ sourcewas defined as the diffel'et_ce betwee_ _t_ism_alyzing power and tt_(::a_alyzit_g powerobtained under the standard criteria. The statistical fluctuatic)_ was removed from

the difference, Tl_e total systema.t, ic error is calculated as tl_e (lUa.dra.ti("sum of tl_eerrors from those sources, A detailed descril._tiot_of tl_e study of the syst(-:matic errorsis given in .Appe_dix C. Since n_agnitude of tl_e syste_natic error could be chat_ged

. for each particle, select.i(.)t__ne,Cl_ods, t:,l_eerror was est,i_ated for eact_ me_tl_od.

Three Leading Particle Selection Method _l_(:,systematic errors of tl_e ana-lyzing power frorn the tt_ree sources shown above are summarized in Table 4,6,

i:Most of t,t_esystematic errors are negligible or quite small. This means tha,t tl_e

analysis method gives unbiased analyzing powers.

_ 89

i, =

_-_-

,_r '['l ,,i ,, , ii tlr",' ...... III' "i'llflll " illl li r,,,lll III'I illlI_l i, ..... lll'l_'lll,'llll ..... fill" iI,_' ,,_,'_, .... _i_ IJ lr' _ iIlll .... J_ll_' '_ ' ',r ,, rli,,, i,ri l, l'II ,, i!l,lli,lll i,,

4,8 Systematic Errors Aria.lysis

3

Systematic error

Source Method Global Light1 Heavy_.Da,ckand event selec.tioll Helicity _o 0 _ (1 I _ 0

Modified Helicity _ 0 ,.o 0 I ,.o0Cllirality _., 0 _ 0 I ,'-, 0

Jet finding Helicity ,.o0 _ 0 i _-,0Modified Helicity _.,0 ,-.,0 I _-,0

Chirality _ 0 _ 0 I ,.o 0Analysis Helicity _ 0 ,._ li I +0,001

Modif:ied Helicity _., 0 ,-_ t) i ,--,0Cllirality -0,003 _-, ,, _ _-,0

Total t--Ielicil;y _ 0 _ 0 +-0voN--_0.000I_Iodified Helicity ,.o0 ,,_ 0 ,.o 0

Chiralit, y +0.000 _ 0 ,-.,0, -0,003

Table 4,6: The systematic errors for the 3-particle selection method. Tho total systematic error Is

l;he quach'atic sum of the errors from ali Sotlrc..._S,

N Leading Particle Selection Method The dependence of tile systemalit.', erroron tlle analyzing power on t.le l_ulnber of leadiilg part, ides Nl_,,z is sho\v|l ill Fig-ure 4,37. The statistical errors are also SllOWllin tile figure for comparison. ThesS,sCel_aCic error was c:alc:t_lat.(._das ;t quaclrat, ic su_t of the errors I'r(.)_tali tl_e sources,In gelleral, the systematic error t.)ecolnes large ii1 tile large NI,,.,,¢region. The syst, eII>

atic error is smaller cllall t,lle statistical error in almost the wllole region.

Particle Selection Method based on Rapidity and Momentum Tl_e depen-dence of the systematic error on the analyzing power on P,,_i,,for several con_binations

of ('rh,,,..,,,An) is shown ill Figure d.38, d.39 all¢t ,'l.d0 for t,he global, ligtlt mid lleavytlavor samples, resp_._ctively. Tile st;at,istical errors are also shown ill t;lle figures forcomparison,

The systelnat, ic error was calculated as the quadratic su|n of the errors t'rolll alit,he sources. Tile sysl;ematic error gellerally l.)ecomes large iI_ the lligl_ [).,,vinregio_.The syst;ematie error is s_naller tha_ tlle sCatistical error except_ in tl_e t_igt_Pmi.,region.

9O

_I _'1' "' " 'q_rll'_' ' lt '" I_, ', ,ll ,, r,, 11 "111" ""n'l_l' ,r I_ '" r, r iI1_r , II"' , ,I',1'," ' r,' I_," _11n '" 'lr "rll_'llll ""'"' II'lrI¢,.... " ' rll tl'" _r '_111 ' 'rll'U ,p ',_ '_'1' ,1'_,1 I%'1" II_11_''_ _'1[1_1"'1_" ,It' ' "l_llri',_'""ll'l'"ll " II

Analysis 4,8 Systemtztic Errors

Global

__ _ -Helicity (Avg) Helicity [Max) _ Chimlityi(Avg) Chti'alityi(Mak)O.2 ...... !.......:....... :...............:.......".......................:.......!...... :................:...... "...... :......

- ,,, , ,,

_ 0 ............. ...: ... --' '_ ', ,, ;

, ', ,,- A_sIILL : A_,sILIL A'a,stttl _stal :

-O.2 A'o.sv,_....... : ........... !......... _asys" • ' !......A_,.sys _i c_sy'_i.1.7.....1...... [ .... " ........ _ ............................................................ 1...:...................L..........1..........l.........

6 10 14 18 6 10 14 8 6 10 14 8 6 10 14 18NLead

, Light Flavor. .......................................................-Helicity iAvg) Helicity ',Max) Chii'ality:(Avg) Chii'ality: (Max)

O.2 .........;.............. ": ........:.................. ' .....'.....:....... ? ...................... :....... '_..... i.... '

_ 0 .................

Aastat Aastat : :' _czstat ' Ab,slat

-O.2 A'_s,.,s ............... Aczs,;,s.......... ....... Aczsys ...... -' ;4o.sys...... : ....

6 10 14 18 6 10 14 18 6 10 14 8 6 10 14 8NLead

Heavy Flavor

" Ti_lelicityii_i, gj ............HC;iic-ityiMa-x!i-..........ci{ira-iifv:,(Avg)........]--Clliri(lity'(Max)......--_'O,2 .................. "

_+_ i ' 'Io -' ........ t.......

<1 ' ' : : , [ ',

..... 41_sys- •

6 10 14 18 6 10 14 8 6 "10 14 18 6 10 14 18NLead

l_'igure 4,37: Del)C?,nde.nco of t,ho star;isr, lc.al ot'rot's rind systernAtt;lc errors or). rho _.%ll&lyz[ngpowc.,.r oi1

Nte,,t in the globnl, light and he,avy flnvor sarnf)les.. The light, and dark hatchc:!d areas are shown thestat, isttcal mid syst;em_tic e,rrors, respect, ively.

91

n '1' ..... r' r' 'lip '111,nhrtHq'a' ii 'Irl' ,', ,,_ ,,qq_l,r,I,, ,'_rl ,,I........ IrRp_til .... Illrmim,I1_,, ,H,e' II ''' _ _11_" "lpl_' '_[I'P'_I'P'[IV 'P',..... t' ""'l" ln'el '"' I_1'" '"'lr' '" ' "'_'"'_1 "'r""l'rll"" =,,,',,e, '"Ilpl"" Hl"'_"llllV'"'_m' "'"'"

4.8 Systematic Errors Analysis

+

11 = 2, _Xn= 1......... 111LIX, ................ ___...,_ ........................... , .................. , ................................ ...............

g' - Helicity (Ayg).: iHelicity (Max) :Chirality (Avg); :Chirality (Max)C0,2 -! ' ' " ................. i:_".. .... -' ............. ..::i_.,._:.,.

: ' . . ?

-- , : ', . : • /;:.:

0-: ......................... • - .......................................................i ....

.... ;

- [ Aastat : ,' : ,&cs,still , Aaslttl : _aslat ,-0.2 -- 'Aa_,y,,4...... :........... ACs.sV,_ : " ' -- AozSVS.............. . aa_;ys ...... • ........

:[_.l.....L.._..I.......I...i__J.......,..._t.......[_.L.I.;_t....t....I..Lt.......[._X._-I..2..J.....L_L_LL ........L...L_.t_.L..I_....[._.+...........

0 2,5 0 2,5 0 2,5 0 2,5Pmln(GeV/c)

n _=3, :Xn=l.....,............................................,........................ma ...................................................................................................................

iHelicity (Avg) Helicity (Max) :Chirality (Avg) :Chirality (Max)0.2 --".................... "......... .......................

"_.,_ : ..... ' : : :q) ' . :.:::

0 -'; :::;"::; .................. '' ..................................................<:::1 ........... " ;

-: A0_slal ' ' Ats.sial A_sllil AC(si/li

- _.....L.,_++,,..,,....++,,....,+.,+,t.,.,...............,...., ,.,_.,_,............L....., <+.,,,._,0 2.5 0 2,5 0 2,5 0 2.5

Pmin(GeV/c)ri = 3, An =2

................................................................... llll, t,'_, ..." ....................................................................................................

>, - Helicity (Avg) Helicity (Max) :Chirality (Avg) :Chirality (Max)0,2 ....' ................:............. " .......... : ............+............. ' * ' i ....... 1" .......... I ....

_+ 2 . .

0<::1

- : ' : :i ..

-: A_stlit : '. A0_sllll : ' Ac_sllil : A0_sllit '

-0,2 .... ' ,Act_ys,'...... ................ A(L_yS ..... ',................ Aa_;ys ..... '..... '....... . Aasys _.....-:L,_,__,_l.....,_,..........L_,_,......_,l_,,..........x+,____,.......,_L__.........L,__,_,_,l_,..............0 2.5 0 2,5 0 2,5 0 2,5

Pmin(GeV/c)

Figure 4,38: Dol)OndOnCe of tlm systonmt.lc, and statist, lc,al errors on rho analyzing po,vet on Pr.i,+

for c,orrll)hmttons of (ri,m<,,_,Ai+,)= (2, 1) (top), (3, 1) (middle) and (3, 2) (1)oi;tom)for tile globalsaml)lo, The. light, ,tuld dark hatchod al'oas tu'o iA_c:statistic.al and systonlal;t(', Ot'l'OrS,rosl)oc.t;lvc'ly,

<(J+).Ca

iI 11111, r,,, ' rip "I" ,, '" p ,_' . lr,+ ' ,fill IIil,lU ,ii .... _, .... ' ' I1'1'I1" ' i, 'll'l'l!,lri,lllllll' ii ii,li ,, ,, illlll li, ,il.,i,,i 'lT'11 ,pi, iii, ,, ,ii ,,,i,,Irll, rl,.,,il r tl, u i,pi, .... ,iI m I!' ,l'p'iq, '.lqlr '1111!1''+1 " Ilpl'UII

Analysis 4,8 Systema, tic Errors

n =2, An = 1................................ I11 LI..K ..................... !._ , ..........

-. iHelicity(Avg) Helicity (Max) :Chirality(Avg) Chirality (Max)<_0.2 .... .....+_ ): ............. ..... i,,

_" O..................................................................................................................

- Au.stal ' A_sta[ ' ' Ac(slat : Aastat

-o.2:--1. ......i................................................................ l.....i.....i....,...l.l...i............l...l....,._..I........l....k........1_t._.t...l.....i ..i....__.....l......l. l_._.l..,l 1.i ,..,0 2,5 0 2,5 0 2,5 0 2.5

Pmln(GeV/c)n = 3, An = I

I.................... max, ................. ::_ -; .... ;.................................. 4..................

I_, ....

_'0, -!i::(eiiciiy(ATv[) Helicity(max) .C.hlrallty(Avf,) Chirality (Max)

0 .............................-'4

:. Aomtnt• -0,2 ........Aasv,_' , .... 1..... Amys : ............. Amys..... ........ A'c_sys.....

• 0 2,5 0 2.5 0 2.5 0 2,5Pmin(GeV/c)

' n_ =3, An=2...................................................................nax,..................................................................................................---!l-lelicity(A:vg) !Helicity(Max) '.Chirality(Avg) :Chirality(Max)

_:_0.2 ...."............... :............. !.............. !..............; ........... ..........; ......, '

- /

•<1 7, ,- ' kaslat ' kastlil kasllit ! kc_xslal

-0.2 .......Aasys..... i.......... Aa._ys................... Ac_sys........... Aasys.:l.....,.LL_,_..I_L.,...._i.,_,_,__L_I._,_,......... ,.......I.._..,t__..L_;L.....i__.I....l..................1_.._.,...I....., ,._..I0 2,5 0 2,5 0 2,5 0 2,5

Pmtn (GeV/c)

;' F'igure 4,39: Del)ondorice, on the systeluat, lc. mid statistic.al errors of the, analyzhlg power ori P,,,i,,

; for combiriatiol_s of (n,,,,,, ./M-_,)= (2, 1) (top), (3, 1) (mtddlo) and (3, 2) (bot, t;oni) for tlm light lh.wor_

= smrll)le,. Tho lighl; and dark lattl;ched al'oas are t,lae. stai;lst;t(tal and syst(.:mati(: (Jrrors, resl)eCtivc;ly.

,,I

4

.

{)3

==

. ,,ili,r.,,I I,..... i,l_,llr_I, i'll"' Ull..... III1" Ivil' rH'nii" ,tori, .,, i1,,, ,,/,li lr "'1111,1, ,, ,,,1tltll p ..... r,q,li, til,' ' IIl, UUlllr,ll,il, iii1,, ,, lr ,, iiii, ,ill/ II'' '_I"111"u',..... r_...... ,' ,,, I[I ....

4,8 Systematic Errors Ana, lys'is

n = 2, ,An= 1cn till.IX,.........................

_:__P0,2- :t-lelicity (A'vg) • !Helicity (Max): r._'Chlndity (Avg) 'Chirality (Max)

_ - ,.

_ 0 ...........................................................................................................

_,CLSI[II /_ £_/.SIII I _0t, Sllll ACt.slat

-0,2 ii(- aa_> .... A_,._._ _. A_.._y._ " i A_:sy._0 2.5 0 2,5 0 2,5 0 2.5

Pmln(GeV/c)n =3, An= l

___ ............................ , .................. 111ll_ .............

_," - :Helicity (Avg) :Helicity (Max) ZChirality(Avg) :Chirality (Max)e._0,2 --! ............... :.............. . ............. : ' .... ,-'- .......... :............ : ........

0 ...............................................................................................................

-- ' /_ Ot,S [ lit I l._ Ct.S t III ACZsIIll Aotstat

-0,2--, A_sys .......... I 'a_'sy_...... 11........ A_,y,_...... , A_yS_._].__,....l....I I , ......................l t........I .....[_l...._t_._t_.J..........t..........L_t_._i_.._i._t..........i0 2.5 0 2,5 0 2.5 0 2,5

Pmin(GeV/c)

n_ =3, An=2................................................... , ................... 11' ,_ ...............................................................................................

