Workshop on Quark Gluon Plasma Thermalization, Vienna 2005

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1 Elliptic R.Andrade 1,F.Grassi 1, Y.Hama 1, T.Kodama 2, O.Socolowski Jr. 3, B.Tavares 2 grassi@if.usp.br 1 Instituto de Física, Universidade de São Paulo, Brazil 2 Instituto de Física, Universidade Federal do Rio de Janeiro, Brazil 3 Instituto Tecnológico de Aeronáutica, Centro Técnico Aeroespacial, Brazil Workshop on Quark Gluon Plasma Thermalization, Vienna 2005

2 Outline Motivation 1 Motivation 2 3 4

3 Motivation: elliptic flow is a tool to study thermalization Hydrodynamics seems a correct tool to describe RHIC collisions however v 2 () is not well reproduced as shown by Hirano et al. results (PRC 65(2001)011901, 66(2002)054905)

4 Hirano suggested this might be due to lack of thermalization. Heinz and Kolb presented a model with partial thermalization (QM2004) to account for this:

5 Question: lack of thermalization is the only explaination?

6 NeXSPheRIO is a junction of two codes. SPheRIO is used to compute the hydrodynamical evolution Smoothed Particle Hydrodynamics was originally developped in astrophysics and adapted to relativistic heavy ion to collisions C.E.Aguiar, T.Kodama, T.Osada & Y.Hama, J.Phys.G27(2001)75 Advantage: incorporate any geometry in the initial conditions

7 NeXus is used to compute the initial conditions H.J. Drescher et al. PRC 65(2002)054902; Y.Hama, T.Kodama & O.Socolowski Jr. Braz.J.Phys. 35(2005)24 In other codes, initial conditions are adjusted to reproduce some selected data AND are very smooth.

8 Method: NeXSPheRIO is run many times and an average over final results is performed. This mimicks experimental conditions.

9 Theoretically, the impact parameter angle φ b is known and varies in the range of the centrality window chosen: v 2 = R dn/dφcos[2(φ φb )] dφ R dn/dφ dφ Experimentally, the impact parameter angle ψ 2 is reconstructed, for example in a Phobos-like way (PRL 89(2002)222301; nucl-ex/ ): v 2 = P i dn/dφ P i cos[2(φ i ψ 2 )] i dn/dφ i where ψ 2 = 1 P 2 tan 1 P i sin 2φ i i cos 2φ i ψ 2 <0 and ψ > < < q <cos[2(ψ <0 2 ψ>0 2 )]> 2 are determined for subevents

10 After averaging on events, we get: (15-25) % Average over 200 events v2 (ch) OPT EoS (EbE - FO, T f =135 MeV, v ( φ ) ) 2 b 1OPT EoS (EbE - FO, T f =135 MeV, v 2( ψ 2 ) ) There is some difference. In order to compare with PHOBOS data, we will use the second (reconstructed angle) method

11 After averaging on events, we get: (15-25) % Average over 200 events v2 (ch) OPT EoS (EbE - FO, T f =135 MeV, v ( φ ) ) 2 b 1OPT EoS (EbE - FO, T f =135 MeV, v 2( ψ 2 ) ) There is some difference. In order to compare with PHOBOS data, we will use the second (reconstructed angle) method

12 Motivation In all comparisons, the same set of initial conditions is used, scaled to reproduce dn/d for T f.out = 135 MeV (15 25)% Average over 200 events 350 dn/d OPT EoS (EbE - FO, T f = 125 MeV) 1OPT EoS (EbE - FO, T f = 135 MeV) v 2 and dn/p t dp t favour T f.out = 135 MeV, used thereafter.

13 Motivation In all comparisons, the same set of initial conditions is used, scaled to reproduce dn/d for T f.out = 135 MeV (15-25) % Average over 200 events v2 (ch) OPT EoS (EbE - FO, T f =125 MeV) 1OPT EoS (EbE - FO, T f =135 MeV) v 2 and dn/p t dp t favour T f.out = 135 MeV, used thereafter.

14 π t Motivation In all comparisons, the same set of initial conditions is used, scaled to reproduce dn/d for T f.out = 135 MeV -2 (2 p ) d N/dy π dp (Gev/c) t (15-25)% (x10 ) (h+ + h-)/2 0.2 < y < 1.4 Average over 200 events 1OPT EoS (EbE - FO, T f = 125 MeV) 1OPT EoS (EbE - FO, T f = 135 MeV) P (Gev/c) t v 2 and dn/p t dp t favour T f.out = 135 MeV, used thereafter.

