Study of the $B_{c}$ ${\to}$ $B_{s}{\pi}$ decay with the perturbative QCD approach

The $B_{c}$ ${\to}$ $B_{s}{\pi}$ decay is studied with the perturbative QCD approach. Three types of wave functions for $B_{s}$ meson are considered. The transition form factor $F_{0}^{B_{c}{\to}B_{s}}(0)$ and the branching ratio ${\cal B}r(B_{c}{\to}B_{s}{\pi})$ are sensitive to the model of the $B_{s}$ meson wave functions. With appropriate inputs, our estimate on ${\cal B}r(B_{c}{\to}B_{s}{\pi})$ is comparable with the recent LHCb measurement. A clear signal of $B_{c}$ ${\to}$ $B_{s}{\pi}$ decay should be easily observed at the Large Hadron Collider.