QM2009 summary: Soft physics: Flow and hydrodynamics

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QM2009 summary: Soft physics:

Flow and hydrodynamics

A. Marin (GSI)

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OUTLINE

• HBT• Flow• Hydrodynamics

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HBT PUZZLE (S. Pratt)

RHIC HBT PUZZLE: flow & spectra OK HBT radii NOT OK ideal hydro (no viscosity)1st order phase transition 0 =1.0 fm/c

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HBT PUZZLE (S. Pratt)

Solution:Early acceleration (t < 1 fm/c)Shear viscosityEoS (crossover)Initial energy profile

Fixing HBT requires increasing explosivityBulk viscosity decreases radial flowEarly flow increases elliptic flowviscosity decreases elliptic flow

S. Pratt, arXiv:0812.4714v1

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Effect of Eccentricity Effect of Eccentricity FluctuationsFluctuationsand Nonflowand Nonflow

on Elliptic Flow Methods on Elliptic Flow MethodsJean-Yves Ollitrault, Art Poskanzer, and Sergei Voloshin

QM09

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Reaction, Participant, and Event Planes

participant plane

coordinate space

momentum space

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Methods“Two-particle”:• v2{2}: each particle with every other particle• v2{subEP}: each particle with the EP of the other subevent• v2{EP} “standard”: each particle with the EP of all the others• v2{SP}: same, weighted with the length of the Q vectorMany-particle:• v2{4}: 4-particle - 2 * (2-particle)2

• v2{q}: distribution of the length of the Q vector• v2{LYZ}: Lee-Yang Zeros multi-particle correlation

review of azimuthal anisotropy:arXiv: 0809.2949

STAR, J. Adams et al., PRC 72, 014904 (2005)

2-part. methods

multi-part. methods

"Because of nonflow and fluctuations the true v2 lies between the lower band and the mean of the two bands.”

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Differences of Measured v2 Values

All differences proportional to

Without additional assumptionscan not separate nonflow and fluctuations

nonflowfluctuations

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Data Corrected to <v2>

published

agreement for mean v2 in participant plane

corrected to PP

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corrected to RP

v2 in the Reaction Plane

in Gaussian fluctuation approximation:

Voloshin, Poskanzer, Tang, and Wang, Phys. Lett. B 659, 537 (2008)

a v2 for theorists

11QM2009, Knoxville, March 30 - April 4 Patricia Fachini 11

Patricia Fachini

for the STAR collaboration

Motivation

Measurements

Results

Conclusions

ρ0 Production in Cu+Cu Collisions at √sNN = 200 and 62.4 GeV in STAR

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• Significant ρ0 v2 measured pT > 1.2 GeV/c v2 ~ 13 ± 4%.

Elliptic Flow

12QM2009, Knoxville, March 30 - April 4 Patricia Fachini

13QM2009, Knoxville, March 30 - April 4 Patricia Fachini 13

Elliptic Flow

• Resonance v2 ρ0(770) production mechanism scale NCQ v2/nππ ρ0 n = 4 or qq ρ0 n = 2

a, b, c, and d constants extracted using KS0 and Λ v2 ρ0 v2 n= 4.7 ± 2.9

pT range covered not sufficient for conclusive statement on the ρ0 production mechanism.

v2(pT,n) = - dn1 + exp[-(pT/n – b)/c]

anX. Dong et al., Phys.Lett. B597 (2004) 328

n=2 n=4

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Differential Measurements of Differential Measurements of Hexadecapole (VHexadecapole (V44) and Elliptic ) and Elliptic

( V( V22) Flow as a Probe for ) Flow as a Probe for

Thermalization at RHIC-Thermalization at RHIC-PHENIXPHENIX

Arkadij TaranenkoArkadij TaranenkoNuclear Chemistry Group Nuclear Chemistry Group

Stony Brook UniversityStony Brook University

for the PHENIX Collaboration

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23/4/2123/4/21 Arkadij Taranenko, QM2009Arkadij Taranenko, QM20091515

KEKETT and CQN Scaling for v and CQN Scaling for v44KEKETT and CQN Scaling for v and CQN Scaling for v44

V4/(nq)2 vs KET /nq scaling observed for V4

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VV44 = k(V = k(V22))2 2 where k is the same for different particle species where k is the same for different particle species

vv44/(v/(v22))22 ratio for different particle species ratio for different particle speciesvv44/(v/(v22))22 ratio for different particle species ratio for different particle species

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23/4/2123/4/21 Arkadij Taranenko, QM2009Arkadij Taranenko, QM20091717

Baryon and meson V2 & V4 scale to a universal curve

as a function of (KET)/nq

PHENIXPreliminary

Flow is universal?Flow is universal?Flow is universal?Flow is universal?

