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

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 → πνν̄ and KL → πνν̄ matrix-elements are reduced by a factor of about 7 and 4, respectively, and similarly for the direct CP-violating contributions to KL → π0e+e− and KL → π0μ+μ−. 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 → πνν̄) and for the direct CP-violating contributions to B ( KL → π0l+l− ) are now completely dominated by those on the short-distance physics.