We show that long-distance contributions to the rare decays K→πνν̄ and K→πℓ+ℓ- can be computed using lattice QCD. The proposed approach requires well established methods, successfully applied in the calculations of electromagnetic and semileptonic form factors. The extra power divergences, related to the use of weak four-fermion operators, can be eliminated using only the symmetries of the lattice action without ambiguities or complicated non-perturbative subtractions. We demonstrate that this is true even when a lattice action with explicit chiral symmetry breaking is employed. Our study opens the possibility of reducing the present uncertainty in the theoretical predictions for these decays. © 2005 Elsevier B.V. All rights reserved.
Isidori, G., Martinelli, G., & Turchetti, P. (2006). Rare kaon decays on the lattice. Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 633(1), 75–83. https://doi.org/10.1016/j.physletb.2005.11.044