s.a. voloshin 2 nd int. workshop on the critical point and onset of deconfinement, bergen, 2005page1...

2nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005

page 1 S.A. Voloshin

Anisotropic Flow and Phase transitions,

…and a little bit on fluctuations/correlations

Sergei Voloshin Wayne State University, Detroit

Outline:

- Anisotropic flow: where to look for a phase transition- v1(y) - directed flow “wiggle”- v2(pt) – constituent quark number scaling- v2(pt) – “mass splitting” and QGP- v2(energy,centrality) – approaching “hydro limit”

- v2/ vs dN/dy/S, any “wiggle/step”?

- Correlation functions and fluctuations.- Centrality dependence of <dpt dpt> and radial flow.

- Conclusions



...)φ)(v)(φv(dydp

Nd

dφdydp

Nd

tt

2cos2cos212

121

23

Directed flow Elliptic flow

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

Anisotropic flow

Fourier decomposition of single particle inclusive spectra:

X

Z b

XZ – the reaction plane

Picture: © UrQMDAnisotropic flow correlationswith respect to the reaction plane

Note large orbital angular momen-tum in the system. - Parity violation - Orbital momentum particle spin.



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



Third flow component as the QGP signal

L.P. Csernai, D. RohrichPRL 458 (1999) 454

“Wiggle is present only for the QGP EoS.

tx pvp 1

This calculations have been done at 11 AGeV. Would the results change for RHIC?



Wiggle from anti-flow: development in time.

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



Wiggle from uRQMD

Marcus Bleicher, Horst StockerPLB 526, (2002) 309-314

“Rich” dependence on the particle type: baryons, antibaryons, mesons



Anti-flow from shadowing

Anti-flow is developingin more peripheral collisions



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”

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

The wiggle is pronounced only at high energiesDoes the picture contradict FOPI resultson different isotope collisions?



QM2002

Warning: Large systematic errors!



Laszlo’s slide from BNL Flow workshop ‘03

The slope of v1(eta) at eta=0is indeed as in antiflowscenario, … but also the sameas always for pions at lowerenergies



PHOBOS, v1(eta)

Qualitatively the samepicture from SPS energiesto highest RHIC energy.



STAR: ZDC-SMD

SMD is an 8 channel by 7 channel hodoscope that sits directly on the face of the 2nd ZDC module

What about ALICE, CMS, do they have something like that?



v1(eta), v1(pt), AuAu@62 GeV,different centralities

STAR preliminary

Qualitatively the picture is very similar at different centralities



Comparison with models. Centrality dependence

STAR preliminarySTAR preliminary

- In order to prove the “wiggle” one needs identified particle measurementsand look for the change of sign of the slope with energy/centrality. At 62 GeV the errorbars are too large, we hope to have it such results for 200 GeV data.

Neither model describes v1(eta) close to midrapidty



Elliptic Flow.

XZ-plane - the reaction plane

Transverse Plane

22

22

xyxy

ε

X

Y

)cos( φ222

22

2yx

yx

pp

ppv

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

Sensitive to “early” times.(Free streaming kills )



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.

In mid and more central collisions elliptic flow is rather well described by hydro model

PHOBOS

It is measured vs:- collision energy- transverse momentum- centrality- rapidity- particle ID



Integrated vIntegrated v2 2 at different energiesat different energies

(0-40% central)(0-40% central)

We still have to analyze carefully the centrality dependence



Constituent quark model + coalescence

Side-notes:a) more particles produced via coalescence rather than

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; Levai, Ko; …-> Eremin, S.V.

R. Fries



Constiuent quark scaling: v2 and RCP

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

Gas of constituent quarks – deconfinement !?

AuAu@62 GeVSTAR Preliminary



AuAu@62 GeVSTAR Preliminary

PHENIX: const. quark scaling, v2 saturates at RHIC energy



Are they thermalized?

S. Pratt, S. Pal , nucl-th/0409038

Two pictures correspond to the same v2 of quarks, buta) v2(B) = 3/2 v2(M) (no thermalization ?) b) v2(B) = v2(M) (freeze-out at constant phase space density)

My conclusion: constituent quark scaling - Deconfinement!- No thermalization (at least in this region of pt) (Freeze-out at constant density in the configuration space)

The same mechanism at sqrt(s_NN) 200 and 62 GeV. If thermalized, disappear at LHC??



v2(pt) at 200 GeV. “Mass splitting”.

Mass dependence is rather well reproduced by hydrodynamical model calculations.Note dependence on the EoS.

