11/18/2003Tetsufumi Hirano (RBRC)1 Rapidity Dependence of Elliptic Flow from Hydrodynamics Tetsufumi...

11/18/2003 Tetsufumi Hirano (RBRC) 1

Rapidity Dependence ofRapidity Dependence ofElliptic FlowElliptic Flow

from Hydrodynamicsfrom HydrodynamicsTetsufumi HiranoTetsufumi Hirano

RIKEN BNL Research CenterRIKEN BNL Research Center(Collaboration with Yasushi Nara, Univ. of Arizona)(Collaboration with Yasushi Nara, Univ. of Arizona)


OutlineOutline

• Introduction• Results so far• Tth dependence of v2()• Initial condition from the CGC and its

consequence• Summary & discussion


Non-central coll. Non-central coll. No cylindrical sym. No cylindrical sym.Non-Bjorken behavior Non-Bjorken behavior No scaling ansatz No scaling ansatz

High energy collisions (@RHIC) High energy collisions (@RHIC) No Cartesian coordinate? No Cartesian coordinate?

Need Need fullfull 3D hydro 3D hydrosimulations in simulations in -- coordinate coordinate

T.H., PRC65,011901(2002).T.H., PRC65,011901(2002).

IntroductionIntroduction

From Experimental Point of ViewFrom Experimental Point of ViewNeed broad acceptance in longitudinal directionNeed broad acceptance in longitudinal directionSee S.Manly’s talkSee S.Manly’s talk

vv22((yy) is supposed to reflect global dynamics…) is supposed to reflect global dynamics… How obtain by hydrodynamics?How obtain by hydrodynamics?


Results so far (1)Results so far (1)•The shape of v2() depends largely on initial longitudinal profile dN/ddN/d

vv22(())

T.H., PRC65,011901(2002).T.H., PRC65,011901(2002).


Local Rapidity ShiftLocal Rapidity Shift

““Shape” at Shape” at ss=4.5=4.5

•Local rapidity shiftLocal rapidity shift(J.Sollfrank (J.Sollfrank et alet al., ., Eur.Phys.J.CEur.Phys.J.C6,6,525525((19991999))))

Third flow?(L.P.Csernai andD.Rohrich, PLB458, 454(1999))

z

x

E(x,s) at b=6.9fm

x

s

Direct charged, TDirect charged, Tthth=140MeV, b=6.9fm=140MeV, b=6.9fm

dN/d v2()


Results so far (2)Results so far (2)•v2 is reduced by chemical non-equilibrium property

• Space-time evolution is completelydifferent from conventional(chemically equilibrated) EOS.

T.H. and K.Tsuda, PRC66,054905(2002).T.H. and K.Tsuda, PRC66,054905(2002).


vv22(() and v) and v22(y)(y)P. Kolb, Heavy Ion Phys.15, 279(2002).

Jacobian as an weight fn.Jacobian as an weight fn.

Jacobian between Jacobian between yy and and Result from 3D hydroResult from 3D hydro


Return game in 200 GeV collisionsReturn game in 200 GeV collisions

Summary (part 1)Summary (part 1)• Ambiguity of init. condition. Smaller flat region would be good. No local rapidity shift• Realistic EOS (chemically non-eq.)


Initial Condition in Long. DirectionInitial Condition in Long. Direction

(x,y)=(0,0)

Emax

flat

Gauss

• Emax=45 GeV/fm3

• flat = 2.0• Gauss = 0.8 No local rapidity shift

# of binary coll. scaling for finite b.# of binary coll. scaling for finite b.Works well as centrality dep. forWorks well as centrality dep. forinitial condition.initial condition.(P.Kolb (P.Kolb et al.et al., Nucl.Phys.A, Nucl.Phys.A696696,,197,197,((20012001))))


TTthth Dependence of v Dependence of v22

As far as pions, TAs far as pions, Tthth is not is notdetermined by pdetermined by pTT slope within slope withinchemically non-equilibriumchemically non-equilibriumEOS model.EOS model.

