Strong isospin-breaking effects in K→2 π at next-to-leading order in the chiral expansion

Abstract

Strong isospin-breaking (IB) contributions to both the octet and 27-plet weak K→ ππ transitions are evaluated at next-to-leading order (NLO) in the chiral expansion. NLO contributions are shown to significantly reduce the leading order result for the potentially large contribution to the ΔI=3/2 amplitude resulting from strong isospin-breaking modifications to the weak ΔI=1/2 amplitude. The ratio of strong IB 27-plet to strong IB octet contributions is found to be small for all decay amplitudes. Combined with recent results on the corresponding electromagnetic contributions, we find that the ratio of the intrinsic strengths of octet and 27-plet effective weak operators can be taken to be that obtained from experimental data, analyzed ignoring isospin breaking, to an accuracy better than of order ∼10%.