RHICRHIC とと LHCLHC における楕円型における楕円型フローの相対論的流体モデルフローの相対論的流体モデル

による解析による解析

東京大学大学院理学系研究科東京大学大学院理学系研究科平野哲文平野哲文

Seminar, Tsukuba Univ., Jan.19, 2011Seminar, Tsukuba Univ., Jan.19, 2011

T.H., P.Huovinen, Y.Nara, arXiv:1012.3955; arXiv:1010.6222(PRC, T.H., P.Huovinen, Y.Nara, arXiv:1012.3955; arXiv:1010.6222(PRC, in press); invited review article in Progress of Particle and Nucleain press); invited review article in Progress of Particle and Nuclear Physics (in preparation)r Physics (in preparation)

OutlineOutline IntroductionIntroduction Some highlights from the hybrid modelSome highlights from the hybrid model Model: QGP fluid + hadronic cascade pictureModel: QGP fluid + hadronic cascade picture Results at RHIC: Results at RHIC:

vv22 source functionsource function

Prediction and Postdiction at RHIC and LHC:Prediction and Postdiction at RHIC and LHC: vv22 in U+U collisions in U+U collisions vv22 in Pb+Pb collisions in Pb+Pb collisions

SummarySummary

IntroductionIntroduction Main aim: Understanding RHIC data based on Main aim: Understanding RHIC data based on

a systematic analysis with QGP perfect fluid pia systematic analysis with QGP perfect fluid picturecture

After press release of perfect fluid discovery in After press release of perfect fluid discovery in 2005 2005 Much progress: hadronic dissipation, Much progress: hadronic dissipation, eccentricity fluctuation, lattice EoS, CGC initial eccentricity fluctuation, lattice EoS, CGC initial condition…condition…

Set a baseline for viscous hydro calculationsSet a baseline for viscous hydro calculations Prediction for U+U at RHIC and Pb+Pb at LHCPrediction for U+U at RHIC and Pb+Pb at LHC

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

Elliptic FlowElliptic FlowHow does the system respond to spatial anisotropy?How does the system respond to spatial anisotropy?

Importance of Hadronic DissipationImportance of Hadronic Dissipation

QGP only QGP+hadron fluids

QGP fluid+hadron gas

Suppression in forward and backward rapiditySuppression in forward and backward rapidityImportance of hadronic viscosityImportance of hadronic viscosity

TH et al.,(’05)

Mass Splitting = Hadronic effectsMass Splitting = Hadronic effects

Mass dependence is o.k. from hydro+cascade. When mass splitting appears?

20-30%

Proton

Pion

Mass ordering comes fromhadronic rescattering effect. Interplay btw. radial and elliptic flows.

TH et al.,(’08)

Violation of Mass SplittingViolation of Mass Splitting

Au+Au 200 GeVb=7.2fm

TH et al.,(’08)

ModelModel No single model to understand heavy ion collisNo single model to understand heavy ion collis

ion as a whole.ion as a whole. Idea: Employ “cutting edge” modules as far as Idea: Employ “cutting edge” modules as far as

possiblepossible 3D ideal hydro3D ideal hydro Hadronic transport model, JAMHadronic transport model, JAM Lattice EoS + resonance gas in JAMLattice EoS + resonance gas in JAM Monte Carlo Glauber/KLN for initial conditionMonte Carlo Glauber/KLN for initial condition

A Hybrid Approach: A Hybrid Approach: Initial ConditionInitial Condition

0collision axis

time

AuAu AuAu

QGP fluid

hadron gasModel*

•MC-Glauber•MC-KLN (CGC)

• part, R.P.

• Centrality cut

0-10%

10-20%20-30%

…

*H.J.Drescher and Y.Nara (2007)

Initial Condition w.r.t. Participant PlaInitial Condition w.r.t. Participant Planene

Shift: (<x>,<y>)Shift: (<x>,<y>)Rotation:Rotation:

Throw a diceThrow a diceto choose to choose bband calculateand calculateNNpartpart averageaverage

over eventsover events

averageaverageover eventsover events

E.g.)E.g.)NNpartpart

minmin= 279= 279NNpartpart

maxmax= 394= 394in Au+Au collisionsin Au+Au collisionsat 0-10% centralityat 0-10% centrality

Participant planeParticipant plane

Reaction planeReaction plane

partpart and and R.P.R.P.

