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

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


Thanks to

• Sascha Vogel

• Stephane Haussler

• Hannah Petersen

• Diana Schumacher

• Nu Xu


The tool: UrQMDv2.2

• 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


Transverse Momentum Distributions: Proton-Proton

• PP works well

• pQCD needed at RHIC

• PYTHIA included in

UrQMD 2.x and HSD


Proton-Nucleus

• pA is well under control

• CC and SiSi are also under control

• What about AA?

Inv.

slo

pe

System size


Transverse mass spectra

• Standard UrQMD and HSD underestimate the data

• Additional resonances of 2-3 GeV mass may improve the description

mt-m0


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)


Anisotropic flow

i Ri 1t t t t

2 2t x y

dN 1 dN1 2v cos(i( ))

p dp dyd 2 p dp dy

p p p

Fourier expansion of the transverseangular distribution of the emitted particles:

v1– directed flowV2 -- elliptic flow

Reaction PlaneReaction Planecos( ( ))n Rv n

Ollitrault, PRD 46 (1992)Poskanzer & Voloshin, PRC 58 (1998)


Elliptic flow

y

x

py

px

coordinate-space-anisotropy momentum-space-anisotropy

y 2 x 2y 2 x 2

v2 cos2 , tan 1(pypx)

1) V2 of low pt particles is the good measure the EOS of the fireball in the early stage.

2) V2 of high pt particles is the good measure of jet energy loss through the medium.

22

22

xy

xy

Tak

en f

rom

Nu

Xu


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-


‘Partonic’ dof already atlow SPS energy

•Breakdown of v2/<pt> scaling in model coincides with onset of ‘partonic’ matter

signals onset of change of EoS in the early stage


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



Fluctuations are everywhere

• Au+Au at RHIC

• Strong fluctuations of initial state eccentricity


Fluctuations are everywhere

• Au+Au at RHIC

• Strong fluctuations of final elliptic flow


s2 v2 correlation

• Only weak correlation between coordinate and momentum space in single events

• Hydro yields strong correlation


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


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


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

.)


Cumulant method: Rapidity

• Even at large non-flow effects are present

• However, effects are small (<20% of the v2 value)

• Even at large non-flow effects are present

• However, effects are small (<20% of the v2 value)


Cumulant method: PT• 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.


Cross sections: AQM


Nu Xu Plot

• Multi-strange particles break flow scaling

• Sign of early freeze-out

no v2 from hadronic stage?


V2(pt) from UrQMD

Red--Mesons

Blue-Baryons

1) Clear separation of meson and baryon v22) Low pt, v2(meson)>v2(baryon)3) High pt, v2(m)<v2(b)4) The v2’s of multi-strange baryons are comparable to light baryons

1) Clear separation of meson and baryon v22) Low pt, v2(meson)>v2(baryon)3) High pt, v2(m)<v2(b)4) The v2’s of multi-strange baryons are comparable to light baryons


NCQ-scaling

NCQ-scaling of v2 is roughly reproduced in UrQMD!NCQ-scaling of v2 is roughly reproduced in UrQMD!

Note:multi-strange hadrons follow the normal matter


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

Documents

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