Exploratory lattice QCD study of the rare kaon decay $K^+\to\pi^+\nu\bar{\nu}$

Understand

In Ref [1] we have presented the results of an exploratory lattice QCD computation of the long-distance contribution to the $K^+\to\pi^+\nu\bar{\nu}$ decay amplitude.

• In the present paper we describe the details of this calculation, which includes the implementation of a number of novel techniques.
• The $K^+\to\pi^+\nu\bar{\nu}$ decay amplitude is dominated by short-distance contributions which can be computed in perturbation theory with the only required non-perturbative input being the relatively well-known form factors of semileptonic kaon decays.
• The long-distance contributions, which are the target of this work, are expected to be of O(5%) in the branching ratio.