Lectures-on-QCD.Applications.pdf - Lecture Notes in Physics...

Unformatted text preview: Lecture Notes in Physics Editorial Board H. Araki, Kyoto, Japan R. Beig, Vienna, Austria J. Ehlers, Potsdam, Germany U. Frisch, Nice, France K. Hepp, Ziirich, Switzerland R. L. Iaffe, Cambridge, MA, USA R. Kippenhahn, G6ttingen, Germany H. A. Weidenmiiller, Heidelberg, Germany J. Wess, Miinchen, Germany J. Zittartz, K61n, Germany Managing Editor W. Beiglb6ck Assisted by Mrs. Sabine Lehr c/o Springer-Verlag, Physics Editorial Department II Tiergartenstrasse 17, D-69121 Heidelberg, Germany Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Santa Clara Singapore Tokyo The Editorial Policy for Proceedings The series Lecture Notes in Physics reports new developments in physical research and teaching - quickly, informally, and at a high level. The proceedings to be considered for publication in this series should be limited to only a few areas of research, and these should be closely related to each other. 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Lectures on QCD Applications ~ Springer Editors Frieder Lenz Harald Griei]hammer Dieter Stoll Institut ffir Theoretische Physik III Universit~it Erlangen-Nfirnberg Staudtstrasse 7 D-91o58 Erlangen, Germany Cataloging-in-Publication Data applied for. Die Deutsche Bibliothek - CIP-Einheitsaufnahme L e c t u r e s o n Q C D / Frieder Lenz ... (ed.). - Berlin ; Heidelberg ; New York ; Barcelona ; Budapest ; H o n g Kong ; London ; Milan ; Paris ; Santa Clara ; Singapore ; Tokyo : Springer Applications. - 1997 (Lecture notes in physics ; 496) ISBN 3-540-63442-8 ISSN 0075-8450 ISBN 3-540-63442-8 Springer-Verlag Berlin Heidelberg New York 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms 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-Verlag.Violations are liable for prosecution under the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1997 Printed in Germany 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: Camera-ready by the authors/editors Cover design: design&productionGmbH, Heidelberg SPIN: 10556558 55/3144-543210 - Printed on acid-free paper Preface The two volume set "Lectures on QCD" provides an introductory overview of Quantum Chromodynamics, the theory of strong interactions. In a series of articles, the fundamentals of QCD are discussed and significant areas of application are described. Emphasis is put on recent developments. The field-theoretic basis of QCD is the focus of the first volume. The topics discussed include lattice gauge theories, anomalies, finite temperature field theories, sum-rules, the Skyrme model, and supersymmetric QCD. Applications of QCD to the phenomenology of strong interactions form the subject of the second volume. There, investigations of deep inelastic lepton-nucleon scattering, of high energy hadronic reactions and studies of the quark-glnon plasma in relativistic heavy ion collisions are presented. These articles are based on lectures delivered by internationally well known experts on the occasion of a series of workshops organised by the "Graduiertenkolleg on Strong Interaction Physics" of the Universities of Erlangen-N/irnberg and Regensburg in the years 1992-1995. The workshops were held at "Kloster Banz". Kloster Banz is a former monastery overlooking the valley of the river Main and still serves, for some days of the year, as the stage where certain canons and orthodoxies are vigorously formulated. Inspired by the atmosphere of the site, the workshops were set up with the aim of introducing novices in the field to the basics of QCD. Accordingly, the character of the lectures was pedagogical rather than technical. With the organisation of these workshops we have attempted to establish a new form in graduate education. Graduate students of the "Graduiertenkolleg" constituted a large fraction of the audience. They have worked out these articles on QCD in collaboration with the lecturers. Thanks are due to Jutta Geithner and Achim Oppelt for help in the preparation of these proceedings. The support of the "Graduiertenkolleg" by the Deutsche Forschungsgemeinschaft was instrumental in this endeavor and is gratefully acknowledged. Erlangen, August 1997 F. Lenz H. W. Grieflhammer D. Stoll Contents High Energy Collisions and Nonperturbative QCD 0 . Nachtmann ................................. Perturbative QCD (and Beyond) Yu. L . Dokshitzer; Notes in collaboration with R. Scheibl and C. Slotta 87 Quark Matter and High Energy Nuclear Collisions H. Satz; Notes by S. Leupold . . . . . . . . . . . . . . . . . . . . . . . . . 136 Spin~ Twist and Hadron Structure in Deep Inelastic Processes R. L. Jaffe; Notes by H. Meyer and G. Piller 178 ................ Quark-Gluon Structure of the Nucleon K. Rith 250 ..................................... Low-x Physics at H E R A A. Levy; Notes in cooperation with M. Ferstl and A. Gute Subject Index ................................. ........ 347 478 High Energy Collisions and Nonperturbative QCD* O. Nachtmann Institut fiir Theoretische Physik, Universitgt Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany We discuss various ideas on the nonperturbative vacuum structure in QCD. The stochastic vacuum model of Dosch and Simonov is presented in some detail. We show how this model produces confinement. The model incorporates the idea of the QCD vacuum acting like a dual superconductor due to an effective chromomagnetic monopole condensate. We turn then to high energy, small momentum transfer hadronhadron scattering. A field-theoretic formalism to treat these reactions is developed, where the basic quantities governing the scattering amplitudes are correlation functions of light-like Wegner-Wilson lines and loops. The evaluation of these correlation functions with the help of the Minkowskian version of the stochastic vacuum model is discussed. A further surprising manifestation of the nontrivial vacuum structure in QCD may be the production of anomalous soft photons in hadron-hadron collisions. We interpret these photons as being due to "synchrotron radiation from the vacuum". A duality argument leads us from there to the expectation of anomalous pieces proportional to (Q2)I/B in the electric form factors of the nucleons for small Q2. Finally we sketch the idea that in the Drell-Yan reaction, where a quark-antiquark pair annihilates with the production of a lepton pair, a "chromodynamic Sokolov-Ternov effect" may be at work. This leads to a spin correlation of the qq pair, observable through the angular distribution of the lepton pair. Abstract. 1 Introduction In these lectures I would like to review some ideas on the way nonperturbative QCD may manifest itself in high energy collisions. Thus we will be concerned with strong interactions where we claim to know the fundamental Lagrangian for a long time now [1]: cQco(x) = + - (1.1) q Here q(x) are the quark fields for the various quark flavours (q = u,d, s, c, b, t) with masses mq. We denote the gluon potentials by G~(x) (a = 1, ..., 8) and the gluon field strengths by a ~ , (x) = o ~ a ; (x) - o~a~ (x) - gAbcG~ ( x ) a ; (x), (1.2) * Grown out of lectures presented at the workshop "Topics in Field Theory" organised by the Graduiertenkolleg Erlangen-P~egensburg, held on October 12th-14thi 1993 in Kloster Banz, Germany 2 O. Nachtmann where g is the strong coupling constant and fabc are the structure constants of SU(3). The covariant derivative of the quark fields is Dxq(x) = (Oh + igG~ + )q(x), (1.3) with ha the Gell-Mann matrizes of the SU(3) group. The gluon potential and field strength matrizes are defined as c~(x) : = c ~ , ( ~ ) ~ , G.xt,(x) : = Gip(x)~. (1.4) The Lagrangian (1.1) is invariant under SU(3) gauge transformations. Let x -+ U(x) be an arbitrary matrix function, where for fixed x the U(x) are SU(3) matrices: U(x)ut(x)= 1, detU(x) 1. (1.5) q(~) + u(~)q(x), (1.6) = With the transformation laws: cA (~) + g(~)c~ (x)v*(x) - y U(x)Oj, Ut (1.7) we find U~p(x) ~ U(x)G~p(x)Ut(x), and invariance of •QCD: £QCD(X) -* Z:QCD(X). (1.8) If we want to derive results from the Lagraugian (1.1), we face problems, the most notable being that £QCD is expressed in terms of quark and gluon fields whose quanta have not been observed as free particles. In the real world we observe only hadrons, namely colourless objects; quark and gluons are permanently confined. Nevertheless it has been possible in some cases to derive first principle results which can be compared with experiment, starting from/:QCD (1.1). These are in essence the following: (1) Pure short-distance phenomena: Due to asymptotic freedom [2] the QCD coupling constant becomes small in this regime and one can make reliable perturbative calculations. Examples of pure short distance processes are for instance the total cross section for electron-positron annihilation into hadrons and the total hadronic decay rate of the Z-bosom (2) Pure long-distance phenomena: Here one is in the nonperturbative regime of QCD and one has to use numerical methods to obtain first principle results from £QCD, or rather from the lattice version of £:QCD introduced by Wilson High Energy Collisions and Nonperturbative QCD 3 [3]. Today, Monte Carlo simulations of lattice QCD are a big industry among theorists. Typical quantities one can calculate in this way are hadron masses and other low energy hadron properties. (For an up-to-date account of these methods cf. [4]). There is a third regime of hadronic phenomena, hadron-hadron