Improved estimates of rare K decay matrix-elements from Kl3 decays

TL;DR

This paper refines the estimation of rare K decay matrix-elements by including higher-order effects and radiative corrections, significantly reducing uncertainties and improving the precision of key decay predictions.

Contribution

It extends the analysis of K decay matrix-elements beyond leading order in Chiral Perturbation Theory, incorporating isospin-breaking and QED corrections for improved accuracy.

Findings

Uncertainties on key matrix-elements reduced by factors of 7 and 4.

Errors now dominated by short-distance physics uncertainties.

Potential for further reduction with better experimental data.

Abstract

The estimation of rare K decay matrix-elements from Kl3 experimental data is extended beyond LO in Chiral Perturbation Theory. Isospin-breaking effects at NLO (and partially NNLO) in the ChPT expansion, as well as QED radiative corrections are now accounted for. The analysis relies mainly on the cleanness of two specific ratios of form-factors, for which the theoretical control is excellent. As a result, the uncertainties on the K+ --> pi+ nu nubar and KL --> pi0 nu nubar matrix-elements are reduced by a factor of about 7 and 4, respectively, and similarly for the direct CP-violating contribution to KL --> pi0 l+ l-. They could be reduced even further with better experimental data for the Kl3 slopes and the K+l3 branching ratios. As a result, the non-parametric errors for B(K --> pi nu nubar) and for the direct CP-violating contributions to B(KL --> pi0 l+ l-) are now completely dominated by those on the short-distance physics.