r. lacey, suny stony brook 1 arkadij taranenko helmholtz international summer school: “dense...

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R. Lacey, SUNY Stony Brook

Arkadij Taranenko

Helmholtz International Summer School: “Dense Matter In Heavy Ion Collisions and Astrophysics” Dubna , Russia, July 14-26, 2008

Nuclear Chemistry Group SUNY Stony Brook, USA

Elliptic Flow measurements at RHIC

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Phase diagram (QCD) and RHIC Phase diagram (QCD) and RHIC

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

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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

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Arkadij Taranenko

Helmholtz International Summer School: “Dense Matter In Heavy Ion Collisions and Astrophysics” Dubna , Russia, July 14-26, 2008

Nuclear Chemistry Group SUNY Stony Brook, USA

Elliptic Flow measurements from RHIC to SIS

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

Reaction Plane

-180 -90 0 90 1800

0.1 [

co

rre

cte

d]

ddN

N1

[Deg]

+

-180 -90 0 90 1800

0.1 [

co

rre

cte

d]

ddN

N1

[Deg]

+

0.01± = 0.03 1v

0.01± = -0.13 2v+/- 90deg

v2 < 0mid-rapiditymid-rapidity

x

y

ψR

φ=Φ-ΨR

Diogene, M. Demoulins et al., Phys. Lett. B241, 476 (1990)

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

Reaction plane

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-180 -90 0 90 1800

0.1

[c

orr

ecte

d]

ddN

N1

[Deg]

+

-180 -90 0 90 1800

0.1

[c

orr

ecte

d]

ddN

N1

[Deg]

+

0.01± = 0.03 1v

0.01± = -0.13 2v+/- 90deg


Cheuk-Yin WONG , Physics Letters, 88B, p 39 (1979)Sergei Voloshin, Y. Zhang, Z. Phys. C70,(1996), 665

-180 -90 0 90 180

0

0.2

[c

orre

cte

d]

ddN

N1

[Deg]

p < 0.15n 0.05 < y

-180 -90 0 90 180

0

0.2

[c

orre

cte

d]

ddN

N1

[Deg]

p < 0.15n 0.05 < y

0.01± = -0.27 1v

0.01± = -0.02 2v

v1 < 0

+/- 180deg

...)φ)(v)(φv(dydp

Nd

dφdydp

Nd

tt

2cos2cos212

121

23

Directed flow Elliptic flow

Fourier decomposition of single particle (semi) inclusive spectra:

x

y

ψR

φ=Φ-ΨR

KAOS

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Small Elliptic flow, Large Elliptic Flow?

-180 -90 0 90 1800

0.1

[c

orre

cte

d]

ddN

N1

[Deg]

+

-180 -90 0 90 1800

0.1

[c

orre

cte

d]

ddN

N1

[Deg]

+

0.01± = 0.03 1v

0.01± = -0.13 2v+/- 90deg


ROUT/IN=N(900) + N(2700)N(00) + N(1800)

=1- 2 V2

1 + 2 V2

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

SIS

RHIC

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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%

222

4224

4 )(

6)4cos(

yx

yyxx

pp

ppppv

STAR, J. Phys. G34 (2007)

V4~V22 [ Vn~V2

n/2 ]

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Excitation function of elliptic flow – Do we understand it ?Excitation function of elliptic flow – Do we understand it ?

RHIC

SPS

SIS

GANIL/MSU

AGS

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

b – impact parameter

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

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

SPS

SIS

AGS

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 shadowing of participant hadrons by projectile and target spectators

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

x

y

Azimuthal anisotropy in momentum space (elliptic flow)

px

py

dN/d

-/2 0 /2

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

x

y

Azimuthal anisotropy in momentum space (elliptic flow)

px

py

dN/d

-/2 0 /2

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Interplay of passage/expansion times

Passage time: 2R/(βcmγcm)Expansion time: R/cs cs=c√dp/dε - speed of sound

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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/2 or

vT > (1-b/2R) (βcmγcm)

V2 will increase with vT and impact parameter b

(KAOS – Z. Phys. A355 (1996); (E895) - PRL 83 (1999) 1295

Squeeze-out contribution

reflects the ratio : cs/(βcm γcm)

cs=c√dp/dε - speed of sound

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Elliptic Flow@ SIS/AGS

Low Energy:Low Energy:Squeeze-out

High EnergyHigh Energy In-plane

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elliptic flow

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

Determination of the Equation of State of dense matterfrom collective flow of particles

dN/d1 + 2v1cos + 2v2 cos2

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Prologue:Prologue: Constraints for the Hadronic EOSPrologue:Prologue: Constraints for the Hadronic EOS

0.15 ,0.219sN

Kc c cm

Soft and hard EOS

Good Constraints for the EOS Good Constraints for the EOS achieved achieved

Danielewicz, Lacey, Lynch

3410 Pa

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Elliptic flow at RHIC

b – impact parameter

“spectators”

“spectators”

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

Passage time: ~ 0.15 fm/c

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ε drives pressure gradients which result in flow.

time to thermalize the system (0 ~ 0.2 - 1 fm/c)

Bjorken~ 5 - 15 GeV/fm3

dy

dE

RT

Bj0

2

11

s/

P ²

Thermalization2 2

2 2

y x

y x

eccentricity

PRL87, 052301 (2001)

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

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

Phase Transition:

3/1

170

fmGeV

MeVT

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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? ?

