CP Violation in $B_s^0\to K^{-}{\pi }^{+}$, $B^0\to K^{+}{\pi }^{-}$ Decays and Tests for SU(3) Flavor Symmetry Predictions

Abstract

The LHCb collaboration has recently measured the first direct CP violation in $B_s^0$ decays with a rate asymmetry $A_{CP}(B_s^0\to K^{-}{\pi }^{+})$ given by $0.27\pm 0.04(stat)\pm 0.01(syst)$. At the same time they also made the most precise measurement for $A_{CP}(B^0\to K^{+}{\pi }^{-})=-0.080\pm 0.007(stat)\pm 0.003(syst)$. These data confirm the predicted relation, $A_{CP}(B^0\to K^{+}{\pi }^{-})/A_{CP}(B_s^0\to K^{-}{\pi }^{+})=-Br(B_s^0\to K^{-}{\pi }^{+}){\tau }_{B^0}/Br(B^0\to K^{+}{\pi }^{-}){\tau }_{B_s^0}$, in the standard model with SU(3) flavor symmetry. We discuss possible modifications due to SU(3) breaking effects to this relation. There are several other similar relations in B decays. Using current available data we study whether relevant relations hold in $B^0$ and $B_s^0$ to $PP$ and $PV$ decays. Here $P$ and $V$ indicate pesudoscalar and vector mesons in the flavor octet representations.

Comments: RevTex, 16 pages with no figures. A new reference added and some minor modifications