Study on the $\mathrm{{\rm Y}}(1S)$ $\to$ $B_c{D}_s$ decay

The branching ratio and direct $CP$ asymmetry of the $\mathrm{{\rm Y}}(1S)$ $\to$ $B_c{D}_s$ weak decay are estimated with the perturbative QCD approach. It is found that (1) The direct $CP$-violating asymmetry is close to zero. (2) the branching ratio $\mathcal{B}r(\mathrm{{\rm Y}}(1S)\to B_c{D}_s)$ $\gtrsim$ ${10}^{-10}$ might be measurable at the future experiments.