Au+AuAu+Au Cu+CuCu+Cu

•Eccentricity enhanced due to fluctuationEccentricity enhanced due to fluctuation•Significant in small system, e.g., Cu+Cu, perpheal Au+AuSignificant in small system, e.g., Cu+Cu, perpheal Au+Au•MC-KLN > MC-Glauber *MC-KLN > MC-Glauber *

*See, Drescher and Nara, PRC 75, 034905 (2007).*See, Drescher and Nara, PRC 75, 034905 (2007).

A Hybrid Approach: A Hybrid Approach: HydrodynamicsHydrodynamics

0collision axis

time

AuAu AuAu

QGP fluid

hadron gasIdeal Hydrodynamics#

•Initial time 0.6 fm/c•Lattice + HRG EoS*

##Hirano (2002),*Huovinen and Petreczky (2010) + JAM HRGHirano (2002),*Huovinen and Petreczky (2010) + JAM HRG

A Hybrid Approach: A Hybrid Approach: Hadronic CascadeHadronic Cascade

0collision axis

time

AuAu AuAu

QGP fluid

hadron gas Interface• Cooper-Frye formulaat switching temperatureTsw = 155 MeVHadronic afterburner• Hadronic transportmodel based on kinetictheory JAM*

*Y.Nara et al., (2000)

Comparison of Comparison of Hydro+Cascade ResultsHydro+Cascade Results

with Available Datawith Available Data

ppTT Spectra: MC-Glauber Spectra: MC-Glauber

Filled: PHENIX, PRC69, 034909 (2004), Open: Hydro+cascadeFilled: PHENIX, PRC69, 034909 (2004), Open: Hydro+cascadeFrom top to bottom, 0-5, 5-10, 10-15, …, 70-80% centralityFrom top to bottom, 0-5, 5-10, 10-15, …, 70-80% centrality

(1) Absolute value of entropy, (2) soft/hard fraction (1) Absolute value of entropy, (2) soft/hard fraction = = 0.18, and (3) switching temperature T0.18, and (3) switching temperature Tswsw = 155 MeV. = 155 MeV.

ppTT Spectra: MC-KLN Spectra: MC-KLN

(1) Absolute value of saturation scale and (2) scaling (1) Absolute value of saturation scale and (2) scaling parameters parameters =0.28 and (3) switching temperature T=0.28 and (3) switching temperature Tss

ww = 155 MeV = 155 MeV

Filled: PHENIX, PRC69, 034909 (2004), Open: Hydro+cascadeFilled: PHENIX, PRC69, 034909 (2004), Open: Hydro+cascadeFrom top to bottom, 0-5, 5-10, 10-15, …, 70-80% centralityFrom top to bottom, 0-5, 5-10, 10-15, …, 70-80% centrality

vv22(N(Npartpart))

Au+AuAu+Au Cu+CuCu+Cu

MC-GlauberMC-Glauber: : Apparent reproduction. No room for QGP viscosity?Apparent reproduction. No room for QGP viscosity?MC-KLNMC-KLN::Overshoot due to larger eccentricity. How small QGP Overshoot due to larger eccentricity. How small QGP viscosity?viscosity?

ppTT>0>0 ppTT>0>0

PHOBOS, PRC72, 051901 (2005); PRL98, 242302 (2007).PHOBOS, PRC72, 051901 (2005); PRL98, 242302 (2007).

vv22(centrality)(centrality)

Au+AuAu+Au Cu+CuCu+Cu

•ppTT cut enhances v cut enhances v22 by ~10% by ~10%•STAR data in Au+Au corrected by Ollitrault et al.*STAR data in Au+Au corrected by Ollitrault et al.*•vv22 w.r.t. participant plane w.r.t. participant plane

0.15 < p0.15 < pT T < 2 GeV/c< 2 GeV/c0.15 < p0.15 < pT T < 2 GeV/c< 2 GeV/c

*J.Y.Ollitrault, A.M.Poskanzer and S.A.Voloshin, PRC80, 014904 (200*J.Y.Ollitrault, A.M.Poskanzer and S.A.Voloshin, PRC80, 014904 (2009).9).

vv22(p(pTT) for PID Particles) for PID Particles•Results based on MC-Results based on MC-Glauber initializationGlauber initialization•Mass splitting pattern OKMass splitting pattern OK•A little bit overshoot evenA little bit overshoot evenin low pin low pTT region region Centrality dependence Centrality dependence (next slide)?(next slide)?

