Hadronic Rescattering Effects Hadronic Rescattering Effects after Hadronization of QGP after Hadronization of QGP

FluidsFluids

Tetsufumi HiranoTetsufumi Hirano

Institute of Physics, University of Institute of Physics, University of TokyoTokyo

Workshop “Hadronization”Workshop “Hadronization”in 2006 RHIC & AGS annual users’ meetingin 2006 RHIC & AGS annual users’ meeting

Two TopicsTwo Topics

• Hadronic Rescattering Effects after Hadronic Rescattering Effects after Hadronization of QGP fluidsHadronization of QGP fluids– T.Hirano, U.Heinz, D.Kharzeev, R.Lacey, T.Hirano, U.Heinz, D.Kharzeev, R.Lacey,

Y.Nara, PLB636(2006)299; (in Y.Nara, PLB636(2006)299; (in preparation).preparation).

• Hadronization through Jet-Fluid StringsHadronization through Jet-Fluid Strings– T.Hirano,M.Isse,A.Ohnishi,Y.Nara,K.YoshinT.Hirano,M.Isse,A.Ohnishi,Y.Nara,K.Yoshin

o, (in preparation).o, (in preparation).

(CGC +)QGP Hydro+Hadronic (CGC +)QGP Hydro+Hadronic CascadeCascade

0z

t

(Option)(Option)Color GlassColor GlassCondensateCondensate

sQGP coresQGP core(Full 3D(Full 3DIdeal Hydro)Ideal Hydro)

HadronicHadronicCoronaCorona(Cascade, (Cascade, JAM)JAM)

c.f. Similar approach by Nonaka (talk in “perfect fluid” workshop)c.f. Similar approach by Nonaka (talk in “perfect fluid” workshop)

TH et al.(’05-)TH et al.(’05-)

0.6fm/c0.6fm/c

Hydro Meets Data for the First Time Hydro Meets Data for the First Time at RHIC: “Current” Three Pillarsat RHIC: “Current” Three Pillars

1.1. Perfect Fluid (s)QGP CorePerfect Fluid (s)QGP Core• Ideal hydro description of the QGP phaseIdeal hydro description of the QGP phase• Necessary to gain integrated vNecessary to gain integrated v22

2.2. Dissipative Hadronic CoronaDissipative Hadronic Corona• Boltzmann description of the hadron phaseBoltzmann description of the hadron phase• Necessary to gain enough radial flowNecessary to gain enough radial flow• Necessary to fix particle ratio dynamicallyNecessary to fix particle ratio dynamically

3.3. Glauber Type Initial ConditionGlauber Type Initial Condition• Diffuseness of initial geometryDiffuseness of initial geometry

TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06)TH&Gyulassy(’06),TH,Heinz,Kharzeev,Lacey,Nara(’06)

A Lack of each pillar leads to discrepancy!A Lack of each pillar leads to discrepancy!

(1) Glauber and (2) CGC Hydro (1) Glauber and (2) CGC Hydro Initial Conditions Which Clear the Initial Conditions Which Clear the First Hurdle First Hurdle

•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

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.

vv22(N(Npartpart) from ) from QGP Hydro + Hadronic QGP Hydro + Hadronic CascadeCascade

GlauberGlauber:: Early thermalizationEarly thermalization Mechanism? Mechanism? CGCCGC:: No perfect fluid?No perfect fluid? Additional viscosity Additional viscosity

is required in QGPis required in QGP

Importance of better understanding of initial Importance of better understanding of initial conditioncondition

Result of JAM: Courtesy of M.IsseResult of JAM: Courtesy of M.Isse

TH et al.(’06)TH et al.(’06)

Large Eccentricity from CGC Initial Large Eccentricity from CGC Initial ConditionCondition

xx

yy

Pocket formula (ideal hydro):Pocket formula (ideal hydro): vv22 ~ 0.2 ~ 0.2 @ RHIC energies @ RHIC energies

Ollitrault(’92)Ollitrault(’92)

