S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page1 RHI Collisions. Dense Matter. Anisotropic Flow Sergei Voloshin

International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004

page 1 S.A. Voloshin

RHI Collisions. Dense Matter. Anisotropic Flow

Sergei Voloshin Wayne State University

Outline:

- Anisotropic flow as a tool for early dynamics study- Most important results of recent years: - Constituent quark scaling - mass splitting of v2(pt) - Approaching “hydro limit”- First results on directed flow and higher harmonics- Conclusions and what to expect from exp. in the next couple years

How much the nature of hadronization affects anisotropic flow ?Do we have constituent quark plasma?



Directed flow Elliptic flow

Term “flow” does not mean necessarily “hydro” flow – used only to emphasize the collectivebehavior multiparticle azimuthal correlation.

Anisotropic flow. Definitions.

Fourier decomposition of single particle inclusive spectra:

X

Z b

XZ – the reaction plane

Picture: © UrQMDAnisotropic flow correlationswith respect to the reaction plane

S.V., Y.Zhang, 1994

...)φ)(v)(φv(dydp

Nd

dφdydp

Nd

tt

2cos2cos212

121

23



Elliptic Flow – a probe for early time physics.

t (fm/c)

Zhang, Gyulassy, Ko, PL B455 (1999) 45

Elli

pti

c fl

ow

XZ-plane - the reaction plane

Transverse Plane

22

22

xyxy

ε

X

Y

)cos( φ222

22

2yx

yx

pp

ppv

Sensitive to the physics of constituent interactions (needed to convert space to momentum anisotropy) at early times (free-streaming kills the initial space anisotropy)

The characteristic time scale of 2-4 fm is similar in any model: parton cascade, hydro, etc.

v2 > 0, E877, PRL 73 (1994) 2532



Elliptic flow as function of …

- Integrated values of v2 noticeably increase with energy- The slope of v2(pt) increase slowly Most of the increase in integrated v2 comes from the increase in mean pt.

Popular view:In mid and more central collisions elliptic flow is welldescribed by hydro model, and not by microscopic transport models

PHOBOS

It is measured vs:- collision energy- transverse momentum- centrality

- particle ID



MPC (D. Molnar and M. Gyulassy) AMPT+”string melting” (Zi-Wei Lin, C.M.Ko)v

2

HIJING x 80HIJING x 35HIJING x 13HIJING x 1hydro , sBC

Elastic scattering, Baseline (HIJING) parameters: gg= 3 mb, tr= 1 mb;1 gluon 1 charged particle;dNglue/dy=210. opacity = tr dN/dy =210 mb

Constituent quark plasma:tr up 2 - 3 (?) times,dN/dy up > 2 times, Could be close to the data…

“String melting”: a) # of quarks in the system = # of quarks in the hadrons b) “quark” formation time



Constituent quark model + coalescence

Side-notes:a) more particles produced via coalescence vs parton

fragmentation larger mean pt…)b higher baryon/meson ratio)c lower multiplicity per “participant”

coalescence fragmentationLow pt quarks High pt quarks

Taking into account that in coalescence

and in fragmentation ,

there could be a region in quark pt where only few quarks coalesce, but give hadronsin the hadron pt region where most hadrons are produced via coalescence.

, , / 2t quark t mesonp p

, , /t quark t mesonp p z

In the low pt region density is large and most quarks coalesce: N hadron ~ N quark

2 2 / 4 2( )t tBp Bpe e In the high pt region fragmentation eventually wins:

2(( / 2) )n nt tp p

Only in the intermediate region (rare processes) coalescence can be

described by:

2

3

3

3

3

2/

Mq

q

q

M

M pppd

nd

pd

nd)2/(2)( ,2,2 tqtM pvpv

)3/(3)( ,2,2 tqtB pvpv

S.V., QM2002D. Molnar, S.V., PRL 2003

-> D. Molnar, QM2004, in progress-> Bass, Fries, Mueller. Nonaka; Hwa; Levai, Ko; …-> Eremin, S.V.



dNch/dy vs. number of participants

Open symbols: our calculation of Npart

6 mb - open symbolsqq 42 / 9 mb - solid symbolsqq

The ratio Nch/Nq-part slightly decreases with centrality !

