Longitudinal _L63 [lambda] and _L63 ̄ [anti-lambda] polarization at the COMPASS experiment [Elektronische Ressource] / vorgelegt von Donghee Kang

Longitudinal L and L polarization at theCOMPASS ExperimentDonghee KangFAKULTÄT FÜR MATHEMATIK UND PHYSIKALBERT-LUDWIGS-UNIVERSITÄT FREIBURGLongitudinal L and L polarization at theCOMPASS ExperimentInaugural-DissertationzurErlangung des DoktorgradesderFakultät für PhysikderAlbert-Ludwigs-Universität Freiburg im BreisgauvorgelegtvonDonghee Kangaus KoreaSeptember 2007Dekan: Prof. Dr. Jörg FlumLeiter der Arbeit: Prof. Dr. Kay KönigsmannReferent: Prof. Dr. KayKoreferent: Prof. Dr. Ulrich LandgrafTag der Verkündung des Prüfungsergebnisses: 29. Oktober 2007Contents1 Introduction 12 The Spin Structure of Baryons 32.1 Polarized Deep Inelastic Scattering . . . . . . . . . . . . . . . . . . . . . . . 32.1.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.2 Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Structure Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 QCD Evolution of Structure Functions . . . . . . . . . . . . . . . . . . . . . 122.4 First moments of g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1512.5 The Spin Structure of L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Longitudinal L Polarization 233.1 The L Hyperon as a Spin Polarimeter . . . . . . . . . . . . . . . . . . . . . 233.2 L Production in Semi-Inclusive DIS . . . . . . . . . . . . . . . . . . . . . . 283.2.1 Fragmentation in Semi-Inclusive DIS . . . .
Publié le : lundi 1 janvier 2007
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Longitudinal L and L polarization at the
COMPASS Experiment
Donghee Kang
FAKULTÄT FÜR MATHEMATIK UND PHYSIK
ALBERT-LUDWIGS-UNIVERSITÄT FREIBURGLongitudinal L and L polarization at the
COMPASS Experiment
Inaugural-Dissertation
zur
Erlangung des Doktorgrades
der
Fakultät für Physik
der
Albert-Ludwigs-Universität Freiburg im Breisgau
vorgelegt
von
Donghee Kang
aus Korea
September 2007Dekan: Prof. Dr. Jörg Flum
Leiter der Arbeit: Prof. Dr. Kay Königsmann
Referent: Prof. Dr. Kay
Koreferent: Prof. Dr. Ulrich Landgraf
Tag der Verkündung des Prüfungsergebnisses: 29. Oktober 2007Contents
1 Introduction 1
2 The Spin Structure of Baryons 3
2.1 Polarized Deep Inelastic Scattering . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Structure Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 QCD Evolution of Structure Functions . . . . . . . . . . . . . . . . . . . . . 12
2.4 First moments of g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
2.5 The Spin Structure of L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Longitudinal L Polarization 23
3.1 The L Hyperon as a Spin Polarimeter . . . . . . . . . . . . . . . . . . . . . 23
3.2 L Production in Semi-Inclusive DIS . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Fragmentation in Semi-Inclusive DIS . . . . . . . . . . . . . . . . . 29
3.2.2 in e e Annihilation . . . . . . . . . . . . . . . . . . 31
3.2.3 Connection between Fragmentation and Parton Functions . . . . . . 32
3.3 Theoretical Models of Longitudinal L Polarization . . . . . . . . . . . . . . 33
3.3.1 The Current Fragmentation Region . . . . . . . . . . . . . . . . . . 36
3.3.2 The Target Region . . . . . . . . . . . . . . . . . . . 44
3.4 A Brief Overview of the Experimental Situation . . . . . . . . . . . . . . . . 48
4 COMPASS Experiment 51
4.1 The Polarized Muon Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 The Target . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.3 The COMPASS Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3.1 Tracking System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3.2 Particle Identification . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.4 The Trigger System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.5 Data Acquisition System and Detector Control . . . . . . . . . . . . . . . . . 69
4.5.1 Data Acquisition System . . . . . . . . . . . . . . . . . . . . . . . . 69
I
II CONTENTS
4.5.2 Detector Control and Monitoring System . . . . . . . . . . . . . . . 71
5 Data Analysis 73
5.1 Data Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.1 of Primary Vertex . . . . . . . . . . . . . . . . . . . . . . 78
5.2.2 Selection of V Events . . . . . . . . . . . . . . . . . . . . . . . . . 810
5.2.3 Armenteros-Podolanski Plot . . . . . . . . . . . . . . . . . . . . . . 86
5.2.4 Selection of Current Fragmentation . . . . . . . . . . . . . . . . . . 88
5.2.5 Invariant Mass Distribution . . . . . . . . . . . . . . . . . . . . . . . 89
5.3 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.3.1 Event Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.3.2 Parton Distribution Function . . . . . . . . . . . . . . . . . . . . . . 94
5.3.3 Fragmentation Model . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.3.4 Comparison of Data and Monte Carlo . . . . . . . . . . . . . . . . . 99
5.4 Polarization Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.4.1 Reference System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.4.2 Extraction Method of Polarization . . . . . . . . . . . . . . . . . . . 108
5.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.5.1 Results of Longitudinal Polarization . . . . . . . . . . . . . . . . . . 113
5.5.2 of Spin Transfer . . . . . . . . . . . . . . . . . . . . . . . . 116
5.6 Systematic Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
05.6.1 Systematic of the K Background . . . . . . . . . . . . . . . . . . . 118
5.6.2 Systematics of the Estimation Method . . . . . . . . . . . . . . . . . 118
5.6.3 Verification of the Acceptance Correction . . . . . . . . . . . . . . . 123
5.6.4 Systematic Errors from the Detector Setup . . . . . . . . . . . . . . 126
5.6.5 Error on a . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.6.6 Total Systematic Error . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.6.7 Further Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.7 Kinematic Dependences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
5.7.1 Dependence of C on Inclusive Variables . . . . . . . . . . . . . . . 137LL
5.7.2 of C on Semi-Inclusive Variables . . . . . . . . . . . . 140LL
6 Interpretation and Discussion 141
6.1 Comparison with other Experiments and Theory . . . . . . . . . . . . . . . . 141
6.1.1 x and y Dependence of Spin Transfer . . . . . . . . . . . . . . . . . 141
6.1.2 z Dependence of Spin Transfer . . . . . . . . . . . . . . . . . . . . . 143
6.1.3 x of Spin Transfer . . . . . . . . . . . . . . . . . . . . 144F
6.2 Information from the Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . 147
7 Summary and Outlook 149CONTENTS III
A Comparison of Data with Monte Carlo 151
A.1 between Data and Monte Carlo in 2002 . . . . . . . . . . . . . . 151
A.2 Comparison Data and Carlo in 2003 . . . . . . . . . . . . . . 156
B Tables of Systematic Studies 161
C Tables of Kinematic Dependences 165
Bibliography 173
List of Figures 189
List of Tables 193IV CONTENTSChapter 1
Introduction
In the beginning of the twentieth century Rutherford [1] concluded that atoms consist of a
very small nucleus with a cloud of electrons around. More than 50 years after Rutherford’s
discovery, experiments at SLAC [2] showed a scaling invariance property of the ep e X,
where is essentially independence of the momentum transfer between the electron and the
proton. The result might give evidence of a substructure in the proton and was immediately
interpreted by R. P. Feynman. In his initial parton theory [3], now called the Quark Parton
Model (QPM), he assumed that the proton was composed of point-like partons as an expla-
nation both of scaling and of the no momentum transfer dependence for structure functions.
The partons were later identified with the quarks postulated in 1964 independently by M.
Gell-Mann [4] and G. Zweig [5]. In our present understanding all hadrons are composed
of constituent quarks and are bound together with gluons by the strong color force. A the-
ory of the strong interactions among quarks and gluons, Quantum Chromo Dynamic (QCD)
explains why quarks combine in certain configurations to form the observed patterns of par-
ticles.
Despite having been intensively studied by the investigation of the spin structure of hadrons
both theoretically and experimentally during the past several years, the spin structure of
hadrons is still not understood at a fundamental level in QCD. The first puzzling result for
the spin structure of the nucleon was reported by the European Muon Collaboration (EMC)
[6], and later confirmed by the Spin Muon Collaboration (SMC) [7]: Quarks and antiquarks
carry only 30% of the total contribution of spin to the nucleon. This surprising discrepancy
comes from the point of view of the relativistic QPM, which expected the result amounts to
about 60% of the contribution to the nucleon’s spin [8]. This astonishing result leads to the
so-called nucleon spin crisis.
Complementary information on the polarization of strange quarks and antiquarks in the nu-
cleon can be accessed by measuring the longitudinal polarization of L and L hyperon in
lN l L L X. L particles are unique among light hadrons in that their polarization can be
1





