Table Of ContentTheoretical and Mathematical Physics
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W.Beiglböck,InstituteofAppliedMathematics,UniversityofHeidelberg,Germany
J.-P.Eckmann,DepartmentofTheoreticalPhysics,UniversityofGeneva,Switzerland
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J.Yngvason,InstituteofTheoreticalPhysics,UniversityofVienna,Austria
Francisco J. Ynduráin
The Theory of Quark
and Gluon Interactions
Fourth Edition
With94Figures
ABC
ProfessorDr.FranciscoJ.Ynduráin
DepartementodeFísicaTeórica,C-XI
UniversidadAutónomaMadrid
CantoBlanco
28049Madrid,Spain
E-mail:[email protected]
LibraryofCongressControlNumber:2006925846
ISBN-10 3-540-33209-X4thEd.SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-540-33209-14thEd.SpringerBerlinHeidelbergNewYork
3-540-64881-X3rdEd.SpringerBerlinHeidelbergNewYork
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To Elsa, Marcos and Elena
Preface to the Fourth Edition
Asinformereditionsofthisbook,Ihaveexpandedthepresentonetocontain
newsectionsonsubjectsbeyondthosefoundinthepreviouseditions,thereby
filling some of the existing gaps. Thus, we now have a section on heavy
quark effective theories, one of the more powerful methods devised to take
advantage of the existence a large scale (the mass of the heavy quark) for
observables involving at least a heavy quark; a new section on lattice QCD,
a method of calculation that is already giving reasonably reliable results for
a number of observables; and several sections with a detailed discussion of
chiral perturbation theory. There is little doubt that, at least at the one
loop level, chiral perturbation theory has led to an important insight into
pion physics in a region where methods derived from ordinary perturbation
theory are not at applicable, which justifies this substantial addition.
Besidesthis,Ihavecorrectederrorsinthepreviouseditionandimproved,
here and there, the material on several among the various topics; in particu-
lar, including more information on experiment, and on comparison of theory
with experiment. The values of the basic QCD parameters have also been
completely updated.
There are, of course, a large number of topics still not touched upon in
thepresentedition:QCDhasgrownintosuchavastfieldthatnosinglebook
can hope to provide anything near a full coverage of it. But I feel confident
that, with the new additions, the book presents at least a fair sample of the
main areas where QCD allows one to get quantitative results.
It is a pleasure to thank the colleagues that have contributed with
their collaboration, discussions and information, to whatever improvement
this new edition presents: J. Santiago and, above all, J. R. Pela´ez and
J. de Troc´oniz. Correspondence with J. Gasser concerning certain matters
associated with chiral perturbation theory has also been helpful.
Once again, I would like to acknowledge the continued support and un-
derstanding of Springer–Verlag in all editorial matters.
Madrid, January, 2006 F. J. Yndura´in
Preface to the Third Edition
QCD is an ever growing area of physics; when writing a new edition of a
book dealing with it, it is thus impossible not to take into account some at
leastofthenewdevelopmentsinthefield.Inselectingthosetobeincluded,I
havefollowedtheprincipleofincorporatingdevelopmentspertainingtotopics
already treated in the former editions. Thus I have not included sections on
chiraldynamicsoreffectivetheories.*Whathasbeenincludedareexpansions
of a number of sections. In particular of those dealing with deep inelastic
scattering: both on higher order calculations, quite a number of which have
become available in the last few years and, especially, on the small x limit of
structure functions where, triggered by the results of HERA, there has been
considerableactivity.InthischapterdealingwithperturbativeQCDwehave
alsoaddedasectiononτ andZ decays,atpresentthemorereliableprocesses
from which to extract the QCD coupling constant, α .
s
Two more topics have also received special attention. One is the matter
of bound states of heavy quarks, where inclusion of higher order perturba-
tive and nonperturbative evaluations has led to a clarification of the QCD
description, particularly of lowest states of heavy quarkonia: Chapter 6 has
been almost entirely rewritten. The other concerns Chapter 10, expanded
to include the results of high order (four loop) calculations of β, γ ; an
m
updated determination of the parameters of the theory (quark masses, Λ,
condensates); and a few considerations on the character of the perturbative
QCD series, including discussion of saturation and renormalons.
Besidesthis,Ihaveprofitedtoimprovesomeofthefeaturesofthebook:
a general polishing, including updating of Sect. 7.4 and relocating of the sec-
tionsoninstantonsandlatticeQCDfromChapter8totwoseparatechapters
(plus addition of asmallSubsection 9.5iii); and technical improvements such
as replacement of the old fashioned figures by computer generated graphs.
