Thermal production of charm quarks in relativistic heavy-ion collisions

We investigate the thermal production of charm quarks in the strongly interacting quark-gluon plasma (sQGP) created in heavy-ion collisions at relativistic energies. Our study is based on the off-shell parton-hadron-string dynamics (PHSD) transport approach describing the full time evolution of heavy-ion collisions on a microscopic basis with hadronic and partonic degrees of freedom. The sQGP is realized within the effective dynamical quasi-particle model (DQPM) which is adjusted to reproduce the lattice QCD results for the thermodynamic observables of the sQGP. Relying on the fact that the DQPM successfully describes the spatial diffusion coefficients $D_s$ from the lQCD, which control the interaction of charm quarks with thermal partons (expressed in terms of strongly interacting off-shell quasiparticles), we evaluate the production of charm quark pairs through the rotation of Feynman diagrams such that the incoming charm quark and outgoing light parton in elastic scattering diagrams are exchanged. The charm quark annihilation is realized by detailed balance. We find that the number of produced thermal charm quark pairs strongly depends on the charm quark mass in the QGP. While for the heavy charm quarks of mass $m_c=1.8$ GeV it is subdominant compared to the primary charm production by binary nucleon-nucleon collisions at RHIC and LHC energies, the numbers of primary and thermal charm quarks become comparable for a smaller (bare) $m_c=1.2$ GeV. Compared with the experimental data on the $R_{\rm AA}$ of $D$-mesons in heavy-ion collisions at RHIC and LHC energies, it is more favorable for charm quarks in the QGP to gain additional mass due to thermal effects rather than to have a low bare mass.