Parton-Hadron-String Dynamics

This review provides a written version of lectures on non-equilibrium quantum field theory and shows the way from quantum-field theory in two-particle irreducible approximation to the Kadanoff-Baym equations and practical approximation schemes in phase space. This leads to an off-shell transport theory that incorporates the underlying quantum physics and can be solved in a testparticle representation for weak and strong coupling regimes. Applications to dilepton production in heavy-ion reactions and to hadronization from partonic to hadronic degrees of freedom are discussed.

The Parton-Hadron-String Dynamics (PHSD) transport approach is applied to nucleus-nucleus collisions at RHIC energies with respect to differential hadronic spectra in comparison to available data. PHSD is based on DQPM partons matched to lattice-QCD results and includes covariant transition rates for hadronization with all conservation laws. Dynamical studies for Au+Au collisions at top RHIC energy are compared to HSD results and to STAR, PHENIX, BRAHMS and PHOBOS data. The approach gives a reasonable description of rapidity distributions, transverse mass spectra and elliptic flow, and shows approximate quark-number scaling of v2 for hadrons.

The azimuthal anisotropies of the collective transverse flow of charged hadrons are investigated in a wide range of heavy-ion collision energies within the microscopic parton-hadron-string dynamics (PHSD) transport approach which incorporates explicit partonic degrees of freedom in terms of strongly interacting quasiparticles (quarks and gluons) in line with an equation of state from lattice QCD as well as the dynamical hadronization and hadronic collision dynamics in the final reaction phase. The experimentally observed increase of the elliptic flow v_2 of charged hadrons with collision energy is successfully described in terms of the PHSD approach. The PHSD scaling properties of various collective observables are confronted with experimental data as well as with hydrodynamic predictions. The analysis of higher-order harmonics v_3 and v_4 in the azimuthal angular distribution shows a similar tendency of growing deviations between partonic and purely hadronic models with increasing collision energy. This demonstrates that the excitation functions of azimuthal anisotropies reflect the increasing role of quark-gluon degrees of freedom in the early phase of relativistic heavy-ion collisions. Furthermore, the specific variation of the ratio v_4/(v_2)^2 with respect to bombarding energy, centrality and transverse momentum is found to provide valuable information on the underlying dynamics.

We study charm production in ultra-relativistic heavy-ion collisions by using the Parton-Hadron-String Dynamics (PHSD) transport approach. The initial charm quarks are produced by the Pythia event generator tuned to fit the transverse momentum spectrum and rapidity distribution of charm quarks from Fixed-Order Next-to-Leading Logarithm (FONLL) calculations. The produced charm quarks scatter in the quark-gluon plasma (QGP) with the off-shell partons whose masses and widths are given by the Dynamical Quasi-Particle Model (DQPM) which reproduces the lattice QCD equation-of-state in thermal equilibrium. The relevant cross section are calculated in a consistent way by employing the effective propagators and couplings from the DQPM. Close to the critical energy density of the phase transition, the charm quarks are hadronized into D mesons through coalescence and/or fragmentation depending on transverse momentum. The hadronized D mesons then interact with the various hadrons in the hadronic phase with cross sections calculated in an effective lagrangian approach with heavy-quark spin symmetry. Finally, the nuclear modification factor \rm R_{AA} and the elliptic flow v_2 of D^0 mesons from PHSD are compared with the experimental data from the STAR Collaboration for Au+Au collisions at \sqrt{s_{\rm NN}} =200 GeV. We find that in the PHSD the energy loss of D mesons at high p_T can be dominantly attributed to partonic scattering while the actual shape of \rm R_{AA} versus p_T reflects the heavy quark hadronization scenario, i.e. coalescence versus fragmentation. Also the hadronic rescattering is important for the \rm R_{AA} at low p_T and enhances the D-meson elliptic flow v_2.

