Studies of hadronic spin structure in hard scattering processes at the next-to-leading order of QCD [Elektronische Ressource] / vorgelegt von Barbara Jäger

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• Physik

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• Publié par: universitat_regensburg
• Publié le: 01 janvier 2004
• Nombre de lectures: 14
• Langue: Deutsch
• Poids de l'ouvrage: 1 Mo

Extrait

Studies of Hadronic Spin Structure
in Hard Scattering Processes
at the Next-to-Leading Order of QCD
Dissertation
zur Erlangung des
Doktorgrades der Naturwissenschaften
(Dr. rer. nat. )
der Naturwissenschaftlichen Fakult˜at II { Physik
der Universit˜at Regensburg
vorgelegt von
Barbara J˜ager
Regensburg, April 2004Promotionsgesuch eingereicht am: 20. 4. 2004
Die Arbeit wurde angeleitet von: Prof. Dr. A. Sch˜afer
Prufungsaussc˜ hu…: Prof. Dr. W. Wegscheider
Prof. Dr. A. Sch˜afer
Prof. Dr. U. R˜o…ler
Prof. Dr. V. BraunDie Physik erkl˜art die Geheimnisse der Natur nicht,
sie fuhrt˜ sie auf tieferliegende Geheimnisse zuruck.˜
Carl Friedrich von Weizs˜ackerContents
1 Introduction 1
I ConceptsandTechniques 7
2 Basic Concepts of Perturbative QCD 8
2.1 The Lagrangian of QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Renormalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Example: Quark Selfenergy . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 Parton Distributions and Fragmentation Functions . . . . . . . . . . . . . . 20
3 Technical Issues 26
3.1 Born Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Virtual Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2.1 Vertex and Selfenergy Corrections . . . . . . . . . . . . . . . . . . . 36
3.2.2 Box Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3 Helicity Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4 Real Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4.1 Three-Body Phase Space . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4.2 Phase Space Integration . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.5 Cancelation of Singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
II PhenomenologicalApplicationsandResults 53
4 High-p Hadron Production in pp-Collisions 54T
4.1 Setting the Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2 First Numerical Results and Discussion . . . . . . . . . . . . . . . . . . . . 61
4.3 The Double-Spin Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79vi CONTENTS
5 Single-Inclusive Jet Production in pp-Collisions 81
5.1 Jet Deflnition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2 Analytical Calculation of Jet Cross Sections . . . . . . . . . . . . . . . . . . 83
5.2.1 The One-Parton-to-Jet Cross Section d¢?^ . . . . . . . . . . . . . 86j(k)
5.2.2 The Two-P Cross d¢?^ . . . . . . . . . . . . . 89jk
5.2.3 Cancelation of Final State Singularities . . . . . . . . . . . . . . . . 92
5.3 Numerical Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 95
5.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6 Photoproduction of Inclusive Hadrons 104
6.1 The Parton Structure of the Photon . . . . . . . . . . . . . . . . . . . . . . 105
6.2 Some Technicalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
6.3.1 Pionproduction at an Electron-Proton Collider . . . . . . . . . . . . 114
6.3.2 in Fixed-Target Experiments . . . . . . . . . . . . . 122
6.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7 Summary and Conclusions 135
A Feynman Rules 137
B Leading Order 2! 2 Scattering Cross Sections 140
C Passarino-Veltman Decomposition 143
D Parametrization of Momenta 145
E Lorentz Boosts 148
Acknowledgements 150
Bibliography 151Chapter 1
Introduction
One of the longest standing and still not satisfactorily answered questions of mankind is
which fundamental entities constitute the world we are living in. The very concept of
a microscopic structure underlying all matter flrst occurred in ancient Greek philosophy,
when Demokrit suggested that everything consists of small objects, so-called atoms. It
was not before the end of the 19th century, however, that science had developed a flrst
picture of atomic physics, which could be thoroughly understood only with the advent of
quantum mechanics in the early 20th century. At the same time Rutherford’s scattering
experimentsrevealedthatatomsarenotfundamental,buthaveasubstructurethemselves,
whicheventuallywastracedbacktonucleiconsistingofnucleons{protonsandneutrons{
surrounded by electrons. Continuous efiorts in the following decades established the basic