collisions, which are - apart from very low energy collisions- neither pure long-distance nor pure short-distance phenomena. Thus, none of the above-mentioned theoretical methods apply directly. Traditionally one classifies high-energy hadron-hadron collisions as "hard" and "soft" ones: (3) High energy hadron-hadron collisions: (a) hard collisions, (b) soft collisions. A typical hard reaction is the Drell-Yan process, e.g. 7r- + N --+ 7 * + X ¢-~ e+e - (1.9) where l = e, #. All energies and m o m e n t u m transfers are assumed to be large. However, the masses of the n - and N in the initial state stay fixed and thus we are not dealing with a pure short distance phenomenon. T" N Fig. 1. The lowest order diagram for the Drel1-Yan reaction (1.9) in the QCD improved patton model. In the reaction (1.9) we claim to see directly the fundamental q u a n t a of the theory, the patrons, i.e. the quarks and gluons, in action (cf. Fig. 1). In the usual theoretical framework for hard reactions, the QCD improved p a r t o n model (cf. e.g. [5]), one describes the reaction of the partons, in the Drell-Yan case the qq annihilation into a virtual photon, by perturbation theory. This should be reliable, since the parton process involves only high energies and high m o m e n t u m 4 O. Nachtmann transfers. All the long distance physics due to the bound state nature of the hadrons is then lumped into patton distribution functions of the participating hadrons. This is called the factorization hypothesis, which after early investigations of soft initial and final state interactions [6] was formulated and studied in low orders of QCD perturbation theory in [7]. Subsequently, great theoretical effort has gone into proving factorization in the framework of QCD perturbation theory [8]-[10]. The result seems to be that factorization is most probably correct there (cf. the discussion in [11]). However, it is legitimate to ask if factorization is respected also by nonperturbative effects. To my knowledge this question was first asked in [12] -[14]. In Sect. 4 of these lectures I will come back to this question and will argue that there may be evidence for a breakdown of factorization in the Drell-Yan reaction due to QCD vacuum effects. Let us consider now soft high energy collisions. A typical reaction in this class is proton-proton elastic scattering: p + p ---+ p + p (1.10) at c.m. energies Ecm = X/~ >~ 5GeV say and small momentum transfers ~ / ~ = Iql <~ 1GeV. Here we have two scales, one staying finite, one going to infinity: Ecru --4 cx), Iql <~ 1GeV. (1.11) Thus, none of the above mentioned calculational methods is directly applicable. Indeed, most theoretical papers dealing with reactions in this class develop and apply models which are partly older than QCD, partly QCD "motivated". Let me list some models for hadron-hadron elastic scattering at high energies: geometric [15], eikonal [16], additive quark model [17], Regge poles [18], topological expansions and strings [19], valons [20], leading log summations [21], two-gluon exchange [22], the Donnachie-Landshoff model for the "soft Pomeron" [23]. It would be a forbidding task to collect all references in this field. The references given above should thus only be considered as representative ones. In addition I would like to mention the inspiring general field theoretic considerations for high energy scattering and particle production by Heisenberg [24] and the impressive work by Cheng and Wu on high energy behaviour in field theories in the framework of perturbative calculations [25]. I will now argue that the theoretical description of measurable quantities of soft high energy reactions like the total cross sections should involve in an essential way nonperturbative QCD. To see this, consider massless pure gluon theory High Energy Collisions and Nonperturbative QCD 5 where all "hadrons" are massive glueballs. Then we know from the renormalization group analysis that the glueball masses must behave as mglueball (X Me -c/g2(M) (1.12) for M --~ c~, i.e. for g(M) ~ O, due to asymptotic freedom. Here M is the renormalization scale, g(M) is the QCD coupling strength at this scale and c is a constant: g2(M) 4~r2 87r2 C~ A: 12 33 ln(M2/A 2) for M ~ c~, 11' QCD scale parameter. (1.13) Masses in massless Yang-Mills theory are a purely nonperturbative phenomenon, due to "dimensional transmutation". Scattering of glueball-hadrons in massless pure gluon theory should look very similar to scattering of hadrons in the real world, with finite total cross sections, amplitudes with analytic t dependence etc. At least, this would be my expectation. If the total cross section atot has a f...
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