Fortschritte der Physik / Progress of Physics: Volume 34, Number 8 [Reprint 2022 ed.] 9783112613863, 9783112613856

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FORTSCHRITTE DER PHYSIK PROGRESS OF PHYSICS

Volume 3 4 - 1 9 8 6 Number 8 Board of Editors

F. Kaschluhn A. Lösche R. Rompe

Editor-in-Chief E. Kaschluhn

Advisory Board

A. M. Baldin, Dubna J. Fischer, Prague G. Höhler, Karlsruhe K. Lanius, Berlin J. Lopuszariski, Wroclaw A. Salam, Trieste D. V. Shirkov, Dubna A. N. Tavkhelidze, Moscow I. Todorov, Sofia J. Zinn-Justin, Saclay

CONTENTS: F . BAEREIRO

Jets in e+e~-Annihilation and QCD

H P

AKADEMIE-VERLAG • BERLIN

ISSN 0015 - 8208

Fortschr. Phys., Berlin 84 (1986) 8, 503-604

503—604

Instructions to Authors 1. Only papers not published and not submitted for publication elsewhere will be accepted. 2. Manuscripts should be submitted in English, with an abstract in English. Two copies are desired. 3. Manuscripts should be no less than 30 and preferably no more than about 100 pages in length. 4. All manuscripts should be typewritten on one side only, double-spaced and with a margin 4 cm wide. Manuscript sheets should be numerated consecutively from " 1 " onwards. Footnotes should be avoided. 5. The titel of the paper should be followed by the author's name (with first name abbreviated), by the institution and its address from which the manuscript originates. 6. Figures and tables should be restricted to the minimum needed to clarify the text. They should be numbered consecutively and must be referred too in the text and on the margin. Figures and tables should be added to the manuscript on separate, consecutively numerated sheets. The tables should have a headline. Legends of figures should be submitted on a separate sheet. All figures should bear the author's name and number of figure overleaf. Photographs for half-tone reproduction should be in the form of highly glazed prints. Line drawings should be in a form suitable for reproduction. The lettering should be sufficiently large and bold to permit reduction. If requested, original drawings and photographs will be returned to the author upon publication of the paper. 7. Formulae should not be written to small and not with pencil. Separate lines for formulae are desirable. Si-units should be used. Letters in formulae are normally printed in italics, numbers in ordinary upright typeface. Underlining to denote special typefaces should be done in accordance with the following code: Italics: wavy underlined with pencil (only necessary for type written symbols in the text) Boldface italics (vectors): straight forward and wavy underlined Upright letters (all abbreviations like all units (cm, g,...), all elements and particles (H, H e , . . . , n, p,...), elementary mathematical functions like Re, Im, sin, cos, exp,...): black underlined Greek letters: red underlined Boldface Greek letters: red underlined twice Upright Greek letters (symbols of elementary particles): red and black underlined Large letters: underlined with pencil twice Small letters: overlined with pencil twice (This will be necessary for handwritten letters that do not differ in shape, as cC,kE,oO,pP,sS,uU,vV,wW,xX,yY,z Z). It will help the printer if position of subscripts and superscripts is marked with pencil in the following way: at, b>, Mil, M.^, Wn} Please differentiate between following symbols: a, ¡x; a, a, oo; a, d; c, C, c ; e, I, ¡S, e, k, K, x; x, x,X,%, X ; 1,1; o, 0, a, 0; p, Q; U, U, U, V, v,V;q>, , S>, 0 ; &, 0, 0. 8. Each paper should be followed by a list of references with consecutive numeration. The numbers should be placed on the line between squared brackets or typewritten inclined lines. Articles in journals should be cited with author's name and abbreviated first name, title of journal, volume number (underlined), year of publication (in brackets) and page number. In case of books authors' name and abbreviated first name, title, place, and year of publication should be given. 9. Manuscripts should be submitted fit for printing; badly arranged manuscripts are returned. 10. Proof reading should be limited to the correction of typographical errors. Deletions and insertions are not permitted in proof reading. 11. Of every paper published the author(s) will receive 30 reprints free of charge. 12. Within the framework of legal protection the publishers have the right of publication, distribution and translation reserved. Without express permission it is not allowed to produce photocopies, microfilms etc. of this journal or parts of it.

FORTSCHRITTE DER PHYSIK V O L U M E 34

1986

NUMI

Fortschr. Phys. 34 (1986) 8, 5 0 3 - 6 0 4

Jets in e + e _ -Annihilation and QCD1) F E R N A N D O BARREIRO 2 ) Physics Department, Siegen University, Siegen, Federal Republic of Germany

Contents Abstract

.'

504

I.

