K+ →π+ν ν ̄ decay amplitude from lattice QCD

Abstract

In Ref. [1] we have presented the results of an exploratory lattice QCD computation of the long-distance contribution to the K+→π+νν̄ 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+νν̄ decay amplitude is dominated by short-distance contributions which can be computed in perturbation theory with the only required nonperturbative 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+νν̄ 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 mcMS̄(2 GeV)=863 MeV, the techniques presented in this work can readily be applied to a future realistic calculation.

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