Particle Interactions at High Energies: Scottish Universities’ Summer School 1966

420 Pages·1974·36.934 MB·English

by  T. W. Preist B.Sc., Ph.D., L. L. J. Vick B.Sc., Ph.D. (eds.)

PARTICLE INTERACTIONS
AT HIGH ENERGIES
EARLIER VOLUMES IN THIS SERIES
1. Dispersion Relations, edited by G. R. Screaton, M.A., PH.D.
(Scottish Universities' Summer School, 1960)
2. Fluctuation, Relaxation and Resonance in Magnetic Systems,
edited by D. ter Haar, M.A., DR.SC.
(Scottish Universities' Summer School, 1961)
3. Po/arons and Excitons, edited by C. G. Kuper, B.sc., M.A., PH.D. and
G. D. Whitfield, M.A., PH.D.
(Scottish Universities' Summer School, 1962)
4. Strong Interactions and High Energy Physics, edited by
R. G. Moorhouse
(Scottish Universities' Summer School, 1963)
5. Nuclear Structure and Electromagnetic Interaction,
edited by N. MacDonald, B.SC., PH.D.
(Scottish Universities' Summer School, 1964)
6. Phonons in Perfect Lattices and in Lattices with Point Imperfections,
edited by R. W. H. Stevenson, B.sc., PH.D.
(Scottish Universities' Summer School, 1965)
PARTICLE INTERACTIONS
AT HIGH ENERGIES
Scottish Universities' Summer School
1966
Edited by
T. W. PREIST, B.Sc., PH.D.
and
L. L. J. VICK, B.Sc., PH.D.
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
OLIVER AND BOYD LTD
Tweeddale Court
Edinburgh 1
39A Welbeck Street
London, W.l
FIRST PUBLISHED .... .... 1967
ISBN 978-1-4899-5531-9 ISBN 978-1-4899-5529-6 ( eBook)
DOI 10.1007/978-1-4899-5529-6
© 1974, Springer Science+Business Media New York
Originally published by The Authors in 1974
Softcover reprint ofthe hardcover 1st edition 1974
Robert Cunningham and Sons Ltd
Alva, Scotland
PREFACE
T
HE seventh Scottish Universities' Summer School in Physics was held
at Newbattle Abbey, near Edinburgh, from 1st to 20th August. Like
the first and fourth annual Schools this School was devoted to topics
in High Energy Physics. In this field the School is now in competition with
many new successful Schools established since 1960, but nevertheless we had
strong and early evidence that there was a widespread demand for a con
tinuation of the triennial series of High Energy Schools. This early impres
sion was amply confirmed by the number of applications eventually received
-96, of which we were able to accept 55, even though detailed arrangements
for the School were exceptionally delayed this year.
The delays were related to a serious problem that faced the Governing
Committee of the School for the first time. In the past the generous support
of the N.A.T.O. programme for Advanced Study Institutes was offered early
enough for the orgarusers to be assured of adequate financial backing at the
start of planning. This year, however, some understandable hesitation in
view of the number of competing Schools put N.A.T.O. support in question
at a critical state in preliminary organization. Somewhat later the N.A.T.O.
authorities did proffer support, still at a generous level, but in the inter
vening period it had been necessary to contemplate organizing a School on
a reduced scale, financed entirely by the Scottish Universities.
As Director of the School it is my pleasant duty to acknowledge that the
four ancient Universities of Aberdeen, Edinburgh, Glasgow and St. Andrews,
in spite of grave financial stringency, readily sprang to the aid of the Summer
Schools Committee, by offering sufficient emergency support to allow con
tinued planning of the School at essentially the normal level. When subse
quently assurance of considerable N.A.T.O. support was restored, it became
possible to reduce the call on University funds.
While it is clear that present financial conditions will not allow the
Scottish Universities to bear entirely the expense of future Schools, it may
be hoped that the general pattern eventually established this year-with
N.A.T.O. and the Scottish Universities spending comparable sums-may be
permanently retained. This (as well as the task of running the School) may
be made easier by the fact that the number of Scottish Universities is about
to be doubled and it is already understood that the newer Universities are
interested both in participation and in future planning.
The scientific programme of the School was also only finalized after some
delays-partly caused by the events outlined above and partly by a genuine
uncertainty in 1965 as to what topics would be ripe for discussion in August
v
vi PREFACE
1966. In the event the choice made-high energy scattering, electromagnetic
interactions and current algebras, and weak interactions, proved a satis
factory one; many participants have commented on the particular aptness
for their special interests of the choice made.
It is usual for the Director of the School to express his indebtedness to
the other officials of the School. This year other unexpected duties made
my own share in organization far less than a Director's should be and I
have a particularly strong reason to extend my thanks to Drs D. J. Candlin
(Secretary), J. Cumming (Treasurer) and T. W. Preist and L. L. J. Vick (Joint
Editors and Stewards) for making the school the organizational success it