Forthisnewedition,Iwouldliketorecordmygratitudeto,besidespeople
alreadyquotedinformerones,A.Pich,J.VermaserenandYu.Simonov,who
read some of the new material in the manuscript; and to K. Adel for his
program “Kdraw”, used for the computer generation of the figures. Finally,
* Withrespecttothefirst,seebibliographyintext.Forthesecond,theinterested
readermayconsulttheoriginalpaperofCaswellandLepage(1986)andthereviews
of Lepage and Thacker (1988) and Grinstein (1991).
X Preface
the continued support of Springer–Verlag in all editorial matters is warmly
acknowledged.
Madrid, December 1998 F. J. Yndura´in
Preface to the Second Edition
The present book is not merely an elaboration of the 1982 text Quantum
Chromodynamics: An Introduction to the Theory of Quarks and Gluons. In
fact, a lot of material has been added: some of which is entirely new, and
some of which is an extension of topics in the older text. Among the latter
there are two sections dealing with the background field method, and the
expansion of the section devoted to processes describable by perturbative
QCD (other than deep inelastic scattering) into a whole chapter, containing
adetaileddescriptionofDrell–Yanscattering,jetphysics,exclusiveprocesses,
QCD sum rules, etc. Besides this, I have added a completely new chapter on
constituent quark models of hadrons, including a derivation of the quark–
quark potential and, also entirely new, a half chapter containing a detailed
introduction to lattice QCD. An extra short chapter on the parameters of
QCDandanappendixongroupintegrationcontributetomakingthepresent
book a really new text, sufficiently so to justify the change of title to The
Theory of Quark and Gluon Interactions: a change that also emphasizes the
consolidation of QCD as the theory of strong interactions.
Ofcourse,evenwiththeinclusionofnewmaterialtherearewholeareasof
quarkandgluonphysicsnotcoveredatall.Amongthese,letmementionthe
large N limit of QCD (the interested reader may consult ’t Hooft, 1974a,b,
c
Witten,1979b,1980);theinfraredproblemsinQCD,verypoorlyunderstood
(see, e.g., the classic paper of Lee and Nauenberg, 1964; Muller, 1978 and
Zachariasen,1980),and,especially,QCDatfinitetemperature,afashionable
subject at present, which the reader may follow from the review of Gross,
Pisarski and Yaffe (1981).
Besides the people quoted in the preface to the 1982 edition, I would
like to acknowledge the valuable influence of my scientific involvement with
R. Akhoury, F. Barreiro, G. Lo´pez Castro and M. Veltman, and thank again
A. Gonza´lez-Arroyo, who kindly undertook a most useful critical reading of
the part concerning lattice QCD.
Madrid, 1992 F. J. Yndura´in
Preface to the First Edition
Quantum Chromodynamics – An Introductionto the Theory
of Quark and Gluon Interactions
It is almost thirty years since Yang and Mills (1954) performed their pio-
neering work on gauge theories, and it is probably safe to say that we have
in our hands a good candidate for a theory of the strong interactions based,
precisely, on a non-Abelian gauge theory. While our understanding of quan-
tum chromodynamics (QCD) is still incomplete, there have been sufficient
theoretical developments, many of them enjoying a degree of support from
experimentalevidence,tojustifyareasonablysystematictreatiseonthesub-
ject.
Of course, no presentation of QCD can claim to be complete, since the
theory is still in the process of elaboration. The selection of topics reflects
this: I have tried to discuss those parts of the theory that are more likely
to endure, and particularly those developments that can, with a minimum
of rigour, be derived from “first principles”. To be sure, prejudice has also
influencedmychoice:onenecessarilytendstogivemoreattentiontosubjects
with which one is familiar, and to eschew unfamiliar ones. I will not pause
here to point out topics which perhaps should have been included; the list of
references should fill the gaps.
This work grew out of graduate courses I have been teaching for the last
few years: the book is intended to reflect the pedagogical and introductory
nature of those lectures. With this aim in mind, I have tried to write a self-
contained text which avoids as far as possible the maddening circumventions
of sentences like “it can be shown” or “as is well known”. However, I have
assumed the reader to have a basic knowledge of field theory and particle
phenomenology,andhavenodoubtthatoccasionalrecoursetotheliterature
will be necessary.
Whatthis book owes to the standard reviewsand articles on the subject
shouldbeapparentandisrecordedinthereferences.Ihavedirectlybenefited
from collaboration with my colleagues: A. Gonza´lez-Arroyo, C. Becchi, S.
Narison, J. Bernabeu, E. de Rafael, R. Tarrach and, particularly, C. Lo´pez
and P. Pascual (who also spotted several mistakes in a preliminary version
of this work), to name only a few. I also wish to acknowledge the invaluable
secretarial help of Antoinette Malene.
Madrid, 1982 F. J. Yndura´in
