Parton dynamics and hadronization from the sQGP

1. PHSD Parton dynamics and hadronizationfrom the sQGP Wolfgang Cassing Erice 22.09.08

2. Compressing and heating hadronic matter: sQGP • Questions: • What are the transport properties of the sQGP? • How may the hadronization (partons  hadrons) occur?

3. PHSD From hadrons to partons • We need a consistent transport model with • explicit parton-parton interactions (i.e. between quarks and gluons) • explicit phase transition from hadronic to partonic degrees of freedom • QCD EoS for the partonic phase Transport theory: off-shell Kadanoff-Baym equations for the Green-functions G<h(x,p) in phase-space representation for the partonic and hadronic phase Parton-Hadron-String-Dynamics (PHSD) QGP phase described by input from the Dynamical QuasiParticle Model(DQPM)

4. 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 cf. talk by B. Kämpfer 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

5. The Dynamical QuasiParticle Model (DQPM) Spectral functions for partonic degrees of freedom(g, q, qbar): new: quark mass: Nc = 3 gluon width: new ! quark width: new ! with E2(p)= p2 + M2 - γ2 Peshier, Cassing, PRL 94 (2005) 172301; Cassing, NPA 791 (2007) 365: NPA 793 (2007)

6. The running coupling g2 lQCD 3 parameters:Ts/Tc=0.46; c=28.8; l=2.42 Fit to lattice (lQCD) entropy density:  Quasiparticle properties(Nf=3; Tc = 0.185 GeV) huge width for gluons ! large width for quarks !

7. Differential quark ‚density‘ Example:  Large space-like contributions for broad quasiparticles !

8. Time-like and space-like energy densities x: gluons, quarks, antiquarks • space-like energy densities dominate except close to Tc ! • space-like parts are identified with potential energy densities!

9. Potential energy per time-like parton Potential energy: Plasma parameters: liquid huge ! _________________ gas  Partonic liquid should persist at LHC !

10. Potential energy versus parton density Potential energy: Parton density: Gluon fraction:  PHSD

11. Self-energies of time-like partons gluons quarks  PHSD

12. 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 !

13. Transport properties of hot glue Why do we need broad quasiparticles? viscosity ratio to entropy density:

14. PHSD: the partonic phase • Partonic phase: • Degrees of freedom: • quarks and gluons (= ‚dynamical quasiparticles‘)(+ hadrons) • Properties of partons: • off-shell spectral functions (width, mass) defined by DQPM • EoS of partonic phase: from lattice QCD (or DQPM) • elastic parton-parton interactions: • using the effective cross sections from the DQPM • inelastic parton-parton interactions: • quark+antiquark (flavor neutral) <=> gluon(colored) • gluon+ gluon<=> gluon(possible due to large spectral width) • quark + antiquark (color neutral) <=> hadron resonances • Note:inelastic reactions are described by Breit-Wigner cross sections • determined by the spectral properties of constituents (q,qbar,g) ! • off-shell parton propagation: • with self-generated potentials Uq, Ug Cassing, E.B. arXiv:0808.0022 [hep-ph] PRC Cassing, arXiv:0808.0715 [nucl-th] EPJ

15. PHSD: hadronization Based on DQPM: massive, off-shell quarks and gluons with broad spectralfunctions hadronize tooff-shell mesons and baryons: gluons  q + qbar q + qbar  meson q + q +q  baryon • Hadronizationhappens: • when the effective interactions become attractive<= from DQPM • for parton densities 1 < rP < 2.2 fm-3 : Note: nucleon:parton density rPN= Nq / VN=3 / 2.5 fm3=1.2 fm-3 meson:parton density rPm= Nq / Vm= 2 / 1.2 fm3=1.66 fm-3 Parton-parton recombination rate = probability to form bound state during fixed time-interval Dt in volume DV: <= from DQPM and recomb. model Matrix element increases drastically for rP->0 => => hadronization successful !

16. Hadronization rate Local off-shell transition rate:(meson formation) using Wm: Gaussian in phase space Cassing, E.B. arXiv:0808.0022 [hep-ph] PRC 2008

17. PHSD: hadronization (continued) • Conservation lows: • 4-momentum conservation invariant mass and momentum of meson • flavor current conservation  quark-antiquark content of meson • color + anticolor  color neutrality • large parton masses  dominant production of vector mesons • or baryon resonances (of finite/large width) • resonance state (or string) is determined by the weight of its • spectral function at given invariant mass M • hadronic resonances are propagated in HSD (and finally decay to the • groundstates by emission of pions, kaons, etc.)  Since the partons are • massive the formed states are very heavy (strings)  entropy production • in the hadronization phase ! Hadronic phase: hadron-string interactions –> off-shell transport in HSD

18. Expanding partonic fireball I Initial condition: Partonic fireball at temperature 1.7 Tc with ellipsoidal gaussian shape in coordinate space Eccentricity:ε = (σy2 – σx2)/(σy2 + σx2) energy conservation partons and hadrons ε = 0 More hadrons in the final state than initial partons !

19. Expanding fireball II Time-evolution of parton density 8.75 fm 8.75 fm 10 fm 12 fm -8.75 fm Time-evolution of hadron density 10 fm 12 fm -8.75 fm 8.75 fm Expanding grid: Δz(t) = Δz0(1+a t) !

20. Dynamical information gluon decay rate to q+qbar roughly equal to glue formation rate effective cross sections from the DQPM versus parton density become low at high parton density but interaction rate slightly increases with parton density! Cassing, E.B. arXiv:0808.0022 [hep-ph] PRC 2008

21. Hadronization versus the Statistical Model mass distributions for color neutral ‚mesons‘ and ‚baryons‘ after parton fusion: (rotating color dipoles) These ‚prehadrons‘ decay according to JETSET to 0-, 1-,1+ mesons and the baryon octet/decouplet Comparison of particle ratios with the statistical model (SM): A. Andronic 08

22. Expanding fireball III – collective aspects Elliptic flow v2 is defined by an anisotropy in momentum space: v2 = (px2 – py2)/(px2 + py2) Initially: v2 = 0  study final v2 versus initial eccentricity ε ! ε = (σy2 – σx2)/(σy2 + σx2) v2/ε = const. indicates hydrodynamic flow ! This is expected sinceη/s is small in the DQPM

23. v2 excitation function from string-hadronic transport models : Reminder: Collective flow: v2 excitation function cascade • Proton v2 at low energy very sensitive to the nucleon potential ! • Cascade codes fail to describe the exp. data ! • v2 is determined by attractive/repulsive potentials !

24. Expanding fireball II: Differential elliptic flow Time evolution of v2: Quark number scaling v2/nq: parton v2is generated to a large extent by the repulsive partonic forces ! meson to baryon v2 indicates quark number scaling ! Cassing, E.B. arXiv:0808.0022 [hep-ph] PRC 2008

25. Summary • The dynamical quasiparticle model (DQPM) defines the transport input for PHSD (in line with lattice QCD)! • PHSDprovides a consistent description of off-shell parton dynamics; • the repulsive mean fields generate a sizeable partonic flow! • The dynamical hadronization in PHSD yields particle ratios close to the (GC) statistical model at a temperature of about 170 MeV! • The elliptic flow v2 scales with the initial eccentricity in space as in ideal hydrodynamics! • The scaled elliptic flow of mesons and baryons is approximately the same as a function of the scaled transverse kinetic energy, but is smaller than the parton v2(pT) and suggests quark-number scaling!

26. PHSD Thanks to Elena Bratkovskaya Sascha Juchem Andre Peshier