3P" - iHelicity (Avg) iHelicity (Max) :Chirality (Avg) , _hirality (Max)00,2 --! ................ i........... _.............. :....... "--;............... " ' ...... ; ..................

-. ,

,_ .

0 .....................................................................................................

A_stat ; ' Ali.sl;li Au.stnt Aotsttlt '

-0,2 ....... A_sy.q Au.sys .... kctsys .... AfzSyS

0 2,5 0 2.5 0 2,5 0 2,5Pmin(GeV/c)

Figure 4,40: De,l)endenc.c,of the systematic, and statisl;ic,al Ol'I'Ol'SO11 Lh(), Itnld3'zillg powor on P,umrot'combinatAons of (Tr,,,,,,/..M_,)-- (2, 1) (top), (3, 1) (micldle) and (3, 2) (bottx_xn)for the hem,,y flavorsample. The light; a.ncldark hatched _tl'(.;;.tsa,ro t;ho st;a.t,ist,tca.1and systematic errors, respeclah,ely,

,0':1

,nil.tin...... ,i,_"1_.........rl, #1,'_,"l!l'_r _,r_..... ,....... ,, _i,. "_q'llrll,rlllf,"'i_,., _,p,,,l[l_...... ip" ""I'"'"' .... lt" H'H'II ,_' IIIlql 'Iq Ilr_'_ql_,'"'' "" 'II'P'r Ifllll' 'il_ '_'_" el' II1'"'rl_n_IV'_"eltr"!{ill"til' II .... _l_,llPlll'r" "li...... "qlt',"I_""_qllII'_ ,I" "" ,,'uR_Ir

Chapter 5

Summary and Conclusion

5.1 Summary

' Three Leading Particle Selection Methodo

The analyzing i:_owers for tlle global, light flavor and heavy flavor samples are

summarized in Table 5.1. The analyzing powers obtained by this particle selec-

Ana.lyzing Power

o Analysis Global Light flavor Heavy flavor

" _ Helicity --0.029+0.024+0.000 -0.057:t:0.031-_t:0.000 0.007+ 0.036+8:_Mod. Helicity 0.055-_2.0.024-t-0.000 0.056:t:0.031+0.000 0.055+0.036+0.000

, +9.000Chirality -0.0al+ 0,026-0,003 0.052-1-0,038-t-0.000 --0.058-_1:0.035:1:0.000

Table 5.1: Analyzing powers for the llclMt,y-, modified helicity- and chirality-based analyses. Thefirst numbers are the central values of the aaalyzing power. The second and third numbers m'e thestatis_:ical and systematic errors, respectively.

Lion nletho,I are consistent with zero within 2c7 except that the analyzing power on

the basis of 'the modified helicity-based analysis for the global sample is 2.3cr away

- from zero. The modified helicity-based handedness seems to have angular and beam

polarization dependence. However, we can not conclude that the dependence is sig-nificant, because statistics is.;still poor. This method does not give systematic bias to

" the results, therefore, we will obtain more precise results with large statistics.

" Since the analyzing powers are slnall, we set upper limits at 95% confidence

leve, on the analyzing powers as follows. First, the total error Aatot was assumed as

the quadratic sum of the sta_lstmal and _;ystematic errors. Then, we fiad u and l to

. 95

_- _-_=

,'" ,_l' '_r_llqql' ' _lr'l'lqll' pl,.p_l,llll_.llllrlr' ,., II'I"IIPII' '_'ff0'_ ,_, "_Illll...... ,H'',W'lplN'"_rr,,','rl' _,t"le'r,-r,,I, ,q, _,,, ,',,,. _,_' .,' '

5.1 Summary Summary and Conclusion

satisfy the following equations:

1 [-, (z - c_)20,95 = x/_Ac_t.of J.-ooexp 2/Xch_oL

i }1 exp (z-a) 2 dz,0,95 = V/-_Ac_t,,jt -' 2A(_i!ot

for the upper and lower limits at 95% confidence level. The upper limit on themagnitude of the analyzing power was defined as the largest in magnitude of u andl, i.e, rnax(lu ], [II). The upper lin_its o,_ the analyzing powers calculated in this wayare given in Table 5.2.

Upper limit on Analyzing PowerAnalysis Global Light flavor Heavy flavorHelicity 0.069 0.108 0.075

Modified Helicity 0.094 0.108 0.115....

, Ohirality 0,052 0.125 0.115D

Table 5.2: Upper limits at 95 % confidence level on the magnitude of the analyzing powers for the

hclicit, y-, modified helicity- and and chirality-based analyses.

!N Leading Particle Selection Method

' Fig 5.1 shows tlle mlalyzillg powers as a function of NI_,,d. No dependence ofthe analyzing power was fouild frol_l tllis figure, alld the analyzing power is consistentwith zero for all Nt,,..,Lvalues witt_il_ 2ct of its error. We also set the upper limits at95% confidence level on the analyzillg powers by using tlm same calculation givenin the previous sectio_. Tl_e upper li_nits on tt_e magnitude of tlm analyzing powersare shown in Fig 5.2 as a ful_ction of Nl_,.d, For Nt_,,,l <_ 10, the upper limits are inthe range 0.05-0,10. For a larger Nl_,.,,lregion, the upper limits increase due tc) tilereduction in data statistics.

Particle Selection Method Based on Rapidity and Momentum

The analyzing powers are sllowll iii Fig 5.3, Fig 5.4 and Fig 5.5 for the global,light flavor and heavy flavor salnl)les as a f'uuction of p..,., respectively, "i_heresults areplotted for combinations of (n.,.._,, An) = (2, 1), (3, 1) and (3, 2) separately. For thehelicity-based method with 'n,,,,,_:_= 3, tl_e analyzing power becomes negative as/:',,,i,_

: 96i

i!_ ",l, '_r p,,,t '" ,,v ,t_'_ltlla,',Itr_' III.... I',' 'ff_'_t .... II'.... ", "' 'l'_"ll" 'lt' '" ........ ': tl_'"' ,",Ttp ',,rp, '[ "I' "1'111t' ' _' tr, 'U]'I ..... ""'rlltlJ'il'_t ...... , r_', tl "l?"'l'l[I Pl_a' ,11_10 ,l'lt' ' _t"'ll" '1' ,t" Ig 'l?lt "l'r,tl_l'll,f_ll][TM.... lr, ,l""_llp"lllllt",' mphl,aptr,, 'l'l" "r'll'l' " ..... '11il_ltt C[IlI!I'alll,n ',,lllllll

Summary a,nd Conclusion 5.1 Summary

Global

-Hel!city Avg) - Hel!city ,(Max) ] Chii'alityi(Avg) Chii'ality::(Max)

_O '

0 : : .... : ............ ,,]'Til:,"

-'_c'0'2 ..... A'O.ky,,:;:................ A'O.sy.s":.... "! ....... [. " A'ds?s: ...."", ...... - &_,sys"_ ...... i"/ "< :_............].............1..........]....................l..............l..........t...........L.........I..........J..........I.........6 10 14 18 6 10 14 1S 6 10 14 8 6 10 14 18 --

Nl.ead

Light Flavor

f I' .....................................'¢J -Helicity iAV Hc.liclty (Max) Chirality (Avg) Chirality (Max,$ 0.2

o.° -_'.,',<,,'I++i11 ......._.+_f :.i...:.. .... '.....'.........!:+_,,._,1,! ,1,l,t, ::, _ 0 ** +++ " ' ' i :_'_ L_O.SIal &U.slal

-_-0.2 [7 A'fzsys i. A_s.sys ....... AdsyS : ] .... Aetsys: .... i. < 1. l f ...... 1 1................... J........1...........6 10 14 18 6 10 14 18 6 10 14 18 6 10 14 18

NL.ead

Heavy Flavor..................................................Ho.iicit-i' M;4_...............ciiii:7_iiii.........I-Helicity(A,,_) { ] y(ii,...... _Ji_ii:7;iiit:...........

$ 0.2 ....... ;..... :.. , gS y(Mi,x$

,:,>o ++i++ • -';'<','<_* '7, ,_;{ !+_i::_ ' _OCSll.il ' Ag,sial A:,g.siat:, :: A',g,sial i !/1"_-0.2- A'asvs............ " ,,xc,..<.,,.<......... i....,x_._y.<; , .....,......_<,sys........ T< ..........l......................................... .i ...........l................i..........'....................i...........;........i_._...L.

6 "10 14 18 6 10 14 8 6 10 14 8 6 10 14 18NLead

F'igure 5,1: 'I'ho alml)'ziiig power as a function of Ns,<,,,,.#for the global (top), light (micldlo) and. heavy flavor Saml)le (bottol_l). TI_c gwo le['t ancl two right figure, s show the analyzirig power by rho.

helicity- anti chirality-I_asc'cl aimls'ses, resi)ectively, Shown are ave.rage: method (poinlos) and rnaxi-

mum met,hod (Ol)en squares). The; light, and dark hatched regions show st,atist,ical ancl ,,y,,cei..<,_,o<',' '_,"" 'errors, respectively. For eve.ry analyzing power, the st,aiist, ical error is dominant.

i 97 --!

_=

,=

g

........ , .......... i............ ,....... Irl ,,,r,,,l........ ,............... ,, .......... r,.............. ,...... r, ,ii, ..... I_ll_ii,,r..........p,r"_ll,li'r ..... irl _l_llI",,,_,,,,"'u'",H,,,.,. II"" _,'',',r".,,,r,,,,,, 'li,V,ill,' "_lll'll!ilf"rll'H'l_',_',,'tr"_,'i_nr_'_!lllllq','r,__lllll['_,'ll_l,l_l'I'1_'I'I_'"_'_"_Irlill,l!llIl,llllllll

5.1 Summary Summary and Conclusion

GlobalO.4

Helicity, • :Avg ! Chirali(:y ® :AvgC --

o 0,3- -[].',Max..i............... :.......................... i--m.:Max.................. :..............• ._ : : : : - : r._

0.2- ................................................................................................-........' lhQ. -- : C) • ' 'Q_0,1 .............. •.............. : .........o.._.,........................... _..........O''_..... '-'"V ' ...........

......................................................................................................................................

6 10 14 8 6 10 14 18

NLead

Light Flavor

c

o O.3 I-- ........... " -m.:Max..:.......... : .......... _............. "..re-:Max..:.............. :....... • .......__ • _ • m•"7 0.2 f: •- r-:....... : ..... " . l:'i I:l..... l.............. : _'_o _ I:_.....S i - ! : " I:l !

q _

0 F .[..................l........................L................................................1...................1.....................[.................. "6 10 14 18 6 10 14 18

NLead

Heavy Flavor0,4 ...........................................................................

m Helicity • :Avg . Chirality • 'Avg . r:l, ' : ffI

o O,3 ............ Ll-:Max ' _-•- m:Max ", : . •E l:¶ : :E:_-q 0,2 ............ '........... ".............. :.......... ...... • ........

, lp _ ; LJ . [':J ,

'-' 0.1 _- ........... : ..........®_ ..... _:1.......:......................57;_!]__;_ _" r_ ..... !.........:D -_ _ _ _ ,, I:_,- : " _ 0 " : :

0 -:-'..........."[-..............1.............................1..............................................L.......................I.......................1..........................6 10 14 18 6 10 14 18

NLead

F'igure 5.2: Upper limits at, 95 % confidence level on tlm magnitude of the tulalyzing l)ower forthe global (top), light (middle) tt_(l heavy flavor .t,:'Unl:fles(bottom), The left and right figures showthe ul)per limit for the heliciW- and chirality-based analyses, respectively. Shown are the av(.,,vage(points) and maximum (open squares).

1

I 98

,,,,",,,.,,,' _r_q..... ,...........,_rH',',,,., .... ,_,_', ,r, ......_lt ' IprrqI.'""r'en,,,,n.,_,tn,,_'lll,,,. I_lr ,rl_I Jl''_Jj' I'I51_j,lr] 1,ht_.......... IqllS_ljl'rl ", ",.'"",,,'E_ nm I!'tl,",_r""'_'_'_ .....r,_tpl'"_'ll,'qFlOH'lS'lg'qlIHlIl'n_"[jFn'"lhfqI..... n,n'1I

i

Summaly and Conclusion 5.1 Summa,ry

increases, on the contrary, it tends to have positive value for the chirality method,. However, all analyzing power s are consistent with zero within 2a. We set upper lirnits

at 95% confidence level on the analyzing powers for this particle selection method,The upper limits on analyzing powers are shown in Fig 5.6, Fig 5.7 and Fig 5.8 for

. the global, light flavor and heavy flavor samples, respectively, as a function of Pr,tin forthe combinations of AT_and '/t,,,.,_values, separately. This particle selection methodgave the upper limits of anals, zing powers of less than 0.10 for r_,,,,_.,_<3, An < 2 andP'min < 1.5 GeV/c, but gll(:'larger upt)er limits for P_,_iT,> 1.5 GeV/c.

-,.

,

li

=

z

=

I

J

__

= 99

I IIIrl'lil '' '111..... [11 IlIl_III1.... III i,i, _,ll,,i,ii_ I rllll _, ,i,Tlrl,ll,,,,iill ,llelill_,l,l,iM,lllllllllrl, ,,i.... IV,,I_I?......... r,, ,,Urll _ ii I, fillI_1 'l_l'r',Irirll rlII Illl$'l'll'llllll'l[ll_l ml'II_l''l I{Illlll111IIl"llll'l__ I!i I'lrl_..... ii iI"Ulll ........ I],11_I 'll,uiI _[llrll........ ll'lllltllllll I1'

,,, i, , li,t, ,L

5,1 Summ_ry Surnmt_ry and Conclusion

n = 2, An=,1..............................................III_,IX...............__.......-__l...................................................... ,

_; ,'Helicity (Avg) Helicity (Max) Chirality (Avg) ,Chirality (Max)0.2 -! .............. :............. !.... _............ : .............. "............. "......... :......

tt "++t * . '"'+ +'0 -* '....... ':' '..... _+ { -- ';'. . ,, ,

N_:_ Ac_stat Aczstat Ac_stat ', Ac_stnt '

-0,2 --_:.:Aczsys...... ',............... ,_c_sys : ............ _A_sys..... i........... .: A_sys ..... ":.........c-,_ ._L_.L__L__L_L_.]_.L_L_ _._L.._L_.h_i.... L__L_t_.t ..... L_L_L_L_L.L_L_.L .... J_...L---I_J__-L.[_.L_L_

0 2.5 0 2,5 0 2,5 0 2,5

Pmin(GeV/c)

llmax = 3, Arl = l.....![-t-eiic'ity(Avg) ;Helicity (Max) .............Ci{iiaiity-i,_vg) Chirality (Max)

0.2 .......... " ..................

ill i?,; I "++ +++I...."",_ , ' , .