But qualitatively such a mass dependence will be present in any model, for example, in the constituent quark coalescence picture(heavier particle larger difference in constituent quark momenta)

Data: PHENIX, Nucl. Phys. A715, 599, 2003Hydro: P. Huovinen, P. Kolb, U. Heinz, P. Ruuskanen, S.V., Phys. Lett. B503, 58, 2001;



v2(pt) @ 200 and 62 GeV

0 ~ 80 % star p

reliminary

pion

Y. Bai (STAR), DNP ‘04

Pt

min. bias 0 ~ 80%

star preliminary

STAR expects good identified particle v2 measurements up to relatively high pt.Need detailed/tuned hydro calculations for different centralities and identified particles.



Centrality dependence. Hydro and Low Density limits

Hydro: P.F. Kolb, et al

v 2 /

5 10 b (fm)

SV & A. Poskanzer, PLB 474 (2000) 27

hydro

LDL

(pts are RQMD v2.4)

Hydro: v2~

Ollitrault, PRD 46 (1992) 229

Low Density Limit: v2~ dN/dy / A

Heiselberg & Levy, PRC C59 (1999) 2716

RHIC 160 GeV/A

SPS

SPS 40 GeV/A

b (fm)Suppressed scale!



v2/ and phase transitions

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

Dependence on the particle density in the transverse plane: 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



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?- what happens at SPS energies? Any ‘wiggle’?



“Cold” deconfinement, color percolation?

Percolation point by H. Satz, QM2002

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

There is a need for the “next generation”of this plot: better estimates of epsilon,adding more data (in particular 62 GeV)

It is a real pity that NA49 measurements have so large systematic uncertainty. Need detector with better azimuthal acceptance (could be just a simple extra detector used to determine the RP) .

FT RHIC?



But is it surprising?:

pppp

mmp

pv

5~;2~

;5~;~2

v2 stays the same?

STAR SQM04

Charm flow (via electron measurements)



Correlations/fluctuations



2-particle correlation functions

cc

ccccNc

cccNc

cNc

N

R

yyN

yyNyyNNyyNR

yyNNyyNyyyNy}1{

2}1{

11}1{

12

2}1{

11}1{

12

2}1{

11}1{

121}1{

2}{

2}1{

11}1{

121}1{

221}{

2}1{

1}{

1

)()(

)()()()()1(),(

)()()1(),(),();()(

Production via Nc clusters [e.g. independent NN collisions]

Rnn

n)n(nn

n

nn)n(n

n

nn

n

σω n

n

~

11

1

1

2

2

2222

)()(

),(~

211121

2121

yydydy

yyCdydyR

Relation to fluctuations

“Fluctuations” are determined by the “average“ valueof the correlationfunction over momentumregion under study.

“Inclusive”

ISR data. Filled circles – sqrt(s) = 63 GeVRHIC: PHOBOS?

)1(),(;)( 212211 nnyydydynydy

)()(),(),( 211121221 yyyyyyC

)(

),(),(

11

2121 y

yyCyyB

)()(

),(),(

2111

2121 yy

yyCyyR

Distribution of “correlated” pairs:

Distribution of “associated” particles (2) per “trigger” particle (1)

“Probability” to find a “correlated” pair

)(1 yCconst



<pt> fluctuations: observables and observables.

What are the main requirements for a good observable?-- be sensitive to the physics under study -- be defined at the “theoretical level”, be detector/experiment independent -- have clear physical meaning-- not to be limited in scope, provide new venues for further study

;tt,it,i ppδp Possibilities:- test scaling with Nch, Npart, Nbin, etc.-Particles “1” and “2” could be of different type (e.g. same/opposite charge), - taken from different rapidity/azimuthal angle regions (e.g. “same-side” , |y1-y2|>1 correlations as mostly “free” from jet contribution).

