Hard exclusive QCD processes [Elektronische Ressource] / vorgelegt von Wolfgang Kugler

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• Physik

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• Publié par: universitat_regensburg
• Publié le: 01 janvier 2007
• Nombre de lectures: 23
• Langue: Deutsch
• Poids de l'ouvrage: 3 Mo

Extrait

Hard exclusive QCD processes
Dissertation
zur Erlangung des
Doktorgrades der Naturwissenschaften
(Dr. rer. nat.)
der naturwissenschaftlichen Fakult at II - Physik
der Universit at Regensburg
vorgelegt von
Wolfgang Kugler aus Regensburg
Regensburg, Januar 2007Promotionsgesuch eingereicht am: 22.01.2007
Die Arbeit wurde angeleitet von: Prof. Dr. A. Sch afer
Prufungsaussc huss: Prof. Dr. C. Back
Prof. Dr. A. Sch afer
Dr. M. Diehl
Prof. Dr. M. GrifoniContents
1 Introduction 1
2 General framework 5
2.1 Kinematics and de nition of GPDs . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Physical interpretation and properties of GPDs . . . . . . . . . . . . . . . . 9
2.3 Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.4 Modeling the generalized parton distributions . . . . . . . . . . . . . . . . . 15
2.4.1 Model based on dynamics . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.2 Double Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Transition GPDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Exclusive processes in semi inclusive reactions 21
3.1 Exclusive meson production in the leading-twist approximation . . . . . . . . 23
3.2e pseudoscalar meson production . . . . . . . . . . . . . . . . . . . . 28
3.3 Exclusive vector meson production . . . . . . . . . . . . . . . . . . . . . . . 31
3.4 Comparison with data and discussion of power corrections . . . . . . . . . . 37
3.5 Exclusive channels in semi-inclusive pion and kaon production . . . . . . . . 39
4 Higher order corrections to exclusive meson production 49
4.1 The amplitude of exclusive meson production at next-to-leading order . . . . 50
4.2 Scale dependence of the amplitude . . . . . . . . . . . . . . . . . . . . . . . 52
4.3 Numerical treatment of the NLO amplitude . . . . . . . . . . . . . . . . . . 53
4.4 High energy behavior of the amplitude . . . . . . . . . . . . . . . . . . . . . 55
4.5 Modeling of E(x;;t) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.6 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.6.1 Results forH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.6.2 forE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
~ ~4.6.3 Results for the polarized GPDs H(x;;t) and E(x;;t) . . . . . . . . 95
04.6.4 Cross section for exclusive -production . . . . . . . . . . . . . . . . 984 Contents
5 Summary and outlook 101
A Integrals over GPDs within the double distribution model 105
B Distribution of pions or kaons from vector meson decay 109
C Scattering kernels and properties of the amplitude 113
C.1 Hard scattering kernels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
C.2 Real and imaginary part of the amplitude . . . . . . . . . . . . . . . . . . . 121
C.3 High energy expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
D Evolutions kernels for GPDs 129
D.1 Evolution kernels for generalized parton distributions . . . . . . . . . . . . . 129
D.2 Ev of the NLO vector meson amplitude . . . . . . . . . . . . . . . . . 132
Bibliography 1351
Introduction
Revealing the structure of matter is one of the most fundamental questions in physics which
still has no satisfactory answer. Long time ago people started to think about the structure of
matter and one the very rst concepts of the microscopic structure occurred in ancient Greek
philosophy, when Demokrit proposed the idea that everything consists of small objects, the
atoms.
Our knowledge of the structure of matter has improved since then. It was not before the
end of the 19th century that science had developed a picture of atomic physics. But only the
development of quantum mechanics at the beginning of the 20th century made a thorough
understanding of this picture possible. Further on it was observed that atoms themselves
have an internal structure due to the scattering experiments of Rutherford at the beginning
of the last century. He observed that atoms are composed by a massive atomic nucleus with
positive electric charge surrounded by a much larger cloud of electrons with negative charge.
The force acting between the nucleus and the electrons is the electromagnetic force, which
can be described by the theory of Quantum Electrodynamics (QED). We also know that
the nucleus is built up of positively charged protons and neutrally charged neutrons. They
were seen for quite some time as point-like particles. A rst hint that the nucleons are not
