QGP and Dynamics of QGP and Dynamics of Relativistic Heavy Ion Relativistic Heavy Ion

CollisionsCollisions

Tetsufumi HiranoTetsufumi Hirano

The University of Tokyo, The University of Tokyo, KomabaKomaba

Thermal Quantum Field Theories and Their ApplicationsThermal Quantum Field Theories and Their Applications

OUTLINEOUTLINE

• Basic Checks– Energy density– Chemical and kinetic equilibrium

• Dynamics of Heavy Ion Collisions– Elliptic Flow and Perfect Liquid!?– Recent Results from Hydro models– Some Comments on the Discovery

• Summary and Outlook

My Charge: To interpret recentMy Charge: To interpret recent experimental data at RHICexperimental data at RHIC

from a QGP fluid dynamics point of viewfrom a QGP fluid dynamics point of view

Physics of the QGPPhysics of the QGP

•Matter governed by QCD, not QED

•High energy density/temperature frontier Toward an ultimate matter (Maximum

energy density/temperature)

•Understanding the origin of matter which evolves with our universe

•Reproduction of QGP in H.I.C.Reproduction of early universe on the Earth

Quark Gluon Plasma

Hadronization

Nucleosynthesis

History of the UniverseHistory of the Universe ~ History of Matter ~ History of Matter

QGP study

Understandingearly universe

Little Bang!Little Bang!Relativistic Heavy Ion

Collider(2000-)RHIC as a time machine!

100 GeV per nucleonAu(197×100)+Au(197×100)

Collision energy

Multiple production(N~5000)

Heat

sideview

frontview

STAR

STAR

BASIC CHECKSBASIC CHECKS

Basic Checks (I): Energy Basic Checks (I): Energy DensityDensity

Bjorken energy density

: proper timey: rapidityR: effective transverse radiusmT: transverse mass

Bjorken(’83)

observables

Critical Energy Density from Critical Energy Density from LatticeLattice

Stolen from Karsch(PANIC05); Note that recent results seem to be Tc~190MeV

Centrality Dependence of Centrality Dependence of Energy DensityEnergy Density

PHENIX(’05)

cc from lattice from lattice

Well abovec from lattice

in centralcollision at RHIC,

if assuming=1fm/c.

CAVEATS (I)CAVEATS (I)• Just a necessary condition in the sense that

temperature (or pressure) is not measured.

•How to estimate tau?

• If the system is thermalized, the actual energy density is larger due to pdV work.

•Boost invariant?

•Averaged over transverse area. Effect of thickness? How to estimate area?Gyulassy, Matsui(’84) Ruuskanen(’84)

Basic Checks (II): Chemical Basic Checks (II): Chemical Eq.Eq.

Two fitting parameters: Tch, B

direct Resonance decay

Amazing fit!Amazing fit!

T=177MeV, B = 29 MeV

Close to Tc from lattice

CAVEATS (II)CAVEATS (II)•Even e+e- or pp data can be fitted

well!See, e.g., Becattini&Heinz(’97)

•What is the meaning of fitting parameters? See, e.g.,

Rischke(’02),Koch(’03) •Why so close to Tc?

No chemical eq. in hadron phase!? Essentially dynamical problem!

Expansion rate Scattering rate (Process dependent)

see, e.g., U.Heinz, nucl-th/0407067

Basic Checks (III): Radial Basic Checks (III): Radial FlowFlow

Spectrum for heavier particlesis a good place to see radial flow.

Blast wave model (thermal+boost)

Driving force of flowpressure gradient Inside: high pressure

Outside: vacuum (p=0)

Sollfrank et al.(’93)

Spectrum change is seen in Spectrum change is seen in AA!AA!

O.B

ara

nn

ikova,

talk

at

QM

05

Power law in pp & dAu

Convex to Power law

in Au+Au•“Consistent” with thermal + boost picture•Large pressure could be built up in AA collisions

CAVEATS (III)CAVEATS (III)• Not necessary to be thermalized completely

– Results from hadronic cascade models.

• How is radial flow generated dynamically?

• Finite radial flow even in pp collisions? – (T,vT)~(140MeV,0.2)

– Is blast wave reliable quantitatively?

• Consistency? – Chi square minimum located a different point for

and

• Flow profile? Freezeout hypersurface? Sudden freezeout?

Basic Checks Basic Checks Necessary Necessary Conditions to Study QGP at Conditions to Study QGP at RHICRHIC•Energy density can be well above c.

