603-0060603-0060 極限量子構造汎論Ⅱ極限量子構造汎論Ⅱ

Physics of the quark-gluon Physics of the quark-gluon plasma plasma

担当：平野哲文、浜垣秀樹担当：平野哲文、浜垣秀樹Tetsufumi Hirano & Hideki HamagakiTetsufumi Hirano & Hideki Hamagaki

Thur. 16:30-18:00@Rm.207Thur. 16:30-18:00@Rm.2074/9-5/21 (Hirano), 5/28-7/9 (Hamagaki)4/9-5/21 (Hirano), 5/28-7/9 (Hamagaki)

Syllabus (planned, not confirmed)Syllabus (planned, not confirmed)[1] Introduction to hadron physics[1] Introduction to hadron physics[2] Basic features of the quantum chromodynamics[2] Basic features of the quantum chromodynamics(QCD)(QCD)[3] QCD phase transition at extreme conditions[3] QCD phase transition at extreme conditions[4] Relativistic ideal/viscous hydrodynamics[4] Relativistic ideal/viscous hydrodynamics[5] Transport theory for QGP[5] Transport theory for QGP[6] QGP in relativistic heavy ion collisions[6] QGP in relativistic heavy ion collisions[7] Space-time description of the heavy ion[7] Space-time description of the heavy ioncollisionscollisions[8] Observable and signatures of the QCD phase[8] Observable and signatures of the QCD phasetransitiontransition[9] Relativistic heavy ion collider and detector[9] Relativistic heavy ion collider and detectorsystemssystems[10] Recent experimental data [10] Recent experimental data

Introduction to the physicsIntroduction to the physicsof the quark gluon plasma of the quark gluon plasma

Lecture 1Lecture 1

IntroductionIntroductionQ. What is the matter (in the senseQ. What is the matter (in the sense

of of many body systemmany body system) in which) in which““building blocks” play building blocks” play a fundamental role?a fundamental role?

This is the questionThis is the questionwhich I would like towhich I would like to

address in this lecture.address in this lecture.

Building BlocksBuilding Blocks

http://pdg.lbl.gov/http://pdg.lbl.gov/http://www.particleadventure.org/http://www.particleadventure.org/

Fermions in Standard ModelFermions in Standard Model

Bosons in Standard ModelBosons in Standard Model

Baryons as Composite ParticlesBaryons as Composite Particles

Mesons as Composite ParticlesMesons as Composite Particles

Physics of Many bodiesPhysics of Many bodies ““The whole is more than the sum of its parts.” The whole is more than the sum of its parts.”

(Aristotle) (Aristotle) http://en.wikipedia.org/wiki/Holismhttp://en.wikipedia.org/wiki/Holism

““More is different” (P.W. Anderson) More is different” (P.W. Anderson) http://www.sciehttp://www.sciencemag.org/cgi/pdf_extract/177/4047/393ncemag.org/cgi/pdf_extract/177/4047/393

““Wholism is the way to proceed science in the Wholism is the way to proceed science in the 2121stst Century.” Century.” (T.D. Lee, one of the founders o(T.D. Lee, one of the founders of elementary particle physics)f elementary particle physics) http://www.riken.jp/r-wohttp://www.riken.jp/r-world/info/release/news/2000/dec/index.html#fro_01 (Original article in Japrld/info/release/news/2000/dec/index.html#fro_01 (Original article in Japanese)anese)

Elementary Particle PhysicsElementary Particle Physicsas “Reductionism”as “Reductionism”

Condensed Matter Physics of Condensed Matter Physics of Elementary ParticlesElementary Particles

Quark Gluon Plasma QGP:Quark Gluon Plasma QGP:Many-body system of quarks and Many-body system of quarks and gluons under equilibriumgluons under equilibrium Statistical and thermodynamical Statistical and thermodynamical physics of quarks and gluonsphysics of quarks and gluons

Recipes for Quark Gluon PlasmaRecipes for Quark Gluon Plasma

CompressCompressHeat upHeat up hadronic many body systemhadronic many body system

Figure adopted fromFigure adopted fromhttp://www.bnl.gov/rhic/QGP.htmhttp://www.bnl.gov/rhic/QGP.htm

How are colored particles set free How are colored particles set free from confinement? from confinement?

