Table Of ContentParticles
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.
