Suppression of flavor symmetry breaking in B decay sum rules

Abstract

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 $B\to K\pi$ decays, where isospin breaking is shown to be negligible. (2) An SU(3) sum rule for pairs of $B\to K\pi$ and $B\to K{\eta }_8$, generalized to pairs of $B\to K\pi ,B\to K\eta$ and $B\to K{\eta }^{\prime }$.

Comments: 11 pages, small corrections, one reference added, submitted to Physics Letters B