In this review we address the dynamics of relativistic heavy-ion reactions and in particular the information obtained from electromagnetic probes that stem from the partonic and hadronic phases. The out-of-equilibrium description of strongly interacting relativistic fields is based on the theory of Kadanoff and Baym. For the modeling of the partonic phase we introduce a dynamical quasiparticle model (DQPM) for QCD in equilibrium. The widths and masses of the quasiparticles are controlled by transport coefficients in comparison to lattice QCD results. The resulting off-shell transport approach - denoted by Parton-Hadron-String Dynamics (PHSD) - also includes covariant dynamical hadronization and keeps track of the hadronic interactions in the final phase. We show that PHSD captures the bulk dynamics of heavy-ion collisions from SPS to LHC energies and provides a basis for the evaluation of the electromagnetic emissivity, using the same dynamical parton propagators as for the system evolution. Direct photon production in elementary processes and heavy-ion reactions at RHIC and LHC energies is investigated and the status of the photon v2 puzzle - a large elliptic flow of the direct photons observed in A+A collisions - is addressed. We discuss the roles of hadronic and partonic sources for the photon spectra and the flow coefficients v2 and v3 and also the possibility to subtract the QGP signal from observables. Furthermore, the production of dilepton pairs is addressed from SIS to LHC energies. The low-mass dilepton yield is enhanced due to the in-medium modification of the rho-meson and at the lowest energy also due to a multiple regeneration of Delta-resonances. In addition, a signal of the partonic degrees-of-freedom is found in the intermediate dilepton mass regime (1.2GeV

We study the in-medium effects in strangeness production in heavy-ion collisions at (sub-)\-threshold energies of 1 - 2 A GeV based on the microscopic Parton-Hadron-String Dynamics (PHSD) transport approach. The in-medium modifications of the antikaon (\bar K = K^-, \bar K^0) properties are described via the self-consistent coupled-channel unitarized scheme based on a SU(3) chiral Lagrangian which incorporates explicitly the s- and p- waves of the kaon-nucleon interaction. This scheme provides the antikaon potential, spectral functions and reaction cross sections as well as their dependence on baryon density, temperature and antikaon momentum in the nuclear medium, which are incorporated in the off-shell dynamics of the PHSD. The in-medium modification of kaons (K = K^+, K^0) are accounted via the kaon-nuclear potential, which is assumed to be proportional to the local baryon density. The manifestation of the medium effects in observables is investigated for the K and {\bar K} rapidity distributions, p_T-spectra as well as the polar and azimuthal angular distributions, direct (v_1) and elliptic (v_2) flow in C+C, Ni+Ni, and Au+Au collisions. We find - by comparison to experimental data from the KaoS, FOPI and HADES Collaborations - that the modifications of (anti)kaon properties in nuclear matter are necessary to explain the data in a consistent manner. Moreover, we demonstrate the sensitivity of kaon observables to the equation-of-state of nuclear matter.

We investigate dilepton production in heavy-ion, proton-proton, and proton-nucleus collisions from low energies of 1 AGeV (SIS) to ultra-relativistic energies (LHC) using the Parton-Hadron-String Dynamics (PHSD) transport approach. PHSD is a microscopic, non-equilibrium approach that integrates hadronic and partonic degrees of freedom, providing a comprehensive description of relativistic heavy-ion collisions from initial nucleon-nucleon interactions to quark-gluon plasma (QGP) formation, hadronization, and final-state interactions. Key dilepton sources in PHSD include hadronic decays, bremsstrahlung, QGP radiation (q+\bar q \to e^+e^-, \ q+\bar q \to g+ e^+e^-, \ q+g \to q+ e^+e^-), primary Drell-Yan production, and semileptonic decays of correlated charm and bottom pairs. PHSD well describes dilepton data from HADES, STAR, and ALICE experiments. We examine in-medium effects, such as the vector meson spectral function broadening, and present the excitation function for the dilepton "excess" in the invariant mass range 0.4