15 Effect of first order transition vs. cross over We compare results obtained for a quark matter equation of state with first transition to hadronic matter and with a crossover We expect larger v 2 for cross over

16 (15 25)% Average over 200 events 350 dn/d CP EoS (EbE - FO, T f = 135 MeV) 1OPT EoS (EbE - FO, T f = 135 MeV) The and p t distributions are not much affected v 2 is higer, as expected

17 π t Motivation -2 (2 p ) d N/dy π dp (Gev/c) t (15-25)% (x10 ) (h+ + h-)/2 0.2 < y < 1.4 Average over 200 events CP EoS (EbE - FO, T f = 135 MeV) 1OPT EoS (EbE - FO, T f = 135 MeV) P (Gev/c) t The and p t distributions are not much affected v 2 is higer, as expected

18 (15-25) % Average over 200 events v2 (ch) CP EoS (EbE - FO, T f = 135 MeV) 1OPT EoS (EbE - FO, T =135 MeV) f The and p t distributions are not much affected v 2 is higer, as expected

19 Motivation We compare results obtained for freeze out and continuous emission We expect large momentum particles emitted earlier, with less flow, therefore, narrower v 2 ()

20 (15 25)% Average over 200 events 350 dn/d OPT EoS (EbE - CE) 1OPT EoS (EbE - FO, T f = 135 MeV) The and p t distributions are not much affected v 2 is narrower, as expected

21 π t Motivation -2 (2 p ) d N/dy π dp (Gev/c) t (15-25)% (x10 ) (h+ + h-)/2 0.2 < y < 1.4 Average over 200 events 1OPT EoS (EbE - CE) 1OPT EoS (EbE - FO, T f = 135 MeV) P (Gev/c) t The and p t distributions are not much affected v 2 is narrower, as expected

22 (15-25) % Average over 200 events v2 (ch) OPT EoS (EbE - CE) 1OPT EoS (EbE - FO,T f =135 MeV) The and p t distributions are not much affected v 2 is narrower, as expected

23 Motivation Compared to Hiranos pioneering work with smooth initial conditions, the fact that we used event-by-event initial conditions seems crucial: we immediately avoid the two bumb structure what would WE get with smooth initial conditions?

24 Motivation Compared to Hiranos pioneering work with smooth initial conditions, the fact that we used event-by-event initial conditions seems crucial: we immediately avoid the two bumb structure (15-25) % Average over 200 events v2 (ch) OPT EoS (EbE - FO, T f =135 MeV, v ( φ ) ) 2 b 1OPT EoS (EbE - FO, T f =135 MeV, v 2( ψ 2 ) ) what would WE get with smooth initial conditions?

25 PRELIMINARY (15 25)% 350 dn/d OPT EoS (<IC>-FO, T f = 135 MeV) 1OPT EoS (EbE - FO, T f = 135 MeV) The and p t distributions are not much affected We get a two bump structure for v 2 () (The small depression at = 0 is probably numerical)

26 π t Motivation PRELIMINARY -2 (2 p ) d N/dy π dp (Gev/c) t (15-25)% (x10 ) (h+ + h-)/2 0.2 < y < 1.4 1OPT EoS (<IC>-FO, T f = 135 MeV) 1OPT EoS (EbE - FO, T f = 135 MeV) P (Gev/c) t The and p t distributions are not much affected We get a two bump structure for v 2 () (The small depression at = 0 is probably numerical)

27 PRELIMINARY 0.06 (15-25) % 0.05 v2 (ch) OPT EoS (<IC>-FO, T f = 135 MeV) 1OPT EoS (EbE - FO, T f = 135 MeV) The and p t distributions are not much affected We get a two bump structure for v 2 () (The small depression at = 0 is probably numerical)

28 Motivation Event-by-event initial conditions seem important to get right shape of v 2 () at RHIC Other features seem less important: reconstruction of impact parameter direction, f.out temperature, equation of state (w. or wo. crossover), emission mecanism (15-25) % Average over 200 events 0.04 v2 (ch) CP EoS (EbE - CE) CP EoS (EbE - FO,T f =135 MeV) 1OPT EoS (EbE - CE) 1OPT EoS (EbE - FO,T f =135 MeV) Lack of thermalization is not necessary to reproduce v 2 ()

arxiv:hep-ph/ v3 14 Nov 2005

arxiv:hep-ph/ v3 14 Nov 2005 arxiv:hep-ph/596v3 4 Nov 25 3D Relativistic Hydrodynamic Computations Using Lattice-QCD-Inspired Equations of State Yogiro Hama a, Rone P.G. Andrade a, Frédérique Grassi a, Otávio Socolowski Jr. b, Takeshi