What We Have Learned from
the Measurement of Azimuthal
Anisotropy of Identified Particles
in Relativistic Heavy Ion Collisions
Maya Shimomura
University of Tsukuba

October,15, 2009

3rd Joint Meeting of APS and JPS

Contents
Introduction• Azimuthal Anisotropy• Time Evolution

Results• Fundamental Findings of v2 at RHIC
• Systematic Study of v2• Blast-Wave Model Fit

Summary
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Azimuthal Anisotropy, Elliptic Flow (v2)
PyReaction plane (Ψ)

At non central collisionzPz•Small mean free pathPx•Thermalization

Ｙ•Pressure gradientxElliptic flow

Geometrical anisotropy

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
v2 measurement has been considered as a powerful probe forinvestigating the property of the QGP.
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3rd Joint Meeting of APS and JPS

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.

t

Kinematical 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 .
Note whenever the matter interacts each other, v2 could change.

Need a comprehensive understanding fromthermalization through hadronization to freeze-out.

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Fundamental Findings of v2 at RHIC
•Hydro-dynamical behavior•Quark recombination

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v2 explained by hydro model
PRL 91, 182301

v2 at low pT (<~2 GeV/c) can be
explained by a hydro-dynamical
model assuming:Æ Early thermalization(~0.6 fm/c)

Mass Ordering: v2(π)>v2(K)>v2(p)ÆExistence of radial flow.
Single particle spectra also indicatesradial flow.
convex shape due to radial flow.
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3rd Joint Meeting of APS and JPS

PHENIX: Au+Au: PRC 63, 034909 (2004);
p+p: PRC74, 024904 (2006)

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Quark recombination (quark number scaling)
PRL. 98, 162301 (2007)

Au+Au, √sNN = 200GeV

KET (GeV/c)

KET/nq (GeV/c)

KET = mT-m0v2(pT) /nquark vs. KET/nquark becomes one curve independent of particle species.

Significant part of elliptic flow at RHIC develops at quark level.
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the quark number scalingeverywhere
AuAu 62.4GeV
PHENIX/STARAu+Au 200 GeV (Run7)

PHENIX Preliminary

φmeson (Au+Au 200GeV)

SQM06, M. Oldenburg
QM06, A. Taranenko

Cu+Cu 200GeVSTAR preliminary

Au+Au 200GeV (Run7)v4 (Au+Au 200GeV)
QM09, A. Taranenko

Quark number scaling work out up to KET ~1GeV/c.
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3rd Joint Meeting of APS and JPS

8quark number scaling at SPS
v2 of p, π, Λ - C. Alt et al (NA49 collaboration) nucl-ex/0606026 submitted to PRLv2 of K0 (preliminary) - G. Stefanek for NA49 collaboration (nucl-ex/0611003)

Pb+Pb at 17.2 GeV, NA49

-A. Tranenko’s talk at QM06

Quark number + KET scaling doesn’t seem to work out at SPS.
No flow at quark level due to nonexistence of QGP ?

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3rd Joint Meeting of APS and JPS

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

Systematic study of v2•Energy dependence•System size dependece–Au+Au vs. Cu+Cu–Centrality dependence

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Energy dependence
Au+Au 200 vs. 62 GeV
Centrality dependence

Identified particles
v2 vs. pT for π/K/p

PHENIX PRELIMINARY

No significant difference between 200 and 62 GeV.
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Energy dependence up to RHIC
FOPI : Phys. Lett. B612, 713 (2005). E895 : Phys. Rev. Lett. 83, 1295 (1999)
CERES : Nucl. Phys. A698, 253c (2002). NA49 : Phys. Rev. C68, 034903 (2003)
STAR : Nucl. Phys. A715, 45c, (2003). PHENIX : Preliminary.
PHOBOS : nucl-ex/0610037 (2006)

PRL 94, 232302~ 50% increase from SPS to RHIC.
Above 62.4 GeV, v2 seems to be saturated.
Æ The matter reaches thermal equilibrium state at RHIC.
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Au+Au vs. Cu+Cu
Compare v2 normalized by eccentricity (ε) in collisions of different size.
0.2<pT<1.0 [GeV/c]phenix preliminary

Eccentricity scaling suggests
early thermalization.
PHOBOS Collaboration
PRL 98, 242302

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There is a strong Npart dependence.

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Npart Scaling
The dependence can be normalized by Npart1/3.

v2 vs. Npart

Dividing by Npart1/3

v2/ε vs. Npartv2/ε/Npart1/3 vs. Npart

phenix preliminary

0.2<pT<1.0 [GeV/c]phenix preliminary

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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Universal v2
Taking all scaling together, Different Energy and System

v2(KET/nq)/nq/epar/Npart1/3(AuAu200, CuCu200, AuAu62)

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

45 curvesv 2 ( K ET / n q )nq × ε × N

1/ 3part

Scale to one curve.
χ2/ndf = 2.1 (with systematic errors)
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Then, we have a question !
If the matter is thermalized and the pressure
gradient produce the flow, what is the reason for
Npart dependence of v2?

