11/18/2003Tetsufumi Hirano (RBRC)1 Rapidity Dependence of Elliptic Flow from Hydrodynamics Tetsufumi Hirano RIKEN BNL Research Center (Collaboration with.

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Presentation transcript:

11/18/2003Tetsufumi Hirano (RBRC)1 Rapidity Dependence of Elliptic Flow from Hydrodynamics Tetsufumi Hirano RIKEN BNL Research Center (Collaboration with Yasushi Nara, Univ. of Arizona)

11/18/2003Tetsufumi Hirano (RBRC)2 Outline Introduction Results so far T th dependence of v 2 (  ) Initial condition from the CGC and its consequence Summary & discussion

11/18/2003Tetsufumi Hirano (RBRC)3 Non-central coll.  No cylindrical sym. Non-Bjorken behavior  No scaling ansatz High energy collisions  No Cartesian coordinate? Need full 3D hydro simulations in  -  coordinate T.H., PRC65,011901(2002). T.H., PRC65,011901(2002). Non-central coll.  No cylindrical sym. Non-Bjorken behavior  No scaling ansatz High energy collisions  No Cartesian coordinate? Need full 3D hydro simulations in  -  coordinate T.H., PRC65,011901(2002). T.H., PRC65,011901(2002). Introduction From Experimental Point of View Need broad acceptance in longitudinal direction See S.Manly’s talk From Experimental Point of View Need broad acceptance in longitudinal direction See S.Manly’s talk v 2 (y) is supposed to reflect global dynamics…  How obtain by hydrodynamics?

11/18/2003Tetsufumi Hirano (RBRC)4 Results so far (1) The shape of v 2 (  ) depends largely on initial longitudinal profile dN/d  v2()v2()v2()v2() T.H., PRC65,011901(2002).

11/18/2003Tetsufumi Hirano (RBRC)5 Local Rapidity Shift “Shape” at  s =4.5 Local rapidity shiftLocal rapidity shift (J.Sollfrank et al., Eur.Phys.J.C6,525(1999)) Third flow? (L.P.Csernai and D.Rohrich, PL B458, 454(1999)) z x E(x,  s ) at b=6.9fm x ss Direct charged, T th =140MeV, b=6.9fm dN/d  v2()v2()

11/18/2003Tetsufumi Hirano (RBRC)6 Results so far (2) v 2 is reduced by chemical non-equilibrium property Space-time evolution is completely different from conventional (chemically equilibrated) EOS. T.H. and K.Tsuda, PRC66,054905(2002).

11/18/2003Tetsufumi Hirano (RBRC)7 v 2 (  ) and v 2 (y) P. Kolb, Heavy Ion Phys.15, 279(2002). Jacobian as an weight fn. Jacobian between y and  Result from 3D hydro

11/18/2003Tetsufumi Hirano (RBRC)8 Return game in 200 GeV collisions Summary (part 1) Ambiguity of init. condition.  Smaller flat region would be good.  No local rapidity shift Realistic EOS (chemically non-eq.)

11/18/2003Tetsufumi Hirano (RBRC)9 Initial Condition in Long. Direction (x,y)=(0,0) E max  flat  Gauss E max =45 GeV/fm 3  flat = 2.0  Gauss = 0.8 No local rapidity shift # of binary coll. scaling for finite b. Works well as centrality dep. for initial condition. (P.Kolb et al., Nucl.Phys.A696,197,(2001))

11/18/2003Tetsufumi Hirano (RBRC)10 T th Dependence of v 2 As far as pions, T th is not determined by p T slope within chemically non-equilibrium EOS model. v 2 glows also in hadron phase.v 2 glows also in hadron phase. Eventually, v 2 (y) becomes flatEventually, v 2 (y) becomes flat as T th decreases

11/18/2003Tetsufumi Hirano (RBRC)11 dN/d  from a Saturation Model Qs2Qs2  kT2kT2 0 gg  g D. Kharzeev and E. Levin, Phys.Lett.B523,79(2001) Parton-hadron duality  s

11/18/2003Tetsufumi Hirano (RBRC)12 Initial Condition from 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=0.7  2 =0.94 (T th =100MeV) =0.2

11/18/2003Tetsufumi Hirano (RBRC)13 Initial Energy Density Distribution and dN ch /d  b=2.4fm dE T /d  s e(y=0,  s =0)

11/18/2003Tetsufumi Hirano (RBRC)14 v 2 (  ) from CGC+Hydro CGC+Hydro Flat+Gaussian initialization Slightly suppressed near midrapidity region Slightly suppressed near midrapidity region Pressure gradient in longitudinal directionPressure gradient in longitudinal direction Pressure gradient in transverse directionPressure gradient in transverse direction  Stronger longitudinal flow and weaker transverse flow  Stronger longitudinal flow and weaker transverse flow in CGC+hydro case than in flat+Gaussian case.

11/18/2003Tetsufumi Hirano (RBRC)15 Summary & Discussion Consistency check  (y) & p T spectra in forward rapidity (BRAHMS data)  v 2 (p T forward rapidity region ?  v 1 (y) ???  third flow components ? There IS a solution for v 2 (  ) from hydrodynamics. Further systematic studies are needed. Initial condition? T th dependence ? EOS ? CGC+hydro(+jet) model (“Improvement” of I.C.)

11/18/2003Tetsufumi Hirano (RBRC)16 Thank you! CGC+hydro at b=6.9fm in transverse plane

11/18/2003Tetsufumi Hirano (RBRC)17 Flat Energy Flat dN/dy Basic assumption 1.Finite Bjorken rod (-  0 <  s <  0 ) 2.Massless pions 3.Constant T and Boltzmann approximation 2020

11/18/2003Tetsufumi Hirano (RBRC)18 Accepted Events by PHOBOS Not minimus bias! In hydro, average over N part in multiples of 25 up to 325. B.B.Back et al.(PHOBOS), PRL89,222301(2002).

11/18/2003Tetsufumi Hirano (RBRC)19 J.H.Lee(BRAHMS), talk at Forward Physics at RHIC, Oct.9, 2003,BNL Mean p T as a Function of y

11/18/2003Tetsufumi Hirano (RBRC)20 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). Blast Wave Fit in Forward Rapidity Region by BRAHMS

11/18/2003Tetsufumi Hirano (RBRC)21 v 2 (p T 130AGeV Chemical eq. model Chemical non-eq. model p T slopev 2 (p T ) Chem. eq.yesno Chem. non-eq.noyes Table. T th dependence for pions

11/18/2003Tetsufumi Hirano (RBRC)22 Freezeout Hypersurface PCECE tau (fm) Initial temperature (b=6.9fm) MeV MeV 140- MeV 9.6

11/18/2003Tetsufumi Hirano (RBRC)23 Movie CGCFlat+Gaussian

11/18/2003Tetsufumi Hirano (RBRC)24 Longitudinal Acceleration Y L -  s : Deviation from scaling flow Initial transverse energy