How High?How High?

Suppose a closed-pack masSuppose a closed-pack massless pion system,sless pion system,

forfor

Or how low?Or how low?

Where WAS the QGP?Where WAS the QGP?History of the UniverseHistory of the Universe

History of the matterHistory of the matter

NucleosynthesisNucleosynthesis

HadronizationHadronization

Quark Gluon PlasmaQuark Gluon Plasma(after micro seconds of Big Bang)(after micro seconds of Big Bang)

Where IS the QGP?Where IS the QGP?

Front ViewFront View Side ViewSide ViewMultiplicity of hadrons ~ 5000 in aMultiplicity of hadrons ~ 5000 in ahead-on collision at sqrt(shead-on collision at sqrt(sNNNN)=200 GeV)=200 GeV

Fate of Smashing Two NucleiFate of Smashing Two Nuclei

QGP from the 1QGP from the 1stst Principle Principle

Equation of state from lattice QCDEquation of state from lattice QCD•Typical energy density scale of transition : Typical energy density scale of transition : ~1 GeV/fm~1 GeV/fm33

•Pseudo-critical temperature: Pseudo-critical temperature: ~190 MeV~190 MeV•Sound velocity is small in the vicinity of transition regionSound velocity is small in the vicinity of transition region•Lattice QCD is NOT applicable for time evolutionLattice QCD is NOT applicable for time evolution

M.Cheng et al., PRD77,014511 (’08)M.Cheng et al., PRD77,014511 (’08)

Conjectured Phase Diagram of QCDConjectured Phase Diagram of QCD

The region in whichThe region in whichwe can investigatewe can investigateby relativistic heavyby relativistic heavyion collisionsion collisions

Understanding ofUnderstanding ofphase diagramphase diagram “ “Condensed matterCondensed matterphysics of QCD”physics of QCD”

Physics of RelativisticPhysics of RelativisticHeavy Ion CollisionsHeavy Ion Collisions

Primary Goals of Heavy Ion CollisionsPrimary Goals of Heavy Ion Collisionsat Ultrarelativistic Energiesat Ultrarelativistic Energies

Understanding of QCD matter under extreme cUnderstanding of QCD matter under extreme conditions (high T and low nonditions (high T and low nBB)) Confinement, chiral symmetry breakingConfinement, chiral symmetry breaking Relevant to early universeRelevant to early universe Unique opportunityUnique opportunity

Understanding of hadrons and nuclei at very hiUnderstanding of hadrons and nuclei at very high collision energygh collision energy Universal behavior (color glass condensate)Universal behavior (color glass condensate) Not necessary unique, but give a good opportunityNot necessary unique, but give a good opportunity

Big Bang vs. Little BangBig Bang vs. Little Bang

Figure adopted fromFigure adopted fromhttp://www-utap.phys.s.u-tokyo.ac.jp/~sato/index-j.htmhttp://www-utap.phys.s.u-tokyo.ac.jp/~sato/index-j.htm

3D Hubble expansion3D Hubble expansion

beam axisbeam axis

Nearly 1D Hubble expansion*Nearly 1D Hubble expansion*+ 2D transverse expansion + 2D transverse expansion

*Bjorken(’83)*Bjorken(’83)

Big Bang vs. Little Bang (contd.)Big Bang vs. Little Bang (contd.)Big BangBig Bang Little BangLittle Bang

Time ScaleTime Scale 1010-5-5 sec >> m.f.p./c sec >> m.f.p./c 1010-23-23 sec ~ m.f.p./c sec ~ m.f.p./c

Expansion Expansion RateRate 10105-65-6/sec/sec 101022-2322-23/sec/sec

SpectrumSpectrumRedRed-shifted-shifted

(CMB)(CMB)BlueBlue-shifted-shifted

(hadrons)(hadrons)

Local thermalization is not trivial Local thermalization is not trivial in heavy ion collisions.in heavy ion collisions.