ideas of nuclear physics, but remained limited to a phenomenological description of inter-
actions among nuclei. Only when it was realized that nucleons themselves have an inner
structureandconsistofevensmallerparticles, quarksandgluons, afundamentaltheoryof
the force driving the interaction of the smallest building blocks could be developed. Our
present knowledge of the basic entities and forces in nature is summarized in the Standard
Model of elementary particle physics, based on the assumption that all matter consists
of fundamental particles { quarks and leptons { which interact via the exchange of gauge
bosons. Although the gross features of this model are well-established and experimentally
verifled by now, our understanding of elementary particle dynamics is still incomplete in
many aspects, including the issues of a possible existence of additional elementary parti-
cles and a yet smaller substructure underlying all quarks and leptons. It therefore needs
to be improved by ongoing experimental and theoretical efiorts.
In this thesis we are focusing on the theory of the strong interaction, Quantum Chro-
modynamics (QCD), the sector of the Standard Model which at present is believed to
be the fundamental theory of hadronic structure and interactions. QCD is a non-Abelian
quantum fleld theory which describes the interaction of spin-1=2 quarks and spin-1 gluons.
Duetothenon-Abeliancharacterofthegaugeflelds, self-interactionsofthegluonsoccur{
quite in contrast to Quantum Electrodynamics (QED) where the gauge bosons, the pho-
tons, are electrically neutral and couple therefore only to charged fermions. Similar to this
electric charge, quarks and gluons are ascribed a \color-charge". In nature, however, the2 Introduction
colored quarks and gluons cannot be observed as free particles, but only in color-neutral
combinations { hadrons, highly non-trivial bound states such as, e.g., the proton. The
formation of hadrons is due to a central feature of QCD: conflnement. The complexity
of hadronic systems makes the theoretical description of strongly interacting particles an
intricate task, which only becomes feasible through another fundamental characteristic of
QCD: asymptotic freedom [1]. The strength of the strong interaction depends signiflcantly
on the kinematic domain of the reaction. Contrary to the electromagnetic force, which
becomes stronger with decreasing separation of the interacting particles, the strong cou-
pling fi diminishes the smaller the distances become. This feature makes QCD at highs
energies amenable to perturbative methods.
The basic observation underlying any such approach is manifested in factorization
theorems [2]. They state that in certain kinematic domains strong interactions can be
described as a combination of universal \soft" functions, parametrizing the distribution
of quarks and gluons inside hadrons independently of the reaction they are involved in,
and \hard" partonic quantities, which account for the interaction of quasi-free quarks and
gluons emerging from the hadrons which are involved in a speciflc process. In the frame-
work of perturbative QCD (pQCD) these latter pieces are calculated as a series in fi .s
The deflnition and convergence of a perturbative expansion in quantum fleld theories is an
intricate task, far beyond the scope of this thesis. These issues are intimately related to
profound physics, such as a non-trivial, non-perturbative structure of the vacuum and its
excitations [3]. Nonetheless, the results of a pe calculation very often give good
approximations for physical observables. This remarkable feature, tested in a multitude
of reactions, makes pQCD an indispensable tool for a better understanding of hard scat-
tering processes. In the past, calculations have mostly been restricted to the leading order
(LO) in the strong coupling. Thereby, however, only qualitative aspects can be addressed.
Quantitative predictions, freeof largetheoreticaluncertainties, requirean extensionof the
perturbative expansion to, at least, the next-to-leading order (NLO). The internal struc-
tureofhadronsisalong-distancephenomenon, whichcannotbecalculatedperturbatively,
but has to be extracted from experiment or addressed by non-perturbative methods. At
present, the parton distributions of the unpolarized nucleon are well-established [4-7] from
the analysis of a wealth of hard scattering data. The veriflcation of their universality has
given some confldence in the validity of the factorization theorems mentioned above an