${\bar{B}}_s^0\to K\pi ,KK$ decays and effects of the next-to-leading order contribution

Abstract

By employing the perturbative QCD(pQCD) factorization approach, we calculate the branching ratios and CP violating asymmetries of the four ${\bar{B}}_s^0\to K\pi$ and $KK$ decays, with the inclusion of all known next-to-leading order (NLO) contributions. We find numerically that (a) the NLO contribution can interfere with the LO part constructively or destructively for different decay modes; (b) the NLO contribution leads to a $22\%$ decrease for $Br({\bar{B}}_s^0\to K^{+}{\pi }^{-})$, but $\sim 50\%$ enhancements to other three considered ${\bar{B}}_s$ decays, and therefore play an important role in interpreting the measured values of the branching ratios; and (c) for both ${\bar{B}}_s^0\to K^{+}{\pi }^{-}$ and ${\bar{B}}_s^0\to K^{+}{K}^{-}$ decays, the NLO pQCD predictions for the direct and mixing induced CP-violating asymmetries agree very well with the measured values in both the sign and the magnitude.

Comments: 14 pages, 3 figures and 3 tables. arXiv admin note: text overlap with arXiv:0812.2312