${\Upsilon}(nS)$ ${\to}$ $B_{c}{\rho}$, $B_{c}K^{\ast}$ decays with perturbative QCD approach

Inspired by the potential prospects of ${\Upsilon}(nS)$ data samples ($n$ $=$ $1$, $2$, $3$) at LHC and SuperKEKB, ${\Upsilon}(nS)$ ${\to}$ $B_{c}{\rho}$, $B_{c}K^{\ast}$ decays are studied phenomenologically with pQCD approach. Branching ratios for ${\Upsilon}(nS)$ ${\to}$ $B_{c}{\rho}$ and $B_{c}K^{\ast}$ decays are estimated to reach up to ${\cal O}(10^{-11})$ and ${\cal O}(10^{-12})$, respectively. Given the identification and detection efficiency of final states, searching for these weak decay modes should be fairly challenging experimentally in the future.