Collective flow is a key to see whetherCollective flow is a key to see whetherlocal thermalization is achieved.local thermalization is achieved.

Estimated Energy Density at RHICEstimated Energy Density at RHIC

PHENIX(’05)PHENIX(’05)

c from lattice

Well above Well above cc fro from lattice simulatim lattice simulations in central collons in central collision at RHICision at RHIC

Major Discovery atMajor Discovery atRelativistic HeavyRelativistic HeavyIon Collider (RHIC)Ion Collider (RHIC)

Hydrodynamics for QGP at WorkHydrodynamics for QGP at Work

Ollitrault (’92)

Hydro behaviorHydro behavior

Spatial AnisotropySpatial Anisotropy

Momentum AnisotropyMomentum Anisotropy

INPUTINPUT

OUTPUTOUTPUT

Interaction amongInteraction amongproduced particlesproduced particles

dN/d

No secondary interactionNo secondary interaction

0 2dN

/d

0 2

2v2

x

y

What is Elliptic Flow?What is Elliptic Flow?How does the system respond to spatial anisotropy?How does the system respond to spatial anisotropy?

Elliptic Flow in Kinetic TheoryElliptic Flow in Kinetic Theory

b = 7.5fm

generated through secondary collisionsgenerated through secondary collisions saturated in the early stage saturated in the early stage sensitive to cross section (~1/m.f.p.~1/viscosity)sensitive to cross section (~1/m.f.p.~1/viscosity)

vv22 is is

Zhang-Gyulassy-Ko(’99)Zhang-Gyulassy-Ko(’99) ideal hydro limitideal hydro limit

t(fm/c)

v 2 : Ideal hydro: Ideal hydro

: strongly : strongly interactinginteractingsystemsystem

Arrival at Hydrodynamic LimitArrival at Hydrodynamic Limit

Experimental data reach Experimental data reach hydrodynamic limit curve hydrodynamic limit curve for the first time at RHIC.for the first time at RHIC.

xx

yy

QGP as Opaque QCD MatterQGP as Opaque QCD Matter

Perfect liquid is something likePerfect liquid is something likea black ink in a sense of QED.a black ink in a sense of QED.

Jet TomographyJet Tomography

Adopted fromAdopted fromhttp://www.lbl.gov/Science-Articles/Archive/sabl/2008/Feb/jets.htmlhttp://www.lbl.gov/Science-Articles/Archive/sabl/2008/Feb/jets.html

1. Suppression of1. Suppression ofinclusive yieldsinclusive yieldsat high pat high pTT

2. Modification2. Modificationof back-to-backof back-to-backcorrelationcorrelation

Jet QuenchingJet Quenching

An energetic parton loses its energy by emittingAn energetic parton loses its energy by emittinggluons during traversing medium.gluons during traversing medium.•Emitted gluons also interact with medium.Emitted gluons also interact with medium.•Interference effect (LPM effect)Interference effect (LPM effect)•Medium evolves dynamically.Medium evolves dynamically.

Figure adopted from M. van Leeuwen, talk at QM2005.Figure adopted from M. van Leeuwen, talk at QM2005.

f’

High pHigh pTT Spectra Spectra

f

f

D

D

a

b

c

df’

a

b

D’c

D’d

A x

A x

ff: Parton distribution function: Parton distribution functionDD: Fragmentation function: Fragmentation function

AA: Mass number: Mass numberf’ f’ : Parton distribution in a nucleus: Parton distribution in a nucleusD’D’: Modified fragmentation function: Modified fragmentation function

QGP?jet

Proton-proton collisionProton-proton collision Nucleus-nucleus collisionNucleus-nucleus collision

Perturbative QCDPerturbative QCDpp0X

Leading orderLeading order

PHENIX data andPHENIX data andNLO QCD resultsNLO QCD results

How to Quantify Jet QuenchingHow to Quantify Jet QuenchingNuclear modification factorNuclear modification factor

Null caseNull case11

Yield scales with Yield scales with NNcollcoll ? ?

