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Dynamical equilibration of strongly-interacting ‘infinite’ parton matter

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. From hadrons to partons.

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Dynamical equilibration of strongly-interacting ‘infinite’ parton matter

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  1. 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

  2. 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 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 Parton-Hadron-String-Dynamics (PHSD) W. Cassing, E. Bratkovskaya, PRC 78 (2008) 034919; NPA831 (2009) 215; W. Cassing, EPJ ST 168 (2009) 3 QGP phase described by Dynamical QuasiParticle Model (DQPM) A. Peshier, W. Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007)

  3. The Dynamical QuasiParticle Model (DQPM) Basic idea:Interacting quasiparticles -massive quarks and gluons(g, q, qbar)with spectral functions • fit to lattice (lQCD) results(e.g. entropy density)  Quasiparticle properties: large width and mass for gluons and quarks • DQPM matches well lattice QCD • 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 Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007)

  4. DQPM thermodynamics (Nf=3) entropy  pressure P energy density: interaction measure: lQCD:Wuppertal-Budapest group Y. Aoki et al., JHEP 0906 (2009) 088. TC=160 MeV eC=0.5 GeV/fm3 DQPM gives a good description of lQCD results !

  5. PHSD in a box Goal • study of the dynamical equilibration of strongly-interacting parton matter within the PHSD • 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 Realization

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

  7. 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

  8. Partonic interactions in PHSD 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 Inelastic channels Breit-Wigner cross section

  9. Detailed balance • The reactions rates are practically constant and obey detailed balancefor • The elastic collisions lead to the thermalization of all pacticle species (e.g. u, d, s quarks and antiquarks and gluons) • gluon splitting • quark + antiquark fusion • The numbers of partons dynamically reach their equilibrium valuesthrough the inelastic collisions

  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

  11. 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

  12. Dynamical phase transition & different intializations • the transition from partonic to hadronic degrees-of-freedom is complete after about 9 fm/c • asmall 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 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

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

  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

  24. Back up

  25. Equilibration times • fit the explicit time dependence of the abundances and scaled variances ωby • for all particles species and energy densities, the equilibration time is shorter for the scaled variance than for the average values

  26. PHSD: Transverse mass spectra Central Pb + Pb at SPS energies Central Au+Au at RHIC • PHSD gives harder mT spectra and works better than HSD at high energies – 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 W. Cassing & E. Bratkovskaya, NPA 831 (2009) 215 E. Bratkovskaya, W. Cassing, V. Konchakovski, O. Linnyk, NPA856 (2011) 162 26

  27. Partonic phase at SPS/FAIR/NICA energies partonic energy fraction vs centrality and energy all y Dramatic decrease of partonic phase with decreasing energy and/or centrality ! Cassing & Bratkovskaya, NPA 831 (2009) 215

  28. Elliptic flow scaling at RHIC The scaling of v2with the number of constituent quarks nq 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 εcfor all μq • in the present version the DQPM and PHSD treat the quark-hadron transition as a smooth crossover at all μq

  30. Finite quark chemical potentials • the phase transition happens at the same critical energy εcfor 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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