N ' Aczstat ' Aczslat ' : Ao_stat : ' Ao_stat ' "

¢-< _J__L_L_L_L_I__L_I........l__...L...i_l.......I_..].....,.._.I...........L...L.._.I....a.._A_..I.__L....,......._].....L_L__L.._L.[_.,....,_.

0 2,5 0 2.5 0 2,5 0 2,5P,nin(GeV/c)

nma,_= 3, An = 2'--:...........:--;.....' ...... [C.Ilirality(.,,'(vg) 'C.hirality (Max),-.FlelJclty(A',,_) Helicity (Max) l ............... "$0,2 ....... : .... ,

0.-4+{+ *,+t - +++ --.-,',,,:,.-q ;7 I

' AOt.slal ' J i Aczslal : ' Ac..ZSlat A(zslifl-_-0.2 ..... k_gYs .......... ]..... k('t.sys : ........... AO,sys .... A(_.sYs :r"< L_L_L_J._LL.I_L_L.L_.I..... ill--Ii aI_" fill --I----ILl-- II aill li--lt= ...... ]__.I.__.L__L_._I...... l_.I...J...... l.._..L..'..i_.t...'.._1....' ' ..

0 2,5 0 2.5 0 2.5 0 2.5Pmin(GeV/c)

Figure 5.3' The analyzing power as a function of p,,,,.,, for combinations of (n,,,,,, A_z) = (2, 1)(top), (3, 1) (micldle.)mid (3, 2)(}:)oLI.olii)for Llle glol)al sanll)le.. Th(._two lefLmid two riglit, flgtir(.;ssllow die. analyzing l)OWcrby tlm l_eli(.'iLv-_.tll(I(.']lirality.-I)asc,.danalyses, rest)ecti\'c;ly. Shown are Ll_oaVel'ag,.:(points)and nlaxilmllll nlc,tllo(l (oi,eli SClUares).Th,_ ligllt al_d dark hatc'lled regions showstatistical and syste.mati(: errors, resl),.,ctiv(,.ly. For P,,,i, >_''2.5 GeV/c, t}_(:analyzing powers are.show,, mtlltil)lied by 1/,1, be.cause l;l_(.:ati_tl3,zi_lg1)owers iii tile,,high p,,,,,, region have quitu largovaluc:s and errors COmlmredto d_os,.,in tl_e low p,,,,.,, rogi,_m.Vor eve.ry analyzing l)ower, stmtisticalerror is dominant,.

1()0

.......... HII ..... '.... 'lll"q r.... N' ...... ''_"r_"l]'IP'" _'"'_:_III "III"_IN "I[IF '" ..... lip ",ee, "_'_1,,.....]"li"ll 'Jill I,i, ,,rllllt"l, ' liH I_ "ltl'l ',_,i Irl,,ll,,,,r,",ii,r_il,,rli,rlI ii[!l li_" I_'IllllI['ll"rllU'Ullll 1 ,ii'[', ill,,_ii.... ,,, ,, !i_,,illll,lltl i,I ..... r,,i 'I1[1" ''li i'_ .... _'_I' ,...... ii, rl ""

Conclusion 5, 1 Summar!,Summally and " , '

nml. =2, An=l

e::; -........iHelicity,i ..................................(A'.vg) l..................iHelicity (Max)iX..................................[_Chirality (Avg) I...........................................Chirality (Max)

0,2:-i.............................../ i...............!........................Ii i........._ ................i........._o°- i Ii t,i j.t ++4i+t*! r!i+l-! ! : i i / : i I

'N'_' " i Aezstlit : i kczstttt ': kctsttlt i A(xstal ;-0,2 ?.... :A'asys......, ...... I....Aa_;ys.............. f..... Aasy,s......',............... A'a_;yS' ' .......r"

< L_L_i_LL. l_..l....,l.....I.....i..1.....1__.l....l._..l..._.._...........l_.._l_.._.L..__.L_.I.....h..l.......,.__I__.L._..i............I.__L..L....I.__.l___l...l..._,.__0 2,5 0 2,5 0 2,5 0 2,5

' Pmin(GeV/c)

nina =3, An= 1

_ l'" i"4_]icity (A,vg)[ !]4_Iic'[y (M[_x),Chirality (Avg) f iChiraIi[y (M_N)

,i.,,,.

o_0,2 --: ............... :.......... -;............ :............. ; ............... _............. ' ............. ;.........

/ +t,+{ i II' +t T ',t''''f'c_IN

" _" LMtSlal A(_.sllll AU.sliil-0,2 AasTs..... A(zsys , " ' ' 'AaSys : Aasysr"

0 2,5 0 2,5 0 2,5 0 2,5" Pmln(GeV/c)

rl =3, An=2............. nak ....................... ...............................................

-/!;;ieiiC-ity(-ATg).... ] Helicity (Max) :Chirality (Avg) 'Chirality (Max)

0.)0:2._ "_ .... '.......... ' ....... ! ; ........... ; ...... '-; .............. : ...... "- ; ........ '" "

° { ++ t +o .....,.+++},_..+ ....,,<l,<l,+,<:,_..,,,........++++ ...... '!<'","I" ......,C _- i ' ,

'_ - ' ' A0t.sllll Au.sial- Actslal i , Actslal '

"_-0.2 ' L_,asys : I.... Aasys i ...1_Ars.sys Aas:,,s<i::: 7......I l.., l.... I.l.l I I i i .l , . , l.i.l.,. ,, .. l. l..l i i i ,0 2,5 0 2,5 0 2,5 0 2,5

Prain(GeV/c)

Figure 5.4: The almlyziiig l_owcras a t'unc.i;i.....t of p,,,,, for colnbilml,ioi_sof (n,,,,._,A'n) := (2, l)(top), (3, 1) (middle) and (,3, 2) (bot, toin) for the light: fla,vor sl.tn'lplo. '-I'ho two loft and t,wo righi;

figures show t;h(?, a.nalyzing l)()w(._r by the, ile,lic,iW- and c,hiraliW-l)asod ana, lyses, respectively, Shown

" are the average(points) and mrtxiilll.inl me,t.hod (open squares),The light and dark hat;chedr(,gionsshow si;at,istic.al and ,.'4ysg(.;lliati(.'. (.':l'l'(Jl's> l'(_.Sl:)O(,i,iv(.,ly, For ]),nili _ 2,5 (._(),g/c> [,11(_, analyzing pow(.TS

are shown, mult, il)liod by 1/,1, boc,ause Lile analyzirJg l)owe, rs iri l;ho higtl ])mist FOg[OIl ht;l,VO ql.fil, e large

" values and errors COml)aroclt,ot,hose in the lowPmin rogion. For every analyzirig power, the st,at;isttc,alerror is dominant.

101

1,1,',,, II1,,11',,'I.....,.... "_1'"'"......'1I'r,.,i,,,......[_il,l'l,,'............. "_'1_Ilil 3' I1_'_1''lll'l"_l_lilll_...." 'iii.... 'lllil#"ill"llFIIl_'"lllllll_11 I_1 l'l_'ll_'l_lllll'II11' _1[I.... '11111''r,"' ' ,',,_,_U"'"'III'I_"_ "'qlll!llr''IIr'"'llll_,,I[llrl,_,_,,_l,ll _llipl,i,i,,,,,,i,pql[i,.,.,,,,,,,n_l_,,,,_,,i,i!ll_,, i,,

5,1 Sumrna,ry Summa, w a,nd Coriclusioil

n = 2, An = 1................. ml.iX........................................... --7.........

- _elictty (A',vg) _Helicity(Max) ';Chtralityl(, vg) t --_]i-im-ii-[y-iM-a-x)i

_o,__o , "..................................-_.................- _:...........l_ii.,q --_ _ i : i l>" - ' A0tsllit : ' _Ao_sllil ' ' A_stlit Act.sl!li"_-0,2 --. _A'_J'yS...... :................ Ac_Sys .... J............. : 'AC_,y's..... :............. A'm;VS.......

0 2,5 0 2,5 0 2,5 0 2,5Pmin(GeV/c)

........................................................n,,,,,=.?,An,_!.......................................................................-. iHelicity (Avg) Helicity (Max) :Chirality (Avg) :Chirality (Max)

$ 0,2 ---:.............. :.... ' .....

a. 0 --

,_ |1 ' ' i

-_ -0.2 l, AcJ.s_,s I Ac,sys .... ,Xc:_Sys '

0 2,5 0 2,5 0 2,5 0 2,5Pmln(GeV/c)

n =3, An=2........................................................... m {I,x .................. _.................................................. , .._., .......................................

- iHelicity (Ayg) iHelicity (Max) :Chirality (Avg) ,Chirality (Max)

i f ....................+':;.............",.....N •_' Au, still l__(*Sllll Ac_stat AO:Still

,,_ .... I...1...1 l . i I. i. l i ,. I _l _ I. 1.._1...1. i 1 1 .t. _ l l ! _ I0 2,5 0 2,5 0 2,5 0 2,5

Pmin(GeV/c)

Figure 5.5: The analyzii_g power as it fun(.:t:ioilof ])mi,_for confi_lnat,ions of (n,,,,, AT_,)= (2, 1(tool)),(3, 1) (midcllo) and (3, 2) (bottom) for rho heavy flavor sarnl)le. The two l(?.ft,and two rightfigures show t,he analyzing p()wer by the llelicit#- ullcl chiraliLy-based analyses, resl)ectlvely. Shownare Lhctrverage (point,s) and nlaxirlicilii lll(._tliod(Ol)C_nsquares). Tll(.;ligllLand dm'l<hatched re.giorlsshow sLatisLicaland sysLerriat.icerrors, rospoct!,.ely. For Pr,,i,, _ 2,S GeV/c, l;he analyzhlg powersare shown multtl)lie,d by 1/,1, I)ecause the alialyzilig l)owors in tile high P,,i,, region have quite largovalues arid errors compm'oclLothose in the; low'l),,_i,,region. For (.w(;ryanalyzing power, the stat, tsttcalerror is dominant.

102

....... II ,'r3,,,,l ...... ii ..... ,, ,,,,,i ,=troll,,r,li,, ',',r,,rl'_ ,i.... ill., l_,ril_ipir, le,iul lip' 'ffII'l ....... llfi,,,llilmI, qr ..... ,ulll If'Pl II_ ""lIIl ........ ,IPill' ,ui_'q'_" 'Im,,ll r',.' Glr"v ,I",' ,,,,'_l'tlqll, il'#'_',,' Iv"Illl"rlri'_; 'II!'i ' '_ _li_'''r " 'llli"" 1*i_'il'i'r'i' "rl',llli,_ul,,rwll_'ll_"'' u_, ,,l'_i_,

Summary and Conclusion 5,i Surnmaly

" _ 0,4 nmaa = 2, An = 1:7-i_i-e_ii-c-itY-®-i:Avg: : c[airalttyoi :AvgC ' : , '

o 0,3- "'!........... u::..:Max.... :_............ ' -.... i........... u:_.:.Max................. I............_ : : ' ,

:-q 0,2 -)......::......... .... i ....... i ............................ :.......... ::........................... ,

0,1 .:...... .....i ............ ..... ,,,....................... ..... , ........... m....., .........m : m m , i [- ' m ' u '

0 a_____LLLLI, __,kJ _L.L__LL.,_I__L,.....I.__.l__L L._LL_____L_L..LLL__L._LL,_..LLI0 1 2 3 4 0 1 2 3 4

Pmin(GeV/c)

n a =3, An= 10,4 ......................... m x.... , .................................................

c Helicity • 'Avg , . Chirality oi:Avg ,o 0,3- ' ........ Ll::-.:Max. ' ' •...................E:.ll..:Max.E ....

:..-.q0,2- .:.........................!............_...................._.............i...........,i,............".............. O : ' ' W

121., ' ' : . ; mn 'o. 0,1 ...... i............ a '_ .... u ........... :..................................................: • [ i m '

_) L._?.__L_L_.I.._ L.._[...L.....L.A._..|' ii ; ..L. 1._1_1._ L_..L.,; IN l_J..__. I _ I'

.. 0 1 2 3 4 0 1 2 3 4Pmln(GeV/c)

ninax = 3, An = 20,4 _-Helicity ol iAv_ : Cl:lirality .: :Avgr- '-

o 0,3 ..... _: :Max ............... :..... _j.:Max .... :E .:'q 0,2 ._........:................ .:.................. : ,_I,,...

c_ .... ,. ma..."'0,1-..........' " o'........... • ' ' : " "

:D _ m m t am nn ; :

0 :::_--.-'--1-.,....,...,..,._i_,..._._,.,.1_,...,__.,...l.__,...,...,._,• ,..,_'_._,..,.,..,.1....,.....,..,....,....L,...,_.,....,...1.,,.,..,....0 1 2 3 4 0 1 2 3 4

Pmlr,(GeV/c)

Figure 5,6: l)ependenc,e,oi l:heupper limlt.sat:95% confidence level on magnit,ude of the analyzingpower on P,,i, for coml)inadolls of ('u,,,,,r, A,7.):= (2, 1) (I,op), (3, 1) (middle) and (3, 2) (bottonl)

- for l:he global sample. The left. and right, figures show t:he analyzing power for tl_.:heliciW- andchiralit.y-based analyse,s, respecd\,ely, Shown are. t.ho{iA,(Jr/._,ge(points) anct maximum met;hocl (open

squares). For Pmi,a :> 2,5 GeV/c, t,he tipper upper limits are shown multAplled by 1/4, because th_. upper ]lmlt,s in the high p,,i, rogion are Cltlil;(:_large compared t,o those in the, low pmi,, region.

