Branching ratios of $B_s\to (K^{+}{K}^{-},K^0{\bar{K}}^0)$ and B_d\to \pi^+ \pi^- and determination of \boldmath{\gamma (\phi_3)$

Abstract

We explored various cases for the branching ratios (BRs) of $B_s\to K^{+}{K}^{-}$, $B_s\to K^0{\bar{K}}^0$ and $B_d\to {\pi }^{+}{\pi }^{-}$ decays. We study the possibility of determining $\gamma$ by using the following the measurements: (a) BRs of $B_s\to K^{+}{K}^{-}$, and $B_s\to K^0{\bar{K}}^0$; (b) the ratio of direct CP asymmetries in $B_d\to {\pi }^{+}{\pi }^{-}$ and $B_s\to K^{+}{K}^{-}$; (c) the mix-induced CP asymmetry in $B_d\to {\pi }^{+}{\pi }^{-}$; and (d) the angle of $\beta$.

Comments: 12 pages, 5 figures