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### Elliptic Flow measurements at RHIC

### Elliptic Flow measurements from RHIC to SIS

Arkadij Taranenko

Nuclear Chemistry Group SUNY Stony Brook, USA

Helmholtz International Summer School: “Dense Matter In Heavy Ion Collisions and Astrophysics”

Dubna , Russia, July 14-26, 2008

How one can probe this new state of matter (QGP)?

One want to see a probe (phenomena) which is

- Exist only in Heavy-Ion Collisions (HIC)
- Provides reliable estimates of pressure & pressure gradients
- Can address questions related to thermalization
- Gives insides on the transverse dynamics of the medium
- Provides access to the properties of the medium – EOS, viscosity , etc
- Well calibrated : measured at Ganil (MSU), SIS, AGS, SPS energies

Elliptic Flow in Heavy-Ion Collisions

Arkadij Taranenko

Nuclear Chemistry Group SUNY Stony Brook, USA

Helmholtz International Summer School: “Dense Matter In Heavy Ion Collisions and Astrophysics”

Dubna , Russia, July 14-26, 2008

y

ψR

x

v2 < 0

mid-rapidity

+/- 90deg

“Squeeze-Out” - First Elliptic flow signal in HICDiogene, M. Demoulins et al., Phys. Lett. B241, 476 (1990)

Plastic Ball, H.H. Gutbrod et al., Phys. Lett. B216, 267 (1989)

Reaction plane

Reaction Plane

y

ψR

x

v1 < 0

v2 < 0

mid-rapidity

Fourier decomposition of single particle (semi) inclusive spectra:

+/- 90deg

+/- 180deg

Directed flow

Elliptic flow

KAOS

Cheuk-Yin WONG , Physics Letters, 88B, p 39 (1979)

Sergei Voloshin, Y. Zhang, Z. Phys. C70,(1996), 665

mid-rapidity

+/- 90deg

Small Elliptic flow, Large Elliptic Flow?SIS

V2= -0.2 → ROUT/IN = 2 ( two times more particles emitted out-of-plane than in the plane )

1- 2 V2

N(900) + N(2700)

ROUT/IN=

=

N(00) + N(1800)

1 + 2 V2

RHIC

Where to stop or If Elliptic Flow is very large

To balance the minimum a

v4 > (10v2-1)/34 is required

v4 > 4.4% if v2=25%

STAR, J. Phys. G34 (2007)

V4~V22 [ Vn~V2n/2 ]

At E/A < 100 MeV: attractive nuclear mean field potential : rotating system of projectile and target

Low energy heavy-ion collisions: E/A=25 MeV

Excitation function of elliptic flow – 0.4-10 GeV(SIS/AGS) energies

Passage time: 2R/(βcmγcm)

Expansion time:R/cs

cs=c√dp/dε - speed of sound

( time for the development of expansion perpendicular to the reaction plane)

AGS

SPS

SIS

Delicate balance between:

1) Ability of pressure developed early in the reaction zone to affect a rapid transverse expansion of nuclear matter

2) Passage time for removal of the shadowingof participant hadrons by projectile and target spectators

px

dN/d

y

-/2 0 /2

x

If the passage time is long compared to the expansion time (spectator blocking) → squeeze-outAzimuthal anisotropy in momentum space

(elliptic flow)

px

dN/d

y

-/2 0 /2

x

In-plane elliptic flow (due to pressure gradient) at high beam energies.Azimuthal anisotropy in momentum space

(elliptic flow)

Interplay of passage/expansion times

Passage time: 2R/(βcmγcm)

Expansion time:R/cs

cs=c√dp/dε - speed of sound

(E895) - PRL 83(1999) 1295

Squeeze-out Mechanism

Particle emitted in the center-of-mass of the system and moving in a transverse direction with velocity vT will be shadowed by spectators during the passage time: tpass=2R/(βcmγcm)simple geometry estimate→vTtpass/2 > R-b/2or

vT > (1-b/2R) (βcmγcm)