103

!

I.... ,,,q#............ ,n,ur........"'"'" "'l'e_ rill' I1[1',,_..........u' I,,,,,,,"'ll_'p,l,,,........ . r,'_,_,,,,ht..... ,_,, i.......II11pr'U"' r_..... ",,' _,,..... r.... '._ll.... _1r_.... r_,_.p',l,#,,,_,',,',,'.,',_',11,1...... ,r_IMII_,r'nl'"I{[rlllP_"'""'_1'_1,"' ,_'_,rlt_,. ,,I'1_ ,_'ll_l[_'pnlr_,.I, ' ....... ,r,,,,'l_l_I'_'l,_!_ll!glllllt",glt=

5,1 Summ_ry Summary a,nd C,onclu,_.'io.r_

2,an_____= 10,4.= H',Clicltyo:::Avg :: Chirality .::,:Avg :o 0,3 ......!........... n::..:Max. " ..... !........... ni.:Max.

,,

E , : ,

I,- ; q ',

- au am- ; " ' ' ,m

0,1 "i ............ !:....... ! ..... '..... m............W....._ ....a .....m .i.... ......C-_ 1 '

0 :I____.n..L...I__._..__L._LL.L_.LL_L.__L..,....L_..l._._l_____L.._t......J._L_._I__LL.L_L_L..L._Ll._...l_L__L_I_.l__.l_.IL__.L._L..I....0 1 2 3. 4 0 1 2 3 z

Pmln(GeV/c)

nina_=3,An= l0.4 _-[I-e-iicitY---O[i-Avg......':..... [.................C(i;;:[;liiy-oi[Xvg ': ...........................................c

o 0.3- •........cji,:,Max................ '.............................. cj;.:Max.... i............ _...........,-_-__ ,, ,, ,, ,,E - ,

'_ 0,2 '--.................."...................... ::...................:.........................i ......... '.........w ' w • .

CK .... al .......... ........... III , ..... IN . ,

_0,1 .............. • . •0 _L .L..L..L__......._....l__._._,..Il._,, l ,._ ,._ _.,..l.t_,...,...L...._._._ I, 1.,_ [,,_.,

0 1 2 3 4 0 1 2 3 4P,nln(GeV/c)

-3 An=2

_._0,4 I-:'-i]i-¢-iicity oi :A-vg i Cl3irality .! :AvgF ....................................................................

o 0,3 _.....i.......... E,I;.,,.Max.... i....................... ' E,:_,',Max.F.

•-1 0,2 _.......:.............i.................... ,......... i...................:... : .... i .............. =....._.

C_O.1E_....i........... -......... J.......... i.....®,..i ........i........... i.....• ..= .=... i ....Q.

i" : ; li : lD I : ':D t _ , w : i m • .

0 1 2 3 4 0 1 2 3 4Plntn(GeV/c)

la'igure 5,7: Dependene(.; of upl)er IimlLs aL 95% con{id(.mce level (.m magnitude of Lhc analyzingpower on Pmin for combinabiol!s of ('n,,,.,,a:, &n) :.-- (2, 1) (top), (3, 1) (mLdclle)and (3, 2) (bot,t,om)for t.ho light, flavor sample, The IeI'Land rigl_t figures show t,lm analyzl,ng power for tile helictb,- and

chh'aliW-basedanalyses, respectively,Shown arc.!the average(points) and maximum method (opensquares). For Pmin 2 2.5 GEV/(.',, the Ilpl)er uppe, r llmlt, s multiplied are shown by 1/4, because tile

upper lhnlbs in the htgl_ Pmi. region are quite large compm'od to those in t,he low p,-.i,_ region, o

1()4

,ii, ,i i,, , ii, , , ,,,_ i11 _, _, ,,,, , ,,i , , ,

&unma.G _md Conclusiw_ 5,7 Sumr_a.ry

--0" nw.,,- ", Ali - 1i:::f0,4 ...................................................................1,<,_..................................................................................................................................

c " Helicity t! 'Avg CliLrality.: :Avg ' ii, , .

o 0,3 " ". .... u: 'Mnx ' _:..',Mn×,, o.....,_E _ , , , ,

1.30,2 ::......i ............ ; ......... ,....................... m.... ' II :, '

(1) ii ; ' I ' ii III:_ 2 i ii : : _ 'ii. 0,1 .....................:............ ."............,..............................._' i '

- li ii ,' :, ii :, II U , : ' ",

0 !!L_.LL._L._I...L_.___.I...L,._.L_.L.1__....1_L_L_I.I.....L._._....I....LLI_..I__L..L,_L_LLLL_I....L_I_.I_._._L._..._L_L.I0 1 2 3 4 0 1 2 3 4

Pmln(GeV/c)n = 3, An = 1

_i 0,4 ......... m t.i,K ................r- " Helicity • :Avg Chirality • :Avg• iio 0,3 ,, :Max ,, :Max

:3 0,2 ............................ :.......... :................. ii..' ' II

o. .- . .., ' . i +o..0,1 ....ii " i ...... , • ,...... ......

F- ' ... , ii : ' III . ; ;, 0 Ll_.l __[.l._.l..L...I l.l.L.I.._i ._.1_.I.A..i...i..._l_..t..l .[......i.__l_.__..l.I..._i....L_.L_L_.L_i....i._l.._i..._L...i....i_..[...l..l_.i_..l.

0 1 2 3 4 0 1 2 3 4Pmln(GeV/c)

rliral =3, An=2

i:_ 0,4 ...7:tLieiic',iy,!:Ai,g .............. x.......: .........I....ci_{iali{y-" :XC;g.....[......................... .:

o 0,3 " _i :Max , .... [ ',MIIx ,

,-t:_

E _ ii li::-i 0,2 7 _, i

' ' ii

"'0,Q.1 ::.....• ...._ .....i............ i......... _........................" i ....... • ,i

00 1 2 3 4 0 1 2 3 4

Pmln(GeV/c)

tPigure 5,8: Del:JeiKIonc_; of tiplxJr ltmtl_ at, 95% confh:lonco lovel on magnttudo of tl',o mmlyzlng

powc, r oi1 lJ,,,i,i for c,onlblnai;hJll,q of ('n,,,,,, An) :--: (2, 1) (Dol)), (3, 1) (middle) irlld ([1, 2) (I)ott;Oln) {'{Jt'.

" l;h0 heavy flavor sarnl)le, Tllo I+;1'1:_,tll(l right li,gilt'eS show rh<.+tUlitlyziilg powc,r for the helicity-an(l :(',}llralll, y-I)ast:d aliaiysos, resl:J{_('.l;ively, _ghov,'ll iu'b Lili.; lI,vort.ttro (1)Oilil, s) and liiltXlllltllli lilel, ho<l (ollOll

squat'es), For ].lmill _ 7,5 Ceki/c,, i, lic, t.il.ll)er Upl:x.,r lllllLI, s li.f(), SilUWll niull;lplh.;d by 71<1,I:lc;CaUSo I,tl<_

" til:li)or lhnil;s 111l;}lo high .TJnliti regtoli ltl'O ql.lltO large COl/ll)aro(I I,o tlios(! iii i,he low l;h,,i, l'(J[lOll, -_i-

i

J

!

5,2 (Joncluslon 5'utnm_,ry m_d C( nclu,_.'hm

, 5.2 ConclusionI

i We havc_searched fbr jc:!tlia,_de,dness in hadronic, decays of Z Ubosc!lls 1)roducecti] ' by the SLC and detected by til(:;SI_A),wllere quarkand antiquark from Z ° decays were{ highly longltudxnall3 polarized, Tills high polartzatloll of partons may I)otent, ially •i give a large signal of,jet, lla,ld(:!(.1,1eSS,l)(_fi,li,lg ,jet;llandedn(._ss as an asy,nm(Itry i,l tlmI

I ob_._m'vablef2 whic,ll was taken for ¢:_acllj(::t as a triple vecl;or l.)roduct of two l)articl¢:_sI and tt_e,jet' ""axis, '_w_calculated tll(._allalyzi_lg pow_._rfor tllre(:; l.m,rticl(:_sel(:_cti,ollIn(:_tllc._ds'. witll two different (llelici ty mid chiralit:y) _2defll_itlons, However, _._I_(.,.of tl_¢._n_sl lowedi a sig_il]cant, signal of jet l_allde¢lll(:_ss,givil_g al_alyz!_g powers co_lsisl,e._t witl_ zero,I Tl_e upper limits on tla_._magllit,_l¢le (.)f tile analyzi_g pow(_r for t,he,se _n¢_tl_o(tsareI abo_lt 0,2 or less,

! The ro'tor o_1jet l_a_d(::(.ll_essis st:iii (.lol_i_at;ed by t,l_c statistics of tlac datasample, If tl_e statistical err(:)rbcwoll_(:!ssnlall, Lh(::syst(:unaCicerror becon_es d(:nninm_t,t- ] , I i i ,) _ I ' tics illcr(:!as(.:_ by a ['acLor of ['oltl'_ we l_lay be able l;o l:i_cl; I 1_¢__:,{(._¢:.,if the (.laLast,atws" "a sig_al of jet han(le(.ll_ess at the {'ew% level il_jets i_aZ tl decays,

Another way to get a large a,_alyzing power may be to make a new defi_ition of• _f2, 1_ th_s sense, more new tl_eorc,tical st,ucli(:_sfor,je_ l_andect_ess may help us to define

t2 a_(l I:o find a sig_ific:a_t sig_al of l_a_decl_(.!ss, Such Cl_e(.)ret,ical study is useful toutl(.l_:_rstandthe traxlsport, of t;la(2l_art,oll l)olarizat, io_l i_ ,ii:_t,sat_dwliat lial.)pe_s during

I,

t;l_ehadronizatAon 1)ro(.'.ess,

:l.C)(_

r

Appendix A

Polarization for Analyses

This study assllllted t,l_(:_silnl.)lc_stlilodel of decay (.)['a 1)arton, .A part(:)Ii (lec.aysinto two part, icles wllicll carry illt'orlrmt,ioll of llelic,ity of t,lle partoI_, Tllis model givesthe relations betweell f2s of quarks al_d aIlt,iquarl<s. Tllese relatiotls for eacll of tilehelic,ity-al_d chirality-basc:_d ai:alvses,. ,,,:re.,,., the l)olarizat;ion for each analysis,

1¢

Helicity-based analysis

A quark in d"c" --->qi] decays illto two pa,rticles witch momenta kl, k,_as shownin Figure A.I (a). f2h_,lis (.l(:{il_edas:

where [ is a u_liLvect,or of' a l)art,¢)llinolllellt, llrn, 'l"l_ecllarge colL]ugabe (C), l)arity (P)operat;ions mal<¢:_tl_is decay cllallg(_d t,o t;l_(:_sCat;(:_s(b) a_d (c) sl_owl_i_ Figure A,],respectively, Two successive Ol)eratio_l Ct 0 _nakes tl_(:_state (a) changed to the state(d), These four states giv_ t,l_-_tl_e relat;io_s:

Therefore, _2_,¢:¢del)e_ds o1_()1_13"helic,ity of a 1)m't,or_, t,l_e't_el_c:tt,y-bascd 1.)olarizatiol_'Ph_;tis given by'

P

p:=f,f

"Phcl :--- h= _,_, PE drh

_,=f,]h=R,L

107

E=

II.-'"""

................' '.,;v,', .'..',..,','"",,_,"'",'',', "ml_, ="=""'_'"'..........'_11_II1"......._..... " .....' .... ..v,ell' _'1"........ ,,_ll!lr=I1_I,,"I'r nli,l'qp'l_''"_"_ ..... _1.......ii_"",q,,ll!F_'" "'_t_''"'" " ""IF!r"_'..... '_" til,'_,S'ln"_'_'rl!,'_1''_lP,'_llV'"I'1,_''_.m_,''_, .....

Pola,rlz¢_tlon for Andyses Polarlza, tion for Ana, lyses

, k_ e+ E !

), Z 3, Z

Figure A,I' Decays of Imrtolls iii t;l_ellelicit;y-t_ased analysis,

Chirality-based analysis

/\ quarl_ in c+e '- -+ qi] d¢(a.vs illl_ot:wo positive alld llegat,ive charged particleswit:ii _nonmIlta lit- al_d tc_., reSl)ectively, as sl_ow_ i_ Figure e\,2 (a), f2Chiis defi_ed

{

aS', -, '-...,,

f2,._,i= i. (tc+ x tc-'_). (A,4) i

The C, P and CP operal;tons _nake tl_e stat;e (a) changed to t;he st;at;es (b), (c) and(d), respectively. These four st,at,es give t,l_ethe re lal;ions:

Polarization for Analyses Polarization for Analyses

. (a) i _ _ (b) ;[ __1' k+×k- _ [ k+ _,

y z y z

(c) '" (d) x

k+ × k- e+ / -.. e"

k- k+ k+ X k-

Figure A.2: Decays of partons ira tile chirality-based analysis,

fi,:hi(gTL) :- +flm, i(ql_) (A.5)

Therefore, gZd_idepends on not only helicity but also charge of a parton, the 'chirality-

based' polarization for fermion f, 79_i is given by:

sign {f2m_,i(f_'i_)g_cm(Ph)} cs[- v=S,i

,p<_ __ h=,,t,

p=I,i" hzR,L

=.¢

" f2chi depends on particle's cliarge, therefore, f2chiS for up-type and down-type quark

have opposite sign, If Figure A.2 shows the de_.cay of up-type quark, the decay of| ao,.._wno r,,_r'k is obtained by ,_l_l_,_t,it,_lt,ing k- -4 /,_ This _ives the following'_-_ _ _ '' _ _d ,I._ _ _1 ................. ..a.. - * ° _

!__,'

_'I 109,, , _M , ii,r_ ,' ,_' " ' III ,, _rllllllr_,,illt,, IGIII '111" "1 _r ' IIIWI '_ll'tl' _' . " IIIII II"llIHIIl_ _ i'lll!l[lU, 'I_ l]lpll[

Polarizer, ion for An_),lyses Pol_Lriz_),tionfbr Analyses

relations:

_i(d,_) = -_,_i_(_)

fich,i(J,¢) = +fl_hi(un). (A.7)

Thus, the chirality-based polariza.tioil for a sarrll._leis given by'

"r'_t,i= _ ,_'It_.i_',_i, (A,S)f ='u,d,s,c,,b

where, s/is sign of fermioll f. /?,/ is f'raction of .fr events in tlle sample.

