Dynamical equilibration of strongly-interacting ‘infinite’

parton matterVitalii Ozvenchuk,

in collaboration with

E.Bratkovskaya, O.Linnyk, M.Gorenstein, W.CassingNeD Symposium, 26 June 2012

Hersonissos, Crete, Greece

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

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

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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 quark chemical potential and energy density the size of the box is fixed to 93 fm3

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Initialization

light(u,d) and strange quarks, antiquarks and gluons

ratios between the different quark flavors are e.g.

random space positions of partons

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Initial momentum distributions and abundancies

the initial momentum distributions and abundancies of partons are givenby a ‘thermal’ distribution:

where - spectral function

- Bose and Fermi distributions

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

initial number of partons is given

initial parameters: , which define the total energy 7

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Elastic cross sections

cross sections at high energy density are in the order of 2-3 mb but become large close to the critical energy density

Partonic interactions in PHSD

Inelastic channels

Breit-Wigner cross section

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Detailed balance

The reactions rates are practically constant and obey detailed balance for

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

dynamically reach their equilibrium values through the inelastic collisions

gluon splitting quark + antiquark fusion

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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

Chemical equilibration of strange partons

the slow increase of the total number of strange quarks and antiquarks reflects long equilibration time through inelastic processes involving strange partons

the initial rate for is suppressed by a factor of 9

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Dynamical phase transition & different intializations

the transition from partonic to hadronic degrees-of-freedom is complete after about 9 fm/c

a small non-vanishing fraction of partons – local fluctuations of energy density from cell to cell

the equilibrium values of the parton numbers do not depend on the initial flavor ratios

our calculations are stable with respect to the different initializations

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Thermal equilibration

DQPM predictions can be evaluated:

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Spectral function

the dynamical spectral function is well described by the DQPM form in the fermionic sector for time-like partons

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Deviation in the gluonic sector

the inelastic collisions are more important at higher parton energies

the elastic scattering rate of gluons is lower than that of quarks

the inelastic interaction of partons generates a mass-dependent width for the gluon spectral function in contrast to the DQPM assumption of the constant width

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Equation of state

the equation of state implemented in PHSD is well in agreement with the DQPM and the lQCD results and includes the potential energy density from the DQPMlQCD data from S. Borsanyi et al., JHEP 1009, 073 (2010); JHEP 1011, 077 (2010)

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scaled variance:

the scaled variances reach a plateau in time for all observables

due to the initially lower abundance of strange quarks the respective scaled variance is initially larger

Scaled variance ω

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Scaled variance ω

scaled variance:

the scaled variances reach a plateau in time for all observables

due to the initially lower abundance of strange quarks the respective scaled variance is initially larger

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Fractions of the total energy

a larger energy fraction is stored in all charged particles than in gluons

the difference decreases with the energy due to the higher relative fraction of gluon energy

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Cell dependence of scaled variance ω

the impact of total energy conservation in the box volume V is relaxed in the sub-volume Vn.

for all scaled variances for large number of cells due to the fluctuations of the energy in the sub-volume Vn.

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Shear viscosity

The Kubo formula for the shear viscosity is

The expression for the shear tensor is

The shear tensor in PHSD can be calculated:

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Shear viscosity to entropy density

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Summary

Partonic systems at energy densities, which are above the critical energy density achieve kinetic and chemical equilibrium in time

For For all observables all observables the equilibration time is found to be the equilibration time is found to be shortershorter for the scaled variances than for the average values for the scaled variances than for the average values

The The scaled variances scaled variances for the fluctuations in the number of for the fluctuations in the number of different partons in the box show an different partons in the box show an influenceinfluence of the total of the total energy conservationenergy conservation

The scaled variances for The scaled variances for all observablesall observables approach the approach the Poissonian limit Poissonian limit when the cell volume is when the cell volume is much smaller much smaller than that than that of the boxof the box

The procedure of The procedure of extractingextracting of the shear viscosity from the of the shear viscosity from the microscopic simulations as well as the microscopic simulations as well as the ratioratio of the shear of the shear viscosity to the entropy density are presentedviscosity to the entropy density are presented

Back up

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Equilibration times

fit the explicit time dependence of the abundances and scaled variances ω by

for all particles species and energy densities, the equilibration time is shorter for the scaled variance than for the average values

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 26

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) 21527

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

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Finite quark chemical potentials

the phase transition happens at the same critical energy εc for all μq

in the present version the DQPM and PHSD treat the quark-hadron transition as a smooth crossover at all μq

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Finite quark chemical potentials

the phase transition happens at the same critical energy εc for all μq

in the present version the DQPM and PHSD treat the quark-hadron transition as a smooth crossover at all μq