V2 will increase with vT and impact parameter b

Squeeze-out contribution

reflects the ratio : cs/(βcm γcm)

cs=c√dp/dε - speed of sound

Determination of the Equation of State of dense matter

from collective flow of particles

P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592

elliptic flow

dN/dF (1 + 2v1cosF + 2v2 cos2F)

b – impact parameter

“spectators”

Elliptic flow at RHICLongitudinal and transverse expansion => no influence of spectator matter at midrapidity

Passage time: ~ 0.15 fm/c

Significant Energy Density is produced in Au+Au collisions at RHIC

Thermalization

PRL87, 052301 (2001)

eccentricity

time to thermalize the system (t0 ~ 0.2 - 1 fm/c)

eBjorken~ 5 - 15 GeV/fm3

ε drives pressure gradients which result in flow.

Substantial elliptic flow signals should be present for a variety of particle species !

Fine Structure of Elliptic Flow at RHIC

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

Mass ordering of v2 and ideal fluid hydrodynamics

PHENIX : PRL 91, 182301 (2003)

STAR : PRC 72, 014904 (2005)

pT<1.8 GeV (~ 99% of all particles)

Flavor dependence of v2(pT) enters mainly through mass of the particles → in hydro all particles flow with a common velocity !!! v2 results are in a good agreement with the predictions of ideal relativistic hydrodynamics ( rapid thermalization t< 1fm/c and an extremely small η/s ) → small viscosityLarge cross sections

Large cross sections strong couplings

Elliptic Flow: ultra-cold Fermi-Gas

- Li-atoms released from an optical (laser) trap exhibit elliptic flow analogous to what is observed in ultra-relativistic heavy-ion collisions
- Interaction strength among the atoms can be tuned with an exteranl magnetic field (Feshbach res)
- Elliptic flow is a general feature of strongly interacting systems?

Hadronic transport models (e.g. RQMD, HSD, ...) with hadron formation times ~1 fm/c, fail to describe data.

Hydrodynamic

STAR

PHOBOS

HSD Calculation

pT>2 GeV/c

RQMD

Hadron Gas ?Clearly the system is not a hadron gas.

Intermediate pT range : Meson vs Baryon

- Intermediate pT : (2< pT<5 GeV/c):
- elliptic flow v2(pT): saturates and tends to depends on the particle species-type ( meson vs baryon)
- Suppression pattern (RCP orRAA) is different – meson/baryon effect
- p/π ratio – more (anti-)protons than
- pions at intermediate pT ( 2-5 GeV)

P

Transverse kinetic energy scalingScaling breaks

= mT – m

Baryons scale together

Mesons scale together

PHENIX: Phys. Rev. Lett. 98, 162301 (2007)

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

at higher KET

KET + Quark number Scaling

PHENIX: Phys. Rev. Lett. 98, 162301 (2007)

v2 /nq vs KET/nq scaling works for the full measured range with deviation less than 10% from the universal scaling curve!

KET + Number of constituent Quarks (NCQ) scaling

Centrality dependence

- Scaling seems to hold well for different centralities up to 60% centrality

KET/n scaling and beam energy dependence Au+Au (62.4-200 GeV)

STAR Collaboration: Phys. Rev. C 75(2007) 054906

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

KET/n scaling observed across different colliding systems

v4 Scaling

- The similar scaling for v4 is found recently at PHENIX.
- Compatible with partonic flow picture.

KET/n Scaling tests at SPS

C. Blume (NA49) QM2006 talk

V2 vs KET/n scaling breaks at SPS? – the statistical errors are too large : one need to measure v2 of φ meson at SPS

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
- Previous measurements (STAR) have ruled out the K+K- coalescence as φ meson production mechanism -> information should not be changed by hadronic phase
- 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?)

v2 of φ meson and partonic collectivity at RHIC

nucl-ex/0703024

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 φmesons as well

Multi-strange baryon elliptic flow at RHIC (STAR)

