Many Degrees of Freedom in Particle Theory

562 Pages·1978·22.526 MB·English

by  M. Le Bellac (auth.), H. Satz (eds.)

Many Degrees
of Freedom
in Particle Theory
NATO ADVANCED STUDY INSTITUTES SERIES
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Many Degrees
of Freedom
in Particle Theory
Edited by
H.Satz
University of Bielefeld, Federal Republic of Germany
PLENUM PRESS • NEW YORK AND LONDON
Published in cooperation with NATO Scientific Affairs Division
Library of Congress Cataloging in Publication Data
International Summer Institute on Theoretical Physics, 8th, University of Bielefeld,
1976.
Many degrees of freedom in particle theory.
(NATO advanced study institutes series: Series B, Physics; v. 31)
"Published in cooperation with NATO Scientific Affairs Division."
Includes index.
1. Degree of freedom-Congresses. 2. Particles (Nuclear physics)-Congresses. I.
Satz, H. II. Title. III. Series.
QC793.3.D43I57 1976 539.7'21 78-27
ISBN 978-1-4684-2816-2 ISBN 978-1-4684-2814-8 (eBook)
DOI 10.1007/978-1-4684-2814-8
Proceedings of the 1976 International Summer Institute of Theoretical Physics he
at the University of Bielefeld, Federal Republic of Germany, August 23-Septembld
4, 1976, published in two volumes, of which this is the second 'er
© 1978 Plenum Press, New York
Softcover reprint of the hardcover I st edition 1978
A Division of Plenum Publishing Corporation
227 West 17th Street, New York, N. Y. 10011
All righ ts reserved
No part of this book may be reproduced, stored in a retrieval system, or transmitted,
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Preface
Volumes 30 and 31 of this series, dealing with "~1any
Degrees of Freedom," contain the proceedings of the 1976
International Summer Institute of Theoretical Physics,
held at the University of Bielefeld from August 23 to
September 4, 1976. This Institute was the eighth in a
series of summer schools devoted to particle physics and
organized by universities and research institutes in the
Federal Republic of Germany.
Many degrees of freedom and collective phenomena
playa critical role in the description and understanding
of elementary particles. The lectures in this volume
were intended to show how a combination of theoretical
prejudices and experimental results can lead to the crys
tallization of models and theories. Topics ranged from
quark, parton, and bag model~ to du~l unitarization, from
cluster pictures to hadron-nucleus collisions and to
astrophysical implications.
The Institute took place at the Center for Inter
disciplinary Research of the University of Bielefeld. On
behalf of all participants, it is a pleasure to thank the
officials and the administration of the Center for their
cooperation and help before and during the Institute.
Special thanks go to V.C. Fulland, M. Kamper, and A. Kpt
tenkamp for their rapid and competent preparation of the
manuscripts.
v
PREFACE
The Institute was sponsored by the NATO Advanced
Study Institute Programme and supported by the Bundes
minister fur Wissenschaft und Forschung of the Land
Nordrhein-Westfalen. Last, but certainly not least,
the valuable help of I. Andric, V. Enss, F. Jegerlehner,
B. Petersson, and P. Stichel in organizing the institute
is gratefully acknowledged.
March, 1977 H. Satz
Contents
. . . . . .
Reggeon Field Theory with a(O) > 1 • 1
M. Le Bellac
Some Remarks on Implementing Hadrons
as Extended Objects with Applications
to Dual Models • • • • 19
L.C. Biedenharn and H. van Dam
. . . . . .
High Density Matter in the Universe 37
v.
canuto and J. Lodenquai
Dual Unitarisation - A New Approach to . . . . .
Hadronic Interactions • • • 83
Chan Hong-Ho and Tsou Sheung Tsun
Collective Effects in High Energy
Interactions with Nuclei • • • • • 129
G. Eilam
Unified Interactions of Leptons and Quarks • •• 165
H. Fritzsch
The M.I.T. Bag, 1976 Edition. • • • • • • • •• 239
K. Johnson
Charmed Particles and Drell-Yan Photons
as Sources of Direct Leptons • • • • 259
K. Kajantie
vii.
CONTENTS
viii
Three Lectures on Lattice Gauge Theory . . • • • 275
J.B. Kogut
Clustering and Clusters • . • • • • • • • • •• 345
A. Krzywicki
Quark Partons • • • 383
P.V. Landshoff
Lectures on Hadron-Nucleus Collisions
at High Energies ••• . • . • • 417
A.H. Mueller
Heavy Clusters at High Energy.. ..•••• 447
M. Anselmino, A. Ballestrero, and E. Predazzi
Inclusive Correlations in the Central Region 461
G.H. Thomas
Recent Developments in Dual String Models . • •. 493
P. Di Vecchia
Who Needs Clusters in the Dual Bootstrap? • • •• 533
Y. Zarmi
List of Participants 553
Index • 559
REGGEON FIELD THEORY WITH a(O»1
M. Le Beilac
CERN
CH-1211 Geneva 23, Switzerland
I will discuss in these lectures the theory of the
Pomeron when the intercept a(O) is larger than one.
In the first two parts of the lectures I will give the
motivations for such an investigation, as well as a short
introduction to the Reggeon calculus. In the last part
I will describe what I believe to be the solution when
a(O) >1.
I. INTRODUCTION TO THE REGGEON CALCULUS
Let me begin by explaining briefly what a Reggeon
is. Of course it is first a pole in the partial wave
amplitude of the crossed (t)-channel, which leads to a
sa(t) behaviour of the scattering amplitude at high
energy. However this is a very general statement, and
one needs more dynamical information in order to go
further.
Indeed there are many dynamical models which give
in a particular range of sand t, and to a first approxi-
mation, a power law of the sa(t) type. Examples of such
dynamical models are the multiperipheral model, the dual
model, the first order of the topological expansion. A
general characteristic of all these approaches is that
besides the single Regge pole exchange, which is the
first order approximation, they also predict the presence
of multiple Regge exchanges which leads to Regge cuts.
2 M. LE BELLAe
The same conclusion is reached by a more abstract analysis,
based on t-channel unitarity.
A most important point is that all these approaches
agree on the general properties of these Regge cuts,
such as the position of the n-Reggeon branch point at
t=o:
].1n(O) = n(a(0)-1)+1 (1)
or = n].1
(where I have defined ].1 as a(0)-1), and the negative
sign of the two-Reggeon cut (more generally the alter
nating sign of the n-Reggeon cut). Eq. (1) implies that
the high-energy behaviour of 'the total cross-section will
be:
(2)
The extra logs dependence in (2) reflects the presence
of cuts. In principle at least the functions fn can be
calculated in the framework of each of the dynamical
models mentioned above.
Eq. (2) suggest a very simple situation; indeed,
when ].1+0, the Regge pole contribution (NS].1) clearly
dominates when s+oo, and one can simply ignore the exis
tence of cuts, at least asymptotically. Unfortunately
(or maybe fortunately, since it allows to keep some
theorists busy) this situation does not seem to be
realized in nature: ].1<0 implies decreasing cross-sections,
and, as is wellknown, ISR experiments showed 3 years
ago that, on the contrary, total cross-sections are
rising.
We are thus led to consider the case ].1>0, where we
cannot avoid the calculation of fn's and the analysis of
the sum over all multiple reggeon exchanges.
The actual computation of the fn's depends on the
specific Reggeon model under consideration. However there
is a general framework that allows to calculate the f 's
for large s and small t, which incorporates all knownn
dynamical models and is in agreement (and in fact sug
gested by) t-channel unitarity. This framework is Gibrov
Reggeon calculus. (1)