Relativistic Heavy Ion Physics

701 Pages·2010·15.722 MB·English

by  Reinhard Stock (auth.), R. Stock (eds.)

New
Series
Numerical Data
I
· and Functional Relationships
2
3 in Science and Technology
GROUP I VOLUME 23
Elementary Relativistic
Particles,
Nuclei and Atoms
Heavy Ion
R
Physics
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1 23
Landolt-Börnstein
Numerical Data and Functional Relationships in Science and Technology
New Series / Editor in Chief: W. Martienssen†

Group I: Elementary Particles, Nuclei and Atoms
Volume 23

Relativistic
Heavy Ion Physics

J. Aichelin, F. Becattini, P. Braun-Munzinger, D. d'Enterria,
Z. Fodor, R.J. Fries, C. Gale, H. van Hees, U. Heinz, J.I. Kapusta,
S.D. Katz, L. Kluberg, V. Koch, M.A. Lisa, L. McLerran,
H. Oeschler, A.M. Poskanzer, S. Pratt, R. Rapp, H.G. Ritter,
G. Roland, H. Satz, J. Schaffner-Bielich, E. Shuryak,
R. Snellings, J. Stachel, R. Stock, I. Tserruya, S.A. Voloshin,
J. Wambach, U.A. Wiedemann, Nu Xu

Edited by R. Stock
ISSN 1615-1844 (Elementary Particles, Nuclei and Atoms)

ISBN 978-3-642-01538-0 Springer Berlin Heidelberg New York

Library of Congress Cataloging in Publication Data
Zahlenwerte und Funktionen aus Naturwissenschaften und Technik, Neue Serie
Editor in Chief: W. Martienssen†
Vol. I/23: Editor: R. Stock
At head of title: Landolt-Börnstein. Added t.p.: Numerical data and functional relationships in science and technology.
Tables chiefly in English.
Intended to supersede the Physikalisch-chemische Tabellen by H. Landolt and R. Börnstein of which the 6th ed. began publication in 1950 under title:
Zahlenwerte und Funktionen aus Physik, Chemie, Astronomie, Geophysik und Technik.
Vols. published after v. 1 of group I have imprint: Berlin, New York, Springer-Verlag
Includes bibliographies.
1. Physics--Tables. 2. Chemistry--Tables. 3. Engineering--Tables.
I. Börnstein, R. (Richard), 1852-1913. II. Landolt, H. (Hans), 1831-1910.
III. Physikalisch-chemische Tabellen. IV. Title: Numerical data and functional relationships in science and technology.
QC61.23 502'.12 62-53136