!

v

110

_''l ...... H_ ...... II, ' IIhll',llll I ,i I.... i,ill lr ni' I1' r'lr"' Irl Irl I 111TI "1I_ I Illlrl' IIIlllIiIII'IIIlIIllll' ....... rl ,iI _........ I IIIq_llrrI1_'rll Illlllll _'_rll ' '11''l' III IIIrll i,, 11II I I]ll'l_l,' Irlllr'lll 'llll]ll_lllll III rTII'_l,lrt"rllp"lIIl','lr','"' ","',,,n' F, "

Appendix B

Detailed Helicity-based Analysis

For the 3-prong _-decays, the helicity-based analysis gave small analyzing powerwhich was consisCent with zero. Ill this ai)I)erldix, the reason for t,hat will 13(5investi-gated by comparing with l;he,modified helicity-based analysis.

The helicity-based f2 (2.26) is related to the modified heli('ity-based one (2.27),.¢

as follows:

' where/_a is tl_e mornenCuin of the unlike-_grl pion in the 3-charged pion system, i.e.,7r+ for a T- decay or Tr- for a v + decay, k,, is tim momentum of a pion selected frownthe two remaining same-ct_arge pions. Squared invariant masses sz and su are definedas (k_ + ka) '2 and (k2 + ka) 2, respect, ively. If sl is larger(smaller) than s;_, k_(._)is

used as ki. The relation B.1 means that the magnitude of _2_t is the same as that_of f2mod,hel, bu_; _heir signs are sometimes different. The difference depends on sl andsu. Therefore, ig is useful l;o investigate t,lle Dalitz plog for the 3-prcmg decays of r.Figure B.1 shows Ch(-_Dalitz plots for the sign-flip triplets with f21,,t= --_2_,_o_l.t,_andfor the no--flip ones with f2h_,t- f2,,,od.h_t.The two kinds of triplet, s are well separatedin t,t_eDalitz plot,.

The helicity-based analyzing power was calculated for _- decaying into sign-ttiI)and no-flip triplets separately in the same way as the g-leading-particle selectionmethod shown in Section 4.5 Figure B.2 shows '_, ]_.u handectness as a function ofcos 0 and 79. T (lecavii_g into the sign-fiiI) and t,he no-flip l;riplet_has dlff::_(:,__cdeI.)el_-denee on coso and 79, Therefore, the analyzing powers for Cimtwo kinds of _;riI)let;sare different. The dependence of,jet handedness for the sign-flip and no-flip _riplets

, gives the analyzing powers oi' -0.141 + 0.010 and 0.089 + 0.010, respectively, Due to' the opposite contributions from those two triplets, the helicity-based analysis gives

small magnitude of the analyzing power. This means that the helic,ity-based analyz-ing power depends on l;he regions in the Dalitz plot which contain selected triplets,

___

-_-

---_.__-

=

i,_,r_,,,,,ii,_,l,llr,_fl,,i,,fllrll,_[l[_ll(,ll!l,lllrll_lI ,11,,1111,[iI ....... rl!Imlllr".l"llt_II,,,r_l,l,ll,,",',ll_'l!lH_',' "_tlll'_l_':ni_,l_',,lll[_ "r'"' 'll"ll'll'"'l$"' '"_'111_""_'11"['III'''l''..... ,,,,_l"_'"'t,'_r III.... W i]ll,,,_ll,rq_[1,11,1_,,, li,l, ,. ,_1 ,IIRI 'llll,,ll,l,,"l[l[llt_lll¢ _', I"1[........ .I .......... _1_11........ ,t,,i, t'I_ll_..... iT

Deta, iled Helicity-b&_ect Ana,lysis Detailed Helicity-based Ana,lysis

sign(_h_l)=sign(_..,d,h_l) sign(_h_l)=-sign(_.,o,U._O"o'-"1.2 - :: 1,2 f::-

_'_ ' "::' : _ F '

1 - :i:i ¢ 1 .... :,. ..,, ....

........ _...._

_ - ''""":":": ':' c__ 0.8 i'. ::':',::t,:Zt, i:;::::':. ..................E

0.6 ; :i:iiii;;!_._ii_iiiiiii:!. :. : 0.6 -,._,.., ,: :, ::,,,..:...,,..... : .

0.4 :::::'""'':;;' 0.4 ;:-":""'"::'::""':_::"

0,2 - : i'::'!i:i : 0.2 :_, .'. :'..:",._°,"_=:',:',:::,_

0 LLL,J_±L_LLLLLL,._J__I_LL_. 0 :L.LH_L_._I"_"_",'LI_';._.:L_JJ.__LL0 0.25 0.5 0.75 1 1,25 0 0.25 0.5 0,75 1 1,25

ml32(GeV/c2) ml_2(GeV/c2)

Figure B,I' The Dalitz plots for tl_e sign-flil_ (right,) and no flip (left,) triplets, The size of a squareif proportional to the entry iri each region, The, sign-flip and no-flip t,riplets are well separated,

therefore, the invariant mass cut for tl_e triples is important.

To study such invariant mass cut dependence, tl_e following 6 irn,ariant masscuts are considered'

Cut A: No cut on invariant masses for 2-pion and 2-pion systerns,

Cut B: The cut used in the 3-particle selection method.

i,e. 0.62 < m_., rn_a < 0.92 OeV/c _ AND 0.86 < m_ < 1.66 GeV/c _,

Cut C: 0.62 < m_ < 0.92 OeV/c _ AND rn_.a < 0.62 OeV/c _ AND 0,86 < rn_._ <

1,66 OeV/c _OR,

rrh_ < 0.62 G__AND 0.62 < 'Ht_ < 0.92 OeV/c _ AND 0.86 < 'n_,_ < 1.66

OeV/c _,

Cut D: 0.62 < rrh_ < 0.92 GeV/c _ ANl3 0.62 GeV/c _ < rn_a ANl) 0.86 < 'm,_,_,_<

1..66 GeV/c uOil,

0.62 GeV/e _ < rrhu AND 0.62 < 'm,ua < 0.92 GeV/c :_AND 0,86 < rrt_ < 1.66

OeV/c

Cut E: Cut B AND sign(f_h.cl) = sig_(fZ,,o,Lh_:t) and

Detailed Helicity-based Analysis Detailed Helicity-based Analysis

* /

_'_ nsign(_hel)-_lg (,_'-_mod,hel)i -v 0,4 ............................

Pbeam= -0,63 Pbeam= +0,63J _ 0,3

I "c 0,20,1 -

' =_ o . -*---*--:'-----'--,,.............................. -----_----_- .....,., ....... _--O- -0--0 "-'®-0-0 1 -

I -0.2 -

] -0.3-0,4 !-......................l............. 1.....................l..............................................1.....................1....................[ ............... ,.

" - -0,5 0 3,5 1 -0,5 0 0,5

coso cosO

, s ign(f_hel)=-sign(g2mod,he]):zm 0,4 D{................................................................................................................Pbeam=-0'63 Pl,cam= +0,63 ..........................0,3

0.2

_:_- .......e" -_- e--'-e- .e.._o0,1

x o :!- ,i\::,-'"" ......................................- "......... • lr-:-".:O......-0,1 -e •,-)

-0.2 I-0,3

-0.4 ....... 1............_2 ......... L 1. 1 L_....-1 -0.5 0 0.5 -0.5 0 0.5 1

coso coso

Figure B,2: Del)endence of jet handedness on coso and 7) for the sign-flip and no-flip regions,

Detailed Helicity-based Ana.:ysis Detailed ttelicity-b_'ed Analysis

Helicity Mod. Helicity

° 0,,ii......................................i ....................................0.15 0,15 i_ •

i-.e o e o

o_ 0,1 • • 0,1 ___ •0,05 & 0,05

c i_< -0,15 <-0.15

-0.2 ....1 1___l.... /.......',......1........ 0.2 _I__L__L_A B C D E F A B C D E F

Cut Cut

[?igl.lt'e T3,3' Deprmd(,nce (0fthe m-lalyzing power on the in',,ariant mass cuts for 3-prong r decaysgenerated by the Monte .c.larh)simulation.

)=

Cut F: Cut B AND sign(_/,,,l) --- -sig_,(.Q,,,,,u,,l).

. . (_,ut t-lCalld Cut I!' are idc.llt:ica.1 xx,it.ll Cut 13, Cut, Ccn nl_illatic, n of Cut, CJ _-tlld @til; 13, "" '

C and Cut, I5' (Cut D ailcl Cut Ii!;)select, tril)let:s in similar regions izl tile 13a.lit,z plot:,

since sign,flip and llo-t]ip triplets nrc nlaillly loca,ted in t,lle areas deterlnilled by Clut,

C and Cut D, respectively,

The a1_alyzing power for tile llelicity-based analysis is ca lclllai.ed wit,li (-_ac,ll iil-

varia_.t mass cut. Figure B.3 sllows t,lle (.lepel_deilce of the anal3,zillg power on t,he

cuts, Averages of 'c}le analyzing powers for Cut C and Cut D, Cut E and Cut 17

are same as the analyzing power for Cut B, Tile figure also shows dependence of the

modified helicity-based analyzi_g powers on ;be invariant mass cuts for comparison,

The tl_-_licity-based ana.lyzilig l_m\.'ers for CuL C and Ct ll_ D, Cut t)3a]_d Cu(, t;' }_a.ve

opposite sigt_s and Cut, t_' gives largest n,l_al,'>,zitlgpower i_ t_ag_itu'.le,

The invaria_)t mass cuts were ai)plied for jets il_ tl_e data and tl_e (.lel)e_de_ce of

tl_e helicity and _r'odifie.d l_elicity-based al_alyzi_:{e;powers on tl)e (.:ul,s \v;_s i_lv(:_s/:igat:(,.d.

Figure B.4 shows tl_e de.pe_de_ce for tile t,l_ree samples, Ali o[' t.tle m_alyzi_lg powers

for tl_e t_eavy-flavor sample are co_sist,e_t, witl_ zero wicl_ i_ 1,5 co-,C)_ tile ot.l_er l_au_d,

some oi' tt_e analyzi_lg l.)ov',-q's f'or t,l_e ligl_t-flavor s;mll._le, esi)ecially witl_ Cut C _tnd

Cut, I'-', are away frown zero by '2 c_ or _ore. .[l_(>analyzi_g powers seems t.o l_ave

positive value.s for tl_e _nodifi_-_d helicil_y-l.msed mlalysis, However, sit,ce some results

are correlated with each oilier, il_ is _ot clear tl_at t,l_ese _o_>ze.ro ;u_alyzing powers

! !<!

g

'[17 ......... )_r rHrl ,"pill',irl ml I "'I, "lIP' J) rll rlll"l,,p_'_,r I_lllllpII'lip Imp",_ Illl,' II ' ' II_IIInH' ' 'H ,r, ro'II1 ''' IF lpr, ,,,, 'mlip " Irl 'lF,,l_t' UIIr' ii+lliii ,Ulr ..... I_l_'+l,_ _,qqr,rrlp,' ,Pt'l'l,lP lll_lit 'lllllI+lq_ _'''I'N[I q'lll'" Inl[I '[l'r liI1_' iii i,, _'_11_"'_'_.... 1111111',rl'+,_'l

' ° t , "_'Detmled Helicity-based Aria, l)sL Detailed .Helicity-b_ed Analysis.'

Global

0.1 _ 0.1

o 1 _ 01-_c:-02 ........1..........1.......ii...........I ......1.......J...........=_-02 l_..........1 .........1.........1......1..........1.......t ....< A B C D E F < A B C D E F

Cut Cut

Light Flavor02 .............................................................._ 02 ..........................................................

Helicity _ Mod. Helicity

_o°'': ++ o_°1 , + .+.+ _,0 " I [ ............................. _ 0 .................................,- # ='._ -0.1 :i , * '_ -0.1

_ _ 1...........1....................III 1 _ 02 ........1 .... l...........1..........[..........1...........1........." -0.2 ........................< A B C D E F < A B C D E F

Cut Cut

Heavy Flavor02 ........................................................................_ 0.2 ............................................................................

" Helicity _. Mod, Helicity

°01 _ _ 01

o ++ + oo 0 ....O........................... 0 ,e.....................E:Y)c-" c-

•_ -0.1--- [_-0.1...........L........1........l.............1............1............L............._ iL........1.........l...........1..........1..........1...........1= -02 " -02 ......

