Suppression of Flavor Symmetry Breaking in B Decay Sum Rules

While flavor symmetries are useful for studying hadronic B decays, symmetry relations for amplitudes and decay rates are usually violated by first order symmetry breaking corrections. We point out two cases in which first order symmetry breaking is suppressed by a small ratio of amplitudes: (1) An isospin sum rule for four B → Kπ decays, where isospin breaking is shown to be negligible. (2) An SU(3) sum rule for pairs of B → Kπ and B → Kη8, generalized to pairs of B → Kπ, B → Kη and B → Kη. Charmless hadronic B decays provide valuable tests for the pattern of CP violation in the Cabibbo-Kobayashi-Maskawa (CKM) framework. Several methods, using isospin symmetry and flavor SU(3) symmetry relations for decay amplitudes, have been developed for extracting CKM phases [1, 2]. Flavor symmetry relations for amplitudes are expected to involve corrections which are in most cases linear in symmetry breaking parameters. The parameters describing isospin and SU(3) breaking are respectively of order ǫI ≡ md −mu ΛQCD ∼ 0.03 and δSU(3) ≡ ms −md ΛQCD ∼ 0.3 . (1) Submitted to Physics Letters B.