Introduction to Elementary Particle Theory 0080179541

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Yu.V. Novozhilov

INTRODUCTION TO E L E M E N TA RY PA RT I C L E T H E O RY

INTRODUCTION TO

ELEMENTARY PARTICLE THEORY by

YU. V. NOVOZHILOV Leningrad State University

Translated by

JONATHAN L. ROSNER University o f Minnesota

PERGAMON PRESS O X FO R D • NEW YORK TO RO N TO • SY D N EY . BRAUNSCHW EIG

Pergamon Press Ltd., Headington Hill Hall, Oxford Pergamon Press Inc., Maxwell House, Fairview Park, Elmsford New York 10523 Pergamon of Canada Ltd., 207 Queen’s Quay West, Toronto 1 Pergamon Press (Aust.) Pty. Ltd., 19a Boundary Street, Rushcutters Bay, N.S.W. 2011, Australia Pergamon Press GmbH, Burgplatz 1, Braunschweig 3300, West Germany Copyright © 1975 Pergamon Press Ltd. All Rights Reserved . No part o f this publication may be reproduced, stored in a retrieval system, or transmitted , in any form or by any means, electronic , mechanical, photocopying , recording or otherwise , without the prior permission o f Pergamon Press Ltd .

First edition 1975 Library of Congress Cataloging in Publication Data Novozhilov, IUril Viktorovich. Introduction to elementary particle theory. (International series of monographs in natural philosophy, 78) Translation of Vvedenie v teoriiu elementamykh chastits. 1. Particles (Nuclear physics) QC793.2.N6813 1975

539.721

ISBN 0-08-017954-1

Printed in Hungary

I. Title. 74-17036

PREFACE

The present stage of development in the physics of elementary particles began at the end of the 1950s. With the 1960s our view of the elementary (or fundamental) particles and their interactions broadened considerably. Instead of a score of stable or nearly stable particles and several resonances in pion-nucleon scattering, we now know of more than a couple of hundred particles and resonances. Our picture of space-time symmetry underwent still another change as a result of the discovery of the nonconservation of the combined parity CP (or noninvariance with respect to time reversal T), and, consequently, it is possible that the three basic types of interaction have been joined by a fourth—the superweak interac­ tion. During the same time significant information on high-energy scattering and properties of resonances has accumulated. In elementary particle theory the 1960s were an era of symmetry, Regge poles, current algebra, and duality. During this time fruitful schemes of internal symmetry were construct­ ed, described by the groups SU3and St/e, as well as by current algebra and chiral symmetry. At the same time, the basic features of the asymptotic behavior of scattering amplitudes were clarified, and the fundamental nature of the Regge trajectory was established. The notion of duality introduced in recent years may become a basic concept of future theory. The vigorous development of elementary particle physics has made it evident that quan­ tum field theory cannot assume the role of a theory of elementary particles. Nonetheless, the local quantum theory of fields remains the basis from which general principles are adopted and with whose help several models are constructed. The contemporary theory of elementary particles may be called a constructive theory. Starting from well-founded principles of quantum field theory, from experiment, and from guesses, such a theory seeks to select and work out the ideas essential for the description of the elementary particles and resonances. Regge trajectories, unitary and chiral symmetries, current algebra, and duality are successful examples of the constructive approach; they depend on the local theory but cannot be unambiguously obtained from it or proven. The present book is meant as an introduction to such a constructive theory of elementary particles. The author hopes that such a book will be useful as a complement to other texts on elementary particle theory.u “4) The book consists of four parts. The introductory Part I acquaints the reader with the basic description of elementary particles. In Part II questions of relativistic quantum me­ chanics and kinematics are set forth; Part III is devoted to the problem of internal symmetry, and Part IV to those new dynamical approaches which are likely to have the greatest influ­ ence on the development of theory in the future. Quantum electrodynamics and renormalIX