S. Eremin, S.V., PRC 67, 064905( 2003)

Scaled by number of quark participants

Scaled by number of nucleon participants.The dependence usually explained by a combination of ‘soft’ and ‘hard’ physics



Constiuent quark scaling: v2 and RCP

- Constituent quark scaling holds very well. Deviations are where expected.- Elliptic flow saturates at pt ~ 1 GeV, just at constituent quark scale. An accident?



v2(pt) dependence on mass. Blast wave model.

v1(pt) - S.V., PRC 55 (1997) 1630

v2(pt) - Houvinen, Kolb, Heinz, Ruuskanen, S.V., PLB 503 (2001) 58

v2(pt) - STAR Collaboration, PRL 87 (2001) 182301

Elementary source density -

)cos( ss φ221 2

Parameters: T – temperature

0 - radial expansion rapidity

2 - amplitude of azimuthal

variation in expansion rapidity

STAR

T (MeV) 135 20 100 24

0.0 0.04 0.01S2

0a

0.52 0.02 0.54 0.03

0.09 0.02 0.04 0.01

dashed solid

- model fits data well- shape (s2 parameter) agrees with the interferometry measurements



v2(pt) at 200 GeV. Comparison to hydro.

Mass dependence is well reproduced by hydrodynamical model calculations,but can it also be accounted for in the constituent quark coalescence picture?(heavier particle larger difference in constituent quark momenta)

Data: PHENIX, Nucl. Phys. A715, 599 (2003)

Hydro: P. Huovinen et al., Phys. Lett. B503, 58 (2001);Houvinen, Heinz, Kolb

Mass splitting depends on EoS!

Caveats:- centrality bins are very wide- Initial conditions are chosen independently for spectra and v2 descriptions



Heinz, Kolb, Sollfrank

30000400402 /*..dydN

v

Hydro limits

RHIC 160 GeV/A

SPS

SPS 40 GeV/A

b (fm)Suppressed scale!

Hydro: P.F. Kolb, et al

v 2 /

Hydro: v2~ Ollitrault, PRD 46 (1992) 229

Low Density Limit: v2~ dN/dy / SHeiselberg & Levy, PRC C59 (1999) 2716

Questions to address: - is it saturating?- rapidity dependence? (next slide) - what happens at SPS energies? Any ‘wiggle’?



PHOBOS: rapidity dependence (nucl-ex/0406021)

PRL 91, 052303 (2003)

The detailed study of the rapidity dependenceis still to be made, but it looks like v2()

follows very closely dN/d. Low Density Limit?

Difficulty: ()

Steinberg, nucl-ex/0105013 (QM01)



v2/ and phase transitions

Original ideas: Sorge, PRL 82 2048 (’99), Heiselberg & Levy, PRC 59 2716 (’99)

S.V. & A. Poskanzer, PLB 474 (2000) 27

“Cold” deconfinement?

Uncertainties:Hydro limits: slightly dependon initial conditionsData: no systematic errors,shaded area –uncertainty incentrality determinations.Curves: “hand made”

E877 NA49



“Cold” deconfinement, color percolation?

Percolation point by H. Satz

CERN SPS energies b ~ 4 fmRHIC: b ~ 7 fm

Could it be constituent quark deconfinement ?



Charged particle v2 at high-pt

Above 6 – 8 GeV we do not have a reliable answer (yet) for the magnitude of the elliptic flow

phenix preliminarynucl-ex/0305013



Elliptic flow at intermediate pt (jet quenching ?)

STAR, Au+Au, 200 GeV

Hard shellHard shell

Hard sphereHard sphere

Woods-SaxonWoods-Saxon

Hard shell == box density profile (+) extreme quenching E. Shuryak, nucl-th/0112042Hard sphere == -”- (+) realistic quenchingWoods-Saxon == WS density profile (+) realistic quenching



Directed flow at RHIC: (Limiting fragmentation, etc.)