Blast Wave Model Fit

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Blast-wave Model Fitting
Blast-wave model (local thermal equilibrium + collective transverseexpansion) successfully describes the single particle spectra. * Ref: PRC48(1993)2462⎛ m cosh ρ ⎞ ⎛ p sinhρ ⎞RdNI0⎜⎜ T∝ ∫ rdrmT K1⎜⎜ T⎟⎟⎟⎟
0mT dmT⎝ Tfo⎠ ⎝ Tfo ⎠ρ = tanh−1βT⎛r⎞⎝R⎠

βT = β s ⎜ ⎟yspeed of lightzx
βT

PRC69,034909(2004)
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Thermal freeze-out
temperature, Tfo andtransverse velocity, βT are
extracted from this model
fitting. (Normalization factor is also afree parameter)
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Blast Wave Fitting for v2 and Spectra
We use this well-known fitting technique to obtain theinformation of the flow velocity and temperature in andout-of plane separately.
Measured spectra weighted by φ distribution
1/pT dN/dpTdypT

In/out-of plane spectra
1/pT dN/dpTdy

Measured pT spectra

Measured v2

inoutpT
pT

Fitting pT distribution in and out-of plane separately for
π/K/p simultaneously by blast wave, βT and Tfo in and outof plane are obtained separately.
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Npart Dependence of βT and Tfo

βT is clearly different between in and out-of plane.
Tfo and βT agree between Au+Au and Cu+Cu, especially for the inplane.
Since v2 is produced by the difference between in and out-of plane,
the modulation of βT is expected to have important rule to make v2.
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Modulation of radial flow velocity
βT2 – Modulation amplitude of the second harmonic of the βT
βT2 = (β Tin - β Tout) / (β Tin + βTout) / 2v2/ε vs. Npart

v2 ∝ β T 2
v2 vs.βT2

βT2 scaled by eccentricity agrees between Au+Au and Cu+Cu .
βT2/eccentricity is flat at Npart > 40. Æ ε drives βT2 ! . ÆSignal of Thermalization !?!?
v2 is proportional to βT2 if other parameters are fixed.
BUT, v2/ eccentricity is “not” flat Æ What does course Npart dep. of v2 ??
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3rd Joint Meeting of APS and JPS

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Freeze-out Temperature and v2
Tch obtained by statistical model
1/pT dN/dpTdy

Flatter spectra

ApparentTemperaturev2

highsmalllowlarge

inoutpTDr. M.Konno’s thesis

Tfo depends on Npart(while Tch doesn’t) !

1/pT dN/dpTdy

Steeper spectra

inoutpTLarger system size Æ Lower Tfo Æ Steeper spectra Æ Larger v2
Why does larger system have lower freeze out temperature ?
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Freeze-out Temperature and Time
Dr. M.Konno’s thesis

Tch obtained by statistical model

Simple adiabatic expansion modelyspeed of lightzxβT[Assumption]-Cylindrically expanding-Freeze-out condition: λ(t)=R(t)Freeze-out time vs. Npart

The model explains Npart dependence well !
The times until freeze-out can becalculated by this model. Larger systemtakes more time to freeze-out. ÆThis
makes lower Tfo
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Summary• Systematic study of v2 have been done in Au+Au/Cu+Cu at √sNN =62.4/200 GeV.
• v2 values are saturated above 62.4 GeV in Au+Au.
–Local thermalization• v2(pT) follows quark number + KET scaling in Au+Au (200,62GeV) andCu+Cu (200GeV) .
– Flow at quark level Æ QGP phase• v2(Npart) / ε are same between Au+Au and Cu+Cu at 200 GeV.
– Eccentricity scaling Æ Early thermalization• v2(pT) /ε/Npart1/3 scaling works except for small Npart at 62 GeV.
– Existence of a universal v2 scaling at RHIC
– Exception may indicate non-sufficient thermalization region.

<From Blast-wave fit results with v2 and spectra together>•β2/eccentricity is constant not depending on system size (Npart>40).

•Larger system freezes out later at lower temperature.

– Early thermalization !

– cause the Npart dependence of v2/ ε .

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Scaling (others)
QM2006, S. A. Voloshin

QM2006, R. Nouicer• Straight line from SPS to RHIC energy.
• v2 is reaching the hydro limit at central collision ?
LHC may have answer for this !
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