Table Of ContentW. Greiner . A. Schafer
QUANTUM CHROMODYNAMICS
Greiner Greiner
Quantum Mechanics Mechanics I
An Introduction 3rd Edition (in preparation)
Greiner Greiner
Quantum Theory Mechanics II
Special Chapters (in preparation)
(in preparation)
Greiner
Greiner· MUller Electrodynamics
Quantum Mechanics (in preparation)
Symmetries 2nd Edition
Greiner· Neise . Stocker
Greiner Thermodynamics
Relativistic Quantum Mechanics and Statistical Mechanics
Wave Equations
Greiner· Reinhardt
Field Quantization
(in preparation)
Greiner· Reinhardt
Quantum Electrodynamics
2nd Edition
Greiner . Schafer
Quantum Chromodynamics
Greiner· Maruhn
Nuclear Models
(in preparation)
Greiner· MUller
Gauge Theory of Weak Interactions
Walter Greiner· Andreas Schafer
QUANTUM
CH ROMODYNAM ICS
With a Foreword by
D. A. Bromley
With 146 Figures,
and 62 Worked Examples and Exercises
Springer
Professor Dr. Walter Greiner
Professor Dr. Andreas Schăfer
Institut fiir Theoretische Physik der
Johann WoIfgang Goethe-Universităt Frankfurt
Postfach 111932
0-60054 Frankfurt am Main
Germany
Street address:
Robert-Mayer-Strasse 8-10
0-60325 Frankfurt am Main
Germany
Title of the original German edition: Theoretische Physik. Ein Lehr-und Obungsbuch. Band 10:
Quantenchromodynamik © Verlag Harri Oeutsch. Thun 1989
ISBN 978-3-540-78050-2 ISBN 978-3-642-57978-3 (eBook)
DOI 10.1007/978-3-642-57978-3
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© Springer· Verlag Berlin Heidelberg 1994
Originally published by Springer-Ve rlag Berlin Heidelberg New York in I 994
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in
the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations
and therefore free for general use.
Foreword to Earlier Series Editions
More than a generation of German-speaking students around the world have worked
their way to an understanding and appreciation of the power and beauty of modern
theoretical physics - with mathematics, the most fundamental of sciences - using
Walter Greiner's textbooks as their guide.
The idea of developing a coherent, complete presentation of an entire field
of science in a series of closely related textbooks is not a new one. Many older
physicists remember with real pleasure their sense of adventure and disc~very
as they worked their ways through the classic series by Sommerfeld, by Planck
and by Landau and Lifshitz. From the students' viewpoint, there are a great many
obvious advantages to be gained through use of consistent notation, logical ordering
of topics and coherence of presentation; beyond this, the complete coverage of
the science provides a unique opportunity for the author to convey his personal
enthusiasm and love for his subject.
The present five-volume set, Theoretical PhYSics, is in fact only that part of
the complete set of textbooks developed by Greiner and his students that presents
the quantum theory. I have long urged him to make the remaining volumes on
classical mechanics and dynamics, on electromagnetism, on nuclear and particle
physics, and on special topics available to an English-speaking audience as well,
and we can hope for these companion volumes covering all of theoretical physics
some time in the future.
What makes Greiner's volumes of particular value to the student and professor
alike is their completeness. Greiner avoids the all too common "it follows that ... "
which conceals several pages of mathematical manipulation and confounds the
student. He does not hesitate to include experimental data to illuminate or illustrate
a theoretical point and these data, like the theoretical content, have been kept up to
date and topical through frequent revision and expansion of the lecture notes upon
which these volumes are based.
Moreover, Greiner greatly increases the value of his presentation by including
something like one hundred completely worked examples in each volume. Nothing
is of greater importance to the student than seeing, in detail, how the theoretical
concepts and tools under study are applied to actual problems of interest to a
working physicist. And, finally, Greiner adds brief biographical sketches to each
chapter covering the people responsible for the development of the theoretical ideas
and/or the experimental data presented. It was Auguste Comte (1798-1857) in his
Positive Philosophy who noted, "To understand a science it is necessary to know
its history". This is all too often forgotten in modern physics teaching and the
VI Foreword to Earlier Series Editions
bridges that Greiner builds to the pioneering figures of our science upon whose
work we build are welcome ones.
