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Marcus Bleicher, Berkeley, Oct. 2005 Elliptic Flow in High Energetic Nuclear Collisions Marcus Bleicher & Xianglei Zhu FIAS & Institut für Theoretische Physik Goethe Universität Frankfurt Germany

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Marcus Bleicher, Berkeley, Oct. 2005 Thanks to Sascha Vogel Stephane Haussler Hannah Petersen Diana Schumacher Nu Xu

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Marcus Bleicher, Berkeley, Oct. 2005 The tool: UrQMD v2.2 Non-equilibrium transport model Hadrons and resonances String excitation and fragmentation Cross sections are parameterized via AQM or calculated by detailed balance pQCD hard scattering at high energies Generates full space-time dynamics of hadrons and strings

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Marcus Bleicher, Berkeley, Oct. 2005 Transverse Momentum Distributions: Proton-Proton PP works well pQCD needed at RHIC PYTHIA included in UrQMD 2.x and HSD

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Marcus Bleicher, Berkeley, Oct. 2005 Proton-Nucleus pA is well under control CC and SiSi are also under control What about AA? Inv. slope System size

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Marcus Bleicher, Berkeley, Oct. 2005 Transverse mass spectra Standard UrQMD and HSD underestimate the data Additional resonances of 2-3 GeV mass may improve the description mt-m0

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Marcus Bleicher, Berkeley, Oct. 2005 Inverse slope systematics ‘Step’ claimed to be signature of QGP onset (Gazdzicki) High mass resonances improve the description at low and high energies How can we test those scenarios? use v2 to disentangle early and late stage E_CM (AGeV)

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Marcus Bleicher, Berkeley, Oct. 2005 Anisotropic flow Fourier expansion of the transverse angular distribution of the emitted particles: v1– directed flow V2 -- elliptic flow Reaction Plane Ollitrault, PRD 46 (1992) Poskanzer & Voloshin, PRC 58 (1998)

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Marcus Bleicher, Berkeley, Oct. 2005 Elliptic flow y x pypy pxpx coordinate-space-anisotropy momentum-space-anisotropy 1)V 2 of low pt particles is the good measure the EOS of the fireball in the early stage. 2)V 2 of high pt particles is the good measure of jet energy loss through the medium. Taken from Nu Xu

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Marcus Bleicher, Berkeley, Oct. 2005 Hints from elliptic flow High mass resonances can not explain scaled v2 above 40 AGeV Data shows saturation of scaled v2 Strong hint for large pressure and short mean free paths in the early stage of the reaction already from 30 AGeV on ! Data for h-

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Marcus Bleicher, Berkeley, Oct. 2005 ‘Partonic’ dof already at low SPS energy Breakdown of v2/ scaling in model coincides with onset of ‘partonic’ matter signals onset of change of EoS in the early stage

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Marcus Bleicher, Berkeley, Oct. 2005 V2 at RHIC Magnitude of v2 is large Meson-baryon ordering Constituent quark scaling Decrease of v2 at high pt Are these unique QGP signatures? Zhu, Bleicher, Stoecker, nucl-th/0509081

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Marcus Bleicher, Berkeley, Oct. 2005

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Fluctuations are everywhere Au+Au at RHIC Strong fluctuations of initial state eccentricity

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Marcus Bleicher, Berkeley, Oct. 2005 Fluctuations are everywhere Au+Au at RHIC Strong fluctuations of final elliptic flow

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Marcus Bleicher, Berkeley, Oct. 2005 s 2 v 2 correlation Only weak correlation between coordinate and momentum space in single events Hydro yields strong correlation

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Marcus Bleicher, Berkeley, Oct. 2005 Elliptic flow: Centrality dependence Integral flow V2 from UrQMD is about 50% smaller than the data, Left space for parton rescattering? STAR data is from nucl-ex/0409033

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Marcus Bleicher, Berkeley, Oct. 2005 Cumulant method: Centrality Integral flow In the most central bin: The fluctuations give larger v2{6} but smaller v2{4} In the very peripheral bins: The fluctuations give larger v2{6} and v2{4} Agree with the prediction of MCG model BUT: In the semi-central bins: the v2 fluctuations can be neglected. In the most central bin: The fluctuations give larger v2{6} but smaller v2{4} In the very peripheral bins: The fluctuations give larger v2{6} and v2{4} Agree with the prediction of MCG model BUT: In the semi-central bins: the v2 fluctuations can be neglected. Cumulant method:Ollitrault, Borghini, Dinh, PRC 63, PRC 64, nucl-ex/0110016

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Marcus Bleicher, Berkeley, Oct. 2005 Cumulant method results Comparison to STAR data Good agreement of the ratios with STAR data. Decrease of g2 at peripheral bins are also reproduced. (the g2 decrease is possibly from the v2 fluctuations) Good agreement of the ratios with STAR data. Decrease of g2 at peripheral bins are also reproduced. (the g2 decrease is possibly from the v2 fluctuations) (a.u.)

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Marcus Bleicher, Berkeley, Oct. 2005 Cumulant method: Rapidity Even at large non-flow effects are present However, effects are small (<20% of the v 2 value) Even at large non-flow effects are present However, effects are small (<20% of the v 2 value)

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Marcus Bleicher, Berkeley, Oct. 2005 Cumulant method: P T Differential flow v2{2} is heavily affected by the non- flow effects especially at large pt. The non-flow effects have been eliminated in v2{4} and v2{6}. But v2{4} is still a little larger than the exact v2. v2{2} is heavily affected by the non- flow effects especially at large pt. The non-flow effects have been eliminated in v2{4} and v2{6}. But v2{4} is still a little larger than the exact v2.

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Marcus Bleicher, Berkeley, Oct. 2005 Cross sections: AQM

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Marcus Bleicher, Berkeley, Oct. 2005 Nu Xu Plot Multi-strange particles break flow scaling Sign of early freeze-out no v 2 from hadronic stage?

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Marcus Bleicher, Berkeley, Oct. 2005 V 2 (pt) from UrQMD Red--Mesons Blue-Baryons 1) Clear separation of meson and baryon v2 2) Low pt, v2(meson)>v2(baryon) 3) High pt, v2(m)

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Marcus Bleicher, Berkeley, Oct. 2005 NCQ-scaling NCQ-scaling of v 2 is roughly reproduced in UrQMD! Note: multi-strange hadrons follow the normal matter

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Marcus Bleicher, Berkeley, Oct. 2005 Summary At RHIC (transport models w/ strings and hadrons): Part of v2 might also come from hadronic stage Mass ordering is correct Constituent quark scaling (w/o ReCo!) non-flow correlations are correct However, transport models w/o QGP produce to few pressure in the early stage above 30 GeV

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