X

PREFACE

ization are excluded from the present book, as these questions are contained in the standard quantum theory of fields.(5' 7) The author does not give a systematic review of experimental data, but cites only the information essential to illustrate the pattern of phenomena and to connect theory with experiment. The Appendix contains tables of particles, but the reader’s main reference on particle properties should be special annual reviews/8* The list of references contains only those works which, in the author’s opinion, are basic. The reader may acquaint himself with a more complete list in books(9"20) and in reviews referred to here. The plan of the book essentially follows the program of courses on elementary particle theory given in the Physics Faculty of Leningrad University. The reader must be familiar with nonrelativistic quantum mechanics and classical relativity theory. It would also be very useful to have a preliminary acquaintance with the fundamentals of the Lagrangian formulation of quantum field theory and with Feynman diagrams .(5"7) A course in elementary particle field theory usually is preceded by a short course on group theory. We thus assume that the basic facts of group theory are known to the reader/18,19) The author is grateful to A. A. Ansel’m, M. A. Braun, B. V. Medvedev, I. A. Terent’ev, and especially to L. V. Prokhorov, V. A. Frank, and Yu. P. Shcherbin for valuable advice. The author thanks colleagues and students in the nuclear theory and elementary particle theory groups at Leningrad State University for help and discussions. Several chapters of a first version of this book were written during the author’s stay at the Faculty of Physics and Astronomy of Delhi University. The author wishes to use this occasion to express his gratitude to Professors D. S. Kothari and R. S. Majumdar for their hospitality and for pleasant working conditions.

xi

AUTHOR’S PREFACE TO THE ENGLISH EDITION

In t h e time since this book was finished the center of gravity of interest in elementary particle physics has shifted to the weak and electromagnetic interactions. Gauge theories and parton models have become the subject of nearly universal attention. The author, however, has decided to overcome the temptation to write a supplement on gauge fields and expand the chapter on weak interactions, since the book is primarily devoted to the phenomenological foundations of relativistic theory and to the strong inter­ actions from the 5-matrix standpoint. An exposition of gauge theories would have required an introduction to the Lagrangian formalism (which we do not consider separately) and the use of functional integration (which we do not even mention). The author appreciates the careful and exacting work performed by Prof. Rosner in the process of translation. The changes he has made, of which I approve fully, can only serve to improve the treatment. Yu. Novozhilov Paris, July 1974

TR A N SL A T O R ’S PREFACE

T he serious student of elementary particle theory must cope both with rather formal course work and with a highly specialized literature. The relation between the formalism and its application to practical problems often is not transparent at first glance. The present book, by presenting a unified treatment of both, helps in large measure to bridge this gap. The main emphasis of the book is on the strong interactions, where the need for such a “bridge” is greatest. The first two parts present a theoretical framework which is then used extensively in dealing with concrete problems in the last two parts. It was partly my appreciation for the particular fortunate combination of “theory” and “practice” in this book— which cor­ responded very closely to the way I happened to learn the subject—that led me to undertake the translation. I would like to express deep gratitude to Professor Novozhilov for his constant interest and encouragement, for his patient help in clarifying points in the text, and for making available a list of misprints in the Russian edition. I would also like to ask his indulgence regarding the minor modifications (that a practising theorist cannot help making) which I felt would bring portions of the material more up to date. In general, however, the trans­ lation attempted to follow the text as closely as possible. This was not difficult owing to the exceptional clarity of the original prose. Professor Morton Hamermesh provided much valuable technical advice regarding trans­ lation procedures. I am thankful to Mrs. Valerie Nowak, Mrs. Veronica Goidadin, Miles M. Milligan and S. Williams, Mrs. Janace Ator, and Mrs. Sandra Smith for expert typing. Finally, my special appreciation is reserved for my wife, Joy, whose day-to-day moral support and whose assistance in the final correction of the typescript made a pleasant but protracted task seem shorter and sweeter.

NOM EN CLA TU RE

This book uses units in which h = c — 1.

Indices and abbreviations Indices denoted by the Greek letters //, v, g, . . . , take on the values 0, 1, 2, 3. Indices denoted by the Latin letters i j , fc, . . . , take on the values 1,2, 3. Spinor and isospinor indices are denoted by a, /J, y, . . . = 1,2, but for Dirac bispinors • = 1,2,3,4. Indices denoted by the Latin letters a, b, c, . . . , take on the values 1, 2, 3, . . . , 8. Contra variant components of a vector have the same sign as in the nonrelativistic theory: a* = (ia°, a). The metric tensor gMV= g^v has the signature (-f---------- ). Scalar product: aj.Y = ab = a0b0—a*b. Abbreviations: du = d / d x □ = 0q—02. The antisymmetric pseudo-tensor e ^ ais normalized according to e0123 = —1 or s0iJk = eiJk. Volume elements: d*a = da°cPa, dza = da1da2da?. Commutators and anticommutators: AB—BA = [A, B]_ = [^4,5], AB+BA = [A, B]+ = Hermitian conjugation, complex conjugation, and transposition are denoted respectively by the superscripts + , *, and T.

State vectors and Lorentz group Spin: J\ spin-parity: 7P; spin projection on the z-axis: a\ helicity: A. Normalization of states: ,