Greiner W., Schrammm S., Stein E. Quantum Chromodynamics
Подождите немного. Документ загружается.
W. Greiner · S. Schramm · E. Stein
QUANTUM CHROMODYNAMICS
Greiner
Quantum Mechanics
An Introduction 4th Edition
Greiner
Quantum Mechanics
Special Chapters
Greiner · Müller
Quantum Mechanics
Symmetries 2nd Edition
Greiner
Relativistic Quantum Mechanics
Wave Equations 3rd Edition
Greiner · Reinhardt
Field Quantization
Greiner · Reinhardt
Quantum Electrodynamics
3rd Edition
Greiner · Schramm · Stein
Quantum Chromodynamics
3nd Edition
Greiner · Maruhn
Nuclear Models
Greiner · Müller
Gauge Theory of Weak Interactions
3rd Edition
Greiner
Classical Mechanics
Systems of Particles
and Hamiltonian Dynamics
Greiner
Classical Mechanics
Point Particles and Relativity
Greiner
Classical Electrodynamics
Greiner · Neise · Stöcker
Thermodynamics
and Statistical Mechanics
Walter Greiner ·Stefan Schramm
Eckart Stein
QUANTUM
CHROMODYNAMICS
With a Foreword by
D.A. Bromley
Third Revised and Enlarged Edition
With 165 Figures,
and 66 Worked Examples and Exercises
123
Prof. Dr. Dr. h. c. mult. Walter Greiner
Frankfurt Institute for Advanced Studies (FIAS)
Johann Wolfgang Goethe-Universität
Max-von-Laue-Str. 1
60438 Frankfurt am Main
Germany
email: greiner@fias.uni-frankfurt.de
Prof. Dr. Stefan Schramm
Center for Scientific Computing (CSC)
Johann Wolfgang Goethe-Universität
Max-von-Laue-Str. 1
60438 Frankfurt am Main
Germany
email: schramm@th.physik.uni-frankfurt.de
Dr. Eckart Stein
Physics Department
Maharishi University of Management
6063 NP Vlodrop
The Netherlands
email: EStein@maharishi.net
Title of the original German edition: Theoretische Physik, Ein Lehr- und Übungsbuch, Band 10:
Quantenchromodynamik
c
Verlag Harri Deutsch, Thun, 1984, 1989
ISBN-10 3-540-48534-1 Springer Berlin Heidelberg New York
ISBN-13 978- 3-540-48534-6 Springer Berlin Heidelberg New York
ISBN-10 3-540-66610-9 2nd Ed. Springer Berlin Heidelberg New York
Library of Congress Control Number: 2006938282
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,
specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on mi-
crofilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted
only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission
for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright
Law.
Springer is a part of Springer Science+Business Media
springer.com
c
Springer-Verlag Berlin Heidelberg 1994, 2002, 2007
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.
Typesetting: LE-T
E
X Jelonek, Schmidt & Vöckler GbR
Production: LE-T
E
X Jelonek, Schmidt & Vöckler GbR
Cover: eStudio Calamar S. L., Spain
SPIN 11864288 56/3100YL - 5 4 3 2 1 0 Printed on acid-free paper
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 discovery
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, logi-
cal 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 profes-
sor alike is their completeness. Greiner avoids the all too common “it follows
that ... ” which conceals several pages of mathematical manipulation and con-
founds the student. He does not hesitate to include experimental data to illumi-
nate 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 includ-
ing 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 inter-
est to a working physicist. And, finally, Greiner adds brief biographical sketches
to each chapter covering the people responsible for the development of the the-
oretical 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
VI Foreword to Earlier Series Editions
physics teaching and the 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 mak-
ing 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 trans-
lations 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 to the Third Edition
The theory of strong interactions, quantum chromodynamics (QCD), was for-
mulated more than 30 years ago and has been ever since a very active field
of research. Its continuing importance may be estimated by the Nobel prize in
physics for the year 2004, which was awarded to Gross, Wilczek, and Politzer
for their discovery of asymptotic freedom, one of the key features of QCD. The
underlying equations of motion for the gauge degrees of freedom provided by
QCD are nonlinear and minimally coupled to fermions with global and local
SU(3) charges. This leads to spectacular problems compared with those of QED
since the gauge bosons themselves interact with each other. On the other hand,
it is exactly the self-interaction of the gluons which leads to asymptotic freedom
and the possibility to calcuate quark–gluon interaction at small distances in the
framework of perturbation theory. We discover one of the most complicated but
most beautiful gauge theories which poses extremely challenging problems on
modern theoretical and experimental physics today.
Quantum chromodynamics is the quantum field theory that allows us to cal-
culate the propagation and interaction of colored quarks and gluons at small
distances. Today’s experiments do not allow these colored objects to be detected
directly; instead one deals with colorless hadrons: mesons and baryons seen far
away from the actual interaction point. The hadronization itself is a complicated
process and not yet understood from first principles. Therefore one may won-
der how the signature of quark and gluon interactions can be traced through the
process of hadronization.
Very advanced analytical and numerical techniques have been developed in
order to analyze the world of hadrons on the grounds of fundamental QCD. To-
gether with a much improved experimental situation we seem to be ready to
answer the question wether QCD is the correct theory of strong interactions at
all scales or just an effective high-energy line of a yet undiscovered theory.
