Impact of |ΔI|=5/2 transitions in K→ππ decays

We consider the impact of isospin violation on the analysis of K→ππ decays. We scrutinize, in particular, the phenomenological role played by the additional weak amplitude, of |ΔI|=5/2 in character, incurred by the presence of isospin violation. We show that Watson's theorem is appropriate in Script O sign(m_d-m_u), so that the inferred ππ phase shift at √s=m_K determines the strong phase difference between the I=0 and I=2 amplitudes in K→ππ decay. We find the magnitude of the |ΔI|=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 |ΔI|=5/2 transitions in the CP-violating observable ∈′/∈, we determine that the presence of a |ΔI|=5/2 amplitude impacts the empirical determination of ω, the ratio of the real parts of the |ΔI|=3/2 to |ΔI|=1/2 amplitudes, and that it generates a decrease in the estimation of ∈′/∈.