Dynamical equilibration of strongly- interacting ‘infinite’ parton matter Vitalii Ozvenchuk, in collaboration with E.Bratkovskaya, O.Linnyk, M.Gorenstein, W.Cassing NeD Symposium, 26 June 2012 Hersonissos, Crete, Greece 1

From hadrons to partons In order to study of the phase transition from hadronic to partonic matter – Quark-Gluon-Plasma – we need a consistent non-equilibrium (transport) model with  explicit parton-parton interactions (i.e. between quarks and gluons) beyond strings!  explicit phase transition from hadronic to partonic degrees of freedom  lQCD EoS for partonic phase Parton-Hadron-String-Dynamics (PHSD) QGP phase described by Dynamical QuasiParticle Model DQPM Dynamical QuasiParticle Model (DQPM) Transport theory: off-shell Kadanoff-Baym equations for the Green- functions S < h (x,p) in phase-space representation for the partonic and hadronic phase A. Peshier, W. Cassing, PRL 94 (2005) ; A. Peshier, W. Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007) W. Cassing, E. Bratkovskaya, PRC 78 (2008) ; NPA831 (2009) 215; W. Cassing, EPJ ST 168 (2009) 3 2

The Dynamical QuasiParticle Model (DQPM) Peshier, Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Peshier, Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007)  Quasiparticle properties: large width and mass for gluons and quarks large width and mass for gluons and quarks DQPM matches well lattice QCD DQPM matches well lattice QCD DQPM provides mean-fields (1PI) for gluons and quarks DQPM provides mean-fields (1PI) for gluons and quarks as well as effective 2-body interactions (2PI) DQPM gives transition rates for the formation of hadrons  PHSD DQPM gives transition rates for the formation of hadrons  PHSD Basic idea: Interacting quasiparticles - massive quarks and gluons (g, q, q bar ) with spectral functions - massive quarks and gluons (g, q, q bar ) with spectral functions  fit to lattice (lQCD) results (e.g. entropy density) 3

DQPM thermodynamics (N f =3) entropy  pressure P energy density: interaction measure: DQPM gives a good description of lQCD results ! DQPM gives a good description of lQCD results ! lQCD: Wuppertal-Budapest group Y. Aoki et al., JHEP 0906 (2009) 088. T C =160 MeV e C =0.5 GeV/fm 3 4

PHSD 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 9 3 fm 3 5

Initialization  light(u,d) and strange quarks, antiquarks and gluons  ratios between the different quark flavors are e.g.  random space positions of partons 6

Initial momentum distributions and abundancies  the initial momentum distributions and abundancies of partons are given by 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

8 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

9 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              

10 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 11

12 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

13 Thermal equilibration  DQPM predictions can be evaluated:

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

15 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

16 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 DQPM lQCD data from S. Borsanyi et al., JHEP 1009, 073 (2010); JHEP 1011, 077 (2010)

17  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

18 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

19 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

20 Cell dependence of scaled variance ω  the impact of total energy conservation in the box volume V is relaxed in the sub-volume V n.  for all scaled variances for large number of cells due to the fluctuations of the energy in the sub-volume V n.

21 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:

22 Shear viscosity to entropy density

23 Summary  Partonic systems at energy densities, which are above the critical energy density achieve kinetic and chemical equilibrium in time  For all observables the equilibration time is found to be shorter for the scaled variances than for the average values  The scaled variances for the fluctuations in the number of different partons in the box show an influence of the total energy conservation  The scaled variances for all observables approach the Poissonian limit when the cell volume is much smaller than that of the box  The procedure of extracting of the shear viscosity from the microscopic simulations as well as the ratio of the shear viscosity to the entropy density are presented

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25 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 spectra Central Pb + Pb at SPS energies 26  PHSD gives harder m T spectra and works better than HSD at high energies – 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 partonic phase decreases due to the decrease of the partonic fraction Central Au+Au at RHIC W. Cassing & E. Bratkovskaya, NPA 831 (2009) 215 E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, NPA856 (2011)

Partonic phase at SPS/FAIR/NICA energies partonic energy fraction vs centrality and energy Dramatic decrease of partonic phase with decreasing energy and/or centrality ! Cassing & Bratkovskaya, NPA 831 (2009) all y

Elliptic flow scaling at RHIC 28 The scaling of v 2 with the number of constituent quarks n q is roughly in line with the data E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, NPA856 (2011) 162

29 Finite quark chemical potentials  the phase transition happens at the same critical energy ε c for all μ q  in the present version the DQPM and PHSD treat the quark-hadron transition as a smooth crossover at all μ q

30 Finite quark chemical potentials  the phase transition happens at the same critical energy ε c for all μ q  in the present version the DQPM and PHSD treat the quark-hadron transition as a smooth crossover at all μ q