Impact of [formula presented] transitions in [formula presented] decays

We consider the impact of isospin violation on the analysis of (Formula presented) decays. We scrutinize, in particular, the phenomenological role played by the additional weak amplitude, of (Formula presented) in character, incurred by the presence of isospin violation. We show that Watson’s theorem is appropriate in (Formula presented) so that the inferred (Formula presented) phase shift at (Formula presented) determines the strong phase difference between the (Formula presented) and (Formula presented) amplitudes in (Formula presented) decay. We find the magnitude of the (Formula presented) amplitude thus implied by the empirical branching ratios to be larger than expected from estimates of isospin-violating strong and electromagnetic effects. We effect a new determination of the octet and 27-plet coupling constants with strong-interaction isospin violation and with electromagnetic effects, as computed by Cirigliano, Donoghue, and Golowich, and find that we are unable to resolve the difficulty. Exploring the role of (Formula presented) transitions in the (Formula presented)-violating observable (Formula presented) we determine that the presence of a (Formula presented) amplitude impacts the empirical determination of ω, the ratio of the real parts of the (Formula presented) to (Formula presented) amplitudes, and that it generates a decrease in the estimation of (Formula presented).