Effective QCD and transport description of dilepton and photon production in heavy-ion collisions and elementary processes

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 an effective dynamical quasiparticle model (DQPM) for QCD in equilibrium. In the DQPM, the widths and masses of the dynamical quasiparticles are controlled by transport coefficients that can be compared to the corresponding quantities from lattice QCD. The resulting off-shell transport approach is denoted by Parton-Hadron-String Dynamics (PHSD) and includes covariant dynamical transition rates for hadronization and keeps track of the hadronic interactions in the final phase. It is shown that the PHSD captures the bulk dynamics of heavy-ion collisions from lower SPS to LHC energies and thus provides a solid basis for the evaluation of the electromagnetic emissivity, which is calculated on the basis of the same dynamical parton propagators that are employed for the dynamical evolution of the partonic system. The production of direct photons in elementary processes and heavy-ion reactions is discussed and the present status of the photon v2 “puzzle”-a large elliptic flow v2 of the direct photons experimentally observed in heavy-ion collisions-is addressed for nucleus-nucleus reactions at RHIC and LHC energies. The role of hadronic and partonic sources for the photon spectra and the flow coefficients v2 and v3 is considered as well as the possibility to subtract the QGP signal from the experimental observables. Furthermore, the production of e+e− or μ+μ− pairs in elementary processes and A + A reactions is addressed. The calculations within the PHSD from SIS to LHC energies show an increase of the low mass dilepton yield essentially due to the in-medium modification of the ρ-meson and at the lowest energy also due to a multiple regeneration of Δ-resonances. Furthermore, pronounced traces of the partonic degrees-of-freedom are found in the intermediate dilepton mass regime (1.2GeV