Prospects for a lattice computation of rare kaon decay amplitudes II K → πνν̄ decays

The rare kaon decays K → πνν̄ 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 precise standard model prediction for the braching ratio of K → πνν̄ with controlled uncertainty for both short-distance and long-distance contributions. In this work we demonstrate the feasibility of lattice QCD calculation of the longdistance contribution to rare kaon decays with the emphasis on K+ → π+νν̄. 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 → π`+`−, where the focus was made on the γ-exchange diagrams. 1 ar X iv :1 60 5. 04 44 2v 1 [ he pla t] 1 4 M ay 2 01 6