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Editor
R. Stock
Institut für Kernphysik Frankfurt
Johann-Wolfgang-Goethe-Universität Frankfurt
Max-von-Laue-Str. 1
60438 Frankfurt, Germany
email: [email protected]
Contributors
J. Aichelin Z. Fodor
SUBATECH, Ecole des Mines, Fachgruppe Physik, Bergische Universität
4 rue A. Kastler, La Chantrerie BP 20722, Wuppertal, Gaußstr. 20, 42119 Wuppertal,
44307 Nantes, France, email: Germany, and
[email protected] Department of Theoretical Physics, Eötvös
Quest for the Nuclear Equation of State Loránd University, Pázmány Péter sétány 1/A,
1117 Budapest, Hungary, email:
F. Becattini
[email protected];
Dipartimento di Fisica, Università di Firenze,
[email protected]
Via G. Sansone 1, 50019 Sesto Fiorentino,
Phase Diagram of QCD
Firenze, Italy, email: [email protected]
QCD Confinement Transition: Hadron R.J. Fries
Formation Cyclotron Institute, Texas A&M University,
College Station, TX 77843, USA, and
P. Braun-Munzinger
RIKEN BNL Research Center, Brookhaven
ExtreMe Matter Institute EMMI, GSI
National Laboratory, Upton, NY 11973, USA
Helmholtzzentrum für Schwerionenforschung,
email: [email protected]
Planckstr. 1, 64291 Darmstadt, Germany, and
QCD Confinement Transition: Hadron
Institut für Kernphysik, Technische Universität
Formation
Darmstadt, Schlossgartenstr. 9,
64289 Darmstadt, Germany, and C. Gale
Frankfurt Institute for Advanced Studies FIAS, Department of Physics, McGill University,
Ruth-Moufang-Str. 1, 60438 Frankfurt, 3600 rue University, Montreal, QC,
Germany Canada H3A 2T8, email:
Charmonium from Statistical Hadronization of [email protected]
Heavy Quarks Photon Production in Hot and Dense Strongly
Interacting Matter
D. d'Enterria
PH-EP, Physics Department, CERN, 1211 H. van Hees
Geneva 23, Switzerland, and Institut für Theoretische Physik, Justus-Liebig-
Laboratory for Nuclear Science, Bldg. 26-505, Universität Gießen, Heinrich-Buff-Ring 16,
Massachusetts Institute of Technology, 35392 Gießen, Germany, email:
Cambridge, MA 02139-4307, USA [email protected]
email: [email protected] Chiral Restoration Transition of QCD and Low
Jet quenching Mass Dileptons
VI Contributors
U. Heinz L. McLerran
Department of Physics, Ohio State University, Physics Department and RIKEN BNL Research
191 West Woodruff Avenue, Columbus, Center, Bldg. 510A, Brookhaven National
OH 43210, USA, email: Laboratory, Upton, NY 11973, USA, email:
[email protected] [email protected]
Hydrodynamics and Transport Properties of Gluon Saturation and Formation Stage of
QCD Matter Heavy Ion Collisions
J.I. Kapusta H. Oeschler
School of Physics and Astronomy, University of Institut für Kernphysik, Technische Universität
Minnesota, 116 Church Street S.E., Darmstadt, Schlossgartenstr. 9,
Minneapolis, MN 55455, USA, email: 64289 Darmstadt, Germany, email:
[email protected] [email protected]
Viscous Properties of Strongly Interacting Hadron Production in Heavy Ion Collisions
Matter at High Temperature
A.M. Poskanzer
S.D. Katz Nuclear Science Division, Lawrence Berkeley
Fachgruppe Physik, Bergische Universität National Laboratory, MS70R319,
Wuppertal, Gaußstr. 20, 42119 Wuppertal, 1 Cyclotron Road, Berkeley, CA 94720-8153,
Germany, and USA, email: [email protected]
Department of Theoretical Physics, Eötvös Collective Phenomena in Non-Central Nuclear
Loránd University, Pázmány Péter sétány 1/A, Collisions
1117 Budapest, Hungary, email:
S. Pratt
[email protected]