Cronin peakCronin peak

Yield suppresses?Yield suppresses?

Figure adopted from http://www.star.bnl.gov/central/focus/highPt/Figure adopted from http://www.star.bnl.gov/central/focus/highPt/

Quenched caseQuenched case

Suppression of High pSuppression of High pTT Hadrons Hadrons

Large suppression in central Au+Au collisions!Large suppression in central Au+Au collisions!Slide adopted from D.d’Enterria, talk at QM2004.Slide adopted from D.d’Enterria, talk at QM2004.

Onset of Jet QuenchingOnset of Jet Quenching

(Almost) no jet quenching at SPS(Almost) no jet quenching at SPSJet quenching was discovered for the first timeJet quenching was discovered for the first timeat RHIC. at RHIC.

D.d’Enterria, 0902.2011[nucl-ex]D.d’Enterria, 0902.2011[nucl-ex]

SPSSPS

RHIC, low ERHIC, low E

RHIC, maximum ERHIC, maximum E

Jet AccoplanarityJet Accoplanarity

What happens to away side peak inWhat happens to away side peak inazimuthal angle distribution forazimuthal angle distribution forassociated hadrons?associated hadrons?

Figure adopted fromFigure adopted fromhttp://www.star.bnl.gov/central/focus/highPt/http://www.star.bnl.gov/central/focus/highPt/

Disappearance of Away-Side PeakDisappearance of Away-Side Peak

Away-side peak: Away-side peak: Exists in p+p and d+AuExists in p+p and d+Aucollisions, but disappearscollisions, but disappearsin Au+Au collisionsin Au+Au collisions

Where does the lostWhere does the lostenergy go?energy go? Distributed among Distributed among soft particles?soft particles?

Figure adopted from http://www.star.bnl.gov/central/focus/highPt/Figure adopted from http://www.star.bnl.gov/central/focus/highPt/

Split of Away-Side PeakSplit of Away-Side Peak

Figure adopted from H. Figure adopted from H. BBüüschingsching, talk at QM2005., talk at QM2005.

*Background subtracted*Background subtracted

(trigger) x (associated)(trigger) x (associated)

One away-side peak One away-side peak Two peaks!? Two peaks!?

Mach-Cone in QGP?Mach-Cone in QGP?Mach angleMach angle

(Sound velocity) < (Velocity of a high energy parton)(Sound velocity) < (Velocity of a high energy parton)Information about sound velocity in the mediumInformation about sound velocity in the mediumMach angle ~ 75 deg. Mach angle ~ 75 deg. (Average) sound velocity c(Average) sound velocity css

22 < 0.1 < 0.1 Very soft equation of state?Very soft equation of state?

Other ProbesOther ProbesRare particlesRare particlesat the RHIC energiesat the RHIC energies•heavy quarksheavy quarks•quarkoniaquarkonia•photonsphotons•di-leptons…di-leptons…

See also Hamagaki-san’s lecture.See also Hamagaki-san’s lecture.

Figure adopted fromFigure adopted fromD.d’Enterria, 0902.2011[nucl-ex]D.d’Enterria, 0902.2011[nucl-ex]

Rare probes will beRare probes will beimportant at LHC.important at LHC.

ProspectsProspectsfor LHCfor LHC

Extrapolation to LHC energyExtrapolation to LHC energy

Naïve expectationNaïve expectation::More particles,More particles,higher initial temperature,higher initial temperature,longer lifetime of the QGP,longer lifetime of the QGP,……

Some PredictionsSome Predictions

T.Hirano T.Hirano et alet al., J.Phys.G34,S879(’07)., J.Phys.G34,S879(’07)

Elliptic flow coefficientElliptic flow coefficient Nuclear modification factorNuclear modification factor

D.d’Enterria, 0902.2011[nucl-ex]D.d’Enterria, 0902.2011[nucl-ex]

Extrapolation of the same scenarioExtrapolation of the same scenariofrom RHIC to LHC…from RHIC to LHC…

Understanding of Full Evolution Understanding of Full Evolution at LHC Eraat LHC Era

After some initial time, space-time evolution oAfter some initial time, space-time evolution of created matter is described by hydrodynamicf created matter is described by hydrodynamics reasonably well.s reasonably well.

