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 $\beta$.