Study on the ${\Upsilon}(1S)$ ${\to}$ $B_{c}D_{s}$ decay

The branching ratio and direct $CP$ asymmetry of the ${\Upsilon}(1S)$ ${\to}$ $B_{c}D_{s}$ 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 ${\cal B}r({\Upsilon}(1S){\to}B_{c}D_{s})$ ${\gtrsim}$ $10^{-10}$ might be measurable at the future experiments.
Comment: 15 pages, 2 pages, revtex. arXiv admin note: substantial text overlap with arXiv:1701.04597