Extreme States of Matter in Strong Interaction Physics: An Introduction

244 Pages·2012·3.444 MB·English

by  Helmut Satz (auth.)

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Helmut Satz
Extreme States of
Matter in Strong
Interaction Physics
An Introduction
Prof.Dr.HelmutSatz
FakultätfürPhysik
UniversitätBielefeld
Bielefeld
Germany
ISSN0075-8450 e-ISSN1616-6361
LectureNotesinPhysics
ISBN978-3-642-23907-6 e-ISBN978-3-642-23908-3
DOI10.1007/978-3-642-23908-3
SpringerHeidelbergDordrechtLondonNewYork
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Preface
Over the past fifty years, the thermodynamics of strongly interacting matter has
become a profound and challenging area of modern physics, both in theory and
in experiment. Statistical quantum chromodynamics, through analytical as well as
numerical studies, provides the main theoretical tool; in experiment, high energy
nuclear collisions are the key for extensive laboratory investigations. The field is
therefore an area of overlap between statistical, particle and nuclear physics, con-
ceptuallyandinthemethodsofinvestigationused.
Manyyoungpeoplearetodaystartingtheirscientificresearchinthisfieldandso
thereisaneedforageneralintroduction,emphasizinginparticularthebasiccon-
ceptsandideas.Thatistheaimofthisbook,toexplainwhywearedoingwhatwe
aredoing.Itisnotmeanttocompetewithseveralrecenttextbooks,whichshouldbe
consultedtoobtainthetechnicaltoolsofthetrade.Iwanttoconcentrateheremore
onthedevelopmentoftheunderlyingideas,whichIthinkhavegiventhefieldavery
uniqueflavor.Moreover,Iwillconcentratemainlyonequilibriumthermodynamics.
Nuclearcollisionscertainlyinvolvenon-equilibriumaspects,fromthermalizationto
hydrodynamicflow.Butbeforewecanunderstandthese,wewillhavetounderstand
thestrikingnewfeaturesalreadypresentinequilibrium.
Thegeneralplanofthebookisthefollowing.Wefirstintroducethefundamental
ideasofstronginteractionthermodynamics(Chap.1)andthensummarizethemain
conceptsandmethodsusedinthestudyofcomplexsystems(Chap.2).Afterthese
general preliminaries, we present some models, i.e., simplified phenomenological
pictures,leadingtocriticalbehaviorinhadronicmatterandtohadron-quarkphase
transitions (Chaps. 3 and 4). Given such a conceptual basis, we can then turn to
finite temperature lattice QCD and to the results obtained in computer simulation
studiesofthelatticeformulation(Chap.5).Complementarytothis,weclarifythe
relationoftheresultingcriticalbehaviortosymmetrybreaking/restorationinQCD
(Chap. 6). In Chap. 7, an extension of our considerations to strongly interacting
matter at finite baryon density provides the basis for the study of the QCD phase
diagram. Following this, we investigate in some detail the main features of a new
stateofmatter,thequark-gluonplasma(Chap.8).Thiscompletesourpresentation
ofbulkequilibriumthermodynamics,althoughquiteafewveryinterestingaspects
vii
viii Preface
have not been dealt with in much detail; in particular, the regime of large baryon
density has only been considered quite briefly. But this simply reflects the present
stateofourknowledgeinthatarea.
Followingthismoregeneralpartofthebook,weturntosomespecificfeatures
which arise when nuclear collisions are considered as a tool for the experimental
study of QCD thermodynamics. In Chap. 9, we introduce the conceptualbasis for
thisendeavor;followingthis,webrieflysurveythemainprobesproposedtoinves-
tigate the properties of the medium produced in such collisions. Finally, the last
twochaptersdealwithhadronproductioninhighenergycollisions—atopicwhich,
more than fifty years ago, started the intimate relation between strong interaction
physicsandthermodynamics.
Sinceourfieldissomultifaceted,Ithoughtitwouldbehelpfultokeepthedif-
ferentchaptersasmuchaspossibleself-contained,sothatareadercouldturntoa
giventopicwithouthavingto read in detailall previous chapters.This necessarily
impliessomerepetition,forwhichIhopeforindulgence.
