Marcus Bleicher, ETD, Montreal 07/2007 Elliptic Flow and Fluctuations in Heavy Ion collisions Marcus...

Marcus Bleicher, ETD, Montreal 07/2007

Elliptic Flow and Fluctuations in Heavy Ion collisions

Elliptic Flow and Fluctuations in Heavy Ion collisions

Marcus Bleicher

Institut für Theoretische Physik

Goethe Universität - Frankfurt

Germany


Thanks to the UrQMD group@ Frankfurt

Thanks to the UrQMD group@ Frankfurt

• Sascha Vogel (Resonances and di-leptons)

• Katharina Schmidt (Di-leptons)

• Stephane Haussler (Event-by-Event Fluctuations)

• Hannah Petersen (Flow)

• Daniel Krieg (Recombination)

• Qingfeng Li (HBT)

• Xianglei Zhu (Charm)


ContentsContents

• Introduction

• v1 and v2

• v2 fluctuations

• Summary


MotivationMotivation

At RHIC: look for signals of partonic matter. (large v2, hydro)

At critRHIC/SPS:look for the mixed phase and the onset of deconfinement(flow stalls, large fluctuations, ideal hydro breaks down)

E. Bratkovskaya, M.B. et al., PRC 2005


The tool: UrQMDv2.2The tool: UrQMDv2.2

• Non-equilibrium transport model• Hadrons and resonances• String excitation and fragmentation• Cross sections are parameterized

via AQM or calculated by detailed balance• pQCD hard scattering at high energies

• Generates full space-time dynamics of hadrons and strings


MultiplicitiesMultiplicities

Comparison to data over the whole energy range

E. Bratkovskaya, M.B. et al., PRC 2005


Droplets: > 10-100 (Mishustin)

Taken from a talk by B. Lungwitz at CPOD 2007

UrQMD data from Lungwitz& Bleicher, arXiv:0707.1788


Maybe HBT can deliver…Maybe HBT can deliver…

• long life times in the mixed phase…

Rischke, Gyulassy, Nucl.Phys.A608:479-512,1996

~ Energy density

10 fold increase in life time during the mixed phase


The HBT puzzle? The HBT puzzle?

• Model calculations of RO/RS or (RO2-RS

2)1/2 are usually larger than the experimental data

Duration time (in the absence of flow):

2

22 )(

SO RR

No indication of long life time in the data

1 10 100 1000 100000

2

4

6

8

(R2 O-R

2 S)1/

2 (fm

)

Eb (A GeV)

Circles: kT=100 MeV/c

Squares: kT=200 MeV/c

Stars: exp. data

Li, Bleicher, Stoecker, arXiv:0706.2091. JPG in press


Flow is important!Flow is important!

• Many observables never fullfilled the promise HBT, fluctuations, J/Psi,… ideally one should be able to study them at all energies

Transverse collective flow is intimately connected to pressure

Flow is sensitive to changes in the equation of state and therefore to phase transitions (H.Stöcker,W.Greiner Phys.Rep. 137 (1986) 277)


Introduction - directed flowIntroduction - directed flowFourier expansion of the azimuthal distribution of the emitted particles :

t

x

p

pv 1

1

cos212

1

iRi

tttt

ivdydpp

dN

dyddpp

dN

Directed flow

measures the total amount of transverse flow

22yxt ppp with

Reaction planeReaction plane

(J.Y. Ollitrault, Phys. Rev. D, 46; A.M. Poskanzer, S.A. Voloshin, Phys. Rev.

C, 58)


Excitation function Excitation function

1-fluid hydro prediction for pxdir :

softest point in the EoS leads to decreasing flow

from D.Rischke, Y.Pürsün et al. (Heavy Ion Physics 1,309,1995)


Antiflow around midrapidityAntiflow around midrapidity

(L.Csernai, Phys.Lett. B 458, 1999)

(J.Brachmann et al., Phys.Rev. C, 61, 2000)

Prediction of antiflow if QGP is produced softening of the EoS leads to flow in the „wrong“ direction


A problem with hydroA problem with hydro

• Hydro is not a good tool to study the onset of deconfinement

• Agreement at top RHIC energies with ‘wrong’ EoS and ‘wrong’ initial c.(see talk by Dumitru)

try transportHeinz, Kolb,STAR


v1 of protons @ 40 AGeVv1 of protons @ 40 AGeV

Comparison of rapidity spectra between model and data:

Largest flow at high rapidity values

Centrality dependence visible

Data

fro

m C

.Alt

et

al.,

Ph

ys.

Rev.

C 6

8,

200

3

Petersen et al, Phys.Rev.C74:064908,2006


v1 of protonsv1 of protons

Slope around midrapidity characterizes shape of the rapidity distribution

Extracted from normalized rapidity distribution via polynomial fit

At low energies: potentials are important

At high energies: data developes negative slope ´wiggle´

QGP-signal? (L.P. Csernai, Phys.Lett. B 458,1999)



Time evolutionTime evolutionPressure Pressure gradients Elliptic flow



Time evolution at RHICTime evolution at RHIC

Elliptic flow builds up in the hadronic stage of the collision

High-pt

Low-pt

Y.

Lu e

t al

, J.

Ph

ys.G

32:1

121-

1130

,200

6


v2 (y) of pions @ 40/160 AGeVv2 (y) of pions @ 40/160 AGeV

Pb+PbPet

erse

n et

al,

Ph

ys.R

ev.C

74:0

6490

8,20

06


v2(y) of protons @40 AGeVv2(y) of protons @40 AGeV

Collapse of elliptic flow?(H.Stöcker, Nucl.Phys. A 750, 2005)

Experimental situation unclear

Transport model calculation is compatible with the data



Energy dependenceEnergy dependence

• Qualitative description OK

• Importance of potentials at low energies

• Lack of pressure shows up at lower SPS energies

Pet

erse

n et

al,

Ph

ys.R

ev.C

74:0

6490

8,20

06


v2 fluctuationsv2 fluctuations

• Tilted axis has to be taken into account with proper (participant) definition of eccentricity

Broniowski et al


Additional fluctuationsAdditional fluctuations

• One would expect additional dynamical fluctuations, if the system is not a perfect liquid

• Degree of perfection is quantified by the Knudsen number Kn

S. Vogel et al., nucl-th/0703031


Fluctuation analysisFluctuation analysis

• To strong fluctuations

• Cross section increase, decreases fluctuations



Extrapolation to small Knudsen numbers

Extrapolation to small Knudsen numbers

• Experimental data requires tiny mean free path

• 1/Kn > 100-1000

Bhalerao, PLB2005



Only ideal hydro can do itOnly ideal hydro can do it

• Calculation by Kodama et al.,

• Fluctuating initial state from Nexus

• Where is viscosity?


SummarySummary

Flow is the ideal tool to study the onset of deconfinement (critRHIC!)

However, ideal hydro fails below top RHIC energy

Unfortunately, hadron/string transport fails above SPS energies

At top RHIC energy: Elliptic flow fluctuations indicate very short mean free path

No sign of ANY turbulence or dynamical fluctuations

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Marcus Bleicher, ETD, Montreal 07/2007 Elliptic Flow and Fluctuations in Heavy Ion collisions Marcus...

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