High-energy heavy-ion collisions have been suggested as a favorable environment for the production of $B_c$ mesons, due to a much larger abundance of charm and bottom quarks compared to elementary reactions. Motivated by recent CMS data for $B_c^{+}$ production in Pb-Pb(5.02 TeV) collisions at the Large Hadron Collider (LHC), we deploy a previously developed transport approach for charmonia and bottomonia to evaluate the kinetics of $B_c$ mesons throughout the fireball formed in these reactions. The main inputs to our approach are two transport parameters: the $B_c$'s reaction rate and equilibrium limit. Both quantities are determined by previous calculations via a combination of charm and bottom sectors. In-medium binding energies of $B_c$ mesons are calculated from a thermodynamic $T$ matrix with a lattice-QCD constrained potential, and figure in their inelastic reaction rates. Temperature-dependent equilibrium limits include charm- and bottom-quark fugacities based on their initial production. We compute the centrality dependence of inclusive $B_c$ production and transverse-momentum $\left(p_T\right)$ spectra using two different recombination models: instantaneous coalescence and resonance recombination. The main uncertainty in the resulting nuclear modification factors, $R_{\mathrm{AA}}$, is currently associated with the $B_c$ cross section in elementary $pp$ collisions, caused by the uncertainty in the branching ratio for the $B_c^{-}\to J/\psi {\mu }^{-}\overline{\nu }$ decay. Our results indicate a large enhancement of the $R_{\mathrm{AA}}$ at low $p_T$, with significant regeneration contributions up to $p_T\simeq 20\mathrm{GeV}$. Comparisons to CMS data are carried out but firm conclusions will require a more accurate value of the branching ratio, or alternative channels to measure the $B_c$ production in $pp$ collisions.

• Received 23 February 2023
• Accepted 25 October 2023

DOI:https://doi.org/10.1103/PhysRevC.109.014906