Department of Physics and Astronomy,
Phase Diagram of QCD
Michigan State University, East Lansing,
L. Kluberg MI 48824, USA, email: [email protected]
LLR, Ecole Polytechnique, Route de Saclay, Femtoscopically Probing the Freeze-out
91128 Palaiseau, France, email: Configuration in Heavy Ion Collisions
[email protected]
R. Rapp
Color Deconfinement and Charmonium
Cyclotron Institute and Physics Department,
Production in Nuclear Collisions
Texas A&M University, College Station,
V. Koch TX 77843-3366, USA, email:
Nuclear Science Division, Lawrence Berkeley [email protected]
National Laboratory, MS70R319, Chiral Restoration Transition of QCD and Low
1 Cyclotron Road,Berkeley, CA 94720-8153, Mass Dileptons
USA, email: [email protected]
H.G. Ritter
Hadronic Fluctuations and Correlations
Nuclear Science Division, Lawrence Berkeley
M.A. Lisa National Laboratory, MS70R319,
Department of Physics, Ohio State University, 1 Cyclotron Road, Berkeley, CA 94720-8153,
191 West Woodruff Avenue, Columbus, USA, email: [email protected]
OH 43210, USA, email: Hadron Production in Heavy Ion Collisions
[email protected]
G. Roland
Femtoscopically Probing the Freeze-out
Department of Physics, Massachusetts Institute
Configuration in Heavy Ion Collisions
of Technology, 77 Massachusetts Avenue,
Cambridge, MA 02139-4307, USA, email:
[email protected]
Hadron Multiplicities in Ultra-Relativistic
Nuclear Collisions
Contributors VII
H. Satz R. Stock
Fakultät für Physik, Universität Bielefeld, Institut für Kernphysik Frankfurt, Johann-
Postfach 100131, 33501 Bielefeld, Germany Wolfgang-Goethe-Universität Frankfurt, Max-
email: [email protected] von-Laue-Str. 1, 60438 Frankfurt, Germany
States of Strongly Interacting Matter and email: [email protected]
Color Deconfinement and Charmonium Introduction
Production in Nuclear Collisions
I. Tserruya
J. Schaffner-Bielich Department of Particle Physics and
Institut für Theoretische Physik, Ruprecht- Astrophysics, Weizmann Institute of Science,
Karls-Universität Heidelberg, Rehovot 76100, Israel, email:
Philosophenweg 16, 69120 Heidelberg, [email protected]
Germany, email: Electromagnetic Probes
[email protected]
S.A. Voloshin
Quest for the Nuclear Equation of State
Department of Physics and Astronomy, Wayne
E. Shuryak State University, 666 W. Hancock, Detroit,
Department of Physics and Astronomy, MI 48201, USA, email: [email protected]
University at Stony Brook, Collective Phenomena in Non-Central Nuclear
NY 11794-3800, USA, email: Collisions
[email protected]
J. Wambach
Structure of Strongly Coupled Quark-Gluon
Institut für Kernphysik, Technische Universität
Plasma
Darmstadt, Schlossgartenstr. 9,
R. Snellings 64289 Darmstadt, Germany, email:
Nikhef, Science Park 105, [email protected]
1098 XG Amsterdam, The Netherlands Chiral Restoration Transition of QCD and Low
email: [email protected] Mass Dileptons
Collective Phenomena in Non-Central
U.A. Wiedemann
Nuclear Collisions
PH-TH, Physics Department, CERN, 1211
J. Stachel Geneva 23, Switzerland, email:
Physikalisches Institut, Ruprecht-Karls- [email protected]
Universität Heidelberg, Philosophenweg 12, Jet Quenching in Heavy Ion Collisions
69120 Heidelberg, Germany, email:
Nu Xu
[email protected]
Nuclear Science Division, Lawrence Berkeley
Charmonium from Statistical Hadronization of
National Laboratory, MS70R319,
Heavy Quarks
1 Cyclotron Road, Berkeley, CA 94720-8153,
USA, email: [email protected]
Hadron Production in Heavy Ion Collisions

