Particles and Fields PDF
Preview Particles and Fields
Particles and Fields Particles and Fields Edited by DAVID H. BOAL and ABDUL N. KAMAL University of Alberta Edmonton, Alberta, Canada Plenum Press· New York and London Library of Congress Cataloging in Publication Data Banff Summer Institute on Particles and Fields, 1977. Particles and fields. Proceedings of the institute held at the Banff Center, Banff, Canada, Aug. 25-Sept. 3, 1977. Includes index. 1. Particles (Nuclear physics)-Congresses. 2. Field theory (Physics)-Congresses. I. Boal, D. H. II. Kamal, A. N. III. Title. QC770.B36 1977 539.7 78-2509 ISBN-13: 978-1-4613-4002-7 e-ISBN-13: 978-1-4613-4000-3 001: 10.1007/978-1-4613-4000-3 Proceedings of the Banff Summer Institute on Particles and Fields held at the Banff Center in Banff, Canada, August 25-September 3,1977 © 1978 Plenum Press, New York Softcover reprint of the hardcover 1s t edition 1978 A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N.Y. 10011 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transm itted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher PREFACE This volume contains the invited lectures and seminars presented at the Banff Summer Institute on Particles and Fields held at the Banff Center in Banff, Canada,from 25 August to 3 September, 1977. The town is situated in the heart of the Canadian Rockies, and the observant reader may notice references in this volume to the bears which roam near the town. The subject matter of the school was recent advances in particle physics and field theory. Lectures were given on such topics as extended objects, lattice gauge theories, quantum chromodynamics and Reggeon field theory. Experimental reviews were given of recent work in charmed particle and neutrino physics. Summaries of the theoretical implications of these experiments were also given. The format of the talks included eight lecture series (of three to four hours each) given by Profs. Abarbanel, Appelquist, Feldman, Gilman, 't Hooft, Jackiw, Mann and Weinstein, seven one-hour seminars given by Profs. Caianiello, Fujii, Johnson, Lam, Phillips, Sherry and Tze, and several short contributed seminars (which do not appear in this volume). There were also small informal seminar groups held at the Center and, we hope, many physics conversations on the hiking trails where most of the participants spent their afternoons. Not included in these proceedings are the banquet speeches by E. Caianiello and S. D. Drell, as well as (for copyright reasons) a seminar by K. Johnson. We would like to thank the following members of the International Advisory Committee for their assistance and advice: E. R. Caianiello, University of Salerno S. D. Drell, Stanford Linear Accelerator Center Y. Fujii, University of Tokyo T. W. B. Kibble, Imperial College C. S. Lam, McGill University Y. Nambu, University of Chicago R. J. N. Phillips, Rutherford Laboratory A. Salam, I.C.T.P., Trieste v vi PREFACE G. Sudarshan, University of Texas M. K. Sundaresan, Carleton University. Much of the detailed work was handled by the five man Local Organizing Committee, whose members, in addition to DHB and ANK were: A. Z. Capri Y. Takahashi H. Umezawa all of the University of Alberta. On the local level, our thanks also go to K. James, secretary at the conference, as well as G. Braun, L. Cech and M. Yiu, who typed the manuscript. Lastly, thanks are due to all those individuals at the University of Alberta who we coerced into folding letters, sealing envelopes and helping with the registration, and to the staff of the Banff Center who contributed to the smooth operation of the Institute. Of course, the Institute was not self-supporting and we gratefully acknowledge the financial support we received from the following organizations: National Research Council of Canada University of Alberta Institute of Particle Physics Theoretical Physics Division, Canadian Association of Physicists Atomic Energy of Canada Ltd. Gulf Oil Canada Ltd. The Institute was organized under the auspices of the Theoretical Physics Division of the Canadian Association of Physics, whose executive for 1976-77 was composed of three members of the Local Organizing Committee (DHB, ANK, HU). C.A.P. attempts to hold a summer school annually at Banff, and the royalties from the sale of the proceedings of this and previous schools will go toward the support of future Summer Institutes. D. H. Boal, A. N. Kamal Edmonton, Canada December, 1977. CONTENTS Contemporary Reggeon Physics 1 H. D. I. Abarbanel