Estimating the charm quark diffusion coefficient and thermalization time from D meson spectra at energies available at the BNL Relativistic Heavy Ion Collider and the CERN Large Hadron Collider

We describe the propagation of charm quarks in the quark-gluon plasma (QGP) by means of a Boltzmann transport approach. Nonperturbative interaction between heavy quarks and light quarks have been taken into account through a quasiparticle approach in which light partons are dressed with thermal masses tuned to lattice quantum chromodynamics (lQCD) thermodynamics. Such a model is able to describe the main feature of the nonperturbative 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, $R_{\text{AA}}$, and the elliptic flow, $v_2$, at both Relativistic Heavy Ion Collider and Large Hadron Collider (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 agreement with experimental data. We also performed calculations within the Langevin approach, which can lead to very similar $R_{\text{AA}}\left(p_T\right)$ as Boltzmann, but the charm drag coefficient as to be reduced by about a $30\%$ and also generates an elliptic flow $v_2\left(p_T\right)$ is about a $15\%$ smaller. We finally compare the space diffusion coefficient $2\pi T{D}_s$ 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 $p\to 0$ limit, of about $4–6\text{fm}/\text{c}$, which is smaller than the QGP lifetime at LHC energy.