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Preface
This new volume, I/23, of the Landolt-Börnstein Data Collection series continues a tradition inaugurated
by the late Editor-in-Chief, Professor Werner Martienssen, to provide in the style of an encyclopedia a
summary of the results and ideas of Relativistic Heavy Ion Physics. Formerly, the Landolt-Börnstein
series was mostly known as a compilation of numerical data and functional relations, but it was felt that
the more comprehensive summary undertaken here should meet an urgent purpose.

Volume I/23 reports on the present state of theoretical and experimental knowledge in the field of
Relativistic Heavy Ion Physics. What is meant by this rather technical terminology is the study of
strongly interacting matter, and its phases (in short QCD matter) by means of nucleus-nucleus collisions
at relativistic energy.

The past decade has seen a dramatic progress, and widening of scope in this field, which addresses one
of the chief remaining open frontiers of Quantum Chromodynamics (QCD) and, in a wider sense, the
"Standard Model of Elementary Interactions". The data resulting from the CERN SPS, BNL AGS and
GSI SIS experiments, and in particular also from almost a decade of experiments carried out at the
"Relativistic Heavy Ion Collider"(RHIC) at Brookhaven, have been fully analyzed, uncovering a wealth
of information about both the confined and deconfined phases of QCD at high energy density.

Concurrent with experimental progress, which has reached a certain maturity by now, theory has
provided for insight of key importance, and even surprise, ranging from major breakthroughs in non-
perturbative QCD theory on the lattice, and in relativistic hydrodynamics, to first hints that the high-
temperature QCD plasma state might be properly understood in a "dual", 5-dimensional string theory. It
will take a few further years before new data from the LHC should be expected to lead to a further
transformation of paradigm in the field. Thus it appeared timely to attempt a temporary summary.

The editor expresses his delight for being able to find outstanding authors for the various chapters. They
should be warmly thanked for their effort and patience.

I also wish to thank the members of the Landolt-Börnstein editorial staff for their devoted effort to bring
this substantial volume into being.

