$\mathrm{{\rm Y}}(nS)$ $\to$ $B_c\rho$, $B_c{K}^{\ast }$ decays with perturbative QCD approach

Inspired by the potential prospects of $\mathrm{{\rm Y}}(nS)$ data samples ($n$ $=$ $1$, $2$, $3$) at LHC and SuperKEKB, $\mathrm{{\rm Y}}(nS)$ $\to$ $B_c\rho$, $B_c{K}^{\ast }$ decays are studied phenomenologically with pQCD approach. Branching ratios for $\mathrm{{\rm Y}}(nS)$ $\to$ $B_c\rho$ and $B_c{K}^{\ast }$ decays are estimated to reach up to $\mathcal{O}({10}^{-11})$ 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.