About PHSD-PHQMD

The Parton-Hadron-String Dynamics (PHSD) is a microscopic off-shell transport approach that 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 as well as hadronization and the subsequent interactions in the hadronic phase. It has been developed by the Giessen/Frankfurt groups on the basis of the Hadron-String Dynamics transport approach (HSD), and in the hadronic sector PHSD is equivalent to HSD.

In PHSD, the transition from the partonic (quarks and gluons) to hadronic degrees of freedom is described by covariant transition rates for the fusion of quark-antiquark pairs to mesonic resonances or three quarks (antiquarks) to baryonic states. This dynamical hadronization obeys flavor current-conservation, color neutrality, and energy-momentum conservation. Two-particle correlations from finite parton spectral widths are treated dynamically by generalized off-shell 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 a quark-gluon plasma in thermodynamic equilibrium. The DQPM supplies mean fields for gluons/quarks and effective two-body interactions implemented in PHSD. Close to the phase transition, dynamical quarks and antiquarks become massive, thus resonant pre-hadronic color-dipole states (q-qbar and qqq) are formed at large invariant mass and then decay sequentially to the meson and baryon octets. The resulting hadronization process increases total entropy and 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 the space-time regions of partonic matter. It provides a consistent description of bulk observables in heavy-ion collisions, including rapidity spectra, transverse-mass distributions, and azimuthal asymmetries (v1, v2, v3, v4) for multiple particle species, and has also been used successfully for dilepton production analyses from hadronic and partonic sources at SPS, RHIC, and LHC energies.

Equilibrium properties of the QGP have also been studied with PHSD simulations in a finite box with periodic boundary conditions at fixed temperature T. In particular, the shear-viscosity to entropy-density ratio from PHSD shows a minimum of about 0.1 near the critical temperature Tc = 160 MeV and approaches the perturbative-QCD limit at higher temperatures, in line with lattice-QCD results. This supports a strongly interacting liquid-like QGP (sQGP) rather than a weakly interacting gas of partons.

The Parton-Hadron-Quantum-Molecular Dynamics (PHQMD) transport approach is designed to provide a microscopic description of nuclear cluster and hypernucleus formation as well as general particle production in heavy-ion reactions at relativistic energies.

In difference to coalescence or statistical models, often used for cluster formation, PHQMD forms clusters dynamically due to interactions between baryons described on the basis of Quantum Molecular Dynamics (QMD), which allows propagation of the n-body Wigner density and n-body correlations in phase-space, essential for cluster formation.

Clusters are identified by the MST (Minimum Spanning Tree) or the SACA (Simulated Annealing Cluster Algorithm), which finds the most bound configuration of nucleons and clusters. Collisions among hadrons, Quark-Gluon-Plasma formation, and parton dynamics in PHQMD are treated in the same way as in the established Parton-Hadron-String Dynamics (PHSD) approach.