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PHENIX Preliminary

Good fits to the vGood fits to the v2 2 & v& v4 4 of charged hadrons of charged hadrons Good fits to the vGood fits to the v2 2 & v& v4 4 of charged hadrons of charged hadrons

Model ansatz extended from v2 to v4. Good fits obtained both for scaled v2 and v4 . What about fits for PID?

2

4 42 2

0

1hd

nv v K

K

npart

KN

1

0

2 1

K

Kvv nhd

2

Two fit parameters: v2

hd and ( is fixed)

24 2v v →

ε – participant eccentricity from Glauber Model

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Event Anisotropy v2 at STARParticle type, Beam energy and Centrality dependence

ShuSu Shi for the STAR collaboration

Nuclear Science Division, Lawrence Berkeley National LaboratoryInstitute of Particle Physics, Central China Normal University

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Test Hydro in Small System

Ideal hydro: P. Huovinen, private communication

pT < 2 GeV/c Smaller v2 for heavier

hadrons as expected from hydrodynamics.

Sizable v2(Ξ) even in small system

Ideal hydro fails to reproduce the data

Fluctuation of v2? Viscosity ? Incomplete thermalization ?

STAR preliminary

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v2 in Cu + Cu (Au +Au) at 200 and 62.4 GeV are comparable within statistical errors

v2 at Cu + Cu 62.4 GeV ~ 12.5 M events- Same procedure used for 200 GeV. - Event plane resolution is 0.088 0.004 in 0 - 60 %, about factor 2 smaller than that in 200 GeV due to lower multiplicity.

STAR Au + Au 200 GeV : PRC77, 054901 (2008) Au + Au 62.4 GeV : PRC75, 054906 (2007)

Energy Dependence

STAR preliminary

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STAR preliminary

Au + Au at 200 GeV

Au + Au : PRC77, 054901 (2008)

System Size Dependence

Does v2 in most central reach ideal hydrodynamic limit ?

v2 scaled by eccentricity Remove the initial

geometry effect

v2 seems solely depending on initial geometry and number of participant in 200 GeV collisions

v2 ∝ v2(ε, Npart)

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STAR preliminary

v2/ε scaling: S. Voloshin (for STAR Collaboration), J.Phys.G34(2007)S883PHENIX π, K and p: nucl-ex/0604011v1CGC eccentricity: H.J. Drescher and Y. Nara, PRC 76 041903 (2007), H.J. Drescher and Y.Nara, PRC 75 034905 (2007)

Ideal Hydro Limit

STAR preliminary

Hydro limit

ΞΛ p K h

STAR preliminary

Ideal Hydro Limit Even in central Au + Au collisions, fitting results indicate

that the system is still away from hydro limit

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Effectiveη/s Extracted from Model

Caveats:Transport model motivated~ best for dilute system of massless particles no phase transition

STAR preliminary

Data shows particle type dependence, not a built-in feature in the modelCan viscous hydrodynamics explain the particle type dependence ?

Inferred η/s depends strongly on the eccentricity model

T: π spectra slope 200 MeVR: Glauber or CGC calculation

H. J. Drescher et al, PRC 76 024905 (2007)

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The World Collection of η/s STAR preliminary

See M. Sharma ’s talk for pT correlation

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Viscous hydrodynamics

Quark Matter 2009

Huichao Song and Ulrich Heinz

The Ohio State University

Supported by DOE

04/02/2009

March 30-April 4, Knoxville, TN

with shear and bulk viscosity

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Luzum & Romatschke, PRC 2008 Glauber CGC

-Glauber vs.CGC ~100% effect on the extracted value of

-A detailed extraction of shear viscosity entropy ratio also requires:

)41(/ s

s/

-viscous late hadronic stage -non-equilibrium chemistry in HG has been studied in ideal hydro

-bulk viscosity ? -Present conservative upper limit:

5

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shear viscosity bulk viscosity

Viscous hydro with shear & bulk viscosity

(2nd order shear-bulk -mixing term (Muronga, Rischke) not included.)