,2,1, tt pp



Multiplicity fluctuations

1)()(

),(~,

~2

~~2)1()1(

11

2

22,

Y bbY aa

Y baba

abdyndd

ddRRRR

nn

nn

n

nn

n

nn

“Charge” fluctuations

42

14

nnRRRD )

~~~(

2

21

21

212

2

22

21

21

212

212

2

112

2

)r(nnD

nn

δnδn

n

)n(

n

)n(

r

)r(

n

nr

!

- Free from “volume” fluctuations - Fails at small < n2 >

- < n++ n-> - “used” multiplicity, subject to cuts and acceptance

Rnn

σω n

n

~1

2

Particle ratios:



Comparison to PHENIX, Fpt (slide from G. Westfall (STAR), QM’04)

200 GeV Au+AuSTAR withPHENIX Cuts

|| < 0.35 = 2x900.2 < pt < 2 GeV

200 GeV Au+AuSTAR Cuts

|| < 1.0 = 3600.1 < pt < 2 GeV

mixedT

mixedTrealT

mixedT

mixedTrealTpt

T

TT F

,

,,

,

,,



STAR Preliminary

Elliptic flow contribution to <dpt dpt>

Shengli Huang (STAR)USTC RHIC Workshop,Hefei, China , Oct. 2004

y

xIn-plane

Out-of-plane

Could be better to plot <dpt dpt> /<pt>^2



correlations: elongation in

ISR data. Filled circles – sqrt(s) = 63 GeV

“Inclusive”R() ~ 1 - ||<R> (Y) ~ 1 - 4/3 Y,where Y= ()max/2

max

Blue dotted lines assume the same .Note difference in slopes (red vs blue) –broadening of R() with centrality

All data on <dpt dpt> are STAR preliminary, taken from talksof G. Westwall (STAR) at QM2004and Nuclear Dynamics WSs ‘04 and ‘05

2,1, tt pp

A way to do it better study directly as function of y1 and y2

2,1, tt pp



Rcc(0)0.66

: centrality dependence

Production via Nc clusters (Nc~Npart/2) [e.g. independent NN collisions]

Data: G. Westfall (STAR), QM2004

NNNNcoll

NNN

nnnN

nnD

coll )1()1(

)1(2

NNttNAAtt ppDppcoll 2,1,2,1,

1)1(~

2

n

nnR

2,1, tt pp

At midrapidity, the probability to find a particle is about 60% larger if one particle has been already detected.

In a superposition of two independent collisions,the ratio of the probability that in a randomly chosen pair both particles are from the same collision to the probability that two particles are from different collisions is about 1.66



“Elementary” NN-collision. Correlation functions.

Correlations are due to local charge(s) conservation, resonances, due to fluctuations in number of produced strings, e.g. number of qq-collisions.

x

y

rapidity

Rcc(0)0.66

)1(),(

)(

21221

1

nnyydydy

nydy

)()(),(),( 211121221 yyyyyyC

)(

),(),(

11

2121 y

yyCyyB

)()(

),(),(

2111

2121 yy

yyCyyR

Distribution of “correlated” pairs:

Distribution of “associated” particles (2) per “trigger” particle (1)

“Probability” to find a “correlated” pair

ISR2

6.1)1( nnn

At midrapidity, the probability to find a particle is about 60% larger if one particle has been already detected.



Radial flow 2- particle correlations

All particles produced in the same NN-collision (qq-string) experience the transverse radial “push” that is(a) in the same direction (leads to correlations in phi)(b) the same in magnitude ( correlations in pt) Position-momentum correlations caused by transverseexpansion “brings” totally new mechanism for momentum correlations, not present in NN-collisions

x

y

rapidity

pp collision

AA collision-Long range rapidity correlations (“bump”- narrow in phi and wide in rapidity, charge independent)-Stronger 2-particle pt correlation in narrow phi bins-Narrowing of the charge balance function( -- increase in mt decreasein rapidity separation) [same as in S. Pratt et al, in “late hadronization scenario”]- Charge correlations in phi. Azimuthal Balance function

Everything evolving with centrality (radial flow)

)sinh( ymp tz



Transverse radial expansion

])cos()sinh()cosh()cosh(

exp[)cosh(0

3

3

T

pyymyymddyrdr

pd

nEd stttstR

stss

Blast wave parameterization (Schnedermann, Sollfrank, Heinz, PRC 48, 2462 (1993), d3n/d3p ~ e-E/T)of the source at freeze-out:

Parameters: T-temperature, velocity profile t r n

STAR Collaboration, PRL 92, 112301 (2004)

)sinh();cosh(;)()(0

012

3

tt

ttt

t

R

tttt T

p

T

mIKmrdr

pddy

nd

AA collision

Note: uniform source densityat r < R has been assumed

y

rapidity

xn=1



Azimuthal correlations

Figures are shown for particles from the same NN collision. Dilution factor to be applied!

No momentum conservation effects has been included. Those would be important for the charge independent first harmonic correlations.

First and second harmonics of the distribution on the left

! - the large values of transverseflow, > 0.25, would contradict “non-flow” estimates in elliptic flow measurements

n=1, T=110 MeV



x correlations

- Charge independent correlations: particles at large rapidities, initially uncorrelated, become correlated, as all of them are pushed by radial flow in the same direction. For those, one needs 2d correlations (rapidity X azimuth) Shown below – hand drawn sketch.

Peripheral Central



Extracting Near-Side Jet Yields

d+Au, 40-100%

Au+Au, 0-5%

STAR preliminary