Thisbookisbasedonthreesetsofcomprehensivelectures,heldattheUniversity
ofBielefeldin1995/96,attheInstitutoSuperiorTécnico(IST)inLisbonin2002/03,
andagainatBielefeldin2010/11.Inaddition,ithasbenefittedmuchfromextensive
lectures at a number of schools, organized by CCAST, CERN, Dubna, Frascati,
VECC,andothers.Thecourseoftheyears,Ithink,hadaveryhealthyinfluencein
placingthings intosome perspective. Let us see whatthe next years will bring. In
themeantime,Ihopethatwhatispresentedheremayhelpinshowingfutureyoung
researchers that ours is a field with much promise, within and beyond its topical
frontiers.
Aconsiderablepartofthebookwaswrittenandeditedduringtwolongstaysat
theISTinLisbon,madepossiblebyagrantoftheCalousteGulbenkianFoundation.
IwanttotakethisopportunitytoexpressmysinceregratitudetoJorgeDiasdeDeus
and João Seixas for their kind hospitality there and to the Gulbenkian Foundation
fortheirgeneroussupport.
Next, it is my great pleasure to thank my colleagues for all the help I have
received over the years in my attempts to understand this fascinating chapter of
physics. My gratitude goes first and foremost to my long-time fellow searchers
(whose conclusions may and often do, of course, differ from mine). On the the-
ory side, I thank Rolf Baier, Jürgen Engels, Rajiv Gavai, Sourendu Gupta, Keijo
Kajantie,FrithjofKarsch,DimaKharzeev,EdwinLaermann,TetsuoMatsui,Larry
McLerran,DavidMiller,KrzysztofRedlich,VesaRuuskanen,EskoSuhonen,Bob
Thews, Ramona Vogt and Xin-Nian Wang; more recently, crucial help came from
PaoloCastorinaandOlafKaczmarek.Ontheexperimentalside,FrancescoBecat-
tini, Peter Braun-Munzinger, Louis Kluberg, Carlos Lourenço, Jürgen Schukraft,
Johanna Stachel and Reinhard Stock have been essential in my search for under-
standing, and they have moreover made sure that the experimental consequences
ofwhatevertheoretical“Hirngespinst”wereneverignoredorforgotten.Thislistof
namesisnecessarilyincomplete,andIwanttoexpressmygratitudealsotoallthe
otherswhohavehelpedmesomuch.
Furthermore, sincere thanks go to Frithjof Karsch, David Miller and Krzysztof
Redlichforacarefulreadingofpartsofthedraft,andespeciallytoCarlosLourenço,
Preface ix
who read and corrected the entire manuscript with great care. This has certainly
helpedmuchineliminatingmanywrongandambiguousformulations;whatremains
faultyisobviouslymyresponsibility.
Someone once said that being a “normal” person married to a physicist is like
being deaf and married to a musician. I dedicate this book to my wife for bearing
withmeduringallthoseendlesshoursofunheardmusic.