– Thermalized?

•“Temperature” can be extracted.– Why freezeout happens so close to Tc?

•Pressure can be built up.– Completely equilibrated?

Importance of Systematic Study Importance of Systematic Study based on Dynamical Frameworkbased on Dynamical Framework

Dynamics of Heavy Dynamics of Heavy Ion Collisions:Ion Collisions:

Elliptic Flow and Perfect Elliptic Flow and Perfect LiquidLiquid

Dynamics of Heavy Ion Dynamics of Heavy Ion CollisionsCollisions

Time scale10fm/c~10-23sec

Temperature scale 100MeV~1012K

Freezeout

“Re-confinement”

Expansion, cooling

Thermalization

First contact (two bunches of gluons)

Why Hydrodynamics?Why Hydrodynamics?StaticStatic•EoS from Lattice QCDEoS from Lattice QCD•Finite Finite TT, , field theory field theory•Critical phenomenaCritical phenomena•Chiral property of hadronChiral property of hadron

Dynamic Phenomena in HICDynamic Phenomena in HIC•Expansion, FlowExpansion, Flow•Space-time evolution ofSpace-time evolution of thermodynamic variablesthermodynamic variables

Once one accepts localOnce one accepts localthermalization ansatz,thermalization ansatz,life becomes very easy.life becomes very easy.

Energy-momentum:Energy-momentum:

Conserved number:Conserved number:

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

Ollitrault (’92)Ollitrault (’92)

Hydro behavior

Spatial Anisotropy

Momentum Anisotropy

INPUTINPUT

OUTPUTOUTPUT

Interaction amongInteraction amongproduced particlesproduced particles

dN

/d

No secondary interaction

0 2

dN

/d

0 2

2v2

x

y

QGPmixedhadron

Anisotropy of energy density distribution Anisotropy of “Momentum” distribution

TH&Gyulassy(’06)TH&Gyulassy(’06)

Time Evolution of a QGP Time Evolution of a QGP FluidFluid

Time Evolution of vTime Evolution of v22 from a from a Parton Cascade ModelParton Cascade Model

b = 7.5fm

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

v2 is

Zhang et al.(’99) ideal hydro limit

t(fm/c)

v2 : Ideal hydro

: strongly interactingsystem

Schematic Picture of Shear Schematic Picture of Shear ViscosityViscosity

See, e.g. Danielewicz&Gyulassy(’85)

Assuming relativistic particles,

Perfect fluid: 0

shear viscosity 0

Shear flow Smearing of flow

Next time step

Basis of the AnnouncementBasis of the AnnouncementPHENIX(’03)STAR(’02)

Multiplicity dependencepT dependenceand mass ordering

Hydro results: Huovinen, Kolb, Heinz,…

resp

on

se =

(outp

ut)

/(in

pu

t) “Hydro limit”

It is found that they reproduce v2(pT) data accidentally. T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.

Recent Hydro Recent Hydro ResultsResults

from Our from Our GroupGroup

Centrality Dependence of vCentrality Dependence of v22

Discovery of “Large” v2 at RHIC• v2 data are comparable with hydro results.• Hadronic cascade cannot reproduce data.• Note that, in v2 data, there exists eccentricity fluctuation which is not considered in model calculations.

Result from a hadronic cascade (JAM)(Courtesy of M.Isse)

TH et al. (’06).

Pseudorapidity Dependence of Pseudorapidity Dependence of vv22

=0 >0<0

•v2 data are comparable with hydro results again around =0•Not a QGP gas sQGP•Nevertheless, large discrepancy in forward/backward rapiditySee next slides

TH(’02); TH and K.Tsuda(’02); TH et al. (’06).

QGP onlyQGP+hadron

Hadron Gas Instead of Hadron Hadron Gas Instead of Hadron FluidFluid

QGP coreQGP core

A QGP fluid surrounded by hadronic gas

QGP: Liquid (hydro picture)Hadron: Gas (particle picture)

“Reynolds number”

Matter proper part: (shear viscosity)(entropy density)

bigin Hadron

smallin QGP

T.Hirano and M.Gyulassy,Nucl.Phys.A769 (2006)71.

See also talk/poster by Nonaka

Importance of Hadronic Importance of Hadronic “Corona”“Corona”

•Boltzmann Eq. for hadrons instead of hydrodynamics•Including viscosity through finite mean free path•Suggesting rapid increase of entropy density•Deconfinement makes hydro work at RHIC!? Signal of QGP!?

