The Parton-Hadron-String Dynamics (PHSD) is a microscopic off-shell transport approach for the description of strongly interacting hadronic and partonic matter in and out-of-equilibrium. It is based on the solution of Kadanoff-Baym equations in first-order gradient expansion in phase space, allowing a causal description of the time evolution of nonperturbative interacting systems. PHSD consistently describes the full evolution of a relativistic heavy-ion collision from the initial hard scatterings and string formation through the dynamical deconfinement phase transition to the quark-gluon plasma, followed by hadronization and subsequent hadronic interactions. The PHSD has been developed by the Giessen/Frankfurt groups on the basis of the Hadron-String Dynamics transport approach (HSD).
In PHSD the transition from partonic (quarks and gluons) to hadronic degrees of freedom is described by covariant transition rates for quark-antiquark fusion to mesonic resonances or three quarks (antiquarks) to baryonic states, i.e. by a dynamical hadronization obeying flavor current-conservation, color neutrality and energy-momentum conservation. The two-particle correlations resulting from finite parton spectral widths are treated dynamically by generalized off-shell Cassing-Juchem transport equations that go beyond mean-field or Boltzmann approximations.
The transport-theoretical description of quarks and gluons in PHSD is based on the Dynamical Quasi-Particle Model (DQPM), constructed to reproduce lattice-QCD results for the quark-gluon plasma in thermodynamic equilibrium. DQPM provides mean fields and effective two-body interactions for gluons and quarks. Close to the phase transition, dynamically massive quarks and antiquarks form resonant pre-hadronic color-dipole states (q-qbar or qqq) with high invariant mass that sequentially decay to meson and baryon octets. The resulting hadronization increases total entropy and thus remains consistent with the second law of thermodynamics.
The PHSD approach has been applied to nucleus-nucleus collisions from low SPS to LHC energies to explore space-time regions of partonic matter. It provides a consistent description of bulk heavy-ion observables - rapidity spectra, transverse-mass distributions, and azimuthal asymmetries (v1, v2, v3, v4) - and has been successfully used for dilepton analyses from hadronic and partonic sources.
Equilibrium properties of QGP were also studied with PHSD in a finite box with periodic boundary conditions at fixed temperature T. The ratio of shear viscosity to entropy density shows a minimum close to Tc = 160 MeV and approaches the perturbative QCD limit at higher temperatures, in line with lattice-QCD results. This indicates a strongly interacting liquid-like QGP rather than a weakly interacting gas of partons.