QLBT: A linear Boltzmann transport model for heavy quarks in a quark-gluon plasma of quasi-particles

We develop a new heavy quark transport model, QLBT, to simulate the dynamical propagation of heavy quarks inside the quark-gluon plasma (QGP) created in relativistic heavy-ion collisions. Our QLBT model is based on the linear Boltzmann transport (LBT) model with the ideal QGP replaced by a collection of quasi-particles to account for the non-perturbative interactions among quarks and gluons of the hot QGP. The thermal masses of quasi-particles are fitted to the equation of state from lattice QCD simulations using the Bayesian statistical analysis method. Combining QLBT with our advanced hybrid fragmentation-coalescence hadronization approach, we calculate the nuclear modification factor $R_\mathrm{AA}$ and the elliptic flow $v_2$ of $D$ mesons at the Relativistic Heavy-Ion Collider and the Large Hadron Collider. By comparing our QLBT calculation to the experimental data on the $D$ meson $R_\mathrm{AA}$ and $v_2$, we extract the heavy quark transport parameter $\hat{q}$ and diffusion coefficient $D_\mathrm{s}$ in the temperature range of $1-4~T_\mathrm{c}$, and compare them with the lattice QCD results and other phenomenological studies.