Recombination of B c mesons in ultrarelativistic heavy-ion collisions

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. Here, 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 ($p_T$) spectra using two different recombination models: instantaneous coalescence and resonance recombination. The main uncertainty in the resulting nuclear modification factors, $R_{AA}$, is currently associated with the $B_c$ cross section in elementary $pp$ collisions, caused by the uncertainty in the branching ratio for the $B^–_c → J/ψμ^– \bar{v}$ decay. Our results indicate a large enhancement of the $R_{AA}$ at low $p_T$, with significant regeneration contributions up to $p_T$ ≃ 20 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.