Statistical Production of $B_c$ Mesons in Heavy-Ion Collisions at the LHC Energy

The recombination production of $B_c$ mesons in heavy-ion collisions at the LHC energy is facilitated by the abundant and highly thermalized charm ($c$) quarks transported in the deconfined medium created. We study the production of $B_c$ mesons via $c$ and bottom ($b$) quark recombination in a statistical fashion by placing $B_c$ in the position of a member of the family of open $b$ hadrons, which allows us to make quantitative predictions for the modifications of the production fraction ($f_c$) of $B_c$ mesons and its relative production to $B$ mesons in $\sqrt{s_{\rm NN}}=5.02$ TeV Pb-Pb collisions with respect to proton-proton ($pp$) collisions at the same energy. The statistical production yield of $B_c$ mesons is converted into the transverse momentum ($p_T$) distribution with the shape computed from resonance recombination using the $c$- and $b$-quark phase space distributions that have been simulated via Langevin diffusion and constrained by open $c$- and $b$-hadron observables. Supplemented with the component fragmented from $b$-quark spectrum that dominates at high $p_T$, the total $p_T$ spectrum of $B_c$ mesons is obtained and converted into the $p_T$ dependent nuclear modification factor ($R_{\rm AA}$). Both $f_c$ and the integrated $R_{\rm AA}$ exhibit a $\sim5$-fold enhancement in central Pb-Pb collisions relative to the $pp$ reference. Comparison with data measured by the CMS experiment shows decent agreement within theoretical and experimental uncertainties.