point-like came from the experimental measurements of the magnetic moment of the proton
in the 1940’s [1]. The experimental results were found to be much larger than expected for
a point-like particle. Further measurements of the nucleon form factors F and F in the1 2
1960’s substantiated the assumption that nucleons have an internal structure. The point-like
constituents of the nucleon are found to be fermions of spin 1/2 and were identi ed with
quarks, proposed by Gell-Mann and Zweig [2, 3]. The interaction between quarks is the2 1. Introduction
strong force and is mediated by gluons.
The underlying theory of strong interactions is called Quantum Chromodynamics (QCD).
It describes the interaction of \colored" quarks via the exchange of \colored" gluons. In con-
trast to QED, QCD is a non-Abelian quantum eld theory which allows the self-interaction
of the gauge bosons (gluons) due to the fact that gluons carry a color charge. In QED the
gauge bosons (photons) are electrically neutral and therefore cannot couple to each other.
In nature it is not possible to observe colored quarks and gluons as free particles, but only in
color-neutral combinations (e.g. hadrons). The formation of such highly non-trivial bound
states is due to one of the central features of QCD: con nemen t. The theoretical description
of hadronic system is a very di cult task. It becomes feasible through another central prop-
erty of QCD: asymptotic freedom [4,5]. The strength of the strong interaction is dependent
on the momentum transfer of the reaction. In contrast to QED, where the coupling of two
interacting particles becomes larger for decreasing distance, the strong coupling constants
decreases for smaller distances. Because the decrease of at high energies, QCD becomess
amenable for perturbative methods.
The rst scattering experiments at high energies were performed at the Stanford Linear
Collider (SLAC) in the 1960’s where the internal structure of the nucleon was probed in
inclusive deep-inelastic scattering (DIS). In these experiments a electron is scattered on a
0nucleon, e +N !e +X, and only the rescattered electron is detected. The results for the
2DIS cross section showed an unexpected weak dependence on the photon virtuality Q . It
was possible to extract structure functions from the measured cross section, which encode
information about the internal structure of nucleon. One of the main observations was the
fact that these structure functions are only dependent on a single variable, the Bjorken
2scaling variable x , instead of two (x and Q ) allowed by kinematics. This observationB B
is called Bjorken scaling. A explanation for Bjorken scaling is provided by the asymptotic
2freedom of QCD: at large energies Q the strong coupling constant is small and thes
incoming lepton scatters almost incoherently on the constituents of the nucleon. Therefore
the structure functions can be expressed in terms of quark and gluon parton distribution
2 2functions (PDFs),q(x; ) andg(x; ), where x denotes the momentum fraction carried by
2the di eren t partons. The dependence of the PDFs on the scale is based on the violation
of Bjorken scaling and is only logarithmic. It represents the physical scale at which the
partons are resolved.
A very important step in the description of high energy inelastic scattering processes with
the help of perturbative methods was the formulation of factorization theorems [6{11]. They
state that in certain kinematical regions the process can be described as a combination of
universal \soft" functions, PDFs, which parameterize the distribution of quarks and gluons
inside the nucleon, and \hard" partonic functions. The hard functions are process dependent
and describe the interaction of quasi-free quarks and gluons emerging from the nucleons.
These hard functions can be calculated as a series in within the framework of perturbatives
QCD. The PDFs on the other hand cannot be calculated with perturbative methods and
have to be extracted from experiments or nowadays from lattice calculations. At present,Introduction 3
the PDFs of the unpolarized nucleon are well established [12, 13] and the con rmation of
their universality has given some evidence of the validity of the factorization theorems.
One of the most fundamental properties of elementary particles which is essential for
the complete understanding of the internal structure and the dynamics of interaction of
hadrons is their spin. Information about the spin structure can be obtained in DIS processes
with polarized lepton beams scattering on a polarized target or in polarized proton proton
collisions. It is possible to extract the polarized structure functions g and g from such1 2
experiments. These polarized structure functions can be expressed in terms of the po