What happens at first contact? (Or how does tWhat happens at first contact? (Or how does the hadron/nucleus look at very high energy?)he hadron/nucleus look at very high energy?)

If we would know the particle/entropy producIf we would know the particle/entropy production at first contact, how does the QCD matter tion at first contact, how does the QCD matter under local equilibriumunder local equilibrium form? form?

Parton Distribution in Proton Parton Distribution in Proton at Small xat Small x

x 20!!x 20!!

•Gluons are dominant at sGluons are dominant at small x.mall x.•Small x = High energySmall x = High energy•Hadron/Nucleus as a buncHadron/Nucleus as a bunch of gluons at high energyh of gluons at high energy

Bjorken x ~ Fraction of longitudinal momentum iBjorken x ~ Fraction of longitudinal momentum in protonn protonKinematics in ggKinematics in gg g g

Interplay btw. Emission and Interplay btw. Emission and Recombination at Small xRecombination at Small x

Linear effect (BFKL)Linear effect (BFKL)

Non-linear effectNon-linear effect

Figures adopted from Figures adopted from E.Iancu and R.Venugopalan, in Quark Gluon Plasma 3 (world scientific)E.Iancu and R.Venugopalan, in Quark Gluon Plasma 3 (world scientific)

Non-Linear Evolution and Non-Linear Evolution and Color Glass Condensate (CGC)Color Glass Condensate (CGC)

Rate eq.*Rate eq.*

Figures adopted from Figures adopted from K.Itakura, talk at QM2005.K.Itakura, talk at QM2005.

*More sophisticated equation (BK or JIMWLK) *More sophisticated equation (BK or JIMWLK) based on QCD has been solved.based on QCD has been solved.

small xsmall xhigh energyhigh energy

““Phase Diagram” of hadronsPhase Diagram” of hadrons

0

non

-pe

rtu

rba

tive

regi

on

dilute parton

CGC

geometrical s

calin

g

DGLAP

BFKL•Onset of CGC at RHICOnset of CGC at RHIC

•Some evidences exist.Some evidences exist.•Test of CGC at LHCTest of CGC at LHC

•How to describe How to describe perturbative CGC toperturbative CGC tonon-perturbative QGP?non-perturbative QGP?RHIC

RHIC

LHCLHC

Onset of CGC in d+Au Collisions Onset of CGC in d+Au Collisions at RHICat RHIC

BRAHMS Collaboration, white paperBRAHMS Collaboration, white paper

midrapiditymidrapidity forward rapidityforward rapidity

data

data

theo

ry (C

GC)

theo

ry (C

GC)

D.Kharzeev et al., PRD68,094013(’03).D.Kharzeev et al., PRD68,094013(’03).

y=0,1,2,3

H.Fujii, talk at RCNP workshop(’07)H.Fujii, talk at RCNP workshop(’07)

SummarySummary An almost perfect fluid and opaque QCD mattAn almost perfect fluid and opaque QCD matt

er is created er is created at RHICat RHIC for the first time. for the first time. Concept of strongly interacting quark-gluon many Concept of strongly interacting quark-gluon many

body system is established.body system is established. Toward comprehensive understanding of the Toward comprehensive understanding of the

collision as a whole and the QGP collision as a whole and the QGP at LHCat LHC CGC is the key concept at ultrarelativistic energy.CGC is the key concept at ultrarelativistic energy.

Some exotic phenomena are anticipated.Some exotic phenomena are anticipated. Something like perfect fluidity or shock wave (MacSomething like perfect fluidity or shock wave (Mac

h cone) at RHICh cone) at RHIC