Rare Kaon Decays on the Lattice

TL;DR

This paper proposes a lattice QCD method to accurately compute long-distance effects in rare kaon decays, potentially reducing theoretical uncertainties in their predictions.

Contribution

It introduces a lattice approach that handles divergences and chiral symmetry breaking, enabling precise calculations of rare kaon decay amplitudes.

Findings

Method successfully eliminates extra divergences.

Applicable to lattice actions with broken chiral symmetry.

Potential to improve decay rate predictions.

Abstract

We show that long distance contributions to the rare decays K -> pi nu nu-bar and K -> pi l+ 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.