How much do heavy quarks thermalize in a heavy ion collision?

TLDR

We investigate the thermalization of charm quarks in high‑energy heavy‑ion collisions. We compute the charm‑quark diffusion coefficient in a perturbative quark‑gluon plasma, use it to construct a Langevin model of heavy‑quark evolution, solve the corresponding Fokker‑Planck equation analytically for a Bjorken expansion, and then run the Langevin equations numerically within a hydrodynamic simulation of the collision. The simulation yields the charm‑quark nuclear modification factor R_AA and elliptic flow v₂(p_T) as functions of the diffusion coefficient.

Abstract

We investigate the thermalization of charm quarks in high-energy heavy-ion collisions. To this end, we calculate the diffusion coefficient in the perturbative quark gluon plasma and relate it to collisional energy loss and momentum broadening. We then use these transport properties to formulate a Langevin model for the evolution of the heavy quark spectrum in the hot medium. The model is strictly valid in the nonrelativistic limit and for all velocities $\ensuremath{\gamma}v<\ensuremath{\alpha}{s}^{\ensuremath{-}1/2}$ to leading logarithm in $T/{m}_{D}$. The corresponding Fokker-Planck equation can be solved analytically for a Bjorken expansion and the solution gives a simple estimate for the medium modifications of the heavy quark spectrum as a function of the diffusion coefficient. Finally we solve the Langevin equations numerically in a hydrodynamic simulation of the heavy-ion reaction. The results of this simulation are the medium modifications of the charm spectrum ${R}_{\mathit{AA}}$ and the expected elliptic flow ${v}_{2}({p}_{T})$ as a function of the diffusion coefficient.