Greiner's lectures, which underlie these volumes, are internationally noted for
their clarity, their completeness and for the effort that he .has devoted to making
physics an integral whole; his enthusiasm for his science is contagious and shines
through almost every page.
These volumes represent only a part of a unique and Herculean effort to make
all of theoretical physics accessible to the interested student. Beyond that, they
are of enormous value to the professional physicist and to all others working with
quantum phenomena. Again and again the reader will find that, after dipping into a
particular volume to review a specific topic, he will end up browsing, caught up by
often fascinating new insights and developments with which he had not previously
been familiar.
Having used a number of Greiner's volumes in their original German in my
teaching and research at Yale, I welcome these new and revised English translations
and would recommend them enthusiastically to anyone searching for a coherent
overview of physics.
Yale University D. Allan Bromley
New Haven, CT, USA Henry Ford II Professor of Physics
1989
Preface
Quantum Chromodynamics (QCD) was formulated more than 25 years ago and has
since been a very active field of research. To calculate hadronic properties from
QCD, however, is such a formidable task that progress has been slow and many
problems are still not solved today. The equations to be solved are highly non-linear,
one is dealing with formulas for infinitely many relativistic particles, and one is
dealing with a quantum field theory requiring careful renormalization. Thus QCD
presents one of the most challenging problems of theoretical physics. To avoid the
extreme complexity of real QCD many phenomenological 'QCD-inspired' models
have been developed, often with astonishing success.
Presently, however, this situation is changing. The continuous slow progress in
computational and analytic techniques has now reached a point where real QCD
calculations have become feasible for a rapidly increasing number of problems
in hadron physics. Together with the much improved experimental situation this
should trigger an enormous boost for hadron physics in the years ahead.
In this book we try to give a pedestrian approach to QCD, stressing the prac
titioner's point of view. We start with an elementary introduction and review
Quantum Electrodynamics (Chap. 2). Chapter 3 analyzes lepton-nucleon scattering,
which offers so far the most successful approach to learning about QCD. Also the
MIT bag model is introduced, which serves as an illustrative example for a QCD
oriented model. In Chap. 4 we then tum to QCD proper and focus on the momentum
dependence of its coupling constant, which is the most important property of QCD.
We demonstrate explicitly how QCD is renormalized and how the running cou
pling constant is obtained. Chapter 5 is devoted to the application of QCD to the
description of lepton-hadron scattering: the Gribov-Lipatov-Altarelli-Parisi equa
tions are derived, model calculations for the structure functions are presented, the
very active and promising field of polarized hadron reactions is sketched, and the
fundamental techniques of operator product expansion and renormalization group
analyses are discussed. Chapter 6 presents applications to hadron-hadron reactions,
most notably, the Drell-Yan process. The techniques discussed allow us to present
a currently much debated problem, namely small-x physics. Chapter 7 is then de
voted to non-perturbative approaches to QCD, namely lattice gauge calculations
and sumrule techniques. Our presentation ends with some remarks on the QCD
ground state and its modification at high temperature and/or baryon density (the
so-called quark gluon plasma) in Chap. 8.
We have tried to give a pedagogical introduction to the concepts and techniques
of QCD. Much had to be left out and we often avoided more formal considerations
for the sake of better readability.
VIII Preface
In writing this book we profited substantially from a number of existing text
books, most notably J.J.R. Aitchison and AJ.G. Hey: 'Gauge Theories in Particle
Physics', O. Nachtmann: 'Elementarteilchenphysik', B. Muller: 'The Physics ofthe
Quark-G1uon Plasma', P. Becher, M.Boehm and H. Joos: 'Eichtheorien', J. Collins:
'Renormalization', R.D. Field: 'Application ofPerturbative QCD', and M. Creutz:
'Quarks, G1uons and Lattices', and several review articles, especially: L.V. Gri
bov, E.M. Levin and M.G. Ryskin: 'Semihand processes in QCD', Phys. Rep. 100
(1983) 1, L.S. Reinders, H. Rubinstein, S. Yazaki: 'Hadron properties from QCD
sumrules', Phys. Rep. 127 (1985) l.
