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 next-to-leading order (and partially next-to-next-to-leading order) in the chiral perturbation theory 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+→π+νν and KL→π0νν 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 Kl3+ branching ratios. As a result, the nonparametric errors for B(K→πνν) and for the direct CP-violating contributions to B(KL→π0l+l-) are now completely dominated by those on the short-distance physics