R. Lacey, SUNY Stony Brook 1 Arkadij Taranenko Quark Matter 2006 November 13-20, Shanghai, China...

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R. Lacey, SUNY Stony Brook

Arkadij Taranenko

Quark Matter 2006 November 13-20, Shanghai, China

Nuclear Chemistry Group SUNY Stony Brook, USA

PHENIX Studies of the Scaling Properties of Elliptic Flow at RHIC

energies

for the PHENIX Collaboration

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Why Elliptic Flow ?

• The probe for early time– The dense nuclear overlap is

ellipsoid at the beginning of heavy ion collisions

– Pressure gradient is largest in the shortest direction of the ellipsoid

– The initial spatial anisotropy evolves (via interactions

and density gradients ) Momentum-space anisotropy

– Signal is self-quenching with time

...])φ[2(2φcos211

2122

3

3

RRT

vvdydp

Nd

pd

NdE

React

ion

plan

e

X

Z

Y

Px

Py Pz

])φ[2cos(2 Rv

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PHENIX Elliptic Flow Data

Detailed differential measurements now available for π, K, p, φ, d, D

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PHENIX Elliptic Flow Data (Posters)

Energy and System Size dependence of Elliptic flow at RHIC (AuAu/CuCu at 62.4-200 GeV) in the poster of Maya Shimomura:

“Measurement of Azimuthal Anisotropy for High Pt charged hadrons at RHIC-PHENIX”.

Poster 38, Room 104 Wind Energy Room

Differential Elliptic flow measurements at forward rapidities in the poster

of I. J. Choi : “Inclusive single muon flow for Au+Au collisions at 200 GeV in the PHENIX experiment at RHIC”

Poster 13, Room 104 Wind Energy Room

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Substantial elliptic flowSubstantial elliptic flow signals signals are observed for a variety of particle are observed for a variety of particle species at RHIC. Indication of species at RHIC. Indication of rapid rapid

thermalizationthermalization? ?

RHIC Elliptic Flow Data

PHENIX : PRL 91, (2003)

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Universal Scaling of Elliptic Flow at RHIC

ε(b,A) – integral elliptic flow of charged hadrons

At midrapidity v2 (pt,M,b,A)/n~ F(KET/n)*ε(b,A)?

KET - transverse kinetic energy n – number of quarks

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Elliptic flow: eccentricity scaling

• Ideal hydro is scale invariant:

v2(pt,b,A)/v2(b,A)~v2(pt)• v2(b,A)/ε(b,A)~const “Integrated v2 reflects momentum

anisotropy of bulk matter and saturates within the first 3-4 fm/c just after collision” (Gyulassy,Hirano Nucl.Phys.A769:71-94,2006)

In hydro models integrated v2 is proportional to the eccentricity

2 2

2 2

y x

y x

Bhalerao, Blaizot, Borghini, Ollitrault : Phys.Lett.B627:49-54,2005

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Eccentricity scaling and system size

v2 scales with eccentricityand across system size

Scaling test

nucl-ex/0608033

nucl-ex/0608033k ~ 3.1+/-0.2 obtained from data

New PHENIX article on the scaling properties of elliptic flow: nucl-ex/0608033

For Au+Au collisions the eccentricity from Glauber model ε=k v2(centrality)

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Sound speed & Eccentricity scaled vSound speed & Eccentricity scaled v2 2 Sound speed & Eccentricity scaled vSound speed & Eccentricity scaled v2 2

Bhalerao, Blaizot, Borghini, Ollitrault : Phys.Lett.B627:49-54,2005

22v

Eccentricity scaled v2 has a relatively strong dependence on sound speed

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cs ~ 0.35 ± 0.05(cs

2 ~ 0.12), soft EOSF. Karsch, hep-lat/0601013

v2/ε for <pT> ~ 0.45 GeV/c

See nucl-ex/0608033 for details

3500 MeV/fmp

An effective EOS is softer than that for high temperature QGP, but does not reflect a strong first order phase transition, where Cs=0 during an extended hadronization period

Sound speed & Eccentricity scaled v2Sound speed & Eccentricity scaled v2 Sound speed & Eccentricity scaled v2Sound speed & Eccentricity scaled v2

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Scaling breaks

Elliptic flow scales with KET up to KET ~1 GeV Indicates hydrodynamic behavior Possible hint of quark degrees of freedom become apparent at higher KET

Baryons scale together

Mesons scale together

PHENIX preliminary

= mT – m

Transverse kinetic energy scalingTransverse kinetic energy scaling

( WHY ? )( WHY ? ) 21

2Therm colKE KE KE m u

PP

New PHENIX article on the scaling properties of elliptic flow: nucl-ex/0608033

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Apparent Quark number scaling Hadron mass scaling at low KET (KET < 1 GeV) is preserved.