Chromodynamic Structure and Phenomenology 33 T. Appelquist Non-Perturbative Methods in Field Theory • • • • • 59 E. R. Caianiello, M. Marinaro and G. Scarpetta Charmed Particle Spectroscopy 75 G. J. Feldman Dimensional Regularization and Hyperfunctions 115 Y. Fuj ii Hadron Spectroscopy and the New Particles 127 F. J. Gilman Extended Objects in Gauge Field Theories • • • • • • • • •• 165 G. It Hooft Classical and Semi-Classical Solutions of the Yang-Mills Theory • • • • 199 R. Jackiw, C. Nohl and C. Rebbi Transverse Momentum Distribution of Partons in Quantum Chromodynamics • • • • 259 C. S. Lam Trimuons 277 R. J. N. Phillips An Approach to Measurement in Quantum Mechanics 289 E. C. G. Sudarshan, 1. N. Sherry and S. R. Gautam A Survey of Vortices in Gauge Theories • • 305 H. C. Tze vii viii CONTENTS Lattice Gauge Theories • 321 M. Weinstein Some Recent Advances in Neutrino Physics • 381 A. K. Mann Participants • 451 Index 459 CONTEMPORARY REGGEON PHYSICS Henry D.I. Abarbanel Fermi National Accelerator Laboratory Batavia, Illinois, U. S. A. 1. INTRODUCTION AND OUTLINE This set of lectures aims to introduce the reader to the physics behind Reggeon field theories (RFT) and the developments in that subject. The goal of RFT is a coherent basis for the effects, in physical processes at large collision energies and small momentum transfers, of diffraction scattering subsumed in the form of the Pomeron Regge trajectory which has 0.(0) = 1, the maximum allowed by unitarity. Time, the patience of the listener, and the attention span of the lecturer did not permit a complete covering of all topics in RFT. Indeed, many have been left untouched. With extended apologies to the appropriate authors I refer the reader to the reviews in Reference 1. Here we treat the following topics: 1. Physical and Experimental Basis for Reggeon Physics 2. Theory of Regge Poles - The Multiperipheral Model 3. Reggeon Unitarity 4. A Suggestive Analogy 5. Critical Behavior in RFT and the "Ordered Phase" of RFT, which should serve as an introduction to the literature and the subject as a whole. 2 H. D. I. ABARBANEL 2. EXPERIMENTAL AND PHYSICAL BASIS FOR REGGEON PHYSICS We will be concerned at first with the elastic collision of equal mass, spinless hadrons as shown in Figure 1, where T(s,t) is the elastic scattering am~litude as a function of an energy variable s = (PA + PB)2 = 4Ecm and t = (PA - PAd 2 = -2p~m(1- cos6); Ecm' Pcm' and 6 are respectively the energy, momentum and scatter ing angle in the barycentric system. The differential cross section comes from T(s,t) dG(szt) 1 IT(s,t)1 2, (1) dt l6lT2s2 and via the optical theorem the total cross section is 1m T(s,O) 1m T(s,t) s s GT(s) (2) s large s Is (s-4m2) Our interest will be in such processes at large s, fixed t. Since dcr(s,t)/dt falls very rapidly as t moves away from 0 (typically as exp-[(B or 10)t/(GeV/c)2]), we are discussing the majority of hadron collision events. Now the basic facts we need are as follows: If in the t AA' channel (the direction of in Figure 1) the isospin is not zero; - 0 for example, It = 1 in IT p+rr n, then -ilTIlI(t) ± e ) TI(s,t) (3) :;:! sin lTll (t) s large I t fixed where ilr(t) , called the Regge trajectory, can be accurately approximated by A A' B B' Fig. 1. The two-to-two hadron scattering amplitude T(s,t) as a function of energy s = (PA+PB)2 and momentum transfer t= (PA-PA,)2. For equal mass particles the physical region is s ~ 4m2, t ~ O. CONTEMPORARY REGGEON PHYSICS 3 =a +a't, (4) o 0 and T (the signature) depends on the particular quantum numbers in the t-channe1. For the case when the allowed quantum numbers are those of the p-meson such processes have been studied over a large range of sand t and are accurately represented by T = -1 and p a (t) = 0.53 + 0.91 t/ (GeV/c)2 , (5) p which may approximately be read as a (t) = 0.5 + t. When this straight line is projected from the s~attering region (t ~ 0) where it is measured to the time1ike region (t > 0) where the real p-meson lives one has to good accuracy the trajectory shown in Figure 2, which shows how a Regge trajectory connects scattering and resonances (here p and g mesons). If the t-channe1 allows the quantum numbers of the vacuum (elastic scattering, for example), the situation is different Tp(s,t) ~ (log s) n , (6) s large t fixed where the Pomeron or vacuum trajectory is ap(t) = 1 + 0.287 t/ (GeV/c) 2 (7) 2.5 t/ (Gev/ c Fig. 2. The Chew-Frautschi a(t) vs. t plot for the p-meson trajectory.
The list of books you might like
