R. Lacey, SUNY Stony Brook 1 Arkadij Taranenko Winter Workshop on Nuclear Dynamics Big Sky, MT February 12-17,2007 Nuclear Chemistry Group SUNY Stony Brook,

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R. Lacey, SUNY Stony Brook

Arkadij Taranenko

Winter Workshop on Nuclear Dynamics

Big Sky , MT February 12-17,2007

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

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RRT

vvdydp

Nd

pd

NdE

React

ion

plan

e

X

Z

Y

Px

Py Pz

])φ[2cos(2 Rv

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Resent PHENIX Elliptic Flow Data

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

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

RHIC Elliptic Flow Data

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Elliptic flow at RHIC and perfect fluid hydrodynamics Elliptic flow at RHIC and perfect fluid hydrodynamics Elliptic flow at RHIC and perfect fluid hydrodynamics Elliptic flow at RHIC and perfect fluid hydrodynamics

The v2 measurements at RHIC are in a good agreement with the predictions of ideal relativistic hydrodynamics ( rapid thermalization t< 1fm/c and an extremely small ratio of shear viscosity to entropy density η/s ).

Looking for scaling properties of elliptic flow in the data – compatible with this picture

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Elliptic flow: eccentricity scaling

• Ideal hydro is a 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)

PHENIX article submitted to PRL: nucl-ex/0608033

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Estimation of the speed of sound Estimation of the speed of sound

<cs > ~ 0.35 ± 0.05(< cs

2 > ~ 0.12), soft EOS

v2/ε for <pT> ~ 0.45 GeV/c

See nucl-ex/0604011 for details

22v

3500 MeV/fmp

Eccentricity scaled v2 has a relatively strong dependence on sound speed

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

<cs > - average value over the time period 2R/cs

(the time over the flow develops )

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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

PHENIX article submitted to PRL: 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 PHENIX article submitted to PRL: 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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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 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 multistrange hadrons (φ, Ξ and ) with their large masses and small hadronic behave like other particles → consistent with the creation of elliptic flow on partonic level before hadron

formation

Multi-strange baryon elliptic flow at RHIC (STAR)

STAR preliminary

200 GeV Au+Au

From M. Oldenburg SQM2006 talk (STAR)

J. Phys G 32, S563 (2006)Scaling test

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Elliptic flow of D meson

All non-photonic electron v2 (pT < 2.0 GeV/c) were assumed to come from D decay D-> e, Pt spectrum constrained by the data Different assumptions for the shape of D meson v2(pt): pion,kaon and proton v2(pt) shapes

Measurements and simulations: Shingo Sakai (PHENIX)(See J. Phys G 32, S 551 and his SQM06,HQ06,QM06 talks for details )

Robust measurements of elliptic flow of non-photonic electrons (PHENIX)

Simulations for D meson v2(pt):

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Elliptic flow of D meson: Scaling test

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

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

(η/s) ~ (1.1-2.5)/4π

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Constraining /s with PHENIX datafor RAA & v2 of non-photonic electrons

• Rapp and van Hees Phys.Rev.C71:034907,2005 – Simultaneously describe PHENIX

RAA(E) and v2(e) with diffusion coefficient in range DHQ (2T) ~4-6

• Moore and Teaney Phys.Rev.C71:064904,2005 – Find DHQ/(/(+p)) ~ 6 for Nf=3

• Combining– Recall +p = T s at B=0

– This then gives /s ~(1.5-3)/4– That is, within factor of 2-3 of

conjectured lower bound

PHENIX article submitted to PRL nucl-ex/0611018

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Au+Au

KET (GeV)

0 1 2 3 4

v 2

0.00

0.05

0.10

0.15

0.20

0.25

Moore

K K p pD

200 NNs GeV

PHENIX PRELIMINARYDATA

3~ ~ 0.5

2D fm

T

D-meson essentially thermal ? D-meson essentially thermal ? Re

1~ 4lax

D

MD fm

T

Transport Coefficients estimate

Moore and Teaney Phys.Rev.C71:064904,2005

R. Lacey (nuc-ex/0610029)

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Shear viscosity to entropy density estimates from RHIC data

(η/s) ~ (1.0-3.8)/4π

S Gavin and M. Abdel-Aziz , Phys. Rev. Lett 97, 162302 (2006)

“Measuring Shear Viscosity using transverse momentum correlations”.

(η/s) ~ (1.1-2.5)/4π

R. Lacey et. al., nucl-ex/0609025 (accepted by PRL)

“Has the QCD Critical Point been Signaled by Observations at RHIC?”.

(η/s) ~ (1.5-3.0)/4π

A. Adare et. al., (PHENIX), nucl-ex/0609025 (submitted to PRL)

“Energy Loss and Flow of Heavy Quarks in Au+Au collisions at 200 GeV

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Summary

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

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

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

• Scaled flow values allow constraints for several transport coefficients.

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

– .

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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

C. Blume (NA49) QM2006 talk

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Comparison with models; RAA & v2

for non-photonic electrons (PHENIX)

Two models describes strong suppression and large v2

Rapp and Van Hees Elastic scattering -> small heavy quark relaxation time τ DHQ × 2πT ~ 4 - 6

Moore and Teaney DHQ × 2πT = 3~12

These calculations suggest that small τ and/or DHQ are required to reproduce the data.

Nucl-ex/0611018

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Constraining /s with PHENIX data

• Rapp and van Hees Phys.Rev.C71:034907,2005 – Simultaneously describe PHENIX

RAA(E) and v2(e) with diffusion coefficient in range DHQ (2T) ~4-6

• Moore and Teaney Phys.Rev.C71:064904,2005 – Find DHQ/(/(+p)) ~ 6 for Nf=3– Calculate perturbatively,

argue result also plausible non-perturbatively

• Combining– Recall +p = T s at B=0

– This then gives /s ~(1.5-3)/4– That is, within factor of 2 of

conjectured bound

Documents

R. Lacey, SUNY Stony Brook 1 Arkadij Taranenko Winter Workshop on Nuclear Dynamics Big Sky, MT February 12-17,2007 Nuclear Chemistry Group SUNY Stony Brook,