Study on the ${\Upsilon}(1S)$ ${\to}$ $B_{c}M$ weak decays

Motivated by the prospects of the potential ${\Upsilon}(1S)$ particle at high-luminosity heavy-flavor experiments, we studied the ${\Upsilon}(1S)$ ${\to}$ $B_{c}M$ weak decays, where $M$ $=$ ${\pi}$, ${\rho}$, $K^{(\ast)}$. The nonfactorizable contributions to hadronic matrix elements are taken into consideration with the QCDF approach. It is found that the CKM-favored ${\Upsilon}(1S)$ ${\to}$ $B_{c}{\rho}$ decay has branching ratio of ${\cal O}(10^{-10})$, which might be measured promisingly by the future experiments.