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 $B\to Kπ$ decays, where isospin breaking is shown to be negligible. (2) An SU(3) sum rule for pairs of $B\to Kπ$ and $B\to Kη_8$, generalized to pairs of $B\to Kπ, B\to Kη$ and $B\to Kη'$.