Production of doubly heavy quarkonium associated with two heavy quarks via top quark decays

Abstract

In this paper, we analyze the $1 \rightarrow 4$ decay channel for the production of doubly heavy quarkonium, $(b\bar{c})$ or $(c\bar{c})$, via top-quark decays, $t \to (b\bar{c}) + c + c + \bar{s}$ and $t \to (c\bar{c}) + b + c + \bar{s}$, within the framework of nonrelativistic QCD (NRQCD). The dominant contributions are considered in color-singlet S-wave states, i.e., $(b\bar{c})[^1S_0]$, $(b\bar{c})[^3S_1]$, $(c\bar{c})[^1S_0]$, and $(c\bar{c})[^3S_1]$. Our calculations show that the decay widths for $\bar{B_{c}}$, $\bar{B_{c}^{*}}$, $\eta_{c}$ and $J/\psi$ production are 0.2251, 0.3099, 0.0537 and 0.0555 MeV, respectively, resulting in ${\cal O}(10^{4}\text{--}10^{6})$ level of $\bar{B}_c^{(*)}$ events and ${\cal O}(10^{3}\text{--}10^{5})$ level of charmonium produced at LHC per year. In particular, we find that the dominant contribution to $\eta_{c}$ and $J/\psi$ production via top-quark decays arises from this decay channel proposed in this work. Moreover, this multi-body top-quark decay process can serve as a sensitive probe for validating the narrow-width approximation (NWA). Finally, we provide a detailed analysis of theoretical uncertainties and differential distributions to facilitate the corresponding experimental searches. The production of a hadron associated with three quarks contains rich physical information, providing new insights for the LHC to study $B_c$ mesons and charmonia.