Dynamical equilibration of strongly-interacting ‘infinite’

parton matterVitalii Ozvenchuk,

in collaboration with

E.Bratkovskaya, O.Linnyk, M.Gorenstein, W.CassingCPOD, Wuhan, China

11 November 2011

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steps with kinetic and chemical equilibrium

phase space configurations far from an equilibrium fast expansion

‘big-bang’ of the universe

laboratory ‘tiny bangs’

local thermodynamic equilibrium

MotivationMotivation

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How and on what timescales a global thermodynamic equilibrium can be achieved in heavy-ion collisions?

Crucial questionCrucial question

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From hadrons to partonsFrom hadrons to partons

In order to study of the In order to study of the phase transitionphase transition from from hadronic to partonic matter – hadronic to partonic matter – Quark-Gluon-PlasmaQuark-Gluon-Plasma – – we we need need a a consistent non-equilibrium (transport) model withconsistent non-equilibrium (transport) model withexplicit explicit parton-parton interactionsparton-parton interactions (i.e. between quarks and (i.e. between quarks and gluons) beyond strings!gluons) beyond strings!explicit explicit phase transitionphase transition from hadronic to partonic degrees of from hadronic to partonic degrees of freedomfreedom lQCD EoS lQCD EoS for partonic phasefor partonic phase

PParton-arton-HHadron-adron-SString-tring-DDynamics ynamics ((PHSDPHSD))

QGP phase QGP phase described bydescribed by

DDynamical ynamical QQuasiuasiPParticle article MModel odel (DQPMDQPM)

Transport theoryTransport theory: off-shell Kadanoff-Baym equations for : off-shell Kadanoff-Baym equations for the Green-functions Sthe Green-functions S<<

hh(x,p) in phase-space (x,p) in phase-space representation for therepresentation for the partonic partonic andand hadronic phase hadronic phase

A. A. Peshier, W. Cassing, PRL 94 (2005) 172301;Peshier, W. Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007)

W. Cassing, E. Bratkovskaya, PRC 78 (2008) W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919;034919;

NPA831 (2009) 215; NPA831 (2009) 215; W. Cassing, W. Cassing, EEPJ ST PJ ST 168168 (2009) (2009) 33

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The Dynamical QuasiParticle Model The Dynamical QuasiParticle Model (DQPM)(DQPM)

Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) 793 (2007)

Quasiparticle properties:Quasiparticle properties: large width and mass for gluons and large width and mass for gluons and quarks quarks

•DQPMDQPM matches well matches well lattice QCDlattice QCD

•DQPMDQPM provides provides mean-fields (1PI) for gluons and quarksmean-fields (1PI) for gluons and quarks as well as as well as effective 2-body interactions (2PI)effective 2-body interactions (2PI)

•DQPMDQPM gives gives transition ratestransition rates for the formation of hadrons for the formation of hadrons PHSDPHSD

Basic idea:Basic idea: Interacting quasiparticles Interacting quasiparticles -- massive quarks and gluonsmassive quarks and gluons (g, q, q(g, q, qbarbar)) with with spectral spectral functions :functions : fit to lattice (lQCD) resultsfit to lattice (lQCD) results (e.g. entropy density)(e.g. entropy density)

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DQPM thermodynamics (NDQPM thermodynamics (Nff=3)=3)

entropy entropy pressure P pressure P

energy energy density:density:

interaction measure:interaction measure:

DQPM gives a good description of lQCD DQPM gives a good description of lQCD results !results !

lQCD:lQCD: Wuppertal-Budapest groupWuppertal-Budapest groupY. Aoki et al., JHEP 0906 (2009) 088.Y. Aoki et al., JHEP 0906 (2009) 088.