certainly was. They have been most ably assisted in their clerical work before,
during and after the School by Mrs R. W. Chester, who was also responsible
for a large part of the work involved in preparing lecture notes, and by many
other members of the Tait Institute. During the School Misses Jane McGhee
and Molly Keys ably assisted in the Conference office. I am sure that all
participants in the School will join me in expressing their sincere thanks to
all these willing helpers, as well as to all the members of the Staff of New
battle Abbey, who contributed so essentially to the smooth and pleasant
running of the School.
N. KEMMER
Tait Professor of Mathematical Physics,
University of Edinburgh
EDITORS' NOTE
T
HE LECTURE notes were prepared by the lecturers themselves before
the Summer School and revised, in some cases, during and shortly
after the course of the School in order to incorporate changes produced
by new experimental information. The galley proofs, but not the page
proofs, were checked by the lecturers and so the ultimate responsibility for
errors and misprints lies with the Editors.
EXECUTIVE COMMITTEE-LECTURERS-PARTICIPANTS vii
EXECUTIVE CoMMI1TEE OF THE 1966 SUMMER SCHOOL
Professor N. Kemmer, Edinburgh, Chairman.
Dr J. Cumming, Glasgow, Treasurer.
Dr D. J. Candlin, Edinburgh, Secretary.
Professor J. C. Gunn, Glasgow.
Professor G. Bishop, Glasgow.
Dr T. W. Preist, Edinburgh, Joint Editor.
Dr L. L. J. Vick, Edinburgh, Joint Editor.
LECTURERS
Dr A. Donnachie, C.E.R.N., Geneva.
Professor S. D. Drell, Stanford, California.
Dr R. J. Eden, Cambridge.
Dr P. K. Kabir, Rutherford Laboratory.
Professor L. A. Radicati, Pisa.
Professor E. J. Squires, Durham.
Professor L. Van Hove, C.E.R.N., Geneva.
Professor R. Wilson, Harvard.
PARTICIPANTS
Dr George R. Allcock, Liverpool. Dr John M. Kennedy, Glasgow.
Mr Ananda Man Singh Amatya, Edin- Mr Robert G. Kirsopp, London.
burgh. Mrs Naomi Levy, Haifa.
Mr Nicolas Antoniou, Birmingham. Mr Christopher H. Llewellyn-Smith, Ox-
Mr Jean-Eudes Augustin, Orsay. ford.
Mr James E. Bateman, Glasgow. Dr David Lyth, Birmingham.
Dr Grzegorz Bialkowski, Warsaw. Dr Giuseppe Marchesini, Milan.
Mr Klaus Buchner, Munich. Dr Mladen Martinis, Edinburgh.
Mr Nigel H. Buttermore, Cambridge. Mr Christopher Michael, Oxford.
Mr Peter A. Cook, Manchester. Dr Marvin K. Moss, North Carolina.
Mr Ronald L. Crawford, Glasgow. Mr Emesto Napolitano, Turin.
Dr Amon Dar, Rehovoth. Dr Jean Pestieau, Louvain.
Dr Riccardo D'Auria, Turin. Dr Anthony C. Phillips, Sussex.
Dr Francesco Felicetti, Frascati. Mr Frank Poole, Durham.
Dr Luciano Girardello, Milan. Mr Nuthakki V. P. Rao, Manchester.
Mr GeorgeS. Gordon, Glasgow. Dr Muhammad S. K. Razmi, Edinburgh.
Dr Peter Grassberger, Bonn. Mr George F. Reid, Edinburgh.
Mr Dietrich Haase, Marburg. Mr Gordon Ringland, Durham.
Mr Anthony G. Hall, Newcastle. Mr Alan Ritchie, Edinburgh.
Mr Bodo Hamprecht, Cambridge. Mr Hans Rosdolsky, Michigan.
Mr Geoffrey H. Henderson, Edinburgh. Dr Morton H. Rubin, Wisconsin.
Dr Archibald W. Hendry, Rutherford Lab- Mr Juan J. Salazar, Paris.
oratory. Mr Vanniarachchige K. Samaranayake,
Dr Herbert S. Hoffman, Tel Aviv. London.
Mr Stephen Humble, Durham. Dr Dieter Schildknecht, D.E.S.Y., Ham
Mr Bruce H. Kellet, London. burg.
viii EXECUTIVE COMMITTEE-LECTURERS-PARTICIPANTS
Dr Klaus Schliipmann, C.E.R.N., Geneva. Dr Henry D. D. Watson, Edinburgh.
Mr Graham Shaw, London. Mr Trevor J. Weare, London.
Dr Robert L. Sugar, Columbia. Mr James N.J. White, Edinburgh.
Mr Roger F. Templeman, Manchester. Mr Edwin G. H. Williams, Liverpool.
Mr Robin W. Tucker, Cambridge.
CONTENTS
PAGE
PREFACE v
Executive Committee of the 1966 Summer School vii
Lecturers vii
Participants vii
1. PROPERTIES OF SCATTERING AMPLITUDES AT
HIGH ENERGY R.J. EDEN
1. Introduction
2. Experimental Survey 2
2.1. Total cross sections 3
2.2. Real part of the forward scattering amplitude 4
2.3. The forward peak for elastic scattering 4
2.4. Large angle scattering 6
2.5. High-energy reactions 7
3. Theoretical Background and Assumptions 8
3.1. Kinematics, the optical theorem and partial wave expansions 8
3.2. Dispersion relations and the Mandelstam representation 15
3.3. Complex angular momenta and Regge theory 19
3.4. Review of assumptions 23
4. Upper Bounds on Cross Sections and Other Inequalities 24
4.1. Partial wave amplitudes 24
4.2. Total cross sections; subtractions in dispersion relations 26
4.3. The forward peak, its slope and higher derivatives 27
4.4. Elastic cross sections 29
4.5. Non-forward scattering 31
5. Lower Bounds 32
5.1. Lower bounds for large angle scattering 32
5.2. Lower bounds for forward scattering and total cross sections 37
5.3. The problem of oscillations 39
6. Crossing Symmetry and Analyticity in the Energy 39
6.1. Relations between different processes; the Phragmen-Lindeloff
theorem 39
6.2. The real part of the forward scattering amplitude 42
6.3. Fixed transfer dispersion relations 44
6.4. Martin's enlargement of the Lehmann ellipse 45
7. The Pomeranchuk Theorems 48
7.1. Crossing symmetry and analyticity 48
7.2. Asymptotic equality of total cross sections 50
ix