Dynamical Concepts on Scaling Violation and the New Resonances in e+e− Annihilation

250 Pages·1976·2.41 MB·English

by  Dr. B. Humpert (eds.)

Lecture Notes
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Edited yb .J Ehlers, Menchen, .K Hepp, Zerich,
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Managing Editor: W. BeiglbSck, Heidelberg
45
Dynamical Concepts
no Scaling Violation dna the New
Resonances ni e+e-Annihilation
Edited yb .B Humpert
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Berlin. Heidelberg. weN kroY 6791
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Library of Congress Cataloging in Publication Data
Humpert, B 1942-
Dynamical concepts on sealing violation and the
new resonances in e~e- annihilation.
(Lectume notes in physics ; 45)
Bibliography: p.
Includes index.
i. Annihilation meaetions. 2. Sealing laws
(Nuclear physics) 5. Nuclear magnetic resonance.
4. HadronSo I. Title. If. Series.
QC794.8.E4H85 559.7'54 75-40~17
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DYNAMICAL CONCEPTS ON SCALING VIOLATION AND THE NEW
RESONANCES IN e e ANNIHILATION
by
B. Humpert*
Department of Theoretical Physics
University of Geneva
Geneva - Switzerland
ABSTRACT
We present the essential experimental results on
the total and the single-particle inclusive cross sections
+ -
in e e annihilation. They show scaling violation and
extremely narrow resonances in the energy range beyond
3 Gev. The theoretical ideas about these phenomena are
sketched and their characteristics and implications
explained. New models are proposed.
*Supported by the Swiss National Science Foundation
C O N T E N T S
1. INTRODUCTION
2. EXPERIMENTAL RESULTS
2.1. The Total Cross Section
2.2. The Inclusive Cross Section
2.3. The New Resonances
2.3.1. The Resonances
2.3.2. The Decay Modes
2.3.3. Inclusive Distributions
2.3.4. Hadronic Production
2.3.5. Photoproduction
3. THEORIES ON SCALING AND ITS VIOLATION
3.1. Scaling - Definition and Hypothesis
3.2. Consequences of Scaling
3.2.1. Kinematics
3.2.2. e-p ÷ e-X
+
3.2.3. e e ÷ hadrons
+ -
3.2.4. e e ÷ h + X
+ -
3.2.5. e-p versus e e
3.3. Models : y ÷ hadrons
3.3.1. Physical Vacuum
IV
3.3.2. Partons
)a Partons with Structure
b) Spin-i Partons
c) New Degrees of Freedom
3.3.3. Vector Mesons
3.3.4 Cuts
3.3.5 Fermi Statistical Model
3.3.6 Landau Statistical Model
3.3.7 Heisenberg Statistical Model
3.3.8 Thermodynamic Model
3.3.9 Uncorrelated Jet Model
3.3.10. Cascade Decay Model
3.3.11. New Interactions
a) Leptons with Hadron Behaviour
b) Direct Lepto -Hadron Coupling
c) Lepto -Hadron X
d) Direct Channel "Objects"
3.3.12. Models : General Features
4. THEORIES ON THE NEW RESONANCES
4.1. Hadrons : Higher Symmetry Schemes
4.1.1. Charm
4.1.2. Color
IIV
4.1.3. Other Ideas
4.1.4. Lepton Quarks
4.2. Hadrons : Dynamical Schemes
4.2. i. Consequences
4.2.2. Hadron Bound States
4.2.3. Charmonium
4.2.4. Zweig Selection Rule
4.2.5. Resonance Models, Duality
4.2.6. Zero-Pole System
4.2.7. New Medium Interactions
4.2.8. Varia
4.3. Non-Hadronic Schemes
4.3.1. Weak Neutral Vector Mesons
4.3.2. Heavy Photon
4.3.3.
.5 CONCLUSION
REFERENCES
1. INTRODUCTION
The recent discoveries of totally unexpected features
+ -
in e e - physics have caused a large amount of theoretical
speculations, estimations and predictions on the behaviour
of electromagnetic interactions at extremely short distances.
)*(
In this paper we present the essential experimental dis-
+ -
coveries - the non-scaling behaviour of e e ÷ hadrons )I(
and the narrow resonances )2( - and give an introduction to
the theoretical explanations of these phenomena.
With the construction of high energy electron accelerators,
deep-inelastic electron-proton scattering processes became
experimentally possible which give us information how the
off-shell photon (exchanged between electron and proton)
interacts with the proton. Such experiments permit simul-
taneous variation of the photon mass q/~ as well as the
photon-proton CM-energy (EcM)z = W 2 . In particular, in
the energy region where (_qZ, W )2 becomes very large,
one expects the differential cross section to be only depen-
dent on the dimensionless ratio of these two variables.
The experiments in the region (_q2, W )2 ~ 40 Gev 2 have
)3(
sofar confirmed this scaling property
The construction of e e intersecting storage rings
made similar experiments possible however in the time-like
region of q2 . One expected that scaling would also hold
2
+ -
in e e ÷ Y + hadrons; however, this was not the case.
The scaling hypothesis predicts the energy dependence of
the total hadronic cross section as : ~(e+e - ÷ h)~ i/q 2 ,
whereas the early experimental results indicated ~(e+e - ÷ h)
constant beyond 5 Gev. This scaling violation lead to a large
amount of theoretical activity which we would like to sketch
here )4(
A new aspect of this problem recently became apparent
when extremely narrow resonances were found at 3.1 Gev and
3.7 Gev. A refined analysis of the experiment then showed
more structure around 4.1 Gev and a cross section behaviour
between 2.0 Gev 2 ~ q2 ~ 9.0 Gev 2 which is roughly in agreement
with scaling )5( It is possible that these two features
(scaling violation and narrow resonances) are connected,
however, a convincing dynamical mechanism is still lacking.
At the present time, it is difficult to present a con-
clusive analysis of the theoretical and experimental situation.
We therefore sketch the theoretical schemes which suggest
violation of scaling or non-asymptotic deviations, as well
as the proposed models for the narrow resonances, intentionally
not excluding models which, on the basis of the experimental
information, seem to be in difficulties or which are based
on unusual theoretical assumptions. Our intention is to present
some of the proposed explanations, discussing their pros and
3
cons and to maintain interest in ideas outside the main streams.
This paper is divided in three parts. In the first one
+ -
we present the essential experimenta! results in e e anni-
hilation before the discovery of the narrow resonances and
subsequently discuss the new experimental data of the narrow
resonances. The attempts to understand a possible scaling
violation in the present energy range are sketched in the
second part. In the third part we discuss the proposed
explanations for the newly discovered narrow resonances and
wide enhancement.
2. THE EXPERIMENTAL RESULTS
In this section we will present the experimental
results of (l' 5, )6
+ - (q2)
)i( e e ÷ hadrons : o h
+ - + d-O
(2 e e ÷ h- + X : E--
dp3
+ - + - q2
(3 ee +~ +~ : o ( )
Concerning the first reaction we are interested in the
hadronic total cross section. The single-particle inclusive
cross section of the second reaction gives us information
on the photonic hadron production mechanism. The measurement
results of ~-pair production are in agreement with QED calcu-
lations apart from the narrow resonances which appear in this
channel too )7(
2.1. The total cross section
In the following we will use the notation introduced
in Fig. i. The only invariant variable of this process is
2
the CM-energy square (EcM)2 = q = (p+ + p_)2 . What is
(q2) 2
the asymptotic dependence of o h on q ? For a long
time it was a common belief that this quantity would decrease
2
like i/q