Study of the $\mathrm{{\rm Y}}(1S)$ $\to$ $B_c{D}_s^{\ast }$ decay with pQCD approach

The $\mathrm{{\rm Y}}(1S)$ $\to$ $B_c{D}_s^{\ast }$ weak decay is studied with the perturbative QCD approach firstly. It is found that (1) main contributions to branching ratio come from the longitudinal and parallel helicity amplitudes, (2) branching ratio, longitudinal and parallel polarization fractions are sensitive to the wave functions of the $\mathrm{{\rm Y}}(1S)$ meson, (3) branching ratio for the $\mathrm{{\rm Y}}(1S)$ $\to$ $B_c{D}_s^{\ast }$ decay can reach up to ${10}^{-9}$, which might be promisingly measured by the future experiments.