Wolfgang Cassing Erice Parton dynamics and hadronization from the sQGP

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

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 Parton-Hadron-String-Dynamics (PHSD) QGP phase described by input from the Dynamical QuasiParticle Model DQPM Dynamical QuasiParticle Model (DQPM) 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

Interacting quasiparticles Entropy density of interacting bosons and fermions (G. Baym 1998): gluons quarks antiquarks with d g = 16 for 8 transverse gluons and d q = 18 for quarks with 3 colors, 3 flavors and 2 spin projections Gluon propagator: Δ -1 =P 2 - Π gluon self-energy: Π=M 2 -i2γ g ω Quark propagator S q -1 = P 2 - Σ q quark self-energy: Σ q =m 2 -i2γ q ω Simple approximations  DQPM: cf. talk by B. Kämpfer

The Dynamical QuasiParticle Model (DQPM) Spectral functions for partonic degrees of freedom (g, q, q bar ): quark mass: gluon width: quark width: with with E 2 (p)= p 2 + M 2 - γ 2 N c = 3 Peshier, Cassing, PRL 94 (2005) ; Peshier, Cassing, PRL 94 (2005) ; Cassing, NPA 791 (2007) 365: NPA 793 (2007) Cassing, NPA 791 (2007) 365: NPA 793 (2007) new: new !

The running coupling g 2 3 parameters: T s /T c =0.46; c=28.8; =2.42  Quasiparticle properties (N f =3; T c = GeV)  Quasiparticle properties (N f =3; T c = GeV) lQCD Fit to lattice (lQCD) entropy density: huge width for gluons ! large width for quarks !

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

Time-like and space-like energy densities  space-like energy densities dominate except close to T c !  space-like parts are identified with potential energy densities! x: gluons, quarks, antiquarks

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

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

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

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

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

PHSD: the partonic phase PHSD: the partonic phase Partonic phase: Partonic phase:  Degrees of freedom: quarks and gluons (= ‚dynamical quasiparticles‘) (+ hadrons) quarks and gluons (= ‚dynamical quasiparticles‘) (+ hadrons)  Properties of partons: off-shell spectral functions (width, mass) defined by DQPM off-shell spectral functions (width, mass) defined by DQPM  EoS of partonic phase: from lattice QCD (or DQPM) elastic parton-parton interactions: elastic parton-parton interactions: using the effective cross sections from the DQPM inelastic parton-parton interactions: 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,q bar,g) ! off-shell parton propagation: off-shell parton propagation: with self-generated potentials U q, U g with self-generated potentials U q, U g Cassing, E.B. arXiv: [hep-ph] PRC Cassing, arXiv: [nucl-th] EPJ

PHSD: hadronization Hadronization happens: when the effective interactions become attractive <= from DQPM when the effective interactions become attractive <= from DQPM for parton densities 1 <  P < 2.2 fm -3 : for parton densities 1 <  P < 2.2 fm -3 : gluons  q + qbar q + qbar  meson gluons  q + qbar q + qbar  meson q + q +q  baryon q + q +q  baryon <= from DQPM and recomb. model Note: nucleon: parton density  P  = N q / V N =3 / 2.5 fm 3 =1.2 fm -3 Note: nucleon: parton density  P  = N q / V N =3 / 2.5 fm 3 =1.2 fm -3 meson: parton density  P m = N q / V m = 2 / 1.2 fm 3 =1.66 fm -3 meson: parton density  P m = N q / V m = 2 / 1.2 fm 3 =1.66 fm -3 Parton-parton recombination rate = probability to form bound state during fixed time-interval  t in volume  V : Matrix element increases drastically for  P ->0 => => hadronization successful ! Based on DQPM: massive, off-shell quarks and gluons with broad spectral functions hadronize to off-shell mesons and baryons:

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

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 large parton masses  dominant production of vector mesons or baryon resonances (of finite/large width) or baryon resonances (of finite/large width) resonance state (or string) is determined by the weight of its resonance state (or string) is determined by the weight of its spectral function at given invariant mass M spectral function at given invariant mass M hadronic resonances are propagated in HSD (and finally decay to the hadronic resonances are propagated in HSD (and finally decay to the groundstates by emission of pions, kaons, etc.)  Since the partons are groundstates by emission of pions, kaons, etc.)  Since the partons are massive the formed states are very heavy (strings)  entropy production massive the formed states are very heavy (strings)  entropy production in the hadronization phase ! in the hadronization phase ! Hadronic phase: Hadronic phase: hadron-string interactions –> off-shell transport in HSD

Expanding partonic fireball I Initial condition: Partonic fireball at temperature 1.7 T c with ellipsoidal gaussian shape in coordinate space ellipsoidal gaussian shape in coordinate space Eccentricity: ε = (σ y 2 – σ x 2 )/(σ y 2 + σ x 2 ) ε = 0 energy conservation partons and hadrons More hadrons in the final state than initial partons !

Expanding fireball II Time-evolution of parton density Time-evolution of hadron density Expanding grid: Δz(t) = Δz 0 (1+a t) ! fm 8.75 fm 10 fm12 fm 10 fm12 fm 8.75 fm

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

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

Expanding fireball III – collective aspects Elliptic flow v 2 is defined by an anisotropy in momentum space: v 2 = (p x 2 – p y 2 ) / (p x 2 + p y 2 ) Initially: v 2 = 0  study final v 2 versus initial eccentricity ε ! v 2 /ε = const. v 2 /ε = const. indicates hydrodynamic flow ! This is expected since η/s is small in the DQPM ε = (σ y 2 – σ x 2 )/(σ y 2 + σ x 2 )

Reminder: Collective flow: v 2 excitation function v 2 excitation function from string-hadronic transport models :  Proton v 2 at low energy very sensitive to the nucleon potential !  Cascade codes fail to describe the exp. data !  v 2 is determined by attractive/repulsive potentials ! cascade

Expanding fireball II: Differential elliptic flow Time evolution of v 2 :Quark number scaling v 2 /n q : parton v 2 is generated to a large extent by the repulsive partonic forces ! meson to baryon v 2 indicates quark number scaling ! Cassing, E.B. arXiv: [hep-ph] PRC 2008

Summary The dynamical quasiparticle model (DQPM) defines the transport input for PHSD (in line with lattice QCD)! The dynamical quasiparticle model (DQPM) defines the transport input for PHSD (in line with lattice QCD)! PHSD provides a consistent description of off-shell parton dynamics; PHSD provides 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 dynamical hadronization in PHSD yields particle ratios close to the (GC) statistical model at a temperature of about 170 MeV! The elliptic flow v 2 scales with the initial eccentricity in space as in ideal hydrodynamics! The elliptic flow v 2 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 v 2 (p T ) and suggests quark-number scaling! 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 v 2 (p T ) and suggests quark-number scaling!

Thanks to Elena Bratkovskaya Sascha Juchem Sascha Juchem Andre Peshier Andre Peshier