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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. IV Youth Scientists Conference, Kyiv. 24 October 2012. Motivation. Motivation. ‘big-bang’ of the universe

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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 IV Youth Scientists Conference, Kyiv 24 October 2012

  2. Motivation

  3. Motivation • ‘big-bang’ of the universe • laboratory ‘tiny bangs’ • local thermal and chemical equilibrium • steps with kinetic and chemical equilibrium • phase space configurations • far from an equilibrium • fast expansion

  4. Crucial question How and onwhat timescales a global thermodynamic equilibrium can be achieved in heavy-ion collisions?

  5. 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)

  6. 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)

  7. 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 !

  8. 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 8

  9. 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

  10. 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

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

  12. 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 • initial number of partons is given • four-momenta are distributed according to the distribution by Monte Carlo simulations • initial parameters: , which define the total energy

  13. 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

  14. 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

  15. 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

  16. Different initializations • 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

  17. 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

  18. Dynamical phase transition • 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

  19. 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)

  20. 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

  21. 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

  22. 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

  23. 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.

  24. Summary • Partonic systems at energy densities, which are above the critical energy density achieve kinetic and chemical equilibrium in time • The scaled variances for the fluctuations in the number of different partons in the box are shown. • The scaled variances for all observables approach the Poissonian limit when the cell volume is much smaller than that of the box • PHSD provides a consistent description of off-shell parton dynamics in line with a lattice QCD equation of state and incorporates dynamicalhadronizationin line with conservation laws

  25. Back up

  26. Thermal equilibration • DQPM predictions can be evaluated:

  27. 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

  28. 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

  29. 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

  30. 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 30

  31. 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

  32. 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

  33. 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

  34. 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

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

  36. 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

  37. Effective 2-body interactions of time-like partons 2nd derivatives of interaction densities 9/4  PHSD effective interactions turn strongly attractive below 2.2 fm-3 !

  38. Transport properties of hot glue Why do we need broad quasiparticles? shear viscosity ratio to entropy density:  otherwise η/s will be too high!

  39. e+ q e- e- g* q * e- q q Time-like and space-like quantities Separate time-like and space-like single-particle quantities by Q(+P2), Q(-P2): gluons quarks antiquarks Space-like:Θ(-P2):particles are virtuell and appear as exchange quanta in interaction processes of real particles Time-like:Θ(+P2):particles may decay to real particles or interact Examples: Cassing, NPA 791 (2007) 365: NPA 793 (2007)

  40. Interacting quasiparticles Entropy density of interacting bosons and fermions (G. Baym 1998): gluons quarks antiquarks with dg = 16 for 8 transverse gluons and dq = 18 for quarks with 3 colors, 3 flavors and 2 spin projections Bose distribution function: Fermi distribution function: Simple approximations  DQPM: Gluon propagator: Δ-1 =P2 - Π gluon self-energy: Π=M2-i2γgω Quark propagator Sq-1 = P2 - Σq quark self-energy: Σq=m2-i2γqω (scalar)

  41. The Dynamical QuasiParticle Model (DQPM) quarks gluons: mass: width: running coupling:aS(T) = g2(T)/(4p) Basic idea:Interacting quasiparticles -massive quarks and gluons(g, q, qbar)with spectral functions : E2 = p2+M2-g2 A. Peshier, PRD 70 (2004) 034016 Nc = 3, Nf=3 lQCD: O. Kaczmarek et, PRD 72 (2005) 059903 • fit to lattice (lQCD) results (e.g. entropy density) with 3 parameters:Ts/Tc=0.46; c=28.8; l=2.42  quasiparticle properties (mass, width) DQPM: Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007) 41

  42. PHSD: Hadronization details Local covariant off-shell transition rate for q+qbar fusion => meson formation using • Nj(x,p) is the phase-space density of partonj at space-time position x and 4-momentum p • Wmis the phase-space distribution of the formed ‚pre-hadrons‘: (Gaussian in phase space) • is the effective quark-antiquark interactionfrom the DQPM Cassing, Bratkovskaya, PRC 78 (2008) 034919; Cassing, EPJ ST 168 (2009) 3

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