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Elliptic Flow measurements at RHIC. 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. Phase diagram (QCD) and RHIC.

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elliptic flow measurements at rhic

Elliptic Flow measurements at RHIC

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


Phase diagram (QCD) and RHIC

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

one want to see a probe phenomena which is
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

elliptic flow measurements from rhic to sis

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

squeeze out first elliptic flow signal in hic





v2 < 0


+/- 90deg

“Squeeze-Out” - First Elliptic flow signal in HIC

Diogene, 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






v1 < 0

v2 < 0


Fourier decomposition of single particle (semi) inclusive spectra:

+/- 90deg

+/- 180deg

Directed flow

Elliptic flow


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

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

small elliptic flow large elliptic flow

v2 < 0


+/- 90deg

Small Elliptic flow, Large Elliptic Flow?


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)



N(00) + N(1800)

1 + 2 V2



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

b – impact parameter

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)




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

if the passage time is long compared to the expansion time spectator blocking squeeze out





-/2 0 /2


If the passage time is long compared to the expansion time (spectator blocking) → squeeze-out

Azimuthal anisotropy in momentum space

(elliptic flow)

in plane elliptic flow due to pressure gradient at high beam energies





-/2 0 /2


In-plane elliptic flow (due to pressure gradient) at high beam energies.

Azimuthal anisotropy in momentum space

(elliptic flow)

interplay of passage expansion times
Interplay of passage/expansion times

Passage time: 2R/(βcmγcm)

Expansion time:R/cs

cs=c√dp/dε - speed of sound


(KAOS – Z. Phys. A355(1996);

(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


Elliptic [email protected] SIS/AGS

Low Energy:


High Energy



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)

prologue constraints for the hadronic eos

Danielewicz, Lacey, Lynch

Good Constraints for the EOS


Soft and hard EOS

Prologue: Constraints for the Hadronic EOS
elliptic flow at rhic


b – impact parameter


Elliptic flow at RHIC

Longitudinal and transverse expansion => no influence of spectator matter at midrapidity

Passage time: ~ 0.15 fm/c


Phase Transition:

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


PRL87, 052301 (2001)


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
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 viscosityLarge 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?
hadron gas

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




HSD Calculation

pT>2 GeV/c


Hadron Gas ?

Clearly the system is not a hadron gas.

elliptic flow at sps and ideal hydrodynamics
Elliptic flow at SPS and ideal hydrodynamics


Different picture than at RHIC!?


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)
transverse kinetic energy scaling

( WHY ? )


Transverse kinetic energy scaling

Scaling 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

ke t quark number scaling
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!

ke t number of constituent quarks ncq scaling
KET + Number of constituent Quarks (NCQ) scaling

Centrality dependence

  • Scaling seems to hold well for different centralities up to 60% centrality
ke t n scaling and beam energy dependence au au 62 4 200 gev
KET/n scaling and beam energy dependence Au+Au (62.4-200 GeV)

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

ke t n scaling and system size auau cucu
KET/n scaling and system size (AuAu/CuCu)

KET/n scaling observed across different colliding systems

v 4 scaling
v4 Scaling
  • The similar scaling for v4 is found recently at PHENIX.
  • Compatible with partonic flow picture.
ke t n scaling tests at sps
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 meson and partonic collectivity at rhic
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 meson and partonic collectivity at rhic
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 φmesons as well

multi strange baryon elliptic flow at rhic star
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
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
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
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 ?

ke t n scaling tests for ideal hydro
KET/n Scaling tests for Ideal Hydro

Why Ideal hydro works so bad after close look?

- In ideal hydro ( η = 0 !!! )




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 viscosityLarge cross sections

Large cross sections strong couplings

t hirano highlights from a qgp hydro hadronic cascade model
T. Hirano: Highlights from a QGP Hydro + Hadronic Cascade Model

Hadronic dissipative effects on elliptic flow and spectra


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



hadronic -“ late viscosity”

what is the lowest viscosity at rhic
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 data for r aa v 2 of non photonic electrons
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
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
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.

viscosity to entropy ratio

η/s for several substances

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 ratio

minimum 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)


Eccentricity Calculation

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 :


≈ 2 v2,q ( KET/2 )






≈ 3 v2,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
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 v 2
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

v 2 p t n n qns scaling close look
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


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

PRL 32, 741 (1974)

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

PRL 44, 725 (1980)


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)

  • 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?

Jet Quenching 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 rhic1
Elliptic flow at RHIC


  • 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