< A B C D E F < A B C D E FCut Cut

Figure B,4: De.pc.,ndc.:nc.eof the analyzing powc.:ron thc_,inx,ariant mass cuts for tam global, lighl,-,, and heavy-flavor samples, Ih.,,sultsfl'onl Ct.lt C alld CutoD (Cut E and Cut F) are not correlated,

Tho other results are correlatx;d with e,ach other,

115

Iq, lH '_1_ ......... ,' I[1 r' lp .'"h'llPPlllll'l'le'l"r'_l'fll IW If'lpllpl'Ull"qrltllr"l'"llll ..... Pltll..... le, 'lrlIII ..... lr,...... ,, ,irll"_,_,_,,.,.l!," ,_e ,,,,,,l_,',,','_r,' l_l'll,p'l,lpr]_ I, Ir,pllllll"

De_ailed Helicity-based An_dysi,s' Der;ailed Helicity-based Analysi,._'

_md tile tendency _u'e signific_u_l;,i

1!6

r ,, rllh..... ""' lilt' II"" ' ' i* ,,,Ill,ii........ r_ _l ......... rl ..... _,l ,, ..... II,IIIH .... r't" IF"n ' Ill'Ill ,t''' n'lllp""'_l,"' q"llr""'iihlllVl"l'l ,ntq,lll,, ...... II ',t,,l_ ,,irl_,,ll'l_r II'lit'li ,'11,1I1'_t_1IIIIr"t_'ln,_

M

Appendix C

Systematic Errors

As meill;ioned ill _(-!c,t,i(.)lld,8 ' "_' ,, We ('ol_sidered t,l_efollowing t,hree sou_c¢,s of svs-t_mnatic ro'rots,

1, Track and event selection

'. The crit,eria for track and event; selection are divided into two cat;egories whicllare concerned wit;h (let,ect,or acc(:;pCance and gransvers(:,, momentum, visible (:m-ergy, et;c, Therefore, we considered sa,nu)les v,,it;tlloose and t;ight; cuts for t;llese

" t;wo cat,egories of' t,ra(tl,:al_cl (:_vm_tselect,ion,

2, Jet tindingIn t;his st;udy, t;ll(-_P sctlela(_ (.)fthe ,JADE algorittlm was used as tlle ,jet,-filldiilg

] algorit, llm, 2'1_(._ss,st,c,_lllaCic(:_rrorr.lu¢:_t;o ,iet,-filldiIlg algont,hms' was also stud-led by usil_g PO, E alld E0 sc,hemc:!sI of tile `JA[)E algoritllln, DUR,HAM[37]

III

| and GENEVA[38] algoril;llms were also used, Y,_,t,values are suit,ably chosenI[ to produce sam(_ numl)(?_roff2-jet: events a.s P sclleme of clue JADE algorit:lllzl

rT_t (I q'_ ' _,_,d.S alS(.)wit,ii Y_,.,t_ 0,03, .La :, syst,elnatic error due t,o variation of Y¢,,ut.value , 'I estimated,

3. Analysisrn _ tmlalssls lnet;l_od may int;roduce bias in tile results To esflima,te tlm bias,exactly same a_als'sis was performed using the events genre'at;cd by the Monte

. ' ' "OI" ' ,, Monte Carlo smm_a,_._-_does nc)tCarlo simulation (tlm MC evenl;s) S_nce thet;at<ei_t,(.)a.ccou_t, jet; llm_de(:l_ess, tile, MC ¢:_v(:,.nt;ssl_ould give z(::roj(:_;t_al_d¢:_(.l-heSS. '-i?hcrefore_ th¢_diit'erenc.(:,bet;ween t;he r(:,,sult from these event,s and zr_ro

" is regarded as t,l_e syst;ematic bias due to t;l_e analysis _n(_tl_ocl, About; 2()01<of events ge,rmra,ted b_/_t:i_t_e(l,,[_"-_ET__:,.,.,_, 6 3 program[29] wit]_ the SLD (.l(:_/;r::c.t:or

_Ttm difference in the P, P0, E and E0 sch(.,,n_(._sof the JADE algorithm is tlm calculation ofinvariant mass, Yij (4,4), and rho mct]_odof combination(4,5) [42],

117

---

Sys_erna,tic Errors Systemat;ic Errors

simulation were us'ed in t;llesc:_st;udies, These simulat;k)_l, give t:t• • • s good desc,ript, ioll

of our measured lll('lusive tra(:k _tll(.le,,'el_t t;opology dist,ribul;iolts as SJloWllill:_' " " C,,1 shown CO1TII)_::LrlSOIISO[' t,heSe,ct;lOn4,3, As for the _2 iii t,he a_lalysen, _ lgure '

distribution for data t;o that. for t,he MC eve,nt,s tn whictl spin t;ransporl_ wasnot; simulated, For t;he lleltdt;y-btts(-;d analysis, distribut, ions of sign('/) c,os O)D,h_l

1

are shown for tlm t;hree samples, Those figures show only dtstrlbul;ton for, t;he3-1eadhlg-part, icle select;ion.metllocl, For l;l_eN-leadtng-part, icle and t;he part, icleselection nmt,hod based on raI.)idit,y and inon-m_ltum, difference begween dat;aand l_he MC ev(.:nl:swas not: fotll_d in S"2dtsl_ribut;ion, The dat,a and the MCevellts had also silllilar dist, ribul;iolls of ot;ller (lualll;it,ies, such as cllarged t,rack

mult;iplicil;y of a jet,, rapidit;y a_ld mulnverse rnomeIltum with respect to t;lle ,icl;axis as SllO\\'II in Figures 4,30, ,1,132mid ,11,33,Those quant, il;ies are i_nl._ortanl;because of the felttr;ion \vii;li N¢_,,,¢in t,lle N-leadh_g..parl;icle select_ion met,lmd,I_..,,.:,,, &'ft, gild Pmiu iii the parl;icle sele,cCion method based on raI)idit;y ancl trlo-menl;um, This means t;t_at,t,lie Monroe Carlo program can well simulated t;l_eSLD del;eel:or accept,anee and resolutions, 'Ylie b_as due to the analysis reel;hodwas esl;imat,ed by remo\'i_g sucl_ effects,

Event; samples used i_ t;l_e st;udy of t,hesS, st;emat;ic errors are sumlnarized in']7'a,ble C,,1,

'Fl_e analyzi_g l_Cm'(,rrr.i w_ls c_l_:_llal.eclt'(_' a sa_rll)le i, 'il'llr,ll tile fr)llrm,i_g ,,qua.l_t,ity L\c:t'was deii_cd,

_r:l! == _ _-'i(el:i --(t:"_td)2

F

Ns,,,u,te,_ (C, 1)1

FI'_ 1 i -1', i . e, (al (a2) i_l ._.a_e C,1, andwl_ere i runs ali smnples i_ sa _(:_sr_urce, 9, l'rom ) t(_)N.,..,.p¢_,sin t,b.e nu_l)er of sa_l.)les for same source, e,9, 2 for tile source due toac.cc_l_Cance,a,,t,,zis t:l_ea_als, zit_g l_ower c.alculal_ed \\,il;h l;l_e ,standard" criteria, Tl_e

sysl;emal;ic error Aa>v,, for eacl_ source is defi_md as:

- (<;,u)where Ac_.,,at is t,i_esl;at:lst.eal tluct._lal.ion of t,he tu_alyzi_g l_(.)w_._r,If Aet, is s_naller

t,l_at:&a.,t_,t, t,hesS, st,e_lat;ic (error is tleglected, ()t;lxerwiso, :k&r_,,>,:is regarded as t;liesystemal;ic error, ,.

The syst;ematie error (C,2) was calc.ula.l;ed for eaoll sourc,e except: for t,l_e biasdue t,o the m_alysis _.?,tl_ods, 1..lsi_g t,lle fact t;llat; t,l_e a_alyzi_g power for t,l_eMCev(:,lts should be zero, t:l_esl_il't,of t,l_eallalyzi_g power t'ro_r__,ero gives t,l_ebi_ts of (:_t(.'.l_analysis reel;hod inclu(.li_lgst,_.rtist,ical tluct,uat,io_, l{,er_ovil_gt,l_estat, ist,ical t:l_lcttlat;io_by si_nilar way as (C,2), tl_e bias i_l(,:ludi_lgsigl_ was det,ermilled,

:'TIw st(mdavd criteria Im!I/_s tire (.:rit(.:rl_ doscrlbo(l lit Sectlo_ d,3,

118

........ ,r,,,'_l'r....... ,,,I .... ii,i,,_,v,lll,,,,r,,, !IiiI ........ ,,,............ I],, ,II ..... ,'"'I_'",1..... Pl..........rr"',,'l,'l,..... '" '_,'............. '"' " '"1'1'_'",",1,"'",,rlllH'_,,_'_lr'_lrg""l_l'_....... II_I_....

' ,E_ro_s Syst;ern a,tlc ErrorsSysl;ema_c .," "

Sourcc_ Sanlple # I @ritc_rlaTrack and event se,lect,ion

(_:1.) Loose : no cut on cosO.,_.,kAccel._tmlce. and [cos 0th,,..st < 0,8, '

(a,2) Tight; ' cos0t,r.,,k < 0.75and [cos Oth,,,,._< 0,05,

(i.,1) [._oose: ilo c,ut, ol_Pr.,'ro,Pr, 'ro, zo Zo ttlld _' ,'O't8 '

and Evi._ (b2) Tigllt; : Pt > 0,3 GeV/c, ro < 2,5 crn,zo< 50cmand r.' , Ev,i._> 30 GeV,

Jet; finclillg

. (cl) ' P schelne, wit,li Y,,.t.= 0,0235(c2) E scheme witll Y,,_,t= 0,054

Algorit;llnl ((.'.3) E0 scl_eme wit,h y,,ut = 0,0305_"-_d-_ DUIt.HAM v¢itJ_Yct,t -- 0,008.... (c5) :- GENEVA wi_h _,1_,_,_= 0,O38

(dl) y_..,,t= 0,028Y'J'_'_ _-- :l./,_..t,= C),032

i -i_ .iAnalysis

Met;hod ((:}) I 200I'( ev(:!llt,s generat;edby t;he Molll;e Carlo sirnulat;ioIl

Table C,,1: 'rho sources o[' Lho syst;crna,{Ac on'ors alKl atm_plc, s for cho ostJmaCo of rho systematicOI'POPS,

119

l_i_ ,',I,I_' ,llllml H,,, ' ' _'llV, l_iSi""" ',I'_' '_ lll_, _ ir_'i,' "_Ir"UiV"' _i[,i' II '' ". 'i""' Iii ' ' ' lit' '_'

Sys_em_ttc Errors S,y's_ematJc Errors

The toUal systematic ro'rot was (.',alcula_d as a quadratic sum of tll_ ,s'ystc_math.',errors frotn ali sourer-is, Due i_otllt_bias from the analysis mot,hod, the tot,al systematic iii

errors may not have same magnittid_ il_ positive and negative signs,",' '

The systematic orrors for the-;t,hre_c_-leading-particle sele,ction me_thod arc:_sum-.martzed in TablcJ C,2, The results shows tile systc-mlatic errors are liegltgtble or quite,

F I i tsrnall, .Phts lll.(J{l,ihSl;ha, t uho mefiliod does l_ot give4biases to the analyzing power,

Figure C,2 shows the sysi_ematic errors from each sourcc_shown in Table C,1 forthe N-lcJading-parttcle selection mot,llod,

The systematic ClIOlS4.... frOlll each sotlrcu for the particle selection method basedon rapidity and molrlelltum arc: sllown iii Figure, (3,3, C,4 all(.t C,5 for the global, lightflavor and heavy tlavor saIriples, respectively,

ii

120

,,r , nv ,"Irl,...... lit " '_iI, "_*....Jill"Ill'" I11Illi"'"m" ,,l_li" ,,_,",",'"1111,,,,pi_Irli,lllr,_l'ii irl ..... _G,I,,,_',,_IIilm, iI , ,lll,_rilil_',"IIIl'll'"'r'_l'i'l' '_

System'a_ic Errors Systemat, ic F,rrors

SoUrce Sample Analysis I Global Ligl{t] HeavyTrack and event scdec,t,io_l

Helicity ,-,.,0 _ 0 I _ 0acceptallce (a) Modified helicity _ 0 _ 0 I _ 0

Chirality _ 0 _ 0 I _ 0

I-Ielicit$ N 0 _ 0 ] _ 0lnolrt(:',I1l;_, (:;t;c, (b) l_4odlli(,;dlmlicib' _ 0 ,'_ 0 I ,",,0

Cl_iralib, _.,0 ,---,0 I _ 0Helicity _ 0 ' ,.i0 _-,0

subtot, al Modified he.licity _ 0 _ C) I _ C)Chlral_ty _ C) ,-.,C) I ,--,0

Jet tlndillg...... Helicity ,-.,0 ,--,0 ,.o O-

" Algoritllrn (c) Modified helicity _ 0 ..o 0 _ 0Cllirality ,-_0 _ 0 _ 0....

" Helicity _ 0 ,-,_0 ,,o 0Y,,..t,(d) Modified he,licity ,-.,0 _ 0 _ 0

Cl_iralit;y ,-,-,0 _ 0 _ 0

I-Ielicity ,-.,0 --, 0 ,-, 0subgot;al modified helicity _-,0 _-.,0 ,--,0

Chirality _ 0 ,-,.,0 ,--,0

AnalysisHelicity _ 0 ,.G() -J-0,001

Mc-_t;hod(e) Modified hdicity ,',.,C) _ 0 _ 0Chirality -0,003 _ 0 _ 0

, ,

Helicity 0 _ C) +o,oo_-0,000

total Modified helicity _ 0 _-,0 _ 0C 11n'_.tli ty +0,o0o-o,ooa ,--,0 _ 0

' Table C.21 Tlm syst,omat;lcorrors for t.ho3-1oadlng-parttclesdectton method. The subtot_aliscalculal;odas a quadrai;i(tsunl Of ali sources in Same category, Tho Coralsyst.emat.lc,error ts aquadratic sum of ali sources,

1.21

f

=

l,I.... elnl nllrn li ,irl....... . ........... i]lll.... ' I$1n' _lrl'"'**'...... "' ppn=nn,,¢ _ ii ...... r, ...... le ..... Irpq " ,vii ,I,II,nll ...... I"ll .... lHr'ii" 'lllI"'," , .......... n"lil ' ' " .... II'PlIIp_nl'n'"11"'_[

S ys tem a,t,ic En'oJ's ,S'v,s't:_,m a t;ic_l.;',,j,,_,,_, I

,f

Globalo4 "1500 ...............................q 14elicity Mod, Helicity Chirality0 _ _ gl

_1000 ,i,__,i, ,s"_,, ,,q,.

500 - j l'1 ]'l,I j,l' LI ,i,1I l'Lkt'_t_km .... j/#,tJ , 1 1........ 1........,;b-..L..............0 ............................................ , ..........................

-0,4 ,.0,2 O, 0,2 -0,4 -0,2 O, 0,2 -0,4 -0,2 O, 0,2 0,4

sign(Po.oosO)D.hom sign(Po.oOS0)-Qmod,hoI -.C_ohi

Light Flavor i

o 900 ..................................................................................................................Helicity Mod, Helicity Chirali[y ' ........ ,/(-5

"_ 600.... _"_ ,i,/"4_ . ...... .',','1 "/'c.. ) [!