Elliptic flow of multistrange hadrons (φ, Ξand ) with their large masses and small hadronic s behave like other particles → consistentwith the creation of elliptic flow at partonic level before hadron formation

Elliptic flow of D meson

Measurements of elliptic flow of non-photonic electrons (PHENIX)

Measurements and simulations:

Shingo Sakai (PHENIX)

(See J. Phys G 32, S 551 and his SQM06,HQ06,

QM06 talks for details )

Simulations for D meson v2(pt):

- 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

Elliptic flow of D meson: Scaling test

Heavy-quark relaxation time τR>> τL : τR ~ (Mhq /T)τL ~8 τL for Mhq ~1.4 GeV and T=165 MeV

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

Elliptic Flow at RHIC energies

For a broad range of reaction centralities (impact parameters) elliptic flow at RHIC energies (62.4-200 GeV) depends only (?) on transverse kinetic energy of the particle KET and number of valence quarks nq ?

KET/n Scaling tests for Ideal Hydro

Why Ideal hydro works so bad after close look?

- In ideal hydro ( η = 0 !!! )

pion

Elliptic flow at RHIC and ideal fluid hydrodynamics

From PHENIX White Paper

Nucl. Phys. A757 (2005) 184

Rapid Thermalization ?

For pT <1.5 GeV/c V2(pT) and pT spectra of identified hadrons are in a good agreement with the predictions of ideal relativistic hydrodynamics ( rapid thermalization t< 1fm/c and an extremely small η/s ) → small viscosityLarge cross sections

Large cross sections strong couplings

T. Hirano: Highlights from a QGP Hydro + Hadronic Cascade Model

Hadronic dissipative effects on elliptic flow and spectra

AuAu200

Adapted from S.J.Sanders (BRAHMS) @ QM2006

b=7.2fm

0-50%

hadronic -“ late viscosity”

What is the lowest viscosity at RHIC?

Shear viscosity (η) – how strongly particles interact and move collectively in a body system. In general, strongly interacting systems have smaller (η) than weakly interacting.

But, (η/s) has a lower bound: in standard kinetic theory η=(n<p>λ)/3 , where n - proper density , <p>- average total momentum, λ – momentum degradation transport mean free path. The uncertainty principle implies : λ>1/<p> , for relativistic system, the entropy density (s~4n) and (η/s) > 1/12

(η/s) > 1/12

[from “Dissipative Phenomena in Quark-Gluon Plasmas “

P. Danielewicz, M. Gyulassy Phys.Rev. D31, 53,1985.]

KSS bound (η/s) > 1/4π

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

Phys. Rev. Lett. 98, 172301 (2007)

- Rapp and van Hees Phys.Rev.C71:034907,2005
- Simultaneously describe PHENIX RAA(E) and v2(e) with diffusion coefficient in range DHQ (2pT) ~4-6
- Moore and Teaney Phys.Rev.C71:064904,2005
- Find DHQ/(h/(e+p)) ~ 6 for Nf=3
- Combining
- Recall e+p = T s at mB=0
- This then gives h/s ~(1.5-2)/4p
- That is, within factor of 2-3 of conjectured lower bound

Estimation of h/s from RHIC data

- Damping (flow, fluctuations, heavy quark motion) ~ h/s
- FLOW:Has the QCD Critical Point Been Signaled by Observations at RHIC?,R. Lacey et al., Phys.Rev.Lett.98:092301,2007(nucl-ex/0609025)
- The Centrality dependence of Elliptic flow, the Hydrodynamic Limit, and the Viscosity of Hot QCD, H.-J. Drescher et al., (arXiv:0704.3553)
- FLUCTUATIONS: Measuring Shear Viscosity Using Transverse Momentum Correlations in Relativistic Nuclear Collisions, S. Gavin and M. Abdel-Aziz, Phys.Rev.Lett.97:162302,2006 (nucl-th/0606061)
- DRAG, FLOW: Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at √sNN = 200 GeV (PHENIX Collaboration), A. Adare et al., to appear in Phys. Rev. Lett. (nucl-ex/0611018)

Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?, P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99:172301, 2007

- Calculation:2nd order causal viscous hydro:

(Glauber IC’s

T. Hirano: Hydro + Cascade

QGP viscosity or hadronic viscosity – both ?

