${\bar{B}}_s^0\to K\pi ,KK$ 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.

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

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• Anatomy of $B_s\to PV$ decays and effects of next-to-leading order contributions in the perturbative QCD factorization approach
• The PQCD approach towards to next-to-leading order: a short review
• The $\rho {\gamma }^{\ast }\to \pi (\rho )$ transition form factors in the Perturbative QCD factorization approach
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• Direct $CP$ violation for ${\bar{B}}_s^0\to \varphi {\pi }^{+}{\pi }^{-}$ in Perturbative QCD
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• Inspection of new physics in ${\mathrm{B}}_{\mathrm{s}}^0\to {\mathrm{K}}^{+}{\mathrm{K}}^{-}$ decay mode
• Recent results from the Belle experiment