0)( xT

Conservation laws:

gpuupeT )()(

u

T

T

2

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Evolution equations for shear pressure tensor and bulk presurre:

u

T

Tu

2

1)(

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Shear viscosity vs. bulk viscosity (I)

-Shear viscosity: decelerate cooling process in early stage accelerate cooling process in middle and late stages

-Bulk viscosity: decelerate cooling process

Same initial & final conditionsideal hydro viscous hydro-shear only viscous hydro-bulk only

Local temperature

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Shear viscosity vs. bulk viscosity (II)

-shear viscosity: increases radial flow, results in flatter spectra

-bulk viscosity: decreases radial flow, results in steeper spectra

radial flow spectra

Same Initial & final conditionsideal hydro viscous hydro-shear only viscous hydro-bulk only

0,4/1 c1,0 c

0,0 css //

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Viscous v2 suppression: shear and bulk viscosity ideal hydro visc. hydro:

-at RHIC, 2 x min. bulk viscosity could result in ~50% additional v2 suppression

-when extracting the from RHIC data, bulk viscous effects cannot be neglected s/

20%30%

ss //

1,4/1 c0,4/1 c

2,4/1 c

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Viscous v2 suppression: shear and bulk viscosity ideal hydro visc. hydro:

-at RHIC, 2 x min. bulk viscosity could result in ~50% additional v2 suppression

-when extracting the from RHIC data, bulk viscous effects cannot be neglected s/

20%30%

ss //

1,4/1 c0,4/1 c

2,4/1 c

0

)0( bulk viscosity effects:

(a) Change the flow profile during hydro evolution (b) Additional spectra correction along freeze-out surfacef

Song & Heinz: v2 will decrease, flow corrections only (a), , at freeze-out Monnai & Hirano: v2 will increase, spectra corrections only(b), ideal hydro for evolution

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Effects from initialization of (III)

-viscous effects from bulk viscosity strongly depend on relaxation time and the initialization for bulk pressure

Smaller vs. larger relaxation time

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A Short Summary

-When extracting QGP viscosity from experimental data, bulk viscosity effects should not be neglected

-first attempts to constrain from RHIC data indicate )41(5/ s

a realistic EOS, initialization, bulk viscosity, highly viscous hadronic stage

s/

-More theoretical inputs are needed for bulk viscosity:

No consistent simultaneous treatment yet of:

- relaxation time- initialization for bulk pressure - bulk viscosity of hadronic phase, etc

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Effects of Bulk Viscosity on pT-Spectra and Elliptic Flow Parameter

Akihiko MonnaiDepartment of Physics, The University of Tokyo, JapanCollaborator: Tetsufumi Hirano

Quark Matter 2009March 30th- April 4th, 2009, Knoxville, TN, U.S.A. arXiv:0903.4436 [nucl-th]

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Introduction (II)

Hydrodynamic analyses needs the Cooper-Frye formula at freezeout

(i) for comparison with experimental data,

(ii) as an interface to a cascade model.

Viscous corrections come in two ways:

(3+1)-D viscous hydro required. We estimate this for a multi-component gas.

Cooper & Frye (‘74)

Quark Matter 2009, Knoxville, Tennessee, April 2Quark Matter 2009, Knoxville, Tennessee, April 2ndnd 2009 2009Effects of Bulk Viscosity on Effects of Bulk Viscosity on ppTT-spectra and Elliptic Flow Parameter-spectra and Elliptic Flow Parameter

Introduction (II)Introduction (II)Introduction (I)Introduction (I) Relativistic Kinetic Theory Relativistic Kinetic Theory

variation of the flow modification of the distribution

* :normal vector to the freezeout hypersurface element,

:distribution of the ith particle, :degeneracy.

particles

hadronresonancegas

QGP

freezeout hypersurface Σ

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pT-Spectra

Au+Au, , b = 7.2(fm), pT -spectra of

Model of the bulk pressure:

: free parameter

The bulk viscosity lowers <pT> of the particle spectra.

Elliptic Flow Coefficient Elliptic Flow Coefficient vv22((ppTT))ppTT-Spectra-Spectra


EoS, Transport Coefficients and FlowEoS, Transport Coefficients and Flow

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Elliptic Flow Coefficient v2(pT)

Au+Au, , b = 7.2(fm), v2(pT) of

The bulk viscosity enhances v2(pT).

*Viscous effects might be overestimated for:

(1) No relaxation for is from the Navier-Stokes limit.