Bielefeld,Germany HelmutSatz
Contents
1 TheAnalysisofDenseMatter . . . . . . . . . . . . . . . . . . . . . . 1
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 ThePhysicsofComplexSystems . . . . . . . . . . . . . . . . . . . . 13
2.1 CriticalBehaviorinThermodynamics . . . . . . . . . . . . . . . . 13
2.2 ClusterFormationandPercolation . . . . . . . . . . . . . . . . . 20
2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3 TheLimitsofHadronPhysics . . . . . . . . . . . . . . . . . . . . . . 29
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 TheHadronicSize . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 TheHadronicResonanceSpectrum . . . . . . . . . . . . . . . . . 31
3.3.1 PartitioningIntegers . . . . . . . . . . . . . . . . . . . . . 32
3.3.2 TheStatisticalBootstrapModel . . . . . . . . . . . . . . . 34
3.3.3 TheDualResonanceModel . . . . . . . . . . . . . . . . . 35
3.4 TheIdealResonanceGas . . . . . . . . . . . . . . . . . . . . . . 36
3.5 TheSpeedofSoundinaResonanceGas . . . . . . . . . . . . . . 40
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Appendix TheCriticalStructureoftheHagedornGas . . . . . . . . . 42
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 FromHadronstoQuarks . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1 ClusterFormationinStronglyInteractingMatter . . . . . . . . . . 45
4.2 IdealQuark-GluonPlasmaandIdealHadronGas. . . . . . . . . . 47
4.3 ConfinementandBagPressure . . . . . . . . . . . . . . . . . . . 52
4.4 NucleonRepulsionandExcludedVolume . . . . . . . . . . . . . 56
4.5 StringsandFlip-Flop . . . . . . . . . . . . . . . . . . . . . . . . 59
4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Appendix BoseandFermiGasPartitionFunctions . . . . . . . . . . . 62
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
xi
xii Contents
5 StatisticalQCD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1 TheGaugeFieldTheoryofStrongInteractions . . . . . . . . . . . 65
5.2 LatticeQCDatFiniteTemperature . . . . . . . . . . . . . . . . . 68
5.3 LatticeQCDatFiniteBaryonNumberDensity . . . . . . . . . . . 74
5.4 TheComputerSimulationofGaugeFieldThermodynamics . . . . 75
5.5 TheDeconfinementofQuarksandGluons . . . . . . . . . . . . . 79
5.5.1 SU(3)GaugeTheory. . . . . . . . . . . . . . . . . . . . . 79
5.5.2 FullQCD . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6 BrokenSymmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.1 SymmetryBreakingandCriticalBehavior . . . . . . . . . . . . . 89
6.2 TheDeconfinementTransition. . . . . . . . . . . . . . . . . . . . 91
6.3 ChiralSymmetryRestoration . . . . . . . . . . . . . . . . . . . . 94
6.4 QuarkMassandTransitionStructure . . . . . . . . . . . . . . . . 100
6.5 DeconfinementandChiralSymmetryRestoration . . . . . . . . . 102
6.6 DoesChiralSymmetryRestorationDriveDeconfinement? . . . . . 106
6.7 PercolationandRapidCross-over . . . . . . . . . . . . . . . . . . 108
6.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7 TheQCDPhaseDiagram . . . . . . . . . . . . . . . . . . . . . . . . 111
7.1 StatesofMatterinQCD:ASecondLook . . . . . . . . . . . . . . 111
7.2 InteractionRegimesofHadronicMatter . . . . . . . . . . . . . . 113
7.3 ConstituentQuarksandConstituentQuarkPlasma . . . . . . . . . 117
7.4 TheNambu–Jona-LasinioModel . . . . . . . . . . . . . . . . . . 124
7.5 QCDatFiniteBaryonDensity. . . . . . . . . . . . . . . . . . . . 129
7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
8 TheQuark-GluonPlasma . . . . . . . . . . . . . . . . . . . . . . . . 137
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8.2 ColorChargeScreeningandStringBreaking . . . . . . . . . . . . 138
8.3 InteractionRegimesofthePlasma . . . . . . . . . . . . . . . . . 143
8.4 WeakCouplingApproaches . . . . . . . . . . . . . . . . . . . . . 146
8.5 BagPressureandGluonCondensate . . . . . . . . . . . . . . . . 149
8.6 TheQuasi-particleApproach . . . . . . . . . . . . . . . . . . . . 150
8.7 TheSpeedofSoundintheQGP . . . . . . . . . . . . . . . . . . . 154
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
9 TheLittleBang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
9.1 ApplyingStrongInteractionThermodynamics . . . . . . . . . . . 157
9.2 HighEnergyCollisionsandtheVaporTrail . . . . . . . . . . . . . 158
9.3 PartonInteractionsandThermalization . . . . . . . . . . . . . . . 161
9.4 PartonPercolationandSaturation . . . . . . . . . . . . . . . . . . 166
9.5 ColorGlassCondensateandGlasma . . . . . . . . . . . . . . . . 167
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169