STAR PreliminaryA. Tang, HQ2004

rapidity

v1

Looking for the ‘wiggle’:

Directed flow is most sensitive to the initial conditions

z

x

Radial flow <x px> > 0

rapidity

px, v1

R. Snellings, H. Sorge, S.V., F. Wang, Nu Xu, PRL 84 (2000) 2803

x

rapidity

px

x

Baryon stopping

“wiggle”



v4, v6 @ 200 GeV

1.4 v22

STAR, PRL 92, 062301 (2004)

P. Kolb, hydro

Detailed comparison of the event shape:not really described by any model



SUMMARY

OBSERVATION:

- Anisotropies are strong at RHIC- The magnitude of elliptic flow is close to hydro predictions (for rather central collisions)- The mass splitting in v2(pt) finds natural explanation in hydro model. The magnitude of the splitting requires QGP EoS. - In the intermediate pt region the constituent quark number scaling is observed.- No model describes all the details…

QUESTIONS:

- How well hydro models describe both, spectra and v2, simultaneously? - How much ‘coalescence enhancement’ is reflected in ‘hydro limits’?- ‘Mass splitting’ at low pt – is the hydro explanation unique?- Constituent quark plasma picture – is it supported by theory / lattice QCD? What is the relation to color percolation? Do we have ’cold deconfinement’? WHAT TO EXPECT:

- Elliptic flow of open charm. Does c-quark flow?- Elliptic flow of resonances. Check regeneration in the hadronic phase vs direct production- Elliptic flow up to 10-12 GeV with good accuracy. Check jet quenching mechanism.- Directed flow of identified particle. Baryon stopping, tilted source.- Two particle correlation wrt Reaction Plane. Jets, tilted source- Anisotropic flow in lighter systems (Cu+Cu?). Low Density Limit?



2-particle correlations wrt RP

);,( 2121

2

RPxxdxdx

Nd x – azimuthal angle, transverse momentum, rapidity, etc.

J. Bielcikova, P. Wurm, K. FilimonovS. Esumi, S.V., PRC, 2003

“a” == “trigger particle”

)2cos(21 ,,

,2,2,

baoutin

abba

flowpairs vv

d

dN

2

22

2

22 4

2

4

2

v

vv

v

vv outin

CERES, PRL, 2003

Selection of one (or both) of particles in- or out- of the reaction plane “distorts” the RP determination

Approach: - “remove” flow contribution- parameterize the shape of what is left- study RP orientation dependence of the parameters



Azimuthal correlations from pp to AuAu

pp (non-flow)

AuAu (flow + non-flow)

In VERY peripheral collisions, azimuthal correlation in AuAu are dominated by non-flow.

At high pt in central collisions, azimuthal correlation in AuAu could be dominated by nonflow.



“Wiggle”, Pb+Pb, Elab=40 and 158 GeV

Preliminary

158 GeV/A

Note different scale for 40 and 158 GeV!The “wiggle” is there!

v1 < 0



Centrality dependence. Hydro + RQMD.

LH8 latent heat = 0.8 GeV/fm^3Pt slope parameters are about 20% larger in hydro compared to data

200 400 600 800

dNch/dy

Teaney, Lauret, Shuryak nucl-th/0110037

- v2 increases with dN/dy- Centrality dependence – close to data



CERES/NA45

0-12.5%12.5-23.5%>23.5%

24-30%

Preliminary

STAR

Lines: horizontal – v2=0.1 vertical - pt=1 GeV/c

Talks:NA49 – A. WetzlerNA45 – J. SlivovaSTAR- K. FilimonovPHENIX – S. EsumiPHOBOS – S. Manly

30-80%10-30%0-10%

v2(pT), low transverse momentum

0-55%

1. For midcentral collisions, v2(pt) is quite similar between SPS and RHIC2. For “central” collisions NA49 results are lower than STAR



Directed flow “wiggle” in cascade models

z

x

Radial flow <x px> > 0

rapidity

px, v1

R. Snellings, H. Sorge, S.V., F. Wang, Nu Xu, PRL 84 (2000) 2803

x

rapidity

px

x

Baryon stopping

“wiggle”

UrQMD: Bleicher, Stocker, PRB 526 (2002) 309

R. Snellings, A. Poskanzer, S.V., nucl-ex/9904003

RQMD v2.4

Should be better pronounced at higher energies



Hydro: “antiflow”, “third flow component”

Net baryon density

Csernai, Rohrich, PLB 458 (1999) 454. Magas, Csernai, Strottman, hep-ph/0010307

Brachmann, Soff, Dumitru, Stocker, Maruhn, GreinerBravina, Rischke , PRC 61 (2000) 024909

- Strongest at the softest point ?- The same for pions and protons ?

rapidity

v1

flowantiflo

w

Documents

S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page1 RHI Collisions. Dense Matter. Anisotropic Flow Sergei Voloshin