(2) Derivatives of are larger than those of real viscous flow

Results with Quadratic AnsatzResults with Quadratic Ansatz


ppTT-Spectra-Spectra Elliptic Flow Coefficient Elliptic Flow Coefficient vv22((ppTT))

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A Transport Calculation with an Embedded (3+1)d Hydrodynamic Evolution:

Elliptic Flow Results from Elab=2-160 AGeVQuark Matter 2009,

31.03.09, Knoxville, Tennessee

Hannah Petersen, Universität FrankfurtThanks to: Jan Steinheimer, Michael Mitrovski, Gerhard Burau, Qingfeng Li, Gunnar Gräf, Marcus Bleicher, Horst Stöcker, Dirk Rischke

(H.P. et al., PRC 78:044901, 2008, arXiv: 0806.1695)(H.P. et al., arXiv: 0901.3821, PRC in print)

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Initial State• Contracted nuclei have passed

through each other

– Energy is deposited– Baryon currents have

separated • Energy-, momentum- and baryon

number densities are mapped onto the hydro grid

• Event-by-event fluctuations are taken into account

• Spectators are propagated separately in the cascade

(J.Steinheimer et al., PRC 77,034901,2008)

(nucl-th

/0607018

, nucl-th

/05110

21)

Elab=40 AGeV b=0 fm

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(3+1)d Hydrodynamic EvolutionIdeal relativistic one fluid dynamics employing:

– HG: Hadron gas including the same degrees of freedom as in UrQMD (all hadrons with masses up to 2.2 GeV)

– CH: Chiral EoS from SU(3) hadronic Lagrangian with first order transition and critical endpoint

– BM: Bag Model EoS with a strong first order phase transition between QGP and hadronic phase

D. Rischke et al., NPA 595, 346, 1995,

D. Rischke et al., NPA 595, 383, 1995

Papazoglou et al., PRC 59, 411, 1999

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Freeze-out 1) Transition from hydro to

transport when < 730 MeV/fm³ (≈ 5 *

0) in all cells of one transverse slice (Gradual freeze-out, GF) iso-eigentime criterion

2) Transition when < 5* 0 in all cells(Isochronuous freeze-out, IF)

• Particle distributions are generated according to the Cooper-Frye formula

with boosted Fermi or Bose distributions f(x,p) including mB and mS

• Rescatterings and final decays calculated via hadronic cascade (UrQMD)

Chemical FO by Cleymans et al.

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Initial State for Non-Central CollisionsPb+Pb at Elab=40 AGeV with b= 7fm at tstart=2.83 fm

Energy density profile Weighted velocity profile

Event-by-event fluctuations are taken into account (H.P. et.al., arXiv:0901.3821, PRC in print)

GeV/fm3

GeV/fm3

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Elliptic Flow

• Smaller mean free path in the hot and dense phase leads to higher elliptic flow

• At lower energies: hybrid approach reproduces the pure UrQMD result

• Gradual freeze-out leads to a better description of the data (H.P. et.al., arXiv:0901.3821, PRC in

print)Data from E895, E877, NA49, Ceres, Phenix, Phobos, Star

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v2/ Scaling

• More realistic initial conditions and freeze-out

Qualitative behaviour nicely reproduced

• Uncertainty due to eccentricity calculation

• Uniqueness of the hydro limit is questioned

(H.P. et.al., arXiv:0901.3821, PRC in print)

Data and hydro limits from NA49 collaboration, PRC 68, 034903, 2003

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Eccentricity fluctuation of initial conditions in hydrodynamics

Tetsufumi HiranoDepartment of Physics

Graduate School of ScienceThe University of Tokyo

Quark Matter 2009Quark Matter 2009

Collaborator: Yasushi Nara (Akita Intl. Univ.)Collaborator: Yasushi Nara (Akita Intl. Univ.)

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Eccentricity Fluctuation

Interaction points of participants vary event by Interaction points of participants vary event by event.event. Apparent reaction plane also varies.Apparent reaction plane also varies. The effect is significant for smaller system such The effect is significant for smaller system such as Cu+Cu collisionsas Cu+Cu collisions

Adopted from D.Hofman(PHOBOS),Adopted from D.Hofman(PHOBOS),talk at QM2006talk at QM2006

A sample eventA sample eventfrom Monte Carlofrom Monte CarloGlauber modelGlauber model

i

0

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Initial Condition with an Effect of Eccentricity Fluctuation

Rotate eachRotate each ii

to to truetrue

Throw a diceThrow a diceto choose to choose bb::bbminmin<<bb<<bbmaxmax

averageaverageover eventsover events

averageaverageover eventsover events

E.g.)E.g.)bbminmin= 0.0fm= 0.0fmbbmaxmax= 3.3fm= 3.3fmin Au+Au collisionsin Au+Au collisionsat 0-5% centralityat 0-5% centrality

