Finite-volume effects in long-distance processes with massless leptonic propagators

A method was proposed recently [X. Feng and L. Jin, Phys. Rev. D 100, 094509 (2019)] to calculate QED corrections to hadronic self-energies from lattice QCD without power-law finite-volume errors. In this paper, we extend the method to processes which occur at second order in the weak interaction and in which there is a massless (or almost massless) leptonic propagator. We demonstrate that, in spite of the presence of the propagator of an almost massless electron, such an infinite-volume reconstruction procedure can be used to obtain the amplitude for the rare kaon decay ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}\ensuremath{\nu}\overline{\ensuremath{\nu}}$ from a lattice quantum chromodynamics computation with only exponentially small finite-volume corrections.