•vv22 glows also in hadron phase. glows also in hadron phase.•Eventually, vEventually, v22((yy) becomes flat) becomes flatas Tas Tthth decreases decreases


dN/ddN/d from a Saturation Model from a Saturation Model

Qs2

kT20

gggggg

D. Kharzeev and E. Levin, Phys.Lett.B523,79(2001)

Parton-hadron dualityParton-hadron duality

s


Initial Condition from CGCInitial Condition from CGC(hydrodynamic afterburner for CGC)(hydrodynamic afterburner for CGC)

“CGC + Hydro (+ Jet) model”

Saturation scale at a transverse position:

Momentum rapidity y space time rapidity s

Input for hydrodynamics

where

Unintegrated gluon distribution can be written

K=0.72=0.94 (Tth=100MeV)=0.2


Initial Energy Density DistributionInitial Energy Density Distributionand dNand dNchch/d/d bb=2.4fm=2.4fm

dEdETT//ddss ee((yy=0,=0,ss=0)=0)


vv22(() from CGC+Hydro) from CGC+HydroCGC+HydroCGC+Hydro Flat+Gaussian initializationFlat+Gaussian initialization

• Slightly suppressed near midrapidity regionSlightly suppressed near midrapidity region•Pressure gradient in longitudinal directionPressure gradient in longitudinal direction•Pressure gradient in transverse direction Pressure gradient in transverse direction Stronger longitudinal flow and weaker transverse flowStronger longitudinal flow and weaker transverse flowin CGC+hydro case than in flat+Gaussian case.in CGC+hydro case than in flat+Gaussian case.


Summary & DiscussionSummary & Discussion

• Consistency check <pT>(y) & pT spectra in forward rapidity (BRAHMS data) v2(pT) @ forward rapidity region ? v1(y) ??? third flow components ?

• There IS a solution for v2() from hydrodynamics.• Further systematic studies are needed.

•Initial condition? Tth dependence ? EOS ?• CGC+hydro(+jet) model (“Improvement” of I.C.)


Thank you!

CGC+hydro at b=6.9fm in transverse planeCGC+hydro at b=6.9fm in transverse plane


Flat Energy Flat dN/dyFlat Energy Flat dN/dyBasic assumption1. Finite Bjorken rod (-0<s<0)2. Massless pions3. Constant T and Boltzmann approximation

20


Accepted Events by PHOBOSAccepted Events by PHOBOSNot minimus bias!Not minimus bias!

In hydro, average over NIn hydro, average over Npartpart

in multiples of 25 up to 325.in multiples of 25 up to 325.B.B.Back et al.(PHOBOS), PRL89,222301(2002).

11/18/2003 Tetsufumi Hirano (RBRC) 19J.H.Lee(BRAHMS), talk at Forward Physics at RHIC, Oct.9, 2003,BNLJ.H.Lee(BRAHMS), talk at Forward Physics at RHIC, Oct.9, 2003,BNL

Mean pMean pTT as a Function of y as a Function of y

11/18/2003 Tetsufumi Hirano (RBRC) 20R.Debbie (BRAHMS), proceeding for The 8th Conference on Intersections of R.Debbie (BRAHMS), proceeding for The 8th Conference on Intersections of Particle And Nuclear Physics (CIPANP2003), New York City, New York (May 19-24, 2003).Particle And Nuclear Physics (CIPANP2003), New York City, New York (May 19-24, 2003).

Blast Wave Fit in Forward Rapidity Blast Wave Fit in Forward Rapidity Region by BRAHMSRegion by BRAHMS


vv22(p(pTT) @ 130AGeV) @ 130AGeV

Chemical eq. modelChemical eq. modelChemical non-eq. modelChemical non-eq. model

pT slope v2(pT)

Chem. eq. yes noChem. non-eq.

no yes

Table. TTable. Tthth dependence for pions dependence for pions


Freezeout HypersurfaceFreezeout HypersurfacePCEPCE CECEtau (fm)tau (fm)

7.8

8.7

Initial temperature (b=6.9fm)Initial temperature (b=6.9fm)

100-120MeV120-140MeV140- MeV

9.6


MovieMovieCGCCGC Flat+GaussianFlat+Gaussian


Longitudinal AccelerationLongitudinal Acceleration

YYLL--ss: Deviation from scaling flow: Deviation from scaling flow

Initial transverse energyInitial transverse energy

11/18/2003Tetsufumi Hirano (RBRC)1 Rapidity Dependence of Elliptic Flow from Hydrodynamics Tetsufumi...

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