QGP only QGP+hadron fluids

QGP fluid+hadron gas

T.Hirano et al.,Phys.Lett.B636(2006)299.

QGP Liquid + Hadron Gas QGP Liquid + Hadron Gas Picture Works WellPicture Works Well

Mass dependence is o.k.Note: First result was obtainedby Teaney et al.

20-30%

•Centrality dependence is ok•Large reduction from pure hydro in small multiplicity events

T.Hirano et al.,Phys.Lett.B636(2006)299.

Some Some CommentsComments

on the on the DiscoveryDiscovery

1. Is mass ordering for v1. Is mass ordering for v22(p(pTT) a ) a signal of the perfect QGP fluid?signal of the perfect QGP fluid?

Mass dependence is o.k. fromhydro+cascade.

20-30%

Proton

Pion

Mass ordering comes fromrescattering effect. Interplay btw. radial and elliptic flowsNot a direct sign of the perfect QGP fluid

2. Is viscosity really small in 2. Is viscosity really small in QGP?QGP?

•1+1D Bjorken flow Bjorken(’83) Baym(’84)Hosoya,Kajantie(’85)Danielewicz,Gyulassy(’85)Gavin(’85)Akase et al.(’89)Kouno et al.(’90)…

(Ideal)

(Viscous)

: shear viscosity (MeV/fm2), s : entropy density (1/fm3)/s is a good dimensionless measure

(in the natural unit) to see viscous effects.

Shear viscosity is small in comparison with entropy density!

A Probable Scenario A Probable Scenario TH and Gyulassy (’06)

!•Absolute value of viscosity •Its ratio to entropy density

Rapid increase of entropy density can

make hydro work at RHIC.Deconfinement Signal?!

: shear viscosity, s : entropy density

Kovtun,Son,Starinets(’05)Kovtun,Son,Starinets(’05)

DigressionDigression(Dynamical) Viscosity : ~1.0x10-3 [Pa s] (Water 20℃) ~1.8x10-5 [Pa s] (Air 20℃) Kinetic Viscosity : ~1.0x10-6 [m2/s] (Water 20℃) ~1.5x10-5 [m2/s] (Air 20℃)

[Pa] = [N/m2]

Non-relativistic Navier-Stokes eq. (a simple form)

Neglecting external force and assuming incompressibility.

water > air BUT water < air

3. Is 3. Is /s enough?/s enough?•Reynolds number Iso, Mori, Namiki (’59)

R>>1 Perfect fluid

•Need to solve viscous fluid dynamics in (3+1)D Cool! But, tough! Causality problem (talk by Kunihiro, talk/poster by Muroya)

•(1+1)D Bjorken solution

4. Boltzmann at work?4. Boltzmann at work?

~ 15 * ~ 15 * pert pert !!

Caveat 1: Where is the “dilute” approximation in Boltzmannsimulation? Is ~0.1fm o.k. for the Boltzmann description?Caveat 2: Differential v2 is tricky. dv2/dpT~v2/<pT>.Difference of v2 is amplified by the difference of <pT>.Caveat 3: Hadronization/Freezeout are different.

25-30%25-30%reductionreduction

Molnar&Gyulassy(’00)Molnar&Huovinen(’04)

gluonicgluonicfluidfluid

5. Does v5. Does v22(p(pTT) really tell us ) really tell us smallness of smallness of /s in the QGP /s in the QGP phase?phase?

• Not a result from dynamical calculation, but a “fitting” to data.• No QGP in the model• 0 is not a initial time, but a freeze-out time.• s/0 is not equal to /s, but to 3/4sT00 (in 1+1D).• Being smaller T0 from pT dist., 0 should be larger (~10fm/c).

D.Teaney(’03)

6. Is there model dependence 6. Is there model dependence in hydro calculations?in hydro calculations?

Novel initial conditionsfrom Color Glass Condensatelead to large eccentricity.

For CGC, see alsotalk/poster by Itakura Need viscosity even in

QGP!

Hirano and Nara(’04), Hirano et al.(’06)Kuhlman et al.(’06), Drescher et al.(’06)

Summary and OutlookSummary and Outlook• We have discovered “something” really We have discovered “something” really

intriguing at RHICintriguing at RHIC– Perfect QGP fluid and dissipative hadron gasPerfect QGP fluid and dissipative hadron gas– Hydro at work as a signal of deconfinement(?)Hydro at work as a signal of deconfinement(?)– Large cross section among partons is needed.Large cross section among partons is needed.

