CP violation in \( B_s^0\to {K^{-}}{\pi^{+}} \), B0 → K+π− decays and tests for SU(3) flavor symmetry predictions

The LHCb collaboration has recently measured the first direct CP violation in $ B_s^0 $ decays with a rate asymmetry $ {A_{CP }}\left( {B_s^0\to {K^{-}}{\pi^{+}}} \right) $ given by 0.27 ± 0.04(stat) ± 0.01(syst). At the same time they also made the most precise measurement for ACP (B0 → K +π−) = −0.080 ± 0.007(stat) ± 0.003(syst). These data confirm the predicted relation, $ {A_{CP }}\left( {{B^0}\to {K^{+}}{\pi^{-}}} \right)/{A_{CP }}\left( {B_s^0\to {K^{-}}{\pi^{+}}} \right)=-Br\left( {B_s^0\to {K^{-}}{\pi^{+}}} \right){\tau_{{{B^0}}}}/Br\left( {{B^0}\to {K^{+}}{\pi^{-}}} \right){\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.