In Ref [1] we have presented the results of an exploratory lattice QCD
computation of the long-distance contribution to the K+→π+ννˉ
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+→π+ννˉ 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. Our study
demonstrates the feasibility of lattice QCD computations of the
K+→π+ννˉ decay amplitude, and in particular of the
long-distance component. Though this calculation is performed on a small
lattice (163×32) and at unphysical pion, kaon and charm quark masses,
mπ​=420 MeV, mK​=563 MeV and m_c^{\overline{\mathrm{MS}}}(\mbox{2
GeV})=863 MeV, the techniques presented in this work can readily be applied to
a future realistic calculation.Comment: 74 pages, 12 figure