With the upcoming Large Hadron Collider (LHC) at CERN near Geneva,
a proton-proton collider reaching a center-of-mass energy of 14 TeV per col-
liding nucleon pair, perturbative QCD will be tested with highest precision in
a regime where it is expected to work extremely well. This will allow precision
tests of QCD as the underlying theory of quarks and hadrons. Moreover, calcula-
tions performed using perturbative QCD are essential to define the background
against which all potential signals of new physics – of the Higgs particle, super-
symmetric particles, or exotic things we may not yet think of – will be gauged.
In this book, we try to give a self-consistent treatment of QCD, stressing the
practitioners point of view. For pedagogical reasons we review quantum elec-
VIII Preface to the Third Edition
trodynamics (QED) (Chap. 2) after an elementary introduction. In Chap. 3 we
study scattering reactions with emphasis on lepton–nucleon scattering and intro-
duce the language for describing the internal structure of hadrons. Also the MIT
bag model is introduced, which serves as an illustrative and successful example
for QCD-inspired models.
In Chap. 4 the general framework of gauge theories is described on the basis
of the famous Standard Model of particle physics. We then concentrate on the
gauge theory of quark–gluon interaction and derive the Feynman rules of QCD,
which are very useful for pertubative calculations. In particular, we show explic-
itily how QCD is renormalized and how the often-quoted running coupling is
obtained.
Chapter 5 is devoted to the application of QCD to lepton–hadron scatter-
ing and therefore to the state-of-the-art description of the internal structure
of hadrons. We start by presenting two derivations of the Dokshitzer–Gribov–
Lipatov–Altarelli–Parisi equations. The main focus of this chapter is on the
indispensable operator product expansion and its application to deep inelastic
lepton–hadron scattering. We show in great detail how to perform this expan-
sion and calculate the Wilson coefficients. Furthermore, we discuss perturbative
corrections to structure functions and perturbation theory at large orders, i.e.
renormalons.
After analyzing lepton–hadron scattering we switch in Chap. 6 to the case
of hadron–hadron scattering as described by the Drell–Yan processes. We then
turn to the kinematical sector where the so-called leading-log approximation is
no longer sufficient. The physics on these scales is called small-x physics.
Chapter 7 is devoted to two promising nonperturbative approaches, namely
QCD on the lattice and the very powerful analytical tool called the QCD sum rule
technique. We show explicitely how to formulate QCD on a lattice and discuss
the relevant algorithms needed for practical numerical calculations, including the
lattice at finite temperature. This is very important for the physics of hot and
dense elementary matter as it appears, for example, in high-energy heavy ion
physics. The QCD sum rule technique is explained and applied to the calculation
of hadron masses.
Our presentation ends with some remarks on the nontrivial QCD vacuum and
its modification at high temperature and/or baryon density, including a sketch of
current developments concerning the so-called quark–gluon plasma in Chap. 8.
Modern high-energy heavy ion physics is concerned with these issues.
We have tried to give a pedagogical introduction to the concepts and tech-
niques of QCD. In particular, we have supplied over 70 examples and exercises
worked out in great detail. Working through these may help the practitioner
in perfoming complicated calculations in this challenging field of theoretical
physics.
In writing this book we profited substantially from a number of existing
textbooks, most notably J.J.R. Aitchison and A.J.G. Hey: ‘Gauge Theories in
Particle Physics’, O. Nachtmann: ‘Elementarteilchenphysik’, B. Müller: ‘The
Physics of the Quark–Gluon Plasma’, P. Becher, M. Boehm and H. Joos:
‘Eichtheorien’, J. Collins: ‘Renormalization’, R.D. Field: ‘Application of Per-
turbative QCD’, and M. Creutz: ‘Quarks, Gluons and Lattices’, and several
Preface to the Third Edition IX
review articles, especially: L.V. Gribov, E.M. Levin and M.G. Ryskin: ‘Semi-
hard processes in QCD’, Phys. Rep. 100 (1983) 1, Badelek, Charchula,
Krawczyk, Kwiecinski, ‘Small x physics in deep inelastic lepton hadron scat-
tering’, Rev. Mod. Phys. 927 (1992), L.S. Reinders, H. Rubinstein, S. Yazaki:
‘Hadron properties from QCD sumrules’, Phys. Rep. 127 (1985) 1.
We thank many members of the Institute of Theoretical Physics in Frank-
furt who added in one way or another to this book, namely Dr. J. Augustin,
M. Bender, C. Best, S. Bernard, A. Bischoff, M. Bleicher, A. Diener, A. Dumi-
tru, B. Ehrnsperger, U. Eichmann, S. Graf, N. Hammon, C. Hofmann, A. Jahns,
J. Klenner, O. Martin, M. Massoth, G. Plunien, D. Rischke, and A. Scherdin.
Special thanks go to A. Steidel who drew the figures, to Dr. H. Weber for techni-
cal help, and to Dr. S. Hofmann who supervised the editing process of the second
edition and gave hints for many improvements.
In this new edition, typographical errors have been removed, and data and
references to the literature have been updated. We thank Dr. S. Scherer for his
reliable and efficient assistance throughout the editing process.
Frankfurt am Main, Walter Greiner
November 2006 Stefan Schramm
Eckart Stein