In-medium kinetic theory of $D$ mesons and heavy-flavor transport coefficients

We extend the kinetic theory of $D$ mesons to accommodate thermal and off-shell effects due to the medium modification of the heavy-meson spectral functions. From the Kadanoff-Baym approach we derive the off-shell Fokker-Planck equation which encodes the heavy-flavor transport coefficients. We analyze the thermal width (damping rate) of $D$ mesons due to their scattering off light mesons, focusing on new in-medium effects: off-shell corrections, inelastic channels, and the contribution of the Landau cut. We obtain that the latter effect (absent for vacuum scattering amplitudes) brings sizable corrections at moderate temperatures. We discuss how the heavy-flavor transport coefficients, like the drag and diffusion coefficients, are modified in matter. We find that the $D$-meson spatial diffusion coefficient matches smoothly to the latest results of lattice-QCD calculations and Bayesian analyses at higher temperatures.