Frankfurt, February 2010 The Editor
Contents
1 Introduction (R. STOCK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1
1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1
1.2 History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2
1.3 The QCD Phase Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4
1.4 Physics Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6
2 Theory of Strongly Interacting Matter . . . . . . . . . . . . . . . . . . . . . 2-1
2.1 The States of Strongly Interacting Matter (H. SATZ) . . . . . . . . . . . . . . 2-1
2.1.1 From Hadrons to Quarks and Gluons . . . . . . . . . . . . . . . . . . . . . . . 2-2
2.1.2 Matter at Finite Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
2.1.3 The Order of the Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-9
2.1.4 The Origin of the Transition . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-11
2.1.5 Probing the States of Matter in QCD . . . . . . . . . . . . . . . . . . . . . . . 2-14
2.1.5.1 Hadron Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-15
2.1.5.2 Electromagnetic Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-16
2.1.5.3 Quarkonium Dissocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-17
2.1.5.4 Jet Quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-20
2.1.5.5 Initial State Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-22
2.1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-23
2.2 Lattice QCD and the Phase Diagram of Quantum Chromodynamics
(Z. FODOR, S.D. KATZ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27
2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-27
2.2.1.1 The phase diagram of QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-28
2.2.2 QCD thermodynamics on the lattice . . . . . . . . . . . . . . . . . . . . . . . 2-30
2.2.2.1 The action in lattice QCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-31
2.2.2.2 Correlators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-35
2.2.2.3 Continuum limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-36
2.2.2.4 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-36
2.2.3 Results at zero chemical potential . . . . . . . . . . . . . . . . . . . . . . . . . 2-40
2.2.3.1 Choice of the action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-40
2.2.3.2 T=0 simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-41
2.2.3.2.1 Determination of the LCP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-41
2.2.3.3 The order of the QCD transition . . . . . . . . . . . . . . . . . . . . . . . . . 2-43
2.2.3.4 The transition temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-46
2.2.3.5 Equation of state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-52
2.2.3.6 Note added in proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-56
2.2.4 Finite chemical potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-58
2.2.4.1 Chemical potential on the lattice . . . . . . . . . . . . . . . . . . . . . . . . . 2-59
2.2.4.2 The sign problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-59
2.2.4.3 Multi-parameter reweighting . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-60
2.2.4.3.1 Multi-parameter reweighting with Taylor-expansion . . . . . . . . . . . . . . . 2-62
μ
2.2.4.3.2 Simulations at imaginary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-62
X Contents
2.2.4.3.3 Differences and similarities of the three techniques . . . . . . . . . . . . . . . . 2-63
2.2.4.3.4 Determining the phase diagram by Lee-Yang zeroes . . . . . . . . . . . . . . . 2-64
2.2.4.4 Results for the phase diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-65
2.2.4.4.1 Phase line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-65
2.2.4.4.2 The critical point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-66
μ
2.2.4.5 Equation of state at > 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-68
2.2.5 Conclusions, outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-69
3 Hadronic Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1
3.1 The Quest for the Nuclear Equation of State
(J. AICHELIN, J. SCHAFFNER-BIELICH) . . . . . . . . . . . . . . . . . . . . . . . 3-1
3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1
3.1.2 The EoS and Heavy-Ion Collisions . . . . . . . . . . . . . . . . . . . . . . . . 3-4
3.1.3 The EoS and Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10
3.1.3.1 The nuclear EoS, supernovae and neutron star mergers . . . . . . . . . . . . . . 3-10
3.1.3.2 The nuclear EoS and compact stars . . . . . . . . . . . . . . . . . . . . . . . . 3-11
3.2 Hadron Production in Heavy Ion Collisions
(H. OESCHLER, H.G. RITTER, NU XU) . . . . . . . . . . . . . . . . . . . . . . . 3-24
3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-24
3.2.2 Hadron Production below 2 A GeV . . . . . . . . . . . . . . . . . . . . . . . . 3-25
3.2.2.1 Multiplicities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-26
3.2.2.2 Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-31
3.2.2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-34
3.2.3 Hadron Production from AGS to RHIC . . . . . . . . . . . . . . . . . . . . . . 3-35
3.2.3.1 Systematics of Spectra and Slopes at AGS and SPS . . . . . . . . . . . . . . . . 3-37
3.2.3.2 Spectra and Radial Flow at RHIC . . . . . . . . . . . . . . . . . . . . . . . . . 3-39
3.2.3.3 Partonic Collectivity at RHIC . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-41
3.2.3.4 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-42
3.2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-43
4 The Hadron-Parton Phase Transition . . . . . . . . . . . . . . . . . . . . . . 4-1
4.1 The Chiral Restoration Transition of QCD and Low Mass Dileptons
(R. RAPP, J. WAMBACH, H. VAN HEES) . . . . . . . . . . . . . . . . . . . . . . . 4-1
4.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1
