Isospin breaking in Kl4 decays

TL;DR

This paper discusses how isospin breaking effects, due to electromagnetic interactions and quark mass differences, impact Ke4 decay measurements and their comparison with QCD predictions, resolving previous discrepancies.

Contribution

It provides a detailed analysis of isospin breaking corrections in Ke4 decays, enabling accurate comparison with theoretical pi pi scattering predictions.

Findings

Isospin breaking effects are significant in Ke4 decays.

Correcting for these effects aligns experimental data with QCD predictions.

Discrepancies in previous measurements are resolved after corrections.

Abstract

Data on Ke4 decays allow one to extract experimental information on the elastic pi pi scattering amplitude near threshold, and to confront the outcome of the analysis with predictions made in the framework of QCD. These predictions concern an isospin symmetric world, while experiments are carried out in the real world, where isospin breaking effects - generated by electromagnetic interactions and by the mass difference of the up and down quarks - are always present. We discuss the corrections required to account for these, so that a meaningful comparison with the predictions becomes possible. In particular, we note that there is a spectacular isospin breaking effect in Ke4 decays. Once it is taken into account, the previous discrepancy between NA48/2 data on Ke4 decays and the prediction of pi pi scattering lengths disappears.