Recombination of $B_c$ mesons in ultra-relativistic heavy-ion collisions

Abstract

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 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 ($p_T$) 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 $B_c^{-}\to J/\psi {\mu }^{-}\bar{\nu }$ decay. Our results indicate a large enhancement of the $R_{\mathrm{AA}}$ at low $p_T$, with significant regeneration contributions up to $p_T\simeq 20$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.

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• Production of doubly charmed hadron ${\Xi }_{cc}^{++}$ and $T_{cc}^{+}$ in relativistic heavy ion collisions
• In-medium mass shift of two-flavored heavy mesons, $B_c$, $B_c^{\ast }$, $B_s$, $B_s^{\ast }$, $D_s$ and $D_s^{\ast }$
• Heavy-heavy and heavy-light mesons in cold nuclear matter
• Can charm fluctuation be a better probe to study QCD critical point?
• Nuclear modification of $B_c$ mesons in relativistic heavy-ion collisions based on a linear Boltzmann transport model