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

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 $s/{\rho }_B^{\mathrm{net}}=20$ 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.

Figure 1

Isentropic thermodynamic trajectories at top RHIC energies. The solid line includes the conservation of particle ratios and the dashed line does not.

Figure 2

The temperature dependence of effective chemical potentials for an isentropic hadronic fireball expansion at top RHIC energy for different particle species. Left panel: $\pi$ (solid), $N$ (dashed), $\overline{N}$ (dash-dotted), $\eta$ (dotted), $K$ (dash-dot-dotted). Right panel: ${\eta }^{\prime }$ (solid), $\omega$ (dashed), $\varphi$ (dash-dotted).

Figure 3

The pressure as a function of energy density calculated in our approach (solid) in comparison to the result obtained from the hydrodynamical model [36] (dashed).

Figure 4

The transport coefficients as a function of the initial momentum of the $D$ meson for systems at different temperatures: drag, $A$ (upper panel); transverse diffusion, $B_0$ (middle panel); longitudinal diffusion, $B_1$ (lower panel).

Figure 5

The thermal relaxation rate of the $D$ meson at momentum $p=0.1\mathrm{GeV}$ as a function of temperature with (left panel) and without (right panel) introduction of effective chemical potentials to the hadronic cocktail. The solid lines represent our results, the model estimates from Ref. [27] are shown by the dashed lines, the dash-dot-dotted line depicts the result from Ref. [28] and the calculation from Ref. [31] is presented by the dash-dotted line.

Figure 6

The spatial diffusion coefficient of the $D$ meson at momentum $p=0.1\mathrm{GeV}$ as a function of temperature with (dash-dotted line) and without (solid line) the introduction of effective chemical potentials to the hadronic cocktail in comparison to the results from Ref. [31] (dashed line). The lQCD data are taken from Ref. [54] (symbols).

Figure 7

The nuclear modification factor, $R_{AA}$, and elliptic flow, $v_2$, of $D$ mesons and of single nonphotonic electrons originating from the decays of HF mesons for two scenarios as well as for the pure QGP scenario in comparison to the experimental data from STAR and PHENIX experiments: $R_{AA}$ of $D$ mesons–Ref. [9], $v_2$ of $D$ mesons–Ref. [12], $R_{AA}$ and $v_2$ of decay electrons–Refs. [7, 8].

Figure 8

The thermal relaxation rate (left panel) and the spatial diffusion coefficient (right panel) of $D$ mesons for three different isentropic trajectories as a function of temperature in comparison to the model estimates from Ref. [31] (dashed lines). The results for the spatial diffusion coefficient of $c$ quarks propagating in the partonic medium obtained in Ref. [58] are shown by the dash-dotted lines.