• Still a lot of work neededStill a lot of work needed– Initial stage, thermalization time, …Initial stage, thermalization time, …– and and /s are not sufficient to discuss viscous /s are not sufficient to discuss viscous

aspects in H.I.C. (“Perfect fluid” is a dynamic aspects in H.I.C. (“Perfect fluid” is a dynamic concept.)concept.)

– Beyond Boltzmann/ideal hydro approach?Beyond Boltzmann/ideal hydro approach?– Success and challenge of hydrodynamicsSuccess and challenge of hydrodynamics

Hadron Gas instead of Hadron Hadron Gas instead of Hadron FluidFluid

0z

t

(Option)(Option)Color GlassColor GlassCondensateCondensate

sQGP coresQGP core(Full 3D(Full 3DHydro)Hydro)

HadronicHadronicCoronaCorona(Cascade, (Cascade, JAM)JAM)

Glauber-BGK and CGC Initial Glauber-BGK and CGC Initial ConditionsConditionsWhich Clear the First Hurdle Which Clear the First Hurdle

Glauber-BGK

•Glauber modelGlauber model NNpartpart:N:Ncollcoll = 85%:15% = 85%:15%•CGC modelCGC model Matching I.C. via e(x,y,Matching I.C. via e(x,y,))

Centrality dependenceCentrality dependence Rapidity dependenceRapidity dependence

CGC

ppTT Spectra for identified Spectra for identified hadronshadronsfrom QGP Hydro+Hadronic from QGP Hydro+Hadronic CascadeCascade

Caveat: Other components such as recombination and Caveat: Other components such as recombination and fragmentation should appear in the intermediate-high pfragmentation should appear in the intermediate-high pTT regions. regions.

dN/dy and dN/dpdN/dy and dN/dpTT are o.k. by hydro+cascade. are o.k. by hydro+cascade.

Results from Hydro + Results from Hydro + CascadeCascade

Glauber-BGK CGC

vv22(p(pTT) from Hydro: Past, ) from Hydro: Past, Present and FuturePresent and Future

2000 (Heinz, Huovinen, Kolb…)2000 (Heinz, Huovinen, Kolb…)Ideal hydro w/ chem.eq.hadronsIdeal hydro w/ chem.eq.hadrons2002 (TH,Teaney,Kolb…)2002 (TH,Teaney,Kolb…)+Chemical freezeout+Chemical freezeout2002 (Teaney…)2002 (Teaney…)+Dissipation in hadron phase+Dissipation in hadron phase2005 (BNL)2005 (BNL)““RHIC serves the perfect liquid.”RHIC serves the perfect liquid.”2004-2005 (TH,Gyulassy)2004-2005 (TH,Gyulassy)Mechanism of vMechanism of v22(p(pTT) slope) slope2005-2006(TH,Heinz,Nara,…)2005-2006(TH,Heinz,Nara,…)+Color glass condensate+Color glass condensateFutureFuture““To be or not to be (consistentTo be or not to be (consistentwith hydro), that is THE question”with hydro), that is THE question” -- anonymous-- anonymous

History of differential elliptic flowHistory of differential elliptic flow~History of development of hydro~History of development of hydro~History of removing ambiguity in hydro~History of removing ambiguity in hydro

20-30%

XXXXXXXXXXXXXXXXXXXXXXXXXXXX

??????????????????????????????????

XXXXXXXXXXXXXXXXXXXXXXXXXXXX

Temperature Dependence Temperature Dependence ofof /s/s

•We propose a possible scenario:

Kovtun, Son, Starinets(‘05)

Danielewicz&Gyulassy(’85)•Shear Viscosity in Hadron Gas

•Assumption: /s at Tc in the sQGP is 1/4

No big jump in viscosity at Tc!

Viscosity from a Kinetic Viscosity from a Kinetic TheoryTheory

See, e.g. Danielewicz&Gyulassy(’85)

For ultra-relativistic particles, the shear viscosity is

Ideal hydro: 0

shear viscosity 0Transport cross section

Schematic Picture of Shear Schematic Picture of Shear ViscosityViscosity

See, e.g. Danielewicz&Gyulassy(’85)

Assuming relativistic particles,

Perfect fluid: 0

shear viscosity 0

Shear flow Smearing of flow

Next time step

A Long Long Time Ago…A Long Long Time Ago…

…we obtain the value R (Reynolds number)=1~10…Thus we may infer that the assumption of theperfect fluid is not so good as supposed by Landau.

