Prospects for a lattice computation of rare kaon decay amplitudes. II. K → π ν ν ¯ decays

The rare kaon decays K????¯ are strongly suppressed in the standard model and widely regarded as processes in which new phenomena, not predicted by the standard model, may be observed. Recognizing such new phenomena requires a precise standard model prediction for the branching ratio of K????¯ with controlled uncertainty for both short-distance and long-distance contributions. In this work we demonstrate the feasibility of lattice QCD calculation of the long-distance contribution to rare kaon decays with the emphasis on K+??+??¯. Our methodology covers the calculation of both W?W and Z-exchange diagrams. We discuss the estimation of the power-law, finite-volume corrections and two methods to consistently combine the long-distance contribution determined by the lattice methods outlined here with the short-distance parts that can be reliably determined using perturbation theory. It is a subsequent work of our first methodology paper on K???+??, where the focus was made on the ?-exchange diagrams.