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

The LHCb collaboration has recently measured the first direct CP violation in $B^0_s$ decays with a rate asymmetry $A_{CP}(B^0_s\to K^- π^+)$ given by $0.27 \pm 0.04(stat)\pm 0.01(syst)$. At the same time they also made the most precise measurement for $A_{CP}(B^0 \to K^+ π^-) = -0.080\pm 0.007(stat)\pm 0.003(syst)$. These data confirm the predicted relation, $A_{CP}(B^0 \to K^+ π^-)/A_{CP}(B^0_s \to K^- π^+) = - Br(B^0_s\to K^- π^+)τ_{B^0}/Br(B^0 \to K^+ π^-)τ_{B^0_s}$, 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 $B^0_s$ to $PP$ and $PV$ decays. Here $P$ and $V$ indicate pesudoscalar and vector mesons in the flavor octet representations.