Impact of |ΔI|=5/2 transitions in K→ππ decays -: art. no. 094024

We consider the impact of isospin violation on the analysis of K-->pi pi decays. We scrutinize, in particular, the phenomenological role played by the additional weak amplitude, of \DeltaI\ = 5/2 in character, incurred by the presence of isospin violation. We show that Watson's theorem is appropriate in O(m(d)-m(u)), so that the inferred pi pi phase shift at roots=m(K) determines the strong phase difference between the I=0 and I=2 amplitudes in K-->pi pi decay. We find the magnitude of the \DeltaI\=5/2 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 \DeltaI\ = 5/2 transitions in the CP violating observable epsilon'/epsilon, We determine that the presence of a \DeltaI\ = 5/2 amplitude impacts the empirical determination of omega, the ratio of the real parts of the \DeltaI\ = 3/2 to \DeltaI\ = 1/2 amplitudes, and that it generates a decrease in the estimation of epsilon'/epsilon.