We study the dynamics of open charm production and the dilepton radiation of the semi-leptonic decays of correlated $Dbar D$ pairs versus the quark-gluon plasma (QGP) radiation and hadronic sources in relativistic heavy-ion collisions. Our study is based on the Parton-Hadron-String Dynamics (PHSD) transport approach employing a non-perturbative QCD description of the strongly interacting quark-gluon plasma (sQGP) in terms of dynamical quasiparticles and the EoS based on lattice QCD. We compare the PHSD results for charm observables with the calculations from BAMPS (Boltzmann Approach to Multi-Parton Scatterings) which is based on perturbative QCD with massless partons and interaction cross sections calculated in leading order of the QCD coupling. We compare the $p_T$ dependence of the ratio $R_{AA}$ of $D$-mesons in $A+A$ over $p+p$ collisions scaled by the number of binary collisions $N_{bin}$ as well as the elliptic flow $v_2$ of $D$-mesons calculated within the PHSD and BAMPS at LHC energies. In other study, based on the PHSD calculations we find that the dileptons from correlated $D-$meson semi-leptonic decays dominate the thermal radiation from the QGP in central Pb+Pb collisions at the intermediate masses ($1.2 < M < 3$ GeV) for higher invariant energies However, for invariant energies $sqrt{s_{NN}} < 40$ GeV the QGP radiation overshines the contribution from $D,{bar D}$ decays such that one should observe a rather clear signal from the partonic dilepton radiation. This finding provides promising perspectives to measure the QGP radiation in the dilepton experiments at RHIC BES and the future FAIR/NICA facilities.
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