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More Flavor SU(3) Tests for New Physics in CP Violating B Decays

The recent LHCb measurements of the $B_s \to K^-π^+$ and $B_s \to K^+K^-$ rates and CP asymmetries are in agreement with U-spin expectations from $B_d \to K^+π^-$ and $B_d \to π^+π^-$ results. We derive the complete set of isospin, U-spin, and SU(3) relations among the CP asymmetries in two-body charmless $B \to PP$ and $B \to PV$ decays, some of which are novel. To go beyond the unbroken SU(3) limit, we present relations which are properly defined and normalized to allow incorporation of SU(3) breaking in the simplest manner. We show that there are no CP relations beyond first order in SU(3) and isospin breaking. We also consider the corresponding relations for charm decays. Comparing parametrizations of the leading order sum rules with data can shed light on the applicability and limitations of both the flavor symmetry and factorization-based descriptions of SU(3) breaking. Two factorization relations can already be tested, and we show they agree with current data.