2 CHAPTER 1. INTRODUCTION
easily reconstructed due to their parity-violating weak decay. Since the L contains a strange
quark, it has been proposed that L and L polarization is potentially a powerful way of prob-
ing the polarized s and s quark. Additionally, the L polarization can also be used for other
interesting measurements of polarized fragmentation functions in Deep Inelastic Scattering
(DIS). The knowledge of the hadronization mechanism is playing a very important role in
the interpretation of semi-inclusive DIS, but the description of the fragmentation process is
currently not predicted in the QCD framework.
When a longitudinally polarized lepton beam is scattered off an unpolarized nucleon target,
only quarks of a particular spin orientation participate in this interaction. The outgoing struck
quark is thus polarized and L produced from its fragmentation may remember its spin ori-
entation. Formally such a correlation of longitudinal spin transfer from the quark q to the
L hyperon may be expressed in terms of a polarized fragmentation function. Consequently,
a measurement of the longitudinal polarization of the L hyperon is believed to provide in-
formation on the spin structure of the L hyperon in a certain kinematic limit. There exists a
highly non-trivial spin of the nucleon, and by the same token, it is also interesting to
consider the spin structure of L hyperon. This work exploits an ansatz in order to contribute
an important piece towards solving the spin puzzle of the nucleon and baryon by utilizing the
L polarization.
The COMPASS (COmmon Muon and Proton Apparatus for Structure and Spectroscopy)
experiment at CERN (Conseil Europeen de Rescherche Nucleaire) in Geneva was designed
to explore and disentangle the contribution from the different quark flavors and from gluons
to the nucleon’s spin in DIS [9]. Chapter 2 supplies the theoretical framework needed to
interpret the results of a DIS experiment. The discussion is extended to perturbative QCD,
which clarifies the important role of the spin structure function of the baryons. The physics
topic of this work, the longitudinal L polarization, will be introduced in Chapter 3. This
Chapter will give insight on the longitudinal spin transfer q L via a measurement of the L
polarization. Chapter 4 gives a brief overview of the experimental apparatus at COMPASS.
Chapter 5 is dedicated to explain a strategy for tagging the L and L events. The selection
scheme is applied to the COMPASS data collected during the years 2002 to 2004 with a
longitudinally polarized target. Subsequently, an extraction method of the L polarization
from the acceptance corrected angular distribution of the decay products will be presented.
In the last Chapter all obtained results of the spin transfer of L and L will be discussed and
compared with theoretical predictions.

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