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TTCC=160 MeV=160 MeVeeCC=0.5 =0.5 GeV/fmGeV/fm33

PHSD: Transverse mass spectraPHSD: Transverse mass spectra

Central Pb + Pb at SPS energiesCentral Pb + Pb at SPS energies

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PHSD gives PHSD gives harder mharder mTT spectra spectra and works better than HSD and works better than HSD at high at high energiesenergies – – RHIC, SPS (and top FAIR, NICA) RHIC, SPS (and top FAIR, NICA) however, at low SPS (and low FAIR, NICA) energies the effect of the however, at low SPS (and low FAIR, NICA) energies the effect of the partonic phase decreases due to the decrease of the partonic fraction partonic phase decreases due to the decrease of the partonic fraction

Central Au+Au at Central Au+Au at RHICRHIC

W. Cassing & E. Bratkovskaya, NPA 831 (2009) 215W. Cassing & E. Bratkovskaya, NPA 831 (2009) 215E. Bratkovskaya, W. Cassing, V. Konchakovski, O. E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, Linnyk, NPA856 (2011) 162NPA856 (2011) 162 7

Partonic phase at SPS/FAIR/NICA energies

2 3 4 5 6 7 8 9 100.0

0.1

0.2

0.3

0.4 b [fm] 1 3 5 7 9 11 13

part

onic

ene

rgy

frac

tion

Pb+Pb, 158 A GeV

t [fm/c]

partonic energy fraction vs centrality and energypartonic energy fraction vs centrality and energy

Dramatic decrease of partonic phase Dramatic decrease of partonic phase with with decreasing energy and/or centrality ! decreasing energy and/or centrality !

0 3 5 8 10 13 15 18 200.0

0.1

0.2

0.3

0.4

part

onic

ene

rgy

frac

tion

Tkin

[A GeV] 10 20 40 80 160

Pb+Pb, b=1 fm

t [fm/c]

Cassing & Bratkovskaya, NPA 831 (2009) 215Cassing & Bratkovskaya, NPA 831 (2009) 2158

all y

Elliptic flow scaling at Elliptic flow scaling at RHICRHIC

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The scaling of v2 with the number of constituent quarks nq is roughly in line with the data

E. Bratkovskaya, W. Cassing, V. Konchakovski, O. E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, Linnyk, NPA856 (2011) 162NPA856 (2011) 162

PHSD in a boxPHSD in a box

study of the dynamical equilibration of strongly interacting parton matter within the PHSD

Goal

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PHSD in a boxPHSD in a box

study of the dynamical equilibration of strongly interacting parton matter within the PHSD

Goal

Realization

a cubic box with periodic boundary conditions various values for chemical potential and energy density the size of the box is fixed to 93 fm3

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Initialization

light and strange quarks, antiquarks and gluons with random space positions initial number of partons is given

ratios between the different quark flavors are

Four-momenta are distributed according to the distribution by Monte Carlo simulations

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Chemical equilibrium

A sign of chemical equilibrium is the stabilization of the numbers of partons of the different species in time

The final abundancies vary with energy density

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Detailed balance

The reactions rates are practically constant and obey detailed balance for

The elastic collisions lead to the eventual thermalization of all pacticle species (e.g. u, d, s quarks and antiquarks and gluons) The numbers of partons

dynamically reach the equilibrium values through the inelastic collisions

gluon splitting quark + antiquark fusion

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Thermal equilibration

Comparison between PHSD simulation in the box and the DQPM model

DQPM predictions can be evaluated:

Dynamical calculations are in a good agreement with the DQPM model

The system is in a dynamical equilibrium

Summary

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PHSD provides a consistent description of off-shell parton dynamics in line with a lattice QCD equation of state and incorporates dynamical hadronization in line with conservation laws

PHSD gives harder mT spectra and works better than HSD at RHIC and at high SPS energies

The The quark-number scaling of v2 holds fairly well in PHSD at RHIC

PHSD within a box allows to study the dynamical equilibration of strongly interacting parton matter

Back up

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The Dynamical QuasiParticle Model (DQPM)The Dynamical QuasiParticle Model (DQPM)

Basic idea:Basic idea: Interacting quasiparticles Interacting quasiparticles -- massive quarks and gluonsmassive quarks and gluons (g, q, q(g, q, qbarbar)) with with spectral functions :spectral functions :

DQPM: Peshier, Cassing, PRL 94 (2005) 172301;DQPM: Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007)

mass:mass:

width:width:

gluons:gluons:

NNcc = 3, N = 3, Nff=3=3

3 parameters: 3 parameters: TTss/T/Tcc=0.46; c=28.8; =0.46; c=28.8; =2.42=2.42

running coupling:running coupling:SS(T) = g(T) = g22(T)/(4(T)/(4))

fit to lattice (lQCD) results fit to lattice (lQCD) results (e.g. entropy density)(e.g. entropy density)

quasiparticle propertiesquasiparticle properties18

E2 = p2+M2-2

quarksquarks

1 2 3 4 5 6 7 8 9 100.0

0.5

1.0

1.5

2.0

2.5

T/TC

N=8

S(T)

lQCD: lQCD: O. Kaczmarek et,O. Kaczmarek et,PRD 72 (2005) 059903PRD 72 (2005) 059903

NNjj(x,p)(x,p) is the is the phase-space density of partonphase-space density of parton j at space-time position j at space-time position xx and 4-momentum and 4-momentum pp WWmm is the is the phase-space distribution of the formed ‚pre-hadrons‘:phase-space distribution of the formed ‚pre-hadrons‘:

(Gaussian in phase space)(Gaussian in phase space) is the is the effective quark-antiquark interactioneffective quark-antiquark interaction from the DQPM from the DQPM

PHSD: Hadronization detailsPHSD: Hadronization details

Local covariant off-shell transition rate for q+qbar fusion Local covariant off-shell transition rate for q+qbar fusion => => meson formationmeson formation

using

Cassing, Bratkovskaya, PRC 78 (2008) 034919; Cassing, Cassing, Bratkovskaya, PRC 78 (2008) 034919; Cassing, EEPJ ST PJ ST 168168 (2009) (2009) 3319

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PHSD: hadronization of a partonic fireballPHSD: hadronization of a partonic fireball

Consequences:Consequences: Hadronization:Hadronization: q+q q+qbarbar or 3q or 3q or 3q or 3qbarbar fuse to fuse to

color neutral hadrons (or strings)color neutral hadrons (or strings) which which subsequently subsequently decay into hadrons in adecay into hadrons in a microcanonical fashion, i.e.microcanonical fashion, i.e. obeying all conservation laws obeying all conservation laws (i.e. 4-momentum (i.e. 4-momentum conservation, flavor current conservation)conservation, flavor current conservation) in each event!in each event! Hadronization Hadronization yieldsyields an increase in total entropy San increase in total entropy S (i.e. more hadrons in (i.e. more hadrons in the final state than initial partons )the final state than initial partons ) and not a decrease as in the simple and not a decrease as in the simple recombination models!recombination models!

Off-shell parton transportOff-shell parton transport roughly leads a roughly leads a hydrodynamic evolution hydrodynamic evolution of the of the partonic systempartonic system

E.g.E.g. time evolution of thetime evolution of thepartonic fireball partonic fireball at initial temperature at initial temperature 1.7 T1.7 Tcc at at qq=0=0

W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919;W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919;NPA831 (2009) 215; NPA831 (2009) 215;

W. Cassing, W. Cassing, EEPJ ST PJ ST 168168 (2009) (2009) 3320

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Elliptic flow scaling at RHICElliptic flow scaling at RHIC

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The mass splitting at low pT is approximately reproduced as well as the meson-baryon splitting for pT > 2 GeV/c ! The scaling of v2 with the number of constituent quarks nq is roughly in line with the data .

E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, NPA856 (2011) 162NPA856 (2011) 162

Elliptic flow versus centrality in PHSDElliptic flow versus centrality in PHSD

enhancement of v2 due to the partonic interactions

vv22 from PHSD is larger relative to HSD ( from PHSD is larger relative to HSD (in line with the data from PHOBOSin line with the data from PHOBOS) )

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Au+Au at midrapidity |Au+Au at midrapidity || < 1| < 1

E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, NPA856 (2011) 162NPA856 (2011) 162 or or arXiv:1101.5793 [nucl-th]arXiv:1101.5793 [nucl-th]

Anisotropic flows vAnisotropic flows v22, v, v33, v, v44 vs. centrality vs. centrality

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vv33, v, v44 are only are only weakly sensitive to centrality weakly sensitive to centrality (the impact parameter (the impact parameter bb)) vv22 increases strongly with increases strongly with bb up to peripheral collisionsup to peripheral collisions

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Initialization

light and strange quarks, antiquarks and gluons with random space positions initial number of partons is given

ratios between different quark flavors are

initial energy distribution

initial invariant momentum distribution

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