4.1.1.1 QCD Vacuum and Chiral Restoration . . . . . . . . . . . . . . . . . . . . . . . 4-1
4.1.1.2 Ultrarelativistic Heavy-Ion Collisions . . . . . . . . . . . . . . . . . . . . . . . 4-2
4.1.1.3 Dilepton Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4
4.1.1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-6
4.1.2 Chiral Symmetry, Condensates and Chiral Restoration . . . . . . . . . . . . . . 4-7
4.1.2.1 Condensates and Hadron Spectrum in Vacuum . . . . . . . . . . . . . . . . . . 4-7
4.1.2.2 Phase Diagram and Chiral Restoration . . . . . . . . . . . . . . . . . . . . . . 4-8
4.1.3 Vector Mesons in Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11
4.1.3.1 Dileptons and Electromagnetic Correlation Function . . . . . . . . . . . . . . . 4-11
4.1.3.2 Medium Effects I: Model Independent . . . . . . . . . . . . . . . . . . . . . . 4-14
4.1.3.2.1 Chiral Reduction and Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14
4.1.3.2.2 Lattice QCD and Susceptibilities . . . . . . . . . . . . . . . . . . . . . . . . . 4-14
4.1.3.3 Sum Rules and Order Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 4-16
4.1.3.3.1 Chiral Sum Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-16
4.1.3.3.2 QCD Sum Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-17
4.1.3.4 Medium Effects II: Chiral Effective Models . . . . . . . . . . . . . . . . . . . . 4-19
4.1.3.4.1 Hidden Local Symmetry and Vector Manifestation . . . . . . . . . . . . . . . . 4-19
Contents XI
4.1.3.4.2 Massive Yang-Mills and Hadronic Many-Body Theory . . . . . . . . . . . . . . 4-19
4.1.3.5 Thermal Dilepton and Photon Rates . . . . . . . . . . . . . . . . . . . . . . . 4-23
4.1.4 Interpretation of Dilepton Spectra . . . . . . . . . . . . . . . . . . . . . . . . . 4-25
4.1.4.1 Medium Effects in Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-25
4.1.4.2 Heavy-Ion Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-26
4.1.4.2.1 Thermal Evolution and Dilepton Sources . . . . . . . . . . . . . . . . . . . . . 4-26
4.1.4.2.2 CERN-SPS I: NA60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-29
4.1.4.2.3 CERN-SPS II: CERES/NA45 and WA98 . . . . . . . . . . . . . . . . . . . . . 4-33
4.1.4.2.4 Future Dilepton Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 4-34
4.1.4.3 Critical Appraisal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-36
4.1.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-37
4.2 Electromagnetic Probes (I. TSERRUYA) . . . . . . . . . . . . . . . . . . . . . 4-43
4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-43
4.2.2 Experimental challenge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-46
4.2.3 p+p and p+A collisions: the reference measurements . . . . . . . . . . . . . . . 4-47
4.2.3.1 Reference measurements at SPS. . . . . . . . . . . . . . . . . . . . . . . . . . 4-47
4.2.3.2 Reference measurements at RHIC . . . . . . . . . . . . . . . . . . . . . . . . . 4-49
4.2.4 Low-mass continuum in nuclear collisions . . . . . . . . . . . . . . . . . . . . 4-49
4.2.4.1 Low-mass dileptons at the SPS . . . . . . . . . . . . . . . . . . . . . . . . . . 4-50
4.2.4.1.1 CERES results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-50
4.2.4.1.2 NA60 results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-53
4.2.4.2 Low-mass dileptons at RHIC . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-55
4.2.4.3 Low-mass dileptons at low energies . . . . . . . . . . . . . . . . . . . . . . . . 4-58
4.2.5 Light vector mesons in nuclear collisions . . . . . . . . . . . . . . . . . . . . . 4-59
4.2.6 Intermediate mass region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-62
4.2.6.1 IMR dimuons at SPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-62
4.2.6.2 IMR at RHIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-64
4.2.7 Light vector meson spectroscopy in elementary reactions . . . . . . . . . . . . . 4-65
4.2.8 Thermal photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-68
4.2.9 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-69
4.3 The QCD Confinement Transition: Hadron Formation
(F. BECATTINI, R.J. FRIES) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-75
4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-75
4.3.2 The Statistical Hadronization Model . . . . . . . . . . . . . . . . . . . . . . . 4-75
4.3.2.1 Localized States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-77
4.3.2.2 The Formalism: Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-78
4.3.2.3 Rates of Multiparticle Channels . . . . . . . . . . . . . . . . . . . . . . . . . . 4-80
4.3.2.4 Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-82
4.3.2.5 High Energy Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-83
4.3.2.6 Heavy Ion Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-86
4.3.2.7 Strangeness Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-88
4.3.2.8 Thermalization: How Is It Achieved? . . . . . . . . . . . . . . . . . . . . . . . 4-90
4.3.3 Quark Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-91
4.3.3.1 Parton Fragmentation and Its Limitations . . . . . . . . . . . . . . . . . . . . . 4-92
4.3.3.2 The Recombination Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . 4-93
4.3.3.2.1 Basic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-93
4.3.3.2.2 Different Implementations of Instantaneous Recombination . . . . . . . . . . . . 4-94
4.3.3.2.3 Dynamical Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-95
4.3.3.3 Connection with other Hadronization Models . . . . . . . . . . . . . . . . . . . 4-96
4.3.3.4 Experimental Evidence for Recombination . . . . . . . . . . . . . . . . . . . . 4-97
4.3.3.4.1 Hadron Spectra and Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-98
4.3.3.4.2 Elliptic Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-98
4.3.4 Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-102