We thank all members of the Institute of Theoretical Physics in Frankfurt who
added in one way or another to this book, namely Dr. J. Augustin, M. Ben
der, Ch. Best, S. Bernard, A. Bischoff, M. Bleicher, A. Diener, A. Dumitru,
B. Ehmsperger, Dr. S. Graf, Dr. C. Hofmann, A. Jahns, J. Klenner, o. Martin,
M. Massoth, M. Maul, Dr. G. Plunien, Dr. D. Rischke, Dr. A. Scherdin, and
E. Stein.
Special thanks go to Mrs. A. Steidel who drew the figures, to R. Mattiello
who supervised the editing process, and to Mark Seymour who did a great job as
copy-editor.
We hope that our readers will enjoy this book.
Frankfurt am Main, Walter Greiner
September 1994 Andreas Schafer
Contents
1. The Introduction of Quarks ................................. .
1.1 The Hadron Spectrum ................................... .
2. Review of Relativistic Field Theory ............................ 17
2.1 Spinor Quantum Electrodynamics .......................... 17
2.1.1 The Free Dirac Equation and Its Solution .............. 17
2.1.2 Density and Current Density ........................ 19
2.1.3 Covariant Notation ................................ 20
2.1.4 Normalization of Dirac Spinors ...................... 21
2.1.5 Interaction with a Four-Potential AI-' .................. 22
2.1.6 Transition Amplitudes .............................. 23
2.1.7 Discrete Symmetries ............................... 23
2.2 Scalar Quantum Electrodynamics ........................... 24
2.2.1 The Free Klein-Gordon Equation and Its Solutions ...... 24
2.2.2 Interaction of a 7r+ with a Potential AI-' ................ 27
2.2.3 7r+K+ Scattering .................................. 30
2.2.4 The Cross Section ................................. 32
2.2.5 Spin-I Particles and Their Polarization ................ 42
2.2.5.1 Massive Spin-l Particles ................... 42
2.2.5.2 Massless Spin-I Particles: Photons ........... 46
2.2.6 The Propagator for Virtual Photons ................... 48
2.3 Fermion-Boson and Fermion-Fermion Scattering ............. 53
2.3.1 Traces and Spin Summations ........................ 54
2.3.2 The Structure of the Form Factors
from Invariance Considerations ...................... 63
3. Scattering Reactions and the Internal Structure of Baryons ....... 69
3.1 Simple Quark Models Compared ........................... 69
3.2 The Description of Scattering Reactions ..................... 77
3.3 The MIT Bag Model ..................................... 108
4. Gauge Theories and Quantum-Chromodynamics ................ 131
4.1 The Standard Model - A Typical Gauge Theory .............. 131
4.2 The Gauge Theory of Quark-Quark Interactions .............. 140
4.3 Dimensional Regularization ............................... 154
4.4 The Renormalized Coupling Constant of QCD ................ 168
x Contents
5. Perturbative QeD I: Deep Inelastic Scattering .................. 181
5.1 The Gribov-Lipatov-Altarelli-Parisi Equations ............... 181
5.2 An Alternative Approach to the GLAP Equations ............. 202
5.3 Common Parametrizations of the Distribution Functions
and Anomalous Dimensions ............................... 215
5.4 Renormalization and the Expansion Into Local Operators ....... 224
5.5 The Spin-Dependent Structure Functions ..................... 248
5.6 The Spin-Dependent Structure Functions in the MIT Bag Model 257
6. Perturbative QeD II: The Drell-Yan Process
and the Gribov-Levin-Ryskin Equation ........................ 267
6.1 The Drell-Yan Process ................................... 267
6.2 Small-x Physics and the Gribov-Levin-Ryskin Equation ....... 297
7. Nonperturbative QeD ....................................... 311
7.1 Lattice Gauge Theories ................................... 311
7.2 Lattice Theories at Finite Temperature ...................... 350
7.3 QCD Sum Rules ........................................ 363
8. Phenomenological Models for Non-Perturbative QeD Problems ... 387
8.1 The Ground State of QCD ................................ 387
8.2 The Quark-GIuon Plasma ................................. 401
Subject Index .................................................. 411