PHENIX, PRL91, 182301 (2003)PHENIX, PRL91, 182301 (2003)

0-80%0-80%

vv22(p(pTT) for PID Particles: ) for PID Particles: Centrality DependenceCentrality Dependence

0-20%0-20%

20-40%20-40%

40-60%40-60%

•Hydro+cascade withHydro+cascade withMC-Glauber at workMC-Glauber at workin 0-20% centralityin 0-20% centrality•Need QGP viscosityNeed QGP viscosity•Or, need jet or Or, need jet or recombination/coalescencerecombination/coalescencecomponents?components?•MC-KLN results not availableMC-KLN results not availableyet due to less statisticsyet due to less statistics

PHENIX, PRL91, 182301 (2003)PHENIX, PRL91, 182301 (2003)

vv22(p(pTT) for Charged Particles: Au+Au) for Charged Particles: Au+Au

•Hydro+cascade with MC-Glauber at work in low pHydro+cascade with MC-Glauber at work in low pTT

•ppTT region at work shrinks as moving to peripheral region at work shrinks as moving to peripheral Importance of viscosityImportance of viscosity PHENIX, PRC80, 024909 (2009).PHENIX, PRC80, 024909 (2009).

STAR, PRC72, 014904 (2005). STAR, PRC72, 014904 (2005).

vv22(p(pTT) for Charged Particles: Cu+Cu) for Charged Particles: Cu+Cu

•Tendency is the same as that in Au+Au collisionsTendency is the same as that in Au+Au collisions

PHENIX, PRL98, 162301 (2007).PHENIX, PRL98, 162301 (2007).STAR, PRC81, 044902 (2010). STAR, PRC81, 044902 (2010).

vv22(p(pTT) for Charged Particles: Au+Au) for Charged Particles: Au+Au

•Hydro+cascade with Hydro+cascade with MC-KLNMC-KLN at work at work in central collisionsin central collisions

PHENIX, PRC80, 024909 (2009).PHENIX, PRC80, 024909 (2009).STAR, PRC72, 014904 (2005). STAR, PRC72, 014904 (2005).

MC-KLN vs. MC-GlauberMC-KLN vs. MC-Glauber

Slope of vSlope of v22(p(pTT))steeper in MC-KLNsteeper in MC-KLNthan in MC-Glauberthan in MC-Glauber vv2,MC-KLN2,MC-KLN > v > v2,MC-Glauber2,MC-Glauber

•ppTT dependent viscous dependent viscouscorrection at T=Tcorrection at T=Tswsw

might interpret the datamight interpret the data•Extracted transportExtracted transportcoefficients depend oncoefficients depend oninitial conditioninitial condition

Conventional Femtoscopic AnalysisConventional Femtoscopic AnalysisParticle sourceParticle source

Detector 1Detector 1

Detector 2Detector 2

Hanbury Brown – Twiss (1956)Hanbury Brown – Twiss (1956)Goldhaber – Goldhaber – Lee – Pais (1960)Goldhaber – Goldhaber – Lee – Pais (1960)

Source size of Source size of particle emissionparticle emission(Homogeneity region)(Homogeneity region) Information in Information in configuration spaceconfiguration space

New Technique: Source ImagingNew Technique: Source Imaging

Koonin-Pratt eq.:

Inverse problemInverse problem

Source function and emission rate:Source function and emission rate:

Primed (‘) variables in Pair Center-of-Mass SystemPrimed (‘) variables in Pair Center-of-Mass System

Brown, Danielewicz(1997)Brown, Danielewicz(1997)

1D Source Function for Pions1D Source Function for Pions

With hadronicWith hadronicrescattering and decaysrescattering and decays

Without hadronicWithout hadronicrescattering and decaysrescattering and decays

Non-Gaussian tail in pion source functionNon-Gaussian tail in pion source functionfrom hybrid modelfrom hybrid model

Au+Au, 0-30%Au+Au, 0-30%0.3 < k0.3 < kTT < 0.9 GeV/c < 0.9 GeV/c

Au+Au, 0-30%Au+Au, 0-30%0.3 < k0.3 < kTT < 0.9 GeV/c < 0.9 GeV/c

PHENIX, PRL103, 142301(2009)PHENIX, PRL103, 142301(2009)

1D Source Function for Kaons1D Source Function for Kaons

With hadronicWith hadronicrescattering and decaysrescattering and decays

Without hadronicWithout hadronicrescattering and decaysrescattering and decays

Non-Gaussian tail in kaon source functionNon-Gaussian tail in kaon source functionfrom hybrid modelfrom hybrid model

