Estimating the Charm Quark Diffusion Coefficient and thermalization time from D meson spectra at RHIC and LHC

We describe the propagation of charm quarks in the quark-gluon plasma (QGP) by means of a Boltzmann transport approach. Non-perturbative interaction between heavy quarks and light quarks have been taken into account through a quasi-particle approach in which light partons are dressed with thermal masses tuned to lQCD thermodynamics. Such a model is able to describe the main feature of the non-perturbative dynamics: the enhancement of the interaction strength near $T_c$. We show that the resulting charm in-medium evolution is able to correctly predict simultaneously the nuclear suppression factor, $R_{AA}$, and the elliptic flow, $v_2$, at both RHIC and LHC energies and at different centralities. The hadronization of charm quarks is described by mean of an hybrid model of fragmentation plus coalescence and plays a key role toward the agreeement with experimental data. We also performed calculations within the Langevin approach which can lead to very similar $R_{AA}(p_T)$ as Boltzmann, but the charm drag coefficient as to be reduced by about a $30\%$ and also generates an elliptic flow $v_2(p_T)$ is about a $15\%$ smaller. We finally compare the space diffusion coefficient $2\pi TD_s$ extracted by our phenomenological approach to lattice QCD results, finding a satisfying agreement within the present systematic uncertainties. Our analysis implies a charm thermalization time, in the $p\rightarrow 0$ limit, of about $4-6 \, fm/c$ which is smaller than the QGP lifetime at LHC energy.