Detector Upgrades + RHIC I AuAu 2 nb-1

Example: STAR Time of Flight + DAQ1000

Key Future Test

W baryon (sss) is a stringent test due to the large mass and OZI suppressed hadronic interactions.

Small deviations from scaling will yield insights on novel hadronization process.

Strong indication for a minimum in the vicinity of Tc

L.P.Csernai et al. PRL 97 (2006) 152303; R.Lacey at al. PRL 98 (2007) 092301

Viscosity-to-entropy ratiominimum bias Au+Au, √s=200 GeV

Hydrodynamic scaling

Partonic fluid

Lower bound of η/s=1/4π in the strong coupling limit (P.Kovtun et al. PRL 94 (2005) 111601)

Coalescence/recombination and KET

J.Jia and C. Zhang, Phys. Rev. C 75 (2007) 031901(R)

If one modify the momentum conservation relation into kinetic energy conservation relation in the coalescence formula – one will get :

2v2,q

≈ 2 v2,q ( KET/2 )

mesons

V2,M(KET)=

1+2v22,q

KET/2

3v2,q+3v32,q

≈ 3 v2,q(KET/3)

baryons

V2,B(KT)=

1+6v22,q

KET/3

Problem with conventional quark coalescence models is energy violation ( 2→ 1, 3→ 1 channels ). What to do with it?

Quark Coalescence based on a Transport Equation

L. Ravagli and R. Rapp: http://arxiv.org/abs/0705.0021

- Resonance formation in quark-(anti)quark scattering as the dominant channel for meson production at RHIC – Energy ( 4-momentum ) conservation satisfied via a finite Γ.
- Is it a way to solve the problem?

Constituent Quark Number Scaling (QNS) of v2

- Simple models of hadronization by coalescence/recombination of constituent quarks, which only considers the momentum distribution of quarks and allows quarks with the same pT to coalesce into hadrons→relate quark and hadron v2:
- v2p = v2h(pT/n)/n,
- n is the number of quarks in the hadron
- Models imply
- v2 is developed before hadrons form ( at partonic level )

Coalescence/recombination of constituent quarks can explain both meson/baryon nature of suppression factors and v2 at intermediate pt

Greco, Ko, Levai; Muller, Nonaka, Bass;Hwa,Yang; Molnar, Voloshin

v2(pT/n)/n QNS scaling: close look

- With higher statistics v2 measurements, fine structure
- in QNS is observed:
- pT>2GeV/c: QNS scaling only works at 20% level
- pT<2GeV/c: QNS scaling breakes badly with systematic dependence on the hadron mass: it undershoots the v2 values of light mesons and overshoots the v2 values of heavy baryons

Imperfections of coalescence/recombination approach?

Wrong scaling variable?

Can one get a unified description of hadron production and elliptic flow at low and intermediate pT ?

The idea to use collective flow to Probe the properties of nuclear matter is long-standing

Ne

W. Scheid, H. Muller, and W. Greiner,

PRL 32, 741 (1974)

H. Stöcker, J.A. Maruhn, and W. Greiner,

PRL 44, 725 (1980)

U

M.I. Sobel, P.J. Siemens, J.P. Bondorf, an H.A. Bethe, Nucl. Phys. A251, 502 (1975)

G.F. Chapline, M.H. Johnson, E. Teller, and M.S. Weiss, PRD 8, 4302 (1973)

E. Glass Gold et al. Annals of Physics 6, 1 (1959)

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
- Outlook: mechanism of hadronisation at RHIC, what is the range of (η/s) at RHIC?

Strong quenching of jets, observed in central Au+Au collisions →

Evidence of the extreme energy loss of partons traversing matter containing a large density of color charges

Elliptic flow at RHIC

Z

- 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

Reaction plane

Y

X

Pz

Py

Px

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