,tj/,I l't'l,t 1,I'r l'lt, j,i'i0 'i'lLU 300

4 _ii,

,' "t, _,.tj' .I '"d........... ' ''#:._A4..... t...... "_q_ _P:.... 1..°d,4-0,2 0, 0,2 -0,4 -0.2 0 0,2 -0,4 -0,2 0, 02 0,4

slgn(Po-c°sO)_2hol slgn(Po.cosO)_'_mod.hol _;]chi

Heavy Flavor

I.......... c-iioi(y............................................................................................................o

"_ 600....... t/

LU ," L ", _,, " , i

3001 I,_ k ' "l,l,,_" ':' "_' : z _'L, ........... ..t.,,2.)''.... r'

- ,4 -0,2 o, 0,2 -0,4 -0,2 0, 0,2 -0,'I -0,2 0, 0,2 0,4

slg n(P_,.c°sO)_;-_lml sign(Po.cosO)f_mod,hel _cht

I;'igure CJ,I' Comparisonot' __disLril.;ul,io_lst'or (lata to LhaL[w' l,lu: MC ovents, St_o_nm'e(lal,a(puls symbols whoso vertical lines shiny their sl,_tlsl;lcal errors) and tl-m Monlx_C',arl_)(histograms),

ii,

i

:122

p_# ,, . ' "qqr '"'II' 'liP" IF, ' IP mP' "'" "II_ .... rp" H'rll " II"' ,ii,iH,, ,llVW _r,,, ,,, .i,iii. rlll, '+'"'Irl'' .... uP 'IIP_ _Ifi_' Prllll31111'll l_llIlll" " IP'r' 'II 'II+t_' '

,, Systematic Errors Systematic Errors

Global

-Hel!city (Avg) Hel!city ,(Max) Chii'alityi(Avg) Chii'ality::(Max)o.2 ........:.......,,.......:................................... _...... i.......................... i................

+'_ -- : [ : i j_

A:ascl : Aasel A0_scl AhsclA'ctlet ! ' hiT.ici Ag.jet ' A'..ajel

_-0.2 w A'g'aliftl:..... I &cdmal ........... I &o,:tinal -w A_.qnal ........<_ :.........l.............l..............l............................................1................J..........].............1......... 1...................L........

6 10 14 18 6 10 14 18 6 10 14 18 6 10 14 18aLead

Light Flavor"_ -Hef!city (Avg)` Helicity ,(Max) Chiralityi (Avg) Chii'ality!(Ma x)

o.2 - ..................................._.............................::.......;.......................!....................._ : ;

+-_ - A:asel a'ascl A:ascl ' A:asel '...... A'o_jct :. A_let . : @jet i ': Abqet '_'-0.2 -mA'aa_t_l.............. o_xo:_in_]................ ,, _.an_] .............. X '_xa_inai

" <_ :_........l...............1....................I........................................1.........1............1...................l....................l..........6 0 14 '18 6 10 14 18 6 10 14 18 6 10 14 18

NLead

--Hel!city :Avg) Hel!city (Ma_) Chimlityi(Avg) Chii'ality::(Max)........ 1......... , ....... ,....... , ....... t........ '........ . .... , ............. ,...... ,.............

¢0,2 ..... :................ : ,. : :

-- , , . ,,

+'6 - A:ascl A_sel A:o_scl Ao_scl :.... _0_jct :: A:ajct ! • _jct .: A_jct i

¢'0.2 -11' A'Gh'ri'M................... !1'_Gd flil]........ : ...... II1'A0:dflhl............... '1lD"Al_ifiiii: .............-1.......]........................1...............1........................1......................1..................1.....................]..............I...........I...........

6 0 14 18 6 10 14 8 6 10 14 18 6 10 14 18NLead

• Figure C.2: The systematic orrol's fl.'Olllthe sources for tlm N-particle-selection method. The lightand dark hatched areas show the ss,stcmatic errors from track and event selection and jet finding,respectively. The black area, shows the systematic error ft'ore the analysis method.

ii

:-_ ].23

_

_1,1 'llII, ,,, .... '_ ..... ""rOI'"llll_ "'l,Hlll]l'lflll I_1] ' _r II ' 'l_l'_Olr 'llrlI' " q'IIl_lW'' ,_,.,,_r_ i,i,, rllfj_i_irllll , Ull,,'lll _1_1"_1"

Systernutic Errors Systern<_tic Errors

n =2, An = 1................ max, ........................................ .-........................

"_ - 'l-Ielicity (A.'.vg) .Helicity (Max) ;Chirality (Avg). 'Chirality (Max)

0.2 .................................................,-:.............. .................."-<v i i_ i :;:i=, :: _/_ii:;_'_'=:{_:i!i_/ ' _::::'i ..... :i.:i : : .... :iI ,, .;_i.... :i ,: " ':

e- o _2_:...............i:;,....4.... !:................,i.....,:.....-_.......... "i"......._.........._:/....i_:....I - Aasel ::"._}: Aasol : ::: Aasol % 7 ::. ' Aasel :_:.:,:!i_::L

- Aaict i ::): "....A_jct L::(.' ' Aotjet . ii_7;r::{...:_<"-0.2<,' -i-!.....AaifiiMAajet..... ::.. .... :....il"Adifn_il .... : ........... i'A_ifdal i: - ............ ;m'A_ififfil< --L..L_i___I._X._..L_..L_I.... ,.h..l___l.._J_..1.....1.__._1......1.......]__.I__I__.L_A_..L_._J...............I..._I_..]._._L__L....__.t.........

0 2,5 0 2.5 0 2.5 0 2.5Pmln(GeV/c)

ninax =3, An = 1- ..Helicity(A_,g) :Helicity (Max) 'Chirality (A(,g) _ _Chirality(Max)7-

0.2 .................................. '.......................... !............... ...................

; ; L

<e- 0 .,:;): _ ............--:........... L_:: i......... ,. .................. -.........................Aasel , Ag.sol ' Aascl Aascl _Aqjct ' Artier : ". Aaiet '; Aajci ........ :_::

-0,2 -m 'A6m'nal ....m Adanal ....[] Adi_iuil...... li Ammal : ....... : "__'__...,.._..,._,__.,_._.,:.:.:.............L.l.___L_X_.._l._.i:i!iLLLi..... "< .-__L__L_J___J--_L.._J.--I..-.I.........[_..i__..!....l_.l._.J__L..-i..... .....

0 2.5 0 2,5 0 2,5 0 2.5Pmin(GeV/c)

n = 3, An = 2................... max.................................................................................

- '.Helicity (Avg) !Helicity (Max) Ehirality (Avg) :Chirality (Max)0.2 _ : : : .... ;

1.._, - : ; '

<" Actsol Aasol Aotsol . Ac_scl

'_ - " Aajct ..... ;:......... : dczjct .... Aajct " ' _ Aajct . :::...._- O.2 -- i Aa iiiial --li Ao.iiiiiii ................... ii Aiaifli_il:: " ........ i Ao.atial< 27_.L_L_i.___L._I._.._I......L__i...........I__..L._.a_../.__1........1__1...... L_t__.i._._.l....1_._i._...1_}.............L._.l....h_..l.....l....1.....i......

0 2.5 0 2.5 0 2.5 0 2.5Pmin(GeV/c)

Figure C.3' Tile systomaLic ol'rors fronl i;ho 8ourcos for t,ho particle selection mot, hod based on t,

rapiclit;y and momerlt,ulll for the global sample.. Tlm light and dark halM_ed a,reas show the systoln-

aLic errors from track and event, seh.,.cdonand .jet finding, respect,ively. The black area shows t,hesystematic error from the analysis met:hod.

m

124t

.... IIII '""' ,I ,,, u, rr ' ,, ' ,', .... _1....... illll ..... ri ...... ,r ,, ............ i,v,, , <n,, 11,111,,,,,,' ,'v , _,1,r , ,,Ill ! tI ...... mllll'q" I,_ ,,....... q_IIII,W , llll,,ll, ,u ;1' Iii II1'11,iii ,,, Illlll'"ii, '11',,, ...... II1_1

Systematic En'ors Systematic Errors

M

nm_ = 2, An = 1-- iHelicity (Ayg) iHelicity (Max) :Chirality (Avg) :Chirality (Max)

_" 0.2,7-i .......... ................... _,........................... i ............... :: .......................... ......... .- ' : .... {i:::::%:- : :!i!!i:i:::!:: i •_:i!ii:'i%>. : "!: .:%:. ' :.

8_ 0-:: ..............::!::)..:!)....... :'

% '!.... _aa_ee_ ::J! .... --7'.::.' Aasel i.............Acqct :::" ::"! ...... [I ',!_" ::'/:'ActJclAascl"....... ;_:::............\ ]!/ [-7" Acxsel[ '' "': Ac_Jcl............ \_\i \ ...."// ......_%0.2 -ira 'Ac_ifrigd..... :............ [] Ad,uial....... ....... l-i Ao.adnl 'V ..... l--w Aczanal ' 'V .......

< :_L._,__LL_*__I_A._*.......L.,___,_._I_J..........j__LI_J__LI__L_s_I_L_t_L._L_t___,_._.I_,._L_0 2.5 0 2.5 0 2.5 0 2.5

Pmin(GeV/c)n =3, An=l

.............................................................. max, ................. 2

"_ --._!elici[y..!A.::Vg)..[.._.,7!e.l.i.ci,y..!m,ax!!...f._iChi.r.a')ty.(Avg!t.-Chi.ra"'Y.!Max!....

g0.2

. o:........."i>:: .........t......:"',: ....[-i .......:.....I I-': .... ".........- ' Ao_sel ! ....• ' kossel ! . / ' kc_sel B' / Aczsel ii'

_g-0.2 - : A_jet i 7 '. Ac_jct i | '.: Aajet \ :l / :. A_Jet \ f--I k0.ffrihl ............ ....... [] AAhfi,'il .... : ..... : fill "k'0.fffial' \ /"" [--II 'AEa'fial ' ' \ .... /" < - I ...._..__.____........_.......,.........l.___J_.__,.__a.....L._.I_.J.._.t__L_L__.__,__,....,....____L._I__L__L__L__'.....____<.L..,_

0 2,5 0 2,5 0 2.5 0 2,5Pmin(GeV/c)

n =3, An=2............... .max

- J-Ielicity (A_vg) iHelicity (Max) ,Chirality (Avg): Chirality (Max)_0.2 .....! ................................! ......................... '-? .................::::: ......-!,'................ :: ....

<+ -7:, . ,

_- 0 ..................... :.................. ' ........................... ;..............................................

.._ - Aa,sel : kctscl Aascl , : .: Actscl.... Acqet ' A_jet .... :::: ... : Aajet ,.ii: :(. ::.._<"-0.2 --B-;':::+A12lfiitdkczjet................... m ko_amil ............... ---I AeZilii,il .... m k_iln£11 '

<1 ,,__'___.,___,_._,___,...._.'_...,.....,............I..._____l_..l_.__...........,__l..........._I.._LJ._.._.....,__L.,.__..........l_..L_.,._.l ____.1...,....._._0 2,5 0 2.5 0 2.5 0 2,5

Prnin(GeV/c)

Figure C.4' The systematic e,rrors ft'ore the sources for the particle selection method based on" raI:,idity and moment,urn for the light, flavor sample. The light and dark hat,chcd areas show the

systematic errors from t,rack and event select,ion and .jet finding, respect;ively. The black area showst,he systematic error from Lhcanalysis met;hod.

Ii

125

'a"q,',,'t!q'" till " ,q...... q'_rwpre,.......... I_1....... I'1_II, ,I',' '_I,_',"IPq',_" "tel'e,'. " ''lP1 _' "_pl_,) ' ,,'1', .r, llt,l_lq'q'll...... 1,1,,_ _,",_p..... "'PI_I_"'qtlv'l[ll'"'"'_,"'"_"'"'"'""""lll"_,'_'_t'm'lllt_'r"lr'II_"']II'_"'"""_"IPP' _ll'rl_l e 'IFP' " "'" pv_r'll.,'_..,'l_"_. _' _qn"'. till "'1', r,l,l_'r _l,ll:

, ii,, ,

Systematic Errors Syst.,ma, tlc Errors

n =2, An = 1-a ....... maz,.5 - 'I-Ielicity (A_g) , ']-Ielicity (Max,) ',Chirality (Avg) :Chirality (Max)0,2 -"...............:L ......'+..............":.:......--.............."i........+---;.............'.'......

.<_ -;

+ -,_- 0 _...................................................................................................

A_scl Ao'.sel Ao_scl Ao_scl.... :":Ac_jet Au,Icl ' Armlet ': Ac_let

' _"-0,2 -.m.A.aa.ria].....: ....... [] Aci.'hnlil ....... lm AlT.ifnal........ il Ag.'iffiSI .......<_ L_LJ+__LL_L.]........i.........l t......L__I.........i.......L.+.I.._..L_L.L.......i......... J___h_._t..._L_i............i ......

0 2,5 0 2,5 0 2,5 0 2.5Pmin(GeV/c)

rlma× = 3, An = 1- t-telicity (Ayg) {Helicity(Max) ,Chirality (Avg) ':Chirality (Max)

C 0.2 -! ................ :........ : ....................................................."_ -- , : ', ,

_+ ;--i,,ii:i:i:i+_'_soi..............i Aa,_o,i ' Aasoi;: ' _a,+oi"m -'.:.Aqjet !\ '. Ac,.ict :\ '. Ao+jet . . l A_]et '

_:5m-0,2--m+Aah_ial.....:--I r-i Adilmil.... i- I _A_/+tial + :., : :l--w'Adn_fd + . " :< -LL.,___.L_L.u..... A_.l+..._,__,l_.,._..]._,.... L..__IL_L.I.L:L_........I_.__LL.,_++..L_.,__:LL...... "0 2.5 0 2,5 0 2,5 0 2,5

Pmin(GeV/c)n =3, An=2121_IX.....................................................................................................................

_0,2_ -',-':Helicity...............(Avg):...... I_ !:l-Iel{ci!y (Max.! ......._Gl!i.ra}}}.y..!Av.g).. ........iCh.i.rslity. (MAX)...

,, . :," ".. . ... '/o_,...............................................................I A<,+, ......................'........

