Light - quark Loops in K → πνν̄

We present a comprehensive analysis of the contributions to K → πνν̄ decays not described by the leading dimension-six effective Hamiltonian. These include both dimensioneight four-fermion operators generated at the charm scale, and genuine long-distance contributions which can be described within the framework of chiral perturbation theory. We show that a consistent treatment of the latter contributions, which turn out to be the dominant effect, requires the introduction of new chiral operators already at O(GFp ). Using this new chiral Lagrangian, we analyze the long-distance structure ofK → πνν̄ amplitudes at the one-loop level, and discuss the role of the dimension-eight operators in the matching between shortand long-distance components. From the numerical point of view, we find that these O(GFΛ 2 QCD) corrections enhance the SM prediction of B(K+ → πνν̄) by about ≈ 6%.