Au+Au, 0-30%Au+Au, 0-30%0.3 < k0.3 < kTT < 0.9 GeV/c < 0.9 GeV/c

Au+Au, 0-30%Au+Au, 0-30%0.3 < k0.3 < kTT < 0.9 GeV/c < 0.9 GeV/c

PHENIX, PRL103, 142301(2009)PHENIX, PRL103, 142301(2009)

Emission Rate for PionsEmission Rate for Pions

0-30% Au+Au, pions, 0.3 < p0-30% Au+Au, pions, 0.3 < pxx < 0.9 GeV/c < 0.9 GeV/cWithoutWithout hadronic rescattering or decays hadronic rescattering or decays Negative x-t correlationNegative x-t correlation

Emission Rate for PionsEmission Rate for Pions

0-30% Au+Au, pions, 0.3 < p0-30% Au+Au, pions, 0.3 < pxx < 0.9 GeV/c < 0.9 GeV/cWithWith hadronic rescattering and decays hadronic rescattering and decays Positive x-t correlation(?)Positive x-t correlation(?)

Emission Rate for KaonsEmission Rate for Kaons

0-30% Au+Au, 0-30% Au+Au, kaonskaons, 0.3 < p, 0.3 < pxx < 0.9 GeV/c < 0.9 GeV/cWithoutWithout hadronic rescattering or decays hadronic rescattering or decays Negative x-t correlationNegative x-t correlation

Emission Rate for KaonsEmission Rate for Kaons

0-30% Au+Au, 0-30% Au+Au, kaonskaons, 0.3 < p, 0.3 < pxx < 0.9 GeV/c < 0.9 GeV/cWithWith hadronic rescattering and decays hadronic rescattering and decays Positive x-t correlation(?)Positive x-t correlation(?)

Predictions and Predictions and Postdiction from Postdiction from

Hydro+Cascade ModelHydro+Cascade Model

Collisions of Deformed Nuclei at RHICCollisions of Deformed Nuclei at RHIC

•How vHow v22// behaves as behaves asincreasing multiplicity?*increasing multiplicity?*

•Saturate?Saturate?•Still enhance?Still enhance?

U+U collision in run12U+U collision in run12at RHIC(?)at RHIC(?)•More multiplicityMore multiplicity•Larger eccentricityLarger eccentricity

STAR, PRC66, 034904 (2002)STAR, PRC66, 034904 (2002)*U.Heinz and A. Kuhlman, *U.Heinz and A. Kuhlman, PRL94, 132301 (2005).PRL94, 132301 (2005).

Eccentricity in U+U Collisions at RHICEccentricity in U+U Collisions at RHIC

•Larger eccentricityLarger eccentricity•Finite eccentricity at Finite eccentricity at zero impact parameterzero impact parameterbody-body collisionbody-body collision•Unable to controlUnable to controlconfiguration configuration Need NeedMonte-Carlo study andMonte-Carlo study andevent selection*event selection*

*See, e.g., P.Filip et al. PRC80, 054903 (2009).*See, e.g., P.Filip et al. PRC80, 054903 (2009).

0-5%0-5% 0.146 (MC-Glauber), 0.148 (MC-KLN) 0.146 (MC-Glauber), 0.148 (MC-KLN)

vv22 in U+U Collisions in U+U Collisions

•vv22 increases due to deformation of colliding nuclei. increases due to deformation of colliding nuclei.•vv22// scales with transverse density. scales with transverse density.•Maximum transverse density increases only by ~10%Maximum transverse density increases only by ~10%in central U+U collisions.in central U+U collisions.

Prediction at LHCPrediction at LHC

Eccentricity does notEccentricity does notchange from RHIC to LHC!change from RHIC to LHC!Change due solely to size Change due solely to size

vv22// does not follow does not followRHIC scaling curveRHIC scaling curve

vv22// Scales at Fixed Collision Energy Scales at Fixed Collision Energy

Increase multiplicityIncrease multiplicitywith fixed centrality.with fixed centrality.

Pick up pointsPick up pointswith fixed centralitywith fixed centrality

consistentconsistent

P.F.Kolb et al., PRC62, 054909 (2000)P.F.Kolb et al., PRC62, 054909 (2000)

The First Heavy Ion Data at LHCThe First Heavy Ion Data at LHC

Congrats!!!Congrats!!!