':_ - i Aajct _ / , A%.'t :_ ' Aalet ' Aajet_"3%0.2 -if Aaanal • ,- _ l-i Adalml , ....... [] A_arial ........... ii Afxhnal '

<_ _-'+.+.L_J___L_I._..L.__J__.L.__.._,I...I. t...i.i, i. l+...i.... _.]_t.__L_L..i_...L_i.............J._._t_.._.L_i_..i_,..l.._a.........0 2.5 0 2,5 0 2,5 0 2.5

Pmin(GeV/c)

Figure C,5: The systematic, errors I'rotrt the sources for the particle selection methocl based onrapiclity and momentum for the heavy flavor sample, The light ancl dark hatched areas show tlm "systematic errors from track and evont:seh.w.tionand jet; fincling, respec,tively, The blacl< area showsthe systematic error from the analysis rnetl_od,

lD

Appendix D

The SLD Collaboration

K, Abe 29, I. Abt 14, C. J, Alto 26, T, Akagi 2r, N, J, Allen 2r, W, W, Ash 2r, D, Aston 2r,I(, G. Baird 24, C, Baltay aa, H, R, Band a2, M. B. Barakat aa, C, Baranko 1°,

O, Bardon _6, T. Barklow 27, A, O, Bazarko 11, R, Ben-David aa, A. C, Benvenuti 2,T, Bienz 27, C, M, Bilei 2=, D. Bisdlo 21, C. Blaylock r, J, R, Eogart 2r, T. Bolton u,

" C, 12,,Bower 2r, J, E, Brau _°, M, Breidenbach 2w,W, M. Bugg =s, D, Burke 'at,T, H, Btlrllel; 31 , P, N, 13urrow,.sl(_,W, Busza 16, A, Ca lcaterra la, D, O, Caldwell 6,

'q }D, Calloway 2r, B. Camanzi 1=,M, Carpinelli ua, R. Cassel 2r, R, Castalch "aA, Castro 21, M. Cavalli-Sforza r, E, Church al , H. O, Cohn 2a, J, A, Coller a,

V, Cook al, R, Cotton 4, t-l,,F, Cowan 16' D, @. Coyne 7, A, D'Oliveira a,C, J. S. Darnerell 2s, M, Daoudi ur, 12..De Sangro la, P, De Simone la, R. Dell'Orso 2a,M. Dima _, P, Y. C, Du _'a,R, Dubois 2r, B, I, Eisenstein t4, R, Ella zt, D, Falciai 22,

C, Fan 1°, M, J, Fero 16, R. Frey 2° t<, Furuno u° T, Gillman 2'5,C Cladding 1'1S, Oonzalez 1_, O, D, I--Iallewell2r, E, L, Hart us, Y, Hasegawa 2'a, S, Hedges 'l,

S, S. Hertzbach lw, M, D, Hildreth 2w,J, Huber u°, M, E, Huffe?r, E. W, Hughes 2r,H. Hwang 2°, Y, Iwasaki 29, D, J, Jackson us, P. Jacques _4, J. Jaros 2r, A, S. Johnson a,

J. R., Johnson a2, lR.,A, Johnson 8, T, Junl<2r, R, I(ajikawa) l), M, Kalelkar u4,I, Karliner 14, H, I(awahara 2r, H, W. I(.endall 1_,Y, Kim u6, M. E, King 2r, R, King 2r,

R. R, Kofler lr, N, M. Krishna 1°, R. S, Kroeger la, J. F. Labs 2r, M. Langston 2°,A. Lath la, J. A. Lauber 1°, D, W. G. Leith ur, X, Liu r, M, Loreti _, A, Lu _,

_ '22H. L. Lynch _w J. Ma_ G, Mancinelh , S. Manly _, G. Mantovani _,' ' ' T, Maruyama 27, l_. Massetti 2_, H. Masuda 27, E. Mazzucato _2,• T.W. Markmw_cz 2r,

A, K. McKemey 4, B. T. Meadows _, R, Messner 2z, P. M, Mockett a_, K, C. Moffeit 27,B, Mours 27, G. M_ller 27, D. Muller 27, T. Nagamine 29, U, Nauenberg _°, H. Neal 2z,

' M, Nussbaurn s, Y, Ohnishi l'a, L. S, Osborne _6, R, S, Panvini a°, H, Pa,rk 2°,T. J, Pavel 2r, I. Peruzzi _a, M, Piccolo _a, L. Piemontese _, E, Pieroni =a, K. T, Pitts 2°,

R. J. Plano _4, R. Prepost au, C, Y, Prescott 27, C, D, Punkar 2r, J, Quigley _,B. N. Ratcliff _r, T, W, Reeves a°, P, E, Rensing 2r, L, S. Rochest, er 2w,

1.27

ill;,. ,t,l,al_,,Ntilitt.... ,. ,t i,I _ .... III' . ' 'I_I, ,, .... ' "?ll'rl'__"II*' _llt 't'Iflrl...... ill I[, aPl...... II'l' '_'¢,llr?il_tit, ,,llvlt,llll, " l_..... 111'IrlIl Ip]l'' ,t_ ,il1,t .,i, "I_III ' ""'"' ""_itl_l .... r, ' " ,, ", =,',,,',,_,=tl,_r,',r',,,",r,,_t""ll_'_lli t, .... ,,," ..... _,,_

The SLD Colh._bortl,t:ion The SLD Colhl,bo.vtl,tion

J, E, Rothberg al, P, C, l-h:)\vs()l_II , J, J, R,ussel_7, O, H, Saxton _7, T, Schalk 7,R, H, Schindler 27, U, Schne(_klotA_l¢_,B, A. Schumm 1_, A, Seidm_7, S, Sen aa,

V. V, Serbo z2, M, H, Shaevit;z lI , J. T, Shank a, G, Shapiro Is, S, L, Shapiro r/,D. J, Sherden 27, C, Simopoulos uT,N, B. Sinev u°, S, R,. SmitlY, J, A, Snyder aa,P. Starner 24, H. Steiner is, R.. St:¢:i_(:_P,M, (24.Sti'auss 17, D, StY, F, Suekane u_,

A, Sugiyam_( 1'_,S, Suzukil"_ M. SwarCz_7, A. Szurnilo al , T, Takallaslli uT,F, E, TayloP _, E, Torrenee la, J, D. Turka a,, T. UsheY, J. Va'vra uT,C, Vannini ua,

E. Vella 27, J. P. Venuti a°, 1:I,.Verdict _°, P. @, Verdini _a, S. 1:1.,Wagner uz,A, P. Waite 27, S, J, Watts 4, A, W, \¥eidemanl_ 2s, E, R. Weiss al, J, S, Whitaker a,

S, L. White us, F. J. Wickens 2s, D, A, Williams 7, D. C. Williams la, S, H. Williams uz,S, Willocq aa, R, J. \¥ilson !_,W. J, \,Visniewski s, M. Woods 2_, G, B, \¥0rd 2'1,J, Wyss _1, R, K Yan iamoCo1_,J, M. Yarna.rt;ino 1_,X. Yang u°, S, J, Yellin6_

C. C. Young 27, H. Yuta u!_,61, Zal)a, lac au, T. \_. Zdarko ur, C, Zeitlin u°, Z, Zhang 1¢_a_d J, Zhou :_°

Adelphi Universit;y, Garden City, New York 11.530INFN Sezione eli Bologna, !-d0126 Bologna, Italy

a Boston Univ(;rsity, Boston, Massachusetts 022154 Brunei Universit, y, Uxbridge, Middlesex, UB8 3PH, United Kingdom

_ Califon_ia Institut_.'. of '.[i_ch_ology, Pasadena, California 911256 University c)fCalifor_ia at. S_:_I;aBarbara, Santa Barbara, California 93106

z University of California at Santa Curz, Santa Curz, California 95064s U_iverslty or Ci_('i_at, i, C,i_cinnagi, Ohio 45221

9 Colorado St,ate Ul_iversity, Fort Collins, Colorado 8052310 University of Colorado, Boulder, Colorado 80309_ Columbia, I_.l_iv(.:rsib,, New York, New York 10027

•1_INFN Sezione cii Ferrara and Universith di Ferrara, 1-44100 Ferrara, Italy•_3INFN Lab, Na.zionali di Frascati, 1-00044 Frascati, Italy

_4Universit:y of Illinois, Urbana, Illinois 61801_"_Lawrence Berkeley Labora¢ory, University of California, Berkeley, Clifornia 94720

_ Massachusetts Ins¢iI;ut;e of Tecl_nology, Cambridge, Massachusetts 02139_r University of Massachusetts, Amherst, Massachusetts 01003

_s U_iversity of Mississippi, University, Mississippi 38677_9 Nagoya g_i\,'_:_rsit,y, Chikusa-ku, Nagoya 464 Japan

uo Universit;y of Oregon, Eugene, Oregon 97403 b

u_ INFN Sezio_e di Padova al_d t I_ivm'sith cii Padow:t, 1-35100 Padova, Italyu2 INFN Sezione cii Perugia alld Universitt_ cti Perugia, I-.06100 Perugia, Italy

2a INFN Sezione di Pisa a_(l Universith cii Pisa, 1-56100 Pisa, It;ab,24 1-_,utgersUxliv<:rsity, l:'iscataway, New Jersey 08855

2"_I_,utherford Appleton Laborat;orS', Cliilton, Didcot, Oxon OXll 0QX UnitedKitlgdom

_'! i28

The SLD Col.h_bor_tion The SLD Collaboration

_a Sogang l.lniw_rsib,, Seoul, Korea27 Stanford Linear Accelerator Center, Stanford University, Stanford, California.[..

94309

_s University of.Tennessee, Knoxville, Tennessee 37996, _ Tohoku University, Sendai 980 Japan

ao Vanderbilt University, Nashville, Tenn_;ss(:,e37235al Universit;y of Washington, Seattle, Washington 98195a2 University of Wisconsin, Madisoll, Wisconsin 53706

aa Yale University, New Havell, Con_eeticut 06511

io N

..... irl...rl ....... i, 'INInII"III_I'I'It....... ' ,IP_ql"nill_,'ll r ......... ,, ,'rl,l,I....... ,,,r,,,,q.li!l_n_nl,,,,n,,,nr.,,,,,,,II..,W,.,I_H._I.... i,p,,,'_,n',lgqlr'"rr'llll_[i_n",,'l,"_,npln,,,_,_n','_,',','_,p,n,_,qnlm,.....,_p,n..... Iglmlqlrnr_'ur""'_lrlIl'i_,'"rn'pn.......,vlr,upllln"_[nl'n"n'_q_'.",lIl'_nq_'II_"n_ll_'lrnir_,_p"n'plll'niipl,',-,

The SLD Collaboration The SLD Collabor_z,tion

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Z' r r ( ,purer Ph,y_ic_ Comm'anieations, 13:307--37,) 1{)80

[30] S, ,ladac{l, B, [;', L, Ward, a,,d Z, VV,;Ls','1'110b/Io,,i:eCarlo program I(OI_,ALZ, ver-sioll 3,8, rot t,ll(:,,l(:+l.)t,(.)llor (:lll_:_rl,:pair l)rocl_lct:ioll_ltI.,EP/SLC e,nergies, G'omp'ltt,(.,rPhyxlc,_ G'om'ul,'_utricatio'n.,s_(.,( ,..7(_-..292]gf)I

[81] 13,F', I..,,Ward e,t:al, lVlollt;oCarlo 13HLUMI-2,0] for Bllablla scat:t,e,ring at; lowangle,s:wi t:l_Ye_ t(:._-F'rttut,sc:l_I-Suura e:.:po_(:_lHut;to_,Coml2ute'r P/ty,qic,_Commu-nicatiou,v, 70::3C)5-344, ] ,9!)2,

[32] Ii, A.il_ar_,c:t:al, M(.,_asur¢:_t_t(._lt,or t:l_(:_l)l_ot,c)_ ,s.'cruc:t:urefu_ct:ion t;7(x , (,,_') i_ t:ho, region 0,2 Ge\/_ < Q'2< 7 G(-_\;'2, Zc'_,t,s'c/rriftf'h_'Phyai/c,C34:], ].987,

r _ r-'_r _ _ .-1 "

[M] IL Bru_ ¢_t:a,1, GEAN.I,3 u_or's gu_clo, CI!H_,N.1)D/F_F_/84.1, CF,I_,N,r

r , -_ , - , --_ _. 11.)

:/_14,Novelllb_:!r]L)92,

[35] E, Fallri, Qutuzt,_m cl_roznodyz_m_icsl;osl_rot ,j(:_l:,s,Phyxical R,e'uiewLetter_,39, 1o8_', i[077,

[30] VV,Ba,rl;(?,l(:_I;al, l)2,Xl.)(.!vizzl(.!zzt:al,.sl;udyoz._mult, i-,jet;l)roduct;iozzizze+c' anzzilzilai(.)zzat: PETI{A. (_,_l(.:r,_ti(.:s,Zcit,s,(:h'_'iftf'l_'_'Ph,y,,il,:,r,,_,_,,),_,Jo,.,....), 1986,

[37] S, Bel:l_k(_ct; M, N(:_w,.let,Clust,er Algoritlim,.s: N(:_xt,-to-leadil_gorder QOI) and}_aclronlz_H,iol_corI'ect;lo_s, Nucla_r Ph,y,s'ic,_,13370:3].0-33,t,:1992,

[38] C, I'(r_u_l(:_r_11_11!1,1._1111.)(:!,'].'u'mj(:_t:cross sect:i(.)_liii u+c-- a_il_il_t, io_l, Zc'il,!_ch.'t'ifl,fib' Physit_, C34:497-.522,138_',

[39] SLD Collaborat, ion, @, Pu_kar el; al, MeasuromelH:of t;.heAverage Iii'el;tri-leorbHa:lrous _ SI,l), SLAC-l=)UI.%5595,Sepi;(:,_nb(:r:1.994,

[dO] S, Jt_,dach, Z. \'V_s, 1-LDock(:,,r,and J, H, Kiihn, ':['l_e7"decay library TAUC)LA,-% t_ _version 2,4, Comt)'u,ter khy_'_c,_Communicatio'rt,s, 76:270-.292, 1993,

[41] D, Mull(_r, Priva, t,(:,,coln_m_uicai;ion, 1994,

133

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[42] ,J,A, Laul.:)m',A Study o/,](._tl_'.(ttc,,_,artd a A4e_as'_tT'evtcTttof c_,_at the Z °/_,c,sor_,a'ltce,.... ' ' ['" _ ' 1992, Sc:,,ctton4,3PhD t,llosts, "Unlvc-_rs_[yo (_.,(:lolttdo, ,

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134

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