Impact of |{Delta}I|=5/2 transitions in K{yields}{pi}{pi} decays

Abstract

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