Centrality Dependence of MultiplicityCentrality Dependence of Multiplicity

MC-KLN: Default, MC-Glauber: alpha = 0.08MC-KLN: Default, MC-Glauber: alpha = 0.08ALICE, arXiv:1012.1657ALICE, arXiv:1012.1657

EccentricityEccentricity

crossing in Glaubercrossing in Glauber

Crossing Crossing Due to smearing effects Due to smearing effects

ppTT Spectra of Charged Hadrons Spectra of Charged Hadrons

Spectra at LHC get harder than at RHICSpectra at LHC get harder than at RHIC

Integrated vIntegrated v22

If the Nature chooses MC-KLN, viscous effectsIf the Nature chooses MC-KLN, viscous effectswould be larger at LHC than at RHIC.would be larger at LHC than at RHIC.

Importance of understanding initial conditionsImportance of understanding initial conditionsALICE, PRL105, 0252302(2010).ALICE, PRL105, 0252302(2010).

Differential vDifferential v22

•vv22(p(pTT) at LHC is almost identical to v) at LHC is almost identical to v22(p(pTT) at RHIC,) at RHIC,in particular, in MC-Glauber.in particular, in MC-Glauber.•Steeper slope in MC-CGC leads to larger vSteeper slope in MC-CGC leads to larger v22 even if even ifincrease of mean pincrease of mean pTT in MC-CGC is identical to that in MC-CGC is identical to thatin MC-Glauber.in MC-Glauber. ALICE, PRL105, 0252302(2010).ALICE, PRL105, 0252302(2010).

SummarySummary Current status of the hybrid approachCurrent status of the hybrid approach

Elliptic flowElliptic flow MC-Glauber initialization gives a reasonable agreement with data iMC-Glauber initialization gives a reasonable agreement with data i

n very central collisions.n very central collisions. Results deviate from data as moving away from central collisions.Results deviate from data as moving away from central collisions. QGP viscosity?QGP viscosity?

Source functionSource function Non-Gaussian tail is seen through hadronic rescatterings and decaNon-Gaussian tail is seen through hadronic rescatterings and deca

ysys PredictionPrediction

Results in U+U collisions follow scaling behavior, extend (1/S)dNResults in U+U collisions follow scaling behavior, extend (1/S)dNchch

/d/d by ~10% by ~10% vv22// at LHC does not follow scaling seen at RHIC at LHC does not follow scaling seen at RHIC

Summary (contd.)Summary (contd.)

PostdictionPostdiction QGP viscosity at LHC (higher T) is larger than at RHIC (loQGP viscosity at LHC (higher T) is larger than at RHIC (lo

wer T) in MC-KLN?wer T) in MC-KLN? Understanding of transverse dynamics and initial state iUnderstanding of transverse dynamics and initial state i

s important.s important.

Thank You!Thank You!

Available at

BACKUPBACKUPSLIDESSLIDES

ppTT Spectra in STAR and PHENIX Spectra in STAR and PHENIX

Central:Central:Consistent btw. Consistent btw. STAR and PHENIXSTAR and PHENIX

Peripheral:Peripheral:(STAR) > (PHENIX)(STAR) > (PHENIX)STAR data are 50 %STAR data are 50 %larger than PHENIX datalarger than PHENIX data

STAR, PRC 79, 034909 (2009)STAR, PRC 79, 034909 (2009)PHENIX, PRC69, 034909 (2004)PHENIX, PRC69, 034909 (2004)

Steeper Transverse Profile in CGCSteeper Transverse Profile in CGC

Closer to hard spherethan Glauber

Note: Original KLNmodel (not fKLN)

Event Distributions from Monte CarloEvent Distributions from Monte Carlo

Centrality cut is doneCentrality cut is doneaccording to Naccording to Npartpart

Correlation btw. NCorrelation btw. Npartpart and N and Ncollcoll

Au+AuAu+Au U+UU+U

NNpartpart NNpartpart

NNco

llco

ll

NNco

llco

ll

Eccentricity FluctuationEccentricity Fluctuation

Interaction points of participants vary event by eveInteraction points of participants vary event by event.nt. Apparent reaction plane also varies.Apparent reaction plane also varies. The effect is significant for smaller system such The effect is significant for smaller system such as Cu+Cu collisionsas Cu+Cu collisions

Adopted from D.Hofman(PHOBOS),Adopted from D.Hofman(PHOBOS),talk at QM2006talk at QM2006

A sample eventA sample eventfrom Monte Carlofrom Monte CarloGlauber modelGlauber model

i

0

Event-by-Event EccentricityEvent-by-Event Eccentricity

Normalization in Source FunctionNormalization in Source Function

Source function multiplied by phase space densitySource function multiplied by phase space density

Comparison of Source FunctionsComparison of Source Functions

Both normalized to be unityBoth normalized to be unity

Normalization in PHENIX???Normalization in PHENIX???

(fm

-2)