Introduction

504

II. II. 1. 11.2. 11.3. 11.4. 11.5. 11.6. 11.7. 11.8. A. A.l. A.2. A.3. A.3. B. B.l. B.2.

Theory and Models The QCD Lagrangian: Feynman rules The total cross section for e+e~ -> hadrons The cross section for gluon bremstrahlung J e t s in e+e _ annihilation: the Sterman-Weinberg formula Next to leading corrections to gluon bremstrahlung Infrared stable quantities a) Thrust b) Energy-energy correlations Multiple soft gluon emission: the leading pole approximation Monte Carlo models. Independent fragmentation vs. string picture The independent fragmentation model The Field-Feynman model The Hoyer et al. model The Ali et al. model The Odorico Monte Carlo The string picture The Lund Monte Carlo The Field-Fox-Gottschalk-Wolfram Monte Carlo

506 506 508 509 511 515 519 520 522 529 531 531 531 533 533 534 536 536 541

11.9.

The use and misuse of Monte Carlos

542

III. 111.1. 111.2. 111.3. 111.4. 111.5. 111.6.

Experimental Results Experimental details The total cross section Charged particle multiplicities Inclusive momentum distributions J e t broadening and gluon bremtrahlung • On the energy dependence of jet measures a) Thrust distributions b) J e t opening angle c) J e t masses d) Multiplicity and event topology

545 545 547 548 552 554 562 562 565 565 570

2)

1

"Habilitationsschrift" accepted by the Physics Department, Siegen University On leave of absence from Universidad Autonoma de Madrid Fortschr. Phys. 34 (1986) 8

504

F. BARREIRO, J e t s in e+e _ -Annihilation

111.7. 111.8. TI1.9.

Sterman-Weinberg jots and energy flow Energy-energy correlations Energy moments for quark jets

IV.

Summary, Conclusions and Outlook

571? 57.S 590 599

Appendix I) Energy-Energy Correlation for Ypsilon Direct Decays

599

Acknowledgements

602

References

1502

Abstract The main filatures of t h e hadronic final states measured in e"e~ annihilation at DORIS and P E T l i A energies are reviewed. Comparisons are made between data and QCD predictions. The importance of perturbative versus non-perturbative contributions is critically examined.

I.

Introduction

Hadron production in hadron-hadron, lepton-hadron and lepton-lepton interactions lias been the subject of dedicated theoretical and experimental invertigations during tin; last three decades. One of the most important features characterizing the final states produced in these three processes results from the observation that directions exist in space along which hadrons are preferentially produced : jets. J e t s were actually first seen, fig. 1, in cosmic ray experiments [1], With the advent of high energy proton accelerators and later on with t h a t of proton and electron storage rings, similar structures were observed in hadron-hadron collisions [2], in deep inelastic lepton-hadron scattering [3] and in e r e~ annihilation [4].

t *«

"

"

'*•-

.

y•

•

:

'

A. '

"*'•...

Fig. 1. Jet« in cosmic r a y experimente

' ^

...

F

/

.

*

'

,

505

Fortschr. Phys. 34 (1986) 8

Our understanding of jet phenomena is tied to the understanding of the dynamics underlying the processes under consideration. Thus our approach to jets has evolved parallel to our views on strong interactions. In the early 60's jets were considered to be a consequence of the production and decay of "fireballs". Today jets are considered a manifestation of hard parton reactions expected to occur in any field theory of hadrons with confinement [5]. Fig. 2 shows a schematic representation of the lowest order diagrams responsible for jet production in the various processes mentioned above.

Current jet

Beam jet

Fig. 2. Diagrammatic sketch for hadron-hadron, lepton-hadron and e + e - annihilation in terms of constituents

It is clear that the study of jets is much cleaner in e + e~ than in lepton-hadron, hadron-hadron or hadron-nucleus interactions. This has to do with the pointlike nature of the colliding particles and with the simplicity of their interaction, mainly electromagnetic at present energies. Thus the study of jet formation in e + e~ annihilation is a particularly good testing ground for any theory of strong interactions. The hadronic final states measured in e + e - annihilations at S P E A R and DORIS energies have shown evidence for two-jet production [4]. The connection between the observed two-jet structures and the production and subsequent decay of a quark-antiquark pair was established by looking at the angular distribution of the jet axis with respect to the beam [6]. Moreover the azimuthal distribution of hadrons produced in collisions with transversely polarized beams showed the same structure as that measured for Bhabha and ¡x pair events in the same experiment [6], thus confirming the fermionic nature of the parent partons as expected in the quark-parton model (QPM) [7], With the advent of the high energies available at P E T R A , evidence for a departure from the two jet-topology was found [8]. Our current understanding of multijet production is based on Quantum Chromodynamics (QCD), the dynamical theory of quarks and vector gluons [9]. Thus hadron production in e + e~ annihilation is pictured today as 1*