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

Talk by Y.Nara in “Interaction btw hard probes and the bulk”.Talk by Y.Nara in “Interaction btw hard probes and the bulk”.

vv22(p(pTT) for identified hadrons) for identified hadronsfrom QGP Hydro + Hadronic from QGP Hydro + Hadronic CascadeCascade

Glauber type initial conditionGlauber type initial condition CGC initial conditionCGC initial condition

Mass dependence is o.k.Mass dependence is o.k. vv22(model) > v(model) > v22(data)(data)

20-30% 20-30%

Summary So FarSummary So Far

• An answer to the question, “whether An answer to the question, “whether perfect fluid is discovered”, depends on perfect fluid is discovered”, depends on relatively unknown initial conditions.relatively unknown initial conditions.– Glauber: Early thermalization + perfect Glauber: Early thermalization + perfect

fluid QGPfluid QGP– CGC: No perfect fluid QGP?CGC: No perfect fluid QGP?

• Discovery of EITHER a perfect fluid QGP Discovery of EITHER a perfect fluid QGP OR the CGC + a viscous fluid QGP?OR the CGC + a viscous fluid QGP?

How Large Hadronic How Large Hadronic Rescattering?Rescattering?• Hybrid Model:Hybrid Model:

QGP Fluid + Hadronic QGP Fluid + Hadronic GasGas + Glauber I.C. + Glauber I.C.

• Hydro Model:Hydro Model:

QGP Fluid + Hadronic QGP Fluid + Hadronic FluidFluid + Glauber I.C. + Glauber I.C.

ComparisonComparisonTry to drawTry to drawinformation on hadron gasinformation on hadron gas

Key technique in hydroKey technique in hydro: : •Partial chemical equilibrium in hadron phasePartial chemical equilibrium in hadron phase•Particle ratio fixed at TParticle ratio fixed at Tchch

Chemical equilibrium changes dynamics. Chemical equilibrium changes dynamics. TH and K.Tsuda(’02),TH and M.Gyulassy(’06)TH and K.Tsuda(’02),TH and M.Gyulassy(’06)

Hydro ~ Hydro+Cascade for Hydro ~ Hydro+Cascade for ProtonsProtons

•TTthth ~ 100 MeV ~ 100 MeV•Shape of spectrumShape of spectrumchanges due tochanges due toradial flow ratherradial flow ratherthan hadronicthan hadronicdissipation fordissipation forprotons.protons.

radial flow

Opposite Behaviors for Opposite Behaviors for PionsPions

Softer: Hadronic FluidSofter: Hadronic Fluid(pdV work)(pdV work)

Harder: Hadronic GasHarder: Hadronic Gas(Viscous pressure)(Viscous pressure)

Green line:Green line:

Teaney(’03)Teaney(’03)Caveat:Caveat:Transverse expansionTransverse expansionNon-scaling solutionNon-scaling solution

Hadronic Dissipation Hadronic Dissipation Suppresses Differential Elliptic Suppresses Differential Elliptic FlowFlow

Difference comes Difference comes from dissipation from dissipation only in the hadron only in the hadron phase phase

Caveat: Chemically frozen hadronic fluid is Caveat: Chemically frozen hadronic fluid is essential in differential elliptic flow. (TH and essential in differential elliptic flow. (TH and M.Gyulassy (’06))M.Gyulassy (’06))

•Relevant parameter: Relevant parameter: ss Teaney(’03)Teaney(’03)•Dissipative effect is not soDissipative effect is not solarge due to small expansion large due to small expansion rate (1/tau ~ 0.05-0.1 fmrate (1/tau ~ 0.05-0.1 fm-1-1))

Mass Splitting Comes from the Mass Splitting Comes from the Late Hadronic StageLate Hadronic Stage

Proton

Pion

Pion: Generation of v2in the hadronic stageProton: Radial flow effects Huovinen et al.(’01)

Mass splitting itselfMass splitting itselfis NOT a direct signatureis NOT a direct signatureof perfect fluid QGP.of perfect fluid QGP.

vv22(() from) fromQGP Hydro + Hadronic QGP Hydro + Hadronic CascadeCascade

Suppression due tohadronic dissipation

Excitation Function of v2Excitation Function of v2

Hadronic DissipationHadronic Dissipation•is huge at SPS.is huge at SPS.•still affects v2 at RHIC.still affects v2 at RHIC.•is almost negligible at LHC.is almost negligible at LHC.