With fluctuation effectsWith fluctuation effects

Without fluctuation effectsWithout fluctuation effects

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Inputs in Model Calculations

Parameters are fixed in Au+Au collisionsParameters are fixed in Au+Au collisions

Glauber: Glauber:

KLN: standard parametersKLN: standard parameters

KLN: Kharzeev-Levin-Nardi model

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Eccentricity with Fluctuation Effects

Au+AuAu+Au Cu+CuCu+Cu

Large fluctuation in small system such as Large fluctuation in small system such as Cu+Cu and peripheral Au+AuCu+Cu and peripheral Au+Au

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Centrality Dependence (Glauber)


Large fluctuation effects in Cu+Cu collisionsLarge fluctuation effects in Cu+Cu collisionsCu+Cu data also constrain the modelsCu+Cu data also constrain the models

Glauber initialization undershoots data!?Glauber initialization undershoots data!?

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Centrality Dependence (KLN)

Large fluctuation effects again in Cu+Cu collisionsLarge fluctuation effects again in Cu+Cu collisionsReasonable agreement btw. data and MC-KLN!?Reasonable agreement btw. data and MC-KLN!?


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Backup slides

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HBT nomenclature

x

Actual q distributionBackground q distribution==

The source S can be directly recovered with imaging

Make assumptions about the source

adapted from Annu. Rev. Nucl. Part. Sci. 2005. 55:357-402

DetectorDetector

Simplified foridentical particles

oror

Bose-EinsteinEnhancement atLow q

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Include Fluctuations

in absence of fluctuations

for full events, it is more complicated

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PHOBOS+ Equation for Subevents

Eq.

Fluctuations!

I0,1 are modified Bessel functions

resolution parameter

only function of

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Analytic Correction for Fluctuations

method similar to momentum conservation correction:N. Borghini, P.M. Dinh, J.-Y. Ollitrault, A.M. Poskanzer, and S.A. Voloshin,PRC 66, 014901 (2002)

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Analytic Correction for Nonflow

nonflow

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v2 Fluctuations from part Fluctuations

Assume width with same percent width as part:

2D Gaussian fluctuations in reaction plane lead toBessel-Gaussianfluctuations along theparticipant plane axis

is from standard deviation of nucleon MC Glauber of part

Bessel-Gaussian:

Voloshin et al., Phys. Lett. B659, 537 (2008)

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• Assumptions

Application to Data

MC Glauber participant

less nonflow

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Nonflow and Fluctuationswith my assumptions and parameters:

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K0 =0.7 (from transport calculation)cs = speed of sound [fixed] = eccentricityS = transverse nuclear overlap areadN/dy – total multiplicity per unit rapidity

C.Gombeaud and J-Y.Ollitrault; Phys. Rev. C 77, 054904 (2008)

• Hydro description: – Ideal hydro: scale invariance leads to eccentricity scaling v2/ε ~ const– Real (viscous) hydro: Eccentricity scaling is broken and v2/ε !=const

• Transport description (Ollitrault):– Operational Ansatz: The Boltzmann equation reduces to

hydrodynamics when the mean free path is small– v2/ε is a function of the Knudsen number Kn = λ / R : [ R – transverse size of the system and λ is the mean free path ]

1

0

2 1

K

Kvv nhd

2

c

c

dy

dN

SK s

n

1

Kn→0 (ideal hydro limit) : v2/ε ~ constant

Kn>>1 (low density limit) : v2/ε~ v2hd/ (ε Kn / K0 )

6767

C. Marle, Annales Poincare Phys.Theor. 10,67 (1969).

2 free parameters in the fit = effective partonic cross section (4~6mb) v2

hd = hydrodynamic limit

Extraction of transport coefficients

PHOBOS data, s=200 GeVH-J.Drescher, A.Dumitru, C.Gombeaud, J-Y.Ollitrault; Phys. Rev. C 76, 024905 (2007)

6868

H. Song , U. W. Heinz Phys.Rev.C78:024902,2008

Operational test of hydro calculation

npart

KN

1

0

2 1

K

Kvv nhd

2

69

Results with Quadratic Ansatz

pT -spectra and v2(pT) of with

and the same EoS

Results with Quadratic AnsatzResults with Quadratic Ansatz SummarySummary


Effects of the bulk viscosity is underestimated in quadratic ansatz.

Elliptic Flow Coefficient Elliptic Flow Coefficient vv22((ppTT))

70

Summary & Outlook

Consistent determination of for a multi-particle system

A non-zero trace tensor term is needed for the hadron resonance gas up to the mass of

Visible effects of on particle spectra

Bulk viscosity should be considered to constrain the transport coefficients with better accuracy from experimental data.