/s from Lattice/s from Lattice

A.Nakamura and S.Sakai,PRL94,072305(2005).A.Nakamura and S.Sakai,PRL94,072305(2005).

Shear viscosity to Shear viscosity to entropy ratio fromentropy ratio fromlattice (pure gauge)lattice (pure gauge)+ an assumption + an assumption of spectral functionof spectral functioneta/s < 1eta/s < 1is one of theis one of thepromising results ofpromising results ofapplicability forapplicability forhydro at RHIChydro at RHIC

Challenging calculation!Challenging calculation!

I love toI love tosee this see this region!!region!!

Navier-Stokes Eq. and Navier-Stokes Eq. and Relaxation TimeRelaxation Time

•Non-rela. (Cattaneo (’48))

0: Fourier law

: relaxation time

Heat Eq. (Hyperbolic Eq.)

Finite relaxation time

Telegraph Eq.(Parabolic Eq.)

Balance Eq.

Constitutive Eq.

Violation ofcausality

cf.) 杉山勝、数理科学 (2002 年８月号）

Novel Viscous Fluid DynamicsNovel Viscous Fluid Dynamics

How to get constitutive eqs.?

2nd thermodynamic law

Balance Eqs

ConstitutiveEq.

Mueller,Israel,Stewart,…

1st order 2nd order

Toward determination of Toward determination of transport coefficient of the transport coefficient of the QGPQGP(Linear Response) ＝ (Transport Coefficient) x (Thermodynamic Force)

bulk, shear, heat conductivity

Lattice QCD + Kubo formula

Relaxation for viscosity ：It can be obtain from a comp. btw. BoltzmannEq. and visc. fluid dynamics. Higher order moment for n(1±n)Can it be obtained from Lattice?

•Navier-Stokes eq. (1st order)

•Novel rela. visc. fluid dynamics (2nd order)

Israel,Stewart

Nakamura,Sakai

How Do Partons Get How Do Partons Get Longitudinal Momentum in Longitudinal Momentum in Comoving System?Comoving System?Free Streaming eta=yFree Streaming eta=y

dN/dydN/dy

y

dN/dydN/dy

y

Sum of delta functionSum of delta function Width Width “Thermal” fluctuation“Thermal” fluctuation

Sheet:Sheet:eta=consteta=const

222 Collisions Do Not Help!2 Collisions Do Not Help!

Xu and Greiner, hep-ph/0406278Xu and Greiner, hep-ph/0406278

Only 2Only 22 collisions,2 collisions,partons are still in apartons are still in atransverse sheettransverse sheeteta~y~const.eta~y~const.223 may help.3 may help.

/s from MD simulations/s from MD simulations

Y.Akimura et al., nucl-th/0511019Y.Akimura et al., nucl-th/0511019

eta/s has a minimumeta/s has a minimumin the vicinity of Tin the vicinity of Tcc ! !

No thermal qqbar No thermal qqbar productionproductionPreliminary resultPreliminary result

Statistical Model Fitting to Statistical Model Fitting to ee&ppee&pp

Becattini&Heinz(’97)Becattini&Heinz(’97)

Phase space dominance? Phase space dominance? ““T” prop to E/N?T” prop to E/N? See, e.g., Rischke(’02),Koch(’03)See, e.g., Rischke(’02),Koch(’03)

Hadron phase below THadron phase below Tchch in in H.I.C.H.I.C.

• ““chemically frozen” chemically frozen” Themalization can be Themalization can be maintained through elastic scattering.maintained through elastic scattering.

• There still exit “quasi-elastic” collisions, e.g.There still exit “quasi-elastic” collisions, e.g.

• The numbers of short-lived resonances can The numbers of short-lived resonances can be varied. (Acquirement of chemical be varied. (Acquirement of chemical potential)potential)

• Recent data suggests importance of Recent data suggests importance of (process dependent) hadronic rescattering(process dependent) hadronic rescattering– Hard to describe this by hydro.Hard to describe this by hydro.

A Closer Look Reveals Details A Closer Look Reveals Details of Hadronic Matterof Hadronic Matter S

tole

n fro

m M

.Ble

icher (T

he B

erke

ley S

chool)

How Reliable How Reliable Quantitatively?Quantitatively?

Radial flow in pp collisions?Radial flow in pp collisions?

central

peripheral

SmallSmallrescatteringrescattering

SystemSystemexpandsexpandslike thislike thistrajectory?trajectory?