506

F- BARREIRO, Jets in e+e~-Annihilation

the result of a two step process. In the first step occurring shortly after the interaction took place, a parent quark radiates its color and energy into a cone of finite apperture giving rise to a quark-gluon cascade. In the second step, ocurring after these virtual quanta have reached masses below a characteristic cut-off value, the radiated quarks and gluons condensate into colorless hadrons. This last stage of hadron formation because of its non-perturbative nature, is not yet calculable. Thus any quantitative comparison between data and QCD predictions is shadowed by the presence of fragmentation effects, the magnitude of which is in most cases difficult to estimate or at best model dependent. In this paper we will review the main features of the hadronic final states produced in e + e~ annihilations in the 7.7—34.6 GeV c.m. energy range. Comparisons between theoretical predictions, Sect. II, and data, Sect. I l l , will be made and the importance of perturbative versus non-perturbative contributions will be critically examined. We start from the QCD Lagrangian, Sect. II.1., and the corresponding Feynman rules, Sect. II.2., derive the cross section for gluon bremstrahlung off quarks, Sect. H.3., and use these results to show how the dominance of two-jet final states can be derived from first principles, Sect. II.4., The importance of second order corrections is adressed to in Sect. II.5., while Sect. II.6. is devoted to discuss the infrared stability of various jet measures. We discuss multiple gluon emission in Sect. II.7. thus being in a position to implement various perturbative calculations into models of hadron formation, Sect. II.8. In Sect. I l l we study the properties exhibited by the hadronic final states produced in e + e~ annihilation and measured with the PLUTO detector at DORIS and PETRA, the storage rings at DESY, Hamburg. After a shoit description of the detector, Sect. III.l., we investigate the following topics: cross sections, Sect. III.2., multiplicities, Sect. III. 3., longitudinal and transverse momentum distributions, Sect. III.4. and Sect. III.5., jet measures, Sect. III.6. Sterman-Weinberg cross sections, Sect. III.7. energy-energy correlations, Sect. III.8. and energy moments, Sect. III.9. Occasionally comparisons with results from other groups will also be discussed. Finally Sect. IV. is devoted to summary, conclusions and a discussion of the prospects for the future.

II.

Theory and Models

II.1.

The QCD Lagrangian: Feynman rules

Our current understanding of the basic forces in nature is based on gauge theories. Quantum Electrodynamics (QED) is a renormalizable quantum field theory, exhibiting gauge invariance under the group C7(l). Leptons are associated to the source fields, the photon being the gauge boson. Because the i7(l) symmetry exhibited by the QED Lagrangian is exact, electric charge is conserved and the photon remains massless. While leptons are considered to be pointlike objects, hadrons are believed to be made of spin 1/2 objects: quarks. This is supported by the succes of the conventional quark model in classifying baryon and meson states, and by the QPM description of deep inelastic lepton hadron scattering and e+e~ annihilation into hadrons. Quarks need to carry a new quantum number, color [10], in order to 1. avoid spin-statistics conflicts in the wave functions of lowest lying baryons which are totally symmetric in the quark and spin indices, i.e. \A++, Jz = 3/2) = \u f wf u\), 2. reconcile data on the decay width of 7r° —> yy and on R = • hadrons)/ n — 6. The region in the xu x2 plane for two-jets defined according to the (e, 6) resolution, criterion, can be obtained in the following way. Let us define [23] 6 = (1 + cos 6)12

(36)

the conditions ii), iii) and iv) can be analytically expressed as x, 2=

M (1 — bxi)

for

> n - 6

x1 71 — 6

(37.2)-

x., ^

1 - bx,(2 - x j 1 — bxt

03l > 7i —

(37.3)'

for

(37.1>

while condition i) is simply given by x3 < 2e

(38.1)

< 2s

(38.2>

x2
(e, (5) cuts. Numerical computations for Q(e, (5) are shown in fig. 12 b.

a) Fig. 12. a) The two-, (hatched area) and three-jet regions in the xx — x% plane. In region A all partons are inside the cone, in B less than a fraction e of the c.m. energy is outside. The values (e, 6) = (0.1, 15°) have been chosen b) Numerical evaluation of the Q(e, 6) function

II.5.

Next to leading corrections to gluon bremstrahlung processes

In previous sections we have shown how gluon bremstrahlung off a quark-antiquark pair produced in e+e~ annihilation may lead to deviations from the two-jet topology. These deviations are proportional to the quark-gluon coupling constant in QCD perturbation theory and can therefore be used to measure ccs. A minimal requirement for a meaningful determination of ots or equivalently of the QCD scale parameter A is the inclusion of radiative corrections, $( qqqq are on the other hand non-leading, and have the form oLLA{qqGG) = (