Fine Structure of Elliptic Flow at RHIC

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Mass ordering of v2 and ideal fluid hydrodynamics Mass ordering of v2 and ideal fluid hydrodynamics Mass ordering of v2 and ideal fluid hydrodynamics Mass ordering of v2 and ideal fluid hydrodynamics

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 sectionsLarge cross sections strong couplings

PHENIX : PRL 91, 182301 (2003) STAR : PRC 72, 014904 (2005)

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

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Elliptic Flow: ultra-cold Fermi-GasElliptic 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?

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Hadron Gas ?

0 100 200 300N part

0.0

0.1

0.2

0.3

<v 2>

STAR

HSD CalculationpT>2 GeV/c

Hydrodynamic

STAR

PHOBOS

Hydrodynamic

STAR

PHOBOS

RQMD

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

Clearly the system is not a hadron gas.

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Elliptic flow at SPS and ideal hydrodynamics

CERES

Different picture than at RHIC!?

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Intermediate pIntermediate pTT range : Meson vs Baryon range : Meson vs Baryon Intermediate pIntermediate pTT range : Meson vs Baryon 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 or RAA) is different – meson/baryon effect

•p/π ratio – more (anti-)protons than

pions at intermediate pT ( 2-5 GeV)

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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 more apparent at higher KET

Baryons scale together

Mesons scale together

= mT – m

Transverse kinetic energy scalingTransverse kinetic energy scaling

( WHY ? )( WHY ? ) 21

2Therm colKE KE KE m u

PP

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

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

KEKETT + Quark number Scaling + Quark number Scaling KEKETT + Quark number Scaling + Quark number Scaling PHENIX: Phys. Rev. Lett. 98, 162301 (2007)

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KET + Number of constituent Quarks (NCQ) scaling

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

Centrality dependence

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KEKETT/n scaling and beam energy dependence /n scaling and beam energy dependence

Au+Au (62.4-200 GeV)Au+Au (62.4-200 GeV)

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

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

KET/n scaling observed across different colliding systems

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v4 Scaling

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

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KET/n Scaling tests at SPS

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

C. Blume (NA49) QM2006 talk

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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 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?)

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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

nucl-ex/0703024

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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 at partonic level before hadron

formation

Multi-strange baryon elliptic flow at RHIC (STAR)

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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 )

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

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

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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 ?

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KET/n Scaling tests for Ideal Hydro

Why Ideal hydro works so bad after close look?

- In ideal hydro ( η = 0 !!! )

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proton pion From PHENIX White Paper

Nucl. Phys. A757 (2005) 184

Elliptic flow at RHIC and ideal fluid hydrodynamics Elliptic flow at RHIC and ideal fluid hydrodynamics Elliptic flow at RHIC and ideal fluid hydrodynamics Elliptic flow at RHIC and ideal fluid hydrodynamics

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 sectionsLarge cross sections strong couplings

Rapid Rapid Thermalization Thermalization

??

Rapid Rapid Thermalization Thermalization

??

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

hadronic -“ late viscosity”

b=7.2fm 0-50%Adapted from S.J.Sanders (BRAHMS) @ QM2006

AuAu200Hadronic dissipative effects on elliptic flow and spectra

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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

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

conjectured lower bound

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

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Estimation of /s from RHIC data

• Damping (flow, fluctuations, heavy quark motion) ~ /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)

4π

1)0.2(1.1

s

η 1.21.1

4

1)8.30.1(

s

4

1)0.23.1(

s

4

1)5.29.1(

s

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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

4

1)0.20(

s

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T. Hirano: Hydro + Cascade

QGP viscosity or hadronic viscosity – both ?

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

Key Future Test

Detector Upgrades + RHIC I AuAu 2 nb-1

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

Example: STAR Time of Flight + DAQ1000

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Viscosity-to-entropy ratio

minimum bias Au+Au, √s=200 GeV

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

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

η/s for several substances

Strong indication for a minimum in the vicinity of Tc

Partonic fluid

Hydrodynamic scaling

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Eccentricity Calculation

V2,M(KET)=

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

1+2v22,q KET/2

≈ 2 v2,q ( KET/2 )

V2,B(KT)=3v2,q+3v3

2,q

1+6v22,q KET/3

≈ 3 v2,q(KET/3)

mesons

baryons

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

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Quark Coalescence based on a Transport EquationQuark Coalescence based on a Transport Equation

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?

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

52


Constituent Quark Number Scaling (QNS) of v2Simple 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 = v2

h(pT/n)/n,

n is the number of quarks in the hadron

Models imply

v2 is developed before hadrons form ( at partonic level )

2 2 2 2an22 3

d 3p pM tt

B tt

pv p vv

pv p

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

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

With higher statistics v2 measurements, fine structurein 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 ?

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

Ne

M.I. Sobel, P.J. Siemens, J.P. Bondorf, an H.A. Bethe, Nucl. Phys. A251, 502 (1975)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)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)E. Glass Gold et al. Annals of Physics 6, 1 (1959)

U

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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

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

56


Jet Quenching at RHICJet 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

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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

...])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

r. lacey, suny stony brook 1 arkadij taranenko helmholtz international summer school: “dense...

Documents

sis slide

large elliptic flow

small elliptic flow

elliptic flow signal

mev slide

reaction plane slide

sps energies elliptic

plane sis rhic slide