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We employ recently published cross sections for $D$-mesons with hadrons andcalculate the drag and diffusion coefficients of $D$-mesons in hadronic matteras a function of the momentum of $D$-mesons as well as of the temperature ofthe medium. Calculating in our approach the spatial diffusion coefficient,$D_x$, at zero chemical potential we see a very smooth transition between ourcalculations for the hadron gas and the lattice QCD calculations. Applying theresults for the transport coefficients of $D$-mesons in a Fokker-Planckequation, which describes the evolution of $D$-mesons during the expansion of ahadron gas created in ultrarelativistic heavy-ion collisions, we find that thevalue of $R_{AA}$ is little influenced by hadronic rescattering, whereas in theelliptic flow the effects are stronger. We extend our calculations to thefinite chemical potentials and calculate the spatial diffusion coefficients of$D$-mesons propagating through the hadronic medium following isentropictrajectories, appropriate at future FAIR and NICA heavy-ion experiments. Forthe isentropic trajectory with $s/\rho_B^{\rm net}=20$ we find a perfectmatching of results for $D$-mesons in hadronic matter and for charm quarks inpartonic matter treated within the DQPM approach.

$D$-mesons propagation in hadronic matter and consequences on heavy-flavor observables in ultrarelativistic heavy-ion collisions