3 < pT(trig) < 6 GeV2 < pT(assoc) < pT(trig)

In Au+Au, jet-like correlation sits on top of an additional, approximately flat correlation in

D. Magestro (STAR) –Hard Probes 2004



Brief comparison to data: centrality dependence

Possible reasons for discrepancy:- diffusion, thermalization time - spatial source profile (not uniform density in transverse plane, e.g. cylinder shell)

n=1

n=0.5

2,1, tt pp



correlation summary

1. Transverse radial flow leads to strong space-momentum correlation. In combination with space correlations between particles created in the same NN collision, it leads to characteristic two (and many) particlerapidity, transverse momentum, and azimuthal correlations.

2. This phenomenon provides a natural (at present, qualitative) explanation of the centrality dependence of mean pt pseudorapidity/azimuthal anglecorrelations. It can be further used to study the details of the systemequilibration/thermalization and evolution (e.g. thermalization time, velocityprofile, etc.)

1. Avoid using ratios (n+/n-, K+/K0,…), use to get rid of “volume” fluctuations and be free from problems related to low multiplicities.2. If use normalized variance – correct for the efficiency.

abbbaa RRR~

2~~



EXTRA SLIDES



Rapidity correlations

How to disentangle “initial” correlations at the parton production stage and obtaineddue to the transverse expansion? - Charge dependent and charge independent correlations.

- Correlation of conserved charges (Balance Functions). In this case the correlationsexisted already at the production moment would be modified (narrowed) by radial flow.

- Charge independent correlations: particles at large rapidities, initially uncorrelated, become correlated, as all of them are pushed by radial flow in the same direction.

Charge Balance function

ymymp ttz )sinh(

As <mt> increases due to the transverseradial flow, the balance function gets narrower.

For the BW parameters used above,<mt> indeed increases for about 15-20%,but the centrality dependence is somewhat different from what is observed in the narrowing of the Balance Function.



Initial and freeze-out configurations

Finalinitial

Uncertainty: particles are at the same positionat the moment of production, but the blastwave parameterization is done at freeze-out

Smearing would depend on the - thermalization time (which is supposedly small)- diffusion during the system evolution before freeze-out- non-zero “expansion velocity” in pp

Should we take it as a possibility to study all the above effects?



AA collision. “Single jet tomography”.

The plot on the right shows particle azimuthaldistribution (integrated over all pt’s) with respect to the boost direction.In order to compare with data it should be also convoluted with jet azimuthal distribution relativeto radial direction.

In this picture, the transverse momentum of the (same side, large ) associated particles would be a measure of the space position the hard scattering occurred

AA collision



Sensitivity to the velocity profilen

t r

Results for n=0.5 and n=2 are shown

Mean pt is almost insensitive to the actualvelocity profile.The correlations are.

In general, mean pt is sensitive to the first momentof the respective transverse rapidity distribution while the two particle correlation are measuring the second moment.

)44/()2( 222 nntt



Parity violation study via 3-particle correlations

sin21 ad

dN

a > 0 preferential emission along the angular momentumThe sign can vary event by event, a~Q/N, where Q is the topological charge, |Q|=1,2,…at dN/dy~100, |a|~1%.

And using only one particle instead of the event flow vector

projections onto reaction plane Projections on the direction of angular momentum

)22cos()()2cos(

)sin()sin()cos()cos(

2,1,12

2222

RPbababa

baba

aavv

note that for a rapidity region symmetric with respect to the midrapidity v1=0

hep-ph/0406311

All effects non sensitive to the RPcancel out!

Possible systematics:clusters that flow

cbabacba

cbcacbca

vaavv ,2,1,1 )()2cos(

)sin()sin()cos()cos(

L

Looking for the effect ofD. Kharzeev, hep-ph/0406125



Ebye and inclusive approaches

i

itt pM

p ,

1k

kt

evt p

Np 1

.ppδp tt,it,i ;δpδp jijt,it,

kk

k iit

ttt,it,i M

ppppδp

,

;

),,,(

)],(),(),,,([

),,,(

),,,(

22,11,22,21,1

22,111,122,11,22,1,2,21,1

22,11,22,21,1

22,11,22,1,2,21,1

2,1,

21

21

21

21

tttt

tttttttt

tttt

tttttt

tt

ppdpddpd

ppppppdpddpd

ppdpddpd

ppppdpddpd

pp

Most of the present measurementsare done this way

Would be better, easier to analyze theoretically.

(! Numerically both are very close)

)2,1(C

s.a. voloshin 2 nd int. workshop on the critical point and onset of deconfinement, bergen, 2005page1...

Documents

flow wiggle

hydro flow

critical point

onset of deconfinement

flowelliptic flow term

2005page1 anisotropic

softest point

cascade models z x radial