Summary of the 1Summary of the 1stst Topic Topic• An answer to the question, “whether An answer to the question, “whether

perfect fluid is discovered”, depends on perfect fluid is discovered”, depends on relatively unknown initial conditions.relatively unknown initial conditions.

• Protons: pT slope becomes harder due to Protons: pT slope becomes harder due to radial flow.radial flow.

• Pions: pT slope becomes harder due to Pions: pT slope becomes harder due to dissipation. However, it becomes softer dissipation. However, it becomes softer due to pdV work in the case of no due to pdV work in the case of no viscosity.viscosity.

• The effect of hadronic dissipation is large The effect of hadronic dissipation is large in small multiplicity as expected.in small multiplicity as expected.

Hadronization through Jet-Fluid Hadronization through Jet-Fluid StringsStrings

In Rudy Hwa’s language, this model describesIn Rudy Hwa’s language, this model describes shower-shower, shower-thermal, NOT thermal-shower-shower, shower-thermal, NOT thermal-thermal.thermal.

T.Hirano, M.Isse, Y.Nara, A.Ohnishi, K.Yoshino, (in preparation).T.Hirano, M.Isse, Y.Nara, A.Ohnishi, K.Yoshino, (in preparation).

Space-time evolution of the QGP fluidSpace-time evolution of the QGP fluidOpen data tableOpen data table

StringStringFragmentationFragmentation

PYTHIAPYTHIA(Lund)(Lund)

Energy lossEnergy loss GLV 1GLV 1stst order order

http://nt1.c.u-tokyo.ac.jp/~hirano/parevo/parevo.html

T.Hirano, talk at “Interaction between hard probes and the bulk” (tomorrow)

Comparison btw two Comparison btw two mechanismsmechanisms

Lorentz-boosted thermal parton distributionat T=Tc hyper surface from hydro simulations

ppTT distributions distributions

20-30% centrality

GLV 1st order (simplified) formula

Effective parton density from hydro

Independent fragmentation C=2.5-3.0Jet-fluid string C=8.0

•Fluctuation of the number of emitted gluon•Chemical non-equilibrium in the QGP phase•Higher order in opacity expansion•Cronin effect …

Neglecting many effects

Fitting the pT data is ourstarting point.

vv22 @ intermediate-high p @ intermediate-high pTT

v2(JFS) ~ 0.1 at b~8 fmwithout assuming

an unrealistic hard sphere

20-30% centrality

High pHigh pTT v v22 puzzle!? puzzle!?STAR, PRL93,252301(’04)

Mechanism 1Mechanism 1

In order to compensate thiseffect, one needs additionalparton energy loss in comparison with independentfragmentation scheme.This enhances v2.

Additional push!

Mechanism 2Mechanism 2

Direction of flow~Perpendicular to surface

Direction of jets~Radial on average

Direction of stringmomentum is tiltedto reaction planein comparison withcollinear direction.

Summary of the 2Summary of the 2ndnd topic topic

Hadronization through jet-fluid stringsHadronization through jet-fluid strings– Realistic space-time evolution of Realistic space-time evolution of

thermalized partons is considered thermalized partons is considered through hydrodynamic simulations. through hydrodynamic simulations. (Data table is now available on the (Data table is now available on the web!)web!)

– v2 is enhanced in intermediate-high pT v2 is enhanced in intermediate-high pT regions.regions.

Source Function from 3D Hydro Source Function from 3D Hydro + Cascade+ Cascade

Blink: Ideal Hydro, Kolb and Heinz (2003)Caveat: No resonance decays in ideal hydro

How much the source functionHow much the source functiondiffers from ideal hydrodiffers from ideal hydroin Configuration space?in Configuration space?