D-meson propagation in hadronic matter and consequences for heavy-flavor observables in ultrarelativistic heavy-ion collisions

Abstract

We employ recently published cross sections for $D$ mesons with hadrons and calculate the drag and diffusion coefficients of $D$ mesons in hadronic matter as a function of the momentum of $D$ mesons as well as of the temperature of the medium. Calculating in our approach the spatial diffusion coefficient, ${D}_{x}$, at zero chemical potential we see a very smooth transition between our calculations for the hadron gas and the lattice QCD calculations. Applying the results for the transport coefficients of $D$ mesons in a Fokker-Planck equation, which describes the evolution of $D$ mesons during the expansion of a hadron gas created in ultrarelativistic heavy-ion collisions, we find that the value of ${R}_{AA}$ is little influenced by hadronic rescattering, whereas in the elliptic flow the effects are stronger. We extend our calculations to the finite chemical potentials and calculate the spatial diffusion coefficients of $D$ mesons propagating through the hadronic medium following isentropic trajectories, appropriate at future FAIR (Facility for Antiproton and Ion Research, Darmstadt) and NICA (Nuclotron-Based Ion Collider Facility, Dubna) heavy-ion experiments. For the isentropic trajectory with $s/{\ensuremath{\rho}}_{B}^{\mathrm{net}}=20$ we find a perfect matching of results for $D$ mesons in hadronic matter and for charm quarks in partonic matter treated within the dynamical quasiparticle model approach.