Strong Isospin-Breaking Effects in K-->pi pi at Next-to-Leading Order in the Chiral Expansion

TL;DR

This paper evaluates strong isospin-breaking effects in K→ππ decays at next-to-leading order, showing significant reductions in certain amplitudes and providing insights into the ratio of weak operator contributions with high accuracy.

Contribution

It provides the first NLO analysis of strong isospin-breaking effects in K→ππ decays, refining understanding of amplitude modifications and operator ratios.

Findings

NLO contributions significantly reduce the leading order ΔI=3/2 amplitude.

The ratio of strong IB 27-plet to octet contributions is small.

The ratio of weak operator strengths can be accurately determined from experimental data.

Abstract

Strong isospin-breaking (IB) contributions to both the octet and 27-plet weak K-->2 pi 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 $\Delta I=3/2$ amplitude resulting from strong isospin-breaking modifications to the weak Delta I=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 percent.