Systematic study of the elliptic flow
~ RHIC v2 and ALICE v2 ~Maya Shimomura

March 7,
The workshop for ALICE upgradesby Asian countries (2011)2011

Contents
Introduction• Elliptic Flow (v2)
• Time Evolution

Results• v2 at RHIC
• Comparison of the ALICE v2• Scaling of v2

Summary

March, 7, 2011

Maya SHIMOMURA

2Elliptic Flow (v2)
Azimuthal anisotropy of produced particles is a powerful probe for investigating the characteristic of the QGP.

Reaction plane (Ψ)

At non central collision

PyzPz•Small mean free pathPx•ThermalizationＹ•Pressure gradientx

Geometrical anisotropy

Elliptic flow

Momentum anisotropy

Momentum anisotropy reflects the hot dense matter.
Fourier expansion of the distribution of produced particle angle (φ) to reaction plane (Ψ)

N (φ ) = N 0 {1 + 2v1 cos(φ − Ψ ) + 2v2 cos[ 2(φ − Ψ )] + ...}

vn = cos[ n(φ − Ψ )]v2 is the coefficient of the second term → indicates ellipticity
Thermalization should be occurred very early before the geometrical eccentricity is gone.
March, 7, 2011

Maya SHIMOMURA

3Time Evolution
The matter produced in the high energy heavy ion collision is expected to undergo several
stages from the initial hard scattering to the final hadron emission.

tKinematical freeze-out

Hadron gas
Mixed phase
QGP

Chemical freeze-out
Hadronization
Expansion & Cooling

Thermalization
pre-equilibrium
Hard scatterings
Collision

When the matter is thermalized, we expect

Hydro-dynamical behavior at quark level .

Need a comprehensive understanding fromthermalization through hadronization to freeze-out.
*Note whenever the matter interacts each other, v2 could change.
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v2 at RHIC
PRL 91, 182301

v2 at low pT (<~2 GeV/c) can be
explained by a hydro-dynamical
model assuming:
Early thermalization(~0.6 fm/c)
Mass Ordering: v2(π)>v2(K)>v2(p)Existence of radial flow.

~ 50% increase from SPS to RHIC.
Above 62.4 GeV, v2 seems to besaturated.
 The matter reaches thermal
equilibrium state at RHIC.
March, 7, 2011

Maya SHIMOMURAPRL 94, 232302

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Comparison with ALICE

ALICE --Pb+Pb, √sNN = 2.76 TeV(nucl-ex 0147314)
PHENIX and STAR --Au+Au, √sNN = 200
GeV
PHENIX : Phys. Rev. C 80, 024909 (2009)STAR : Phys. Rev. C 77, 054901 (2008)• Mostly consistent, especially at low pTMarch, 7, 2011

Maya SHIMOMURA

6For a comprehensive understating of the matter and the mechanism of v2 production…

Scaling of v2•Energy dependence•Eccentricity scaling•Npart scaling•Quark number + KET scaling•Universal scalingWordsNpart --- Number of nucleons participating the collision
Eccentricity (ε) --- geometrical eccentricity of participant nucleons- Monte-Carlo simulation with Glauber model
22yx- Nucleus formed by wood-Saxon shape
ε= 2- Participant eccentricity which is calculated with long and shorty + x2axis determined by distribution of participants at each collision
ε vs. Npart(including participant fluctuations.)

Slightly different at small Npart between Au+Au and Pb+Pb.
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Energy dependence
2.76 TeV, 200 GeV, 62.4 GeV
Centrality dependence

Identified particles
v2 vs. pT for π/K/pradial floweffect?

opened black : 2.76 TeV

PHENIX PRELIMINARY

No significant difference above 62.4 GeV at RHIC.
RHIC and LHC are same especially at low pT.
Need to measure PID v2 at 2.76 TeV to see the radial flow effect.
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Energy dependence
200, 62.4, 39, 7.7 GeV
S. Huang, A. Taranenko, R. Lacey (WWND2011)

No energy dependence from 39 GeV to 200 GeV for different collision centralities.
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Energy dependence
200, 62.4, 39, 7.7 GeV
S. Huang, A. Taranenko, R. Lacey (WWND2011)
Preliminary, STAR, PHENIX and E895 data

The v2 at 7.7 GeV Au+Au is much lower than v2 of 39 - 200 GeV.
Partonic flow --> Hadronic flow : between 39 and 7.7 GeV ?
 Need more study for this region.

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Eccentricity scaling
Pb+Pb, Au+Au, Cu+Cu
Compare v2 normalized by eccentricity (ε) in collisions of different size.
0.2<pT<1.0 [GeV/c]phenix preliminary
phenix preliminary

PHOBOS Collaboration
PRL 98, 242302

Eccentricity scaling suggests
early thermalization.
There is a strong Npart dependence.

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Npart Scaling
The dependence can be normalized by N part1/3.

v2 vs. Npart

phenix preliminary

Dividing by Npart1/3

v2/ε vs. Npart

phenix preliminaryv2/ε /Npart1/3 vs. Npart

phenix preliminary

0.2<pT<1.0 [GeV/c]

v2/eccentricity/Npart1/3 scaling works for all collisionsystems except small Npart at 62 GeV.
- This exception may indicate non-sufficient thermalization region.
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Quark number + KET scaling (AuAu 200 GeV)
PRL. 98, 162301 (2007)

KET (GeV/c)

KET = (mT-m0)/nq

KET/nq (GeV/c)v2(pT) /nquark vs. KET/nquark becomes one curve independent of particle species.
Quark number scaling is consistent to the recombination model which assumes thequark level flow at QGP phase.
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Quark number scaling everywhere
AuAu 62.4GeV
PHENIX/STAR

Au+Au 200 GeV (Run7)

PHENIX Preliminary

Cu+Cu 200GeV

v4 (Au+Au 200GeV)

QM09, A. Taranenko

Quark number scaling work out up to KET ~1GeV.
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Quark number scaling everywhere
Au+Au 200GeV (Run7)

Yoshimasa IKEDA (spring JPS 2010)ϕ, Λ and deuteron also follow the scaling.
Significant part of elliptic flow at RHIC develops at quark level. QGP phase

New detector and high statistics enable us to see thebreaking point at KET ~1GeV.

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Universal v2 for identified charged hadrons
Taking all scaling together, Different Energy and System(AuAu200, CuCu200, AuAu62)

 Different Centrality (0-50%)
 Different particles (π/ K /p)

45 curves

v2 ( K ET / nq )nq × ε × N

1/ 3
part

Scale to one curve.
χ2/ndf = 2.1 (with systematic errors)
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Summary• Systematic study of v2 have been done in Au+Au/Cu+Cu at √sNN =62.4/200 GeV and compared with Pb+Pb at √sNN = 2.76 TeV.
• v2 values are saturated above 62.4 GeV in Au+Au and Pb+Pb.
– Local thermalization• v2(pT) follows quark number + KET scaling in Au+Au (200,62GeV) andCu+Cu (200GeV) .
– Flow at quark level  QGP phase• v2(Npart) / ε are same between Au+Au, Pb+Pb, Cu+Cu at 200 GeV ~2.76
TeV.
– Eccentricity scaling  Early thermalization• v2(pT) /ε/Npart1/3 scaling works except for small Npart at 62 GeV.
– Existence of a universal v2 scaling at RHIC and Continue to LHC.
– Exception may indicate non-sufficient thermalization region from
7.7GeV to 39 GeV.

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Scaling on other pT regions

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Scaling on other pT regions

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