Charm-strange meson production in ultrarelativistic heavy-ion collisions at energies available at the CERN Large Hadron Collider

The nuclear modification factor $R_{AA}$ and the elliptic flow coefficient $v_2$ of charm-strange meson $D_s^{+}$ is systematically studied in Pb-Pb collisions at $\sqrt{s_{\mathit{NN}}}=5.02$ and $2.76\mathrm{TeV}$. During the modeling, the coupling strength between the injected charm quark and the incident medium constituents is extracted from the lattice QCD calculations: $2\pi T{D}_s=\text{const}$ (Model-A) and $2\pi T{D}_s=1.3+{(T/T_c)}^2$ (Model-B). We find that, comparing $R_{AA}\left(D_s^{+}\right)$ with $R_{AA}\left(\text{nonstrange}\right)$, the heavy-light coalescence effect is more pronounced for the former one, resulting in an enhancement behavior in the range $2\lesssim p_T\lesssim 5\mathrm{GeV}$. The predictions for $R_{AA}\left(D_s^{+}\right)$ and $R_{AA}\left(\text{nonstrange}\right)$ favor Model-A to have a better description of the measured $p_T$ dependence at both energies, while the predictions for $v_2$ prefer Model-B at moderate $p_T$ ($2\lesssim p_T\lesssim 4\mathrm{GeV}$). Therefore, it is necessary to consider the temperature and/or momentum dependence of $2\pi T{D}_s$ to describe simultaneously $R_{AA}\left(D_s^{+}\right)$ and $v_2\left(D_s^{+}\right)$ in different centrality classes in Pb-Pb collisions.

Figure 1

Charm quark spatial diffusion coefficient $2\pi T{D}_s$ calculated by lattice QCD at zero momentum: pink circle [32], blue square [33], and red triangle [34]. The phenomenological approaches (dashed green and solid black curves) are displayed as well.

Figure 2

Energy loss of charm quarks obtained via (a) Model-A and (b) Model-B; collisional and radiative contributions are shown separately as long-dashed blue and dashed black curves, respectively, in each panel. The combined results are shown as a solid red curve.

Figure 3

Comparison of the coalescence probability contributed by different combinations in central ($0\text{–}10\%$) Pb-Pb collisions at $\sqrt{s_{\mathit{NN}}}=5.02\mathrm{TeV}$: $cd$ (dot-dashed black curve), $cu$ (dashed green curve) and $cs$ (long-dashed blue curve). Both the ground states and the first excited states are considered. The combined results (solid red curve) are presented as well.

Figure 4

$p_T$-differential production cross section of the $D_s^{+}$ meson with $\left|y\right|<0.5$ in $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$. Experimental data were taken from Ref. [45].

Figure 5

Ratios of $D$-meson production cross sections as a function of $p_T$. the measurements for $D_s^{+}/D^0$ (solid) and $D_s^{+}/D^{+}$ (empty) are shown as boxes, while the relevant model predictions are displayed as the bands. Experimental data were taken from Ref. [45].

Figure 6

Comparison of the central predictions of $R_{AA}$ contributed by different hadronization mechanisms: for (a) the nonstrange charmed mesons (average among $D^0$, $D^{+}$, and $D^{*+}$) and (b) the charm-strange meson ($D_s^{+}$), at mid-rapidity ($\left|y\right|<0.5$) in central ($0\text{–}10\%$) Pb-Pb collisions at $\sqrt{s_{\mathit{NN}}}=5.02\mathrm{TeV}$. See legend for details. Experimental data were taken from Ref. [44].

Figure 7

Comparison of $R_{AA}$ for the average of nonstrange $D$ mesons (solid red curves) and $D_s^{+}$ (dashed blue curves) predicted at mid-rapidity ($\left|y\right|<0.5$) in central ($0\text{–}10\%$) Pb-Pb collisions at (a) $\sqrt{s_{\mathit{NN}}}=5.02\mathrm{TeV}$ and (b) $2.76\mathrm{TeV}$, respectively. Experimental data were taken from Ref. [44, 46].

Figure 8

Comparison between the average of nonstrange $D$ mesons and $D_s^{+}$ observables obtained with Model-A and Model-B approaches in Pb-Pb collisions at $\sqrt{s_{\mathit{NN}}}=5.02\mathrm{TeV}$: $R_{AA}$ (upper) in $0\text{–}10\%$ and $v_2$ in $30\text{–}50\%$. Experimental data were taken from Refs. [44, 47].