A (3+1)-dimensional viscous hydrodynamic flow is necessary to see more realistic behavior of the particle spectra.

SummarySummaryResults with Quadratic AnsatzResults with Quadratic Ansatz


pT-spectra : suppressed

v2(pT) : enhancedwhen estimated with an ideal hydrodynamic flow.

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Hybrid Approaches• Hadronic freezeout following a first order hadronization phase transition in

ultrarelativistic heavy ion collisions.S.A. Bass, A. Dumitru, M. Bleicher, L. Bravina, E. Zabrodin, H. Stoecker, W. Greiner, Phys.Rev.C60:021902,1999

• Dynamics of hot bulk QCD matter: From the quark gluon plasma to hadronic freezeout. S.A. Bass, A. Dumitru, Phys.Rev.C61:064909,2000

• Flow at the SPS and RHIC as a quark gluon plasma signature.D. Teaney, J. Lauret, Edward V. Shuryak, Phys.Rev.Lett.86:4783-4786,2001

• A Hydrodynamic description of heavy ion collisions at the SPS and RHIC.D. Teaney, J. Lauret, E.V. Shuryak, e-Print: nucl-th/0110037

• Hadronic dissipative effects on elliptic flow in ultrarelativistic heavy-ion collisions.T. Hirano, U. Heinz, D. Kharzeev, R. Lacey, Y. Nara, Phys.Lett.B636:299-304,2006

• 3-D hydro + cascade model at RHIC.C. Nonaka, S.A. Bass, Nucl.Phys.A774:873-876,2006

• Results On Transverse Mass Spectra Obtained With NexspherioF. Grassi, T. Kodama, Y. Hama, J.Phys.G31:S1041-S1044,2005

• See also recent work of K. Werner

72

Introduction

• Fix the initial state and freeze-out

learn something about the EoS and the effect of viscous dynamics

1) Non-equilibrium

initial conditions

via UrQMD

2) Hydrodynamic evolution or Transport calculation

3) Freeze-out via

hadronic cascade

(UrQMD) UrQMD-2.3 is available at www.th.physik.uni-frankfurt.de/~urqmd

73

Transverse Momentum Dependence

Hydro phase leads to higher flow values, but weak EoS dependence

NA49

(NA

49,

PR

C 6

8,

034903,

200

3)

Protons Pions

74

Conclusions• Integrated approach with the same initial conditions and

freeze-out for different EoS• Particle multiplicities and spectra are reasonably reproduced,

strangeness enhanced• Transverse momentum spectra indicate importance of non-

equilibrium effects• Phase transition is visible in HBT radii, but long fireball

lifetime so far not supported by the existing data• Flow results depend crucially on initial conditions and

freeze-outSee also • Poster 927 by Jan Steinheimer about new chiral EoS including

deconfinement phase transition • Poster 403 by Björn Bäuchle about direct photons

75

Comment on Monte Carlo Approach

How do we consider this?How do we consider this?

Naïve Glauber calculation: Naïve Glauber calculation:

MC-Glauber calculation: MC-Glauber calculation:

Finite Finite nucleonnucleonprofileprofile

76

Comment on Monte Carlo Approach (contd.)

Reduction of eccentricity by ~5-10%Reduction of eccentricity by ~5-10% Necessity of re-tuning parametersNecessity of re-tuning parameters

in Woods-Saxon densityin Woods-Saxon density We have retuned parameters.We have retuned parameters.

77

Comment on v2/ vs. (1/S)dN/dy

Hydro limitHydro limit= (no viscosity) = (no viscosity)

+ (small freezeout T)+ (small freezeout T) Ideal hydro of QGP Ideal hydro of QGP does NOT give a hydrodoes NOT give a hydro

limit curve due to limit curve due to hadronizationhadronization

and finite life time.and finite life time.

““hydro limit”hydro limit”

Exp. data would reflect life time of the QGP Exp. data would reflect life time of the QGP rather than its viscosity.rather than its viscosity.

78

Summary & Outlook

• Implement of eccentricity fluctuation in hydro initial conditions

• Large fluctuation effects seen in small system• MC-Glauber case

– Undershooting the data!? No room for viscosity?• MC-KLN case

– Reasonable results? Viscosity could play a role?• Realistic EOS, viscosity,…

Documents

QM2009 summary: Soft physics: Flow and hydrodynamics