Quark number ScalingQuark number Scaling Quark number ScalingQuark number Scaling New PHENIX article on the scaling properties of elliptic flow: nucl-ex/0608033

Consistent with quark degrees of freedom in the initial flowing matter

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NCQ (pNCQ (pTT/n) scaling compared to KE/n) scaling compared to KETT /n /n

KET/n scaling works for the full measured range with deviation less than 10% from the universal scaling curve NCQ- scaling works only at 20% level for pt>2 GeV/c and breakes below with clear systematic dependence on the mass

PHENIX Preliminary

NCQ- Scaling

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KEKETT/n scaling across collision centralities/n scaling across collision centralities

KET/n scaling observed across centralities

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KEKETT/n scaling and system size (AuAu/CuCu)/n scaling and system size (AuAu/CuCu)

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Elliptic flow of φ meson and partonic collectivity at RHIC.

φ meson has a very small σ for interactions with non-strange particles φ meson has a relatively long lifetime (~41 fm/c) -> decays outside the fireball φ is a meson but as heavy as baryons (p, Λ ) : m(φ)~1.019 GeV/c2 ; (m(p)~0.938 GeV/c2: m(Λ)~1.116 GeV/c2) -> very important test for v2 at intermediate pt ( mass or

meson/baryon effect?)

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v2 of φ meson and partonic collectivity at RHIC

v2 vs KET – is a good way to see if v2 for the φ follows that for mesons or baryons

v2 /n vs KET/n scaling clearly works for φ mesons as well

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Elliptic flow of D meson

The D meson not only flows, it scales over the measured rangeThe D meson not only flows, it scales over the measured range

expected D meson v2 from non-photonic electron v2 (pT < 2.0 GeV/c)

Simulations: Shingo Sakai (PHENIX)(See SQM2006, HQ2006 Talks and proceedings for details)

See Talk of Shingo Sakai (Parallel 2.1 , Sat 3:20 pm )

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Shear viscosity to entropy density ratio estimateFrom R. A. Lacey et al. submitted to PRL (nucl-ex/0609025 ) and nucl-ex/0610029

PHENIX estimate of η/s from the comparison of the measured RAA and v2 of non-photonic electrons with models: η/s ~(1.5-3)/4π, seeTalk of Shingo Sakai (Parallel 2.1 , Sat 3:20 pm )

(η/s) ~ (1.2-2.5)/4π

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Elliptic Flow at SPS (Pb+Pb at 158 GeV, NA49)

The statistical errors are too large to make any statement about the scaling of elliptic flow at SPS energies

V2 of K0 (preliminary) - G. Stefanek for NA49 collaboration (nucl-ex/0611003)

v2 of p, π, Λ - C. Alt et al (NA49 collaboration) nucl-ex/0606026 submitted to PRL

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Summary

• Scaling predictions of perfect fluid hydrodynamics for the elliptic flow coefficient v2 tested and validated

• Development of elliptic flow in the pre-hadronization phase demonstrated

• Scaling of D meson v2 compatible with full thermalization of the charm quark observed.

• Universal scaling of the flow of both mesons and baryons (over a broad transverse kinetic energy range) via quark number scaling observed.

• Scaled flow values allow constraints for several transport coefficients.

• Outlook: we need to find the range where scaling holds and where it breakes.

– .

Results compatible with a plasma having essentially Results compatible with a plasma having essentially perfect liquid-like propertiesperfect liquid-like properties

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Backup Slides

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0 1 2 3 4 5

v 2

0.00

0.05

0.10

0.15

0.20

0.25

0.30 s 200 GeVNNAu Au

0SKp

fsTy

5 < Centrality < 30 %

K

(STAR)

(PHENIX)

(STAR)

(PHENIX)

(PHENIX)

22 0 3 01 2

20 1 1

~ 1 ..T

T k Tk kv y m

T k m k m

2fsT m Ty k y m

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0

( )

( )

I wv

I wBuda-Lund Model

nucl-th/0310040

R.Lacey, QM2005

Equivalent to a kinetic energy Non-relativistic expression

Looking for scaling properties for vLooking for scaling properties for v22

Relativistic effects are importantespecially for light particlesHence, use relativistic formula

KE m m mT T T ( ) 1

Scaling breaks for kaons

wp

m T TT

T y x

2 1 1

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3-D Hydro C. Nonaka

R. Fries, SQM2006

Quark number and quark mass scaling are not incompatible Mass scaling from hydrodynamics is not perturbed by consituent quark scaling

KET /n scaling and hydrodynamics

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Universal Scaling of Elliptic Flow at RHIC!!!

See Tamas Csorgo talk on Wednesday !

M.Csanad, T.Csorgo et al

nucl-th/0605044

Nucl.Phys.A742:80-94,2004

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Signal + BackgroundBackground

Before subtraction

After subtraction

Elliptic flow of resonance particles

Using the robust method for study the elliptic flow of resonance particle developed by N. Borghini and J.Y. Ollitrault (Phys.Rev.C70:064905,2004)

R. Lacey, SUNY Stony Brook 1 Arkadij Taranenko Quark Matter 2006 November 13-20, Shanghai, China...

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