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

TL;DR

This paper extends a lattice QCD method to accurately compute rare kaon decay amplitudes involving massless leptonic propagators, effectively controlling finite-volume effects for such second-order weak processes.

Contribution

The authors adapt an existing finite-volume correction method to processes with massless leptons, enabling precise lattice QCD calculations of rare decay amplitudes.

Findings

Finite-volume effects are exponentially suppressed even with massless leptons.

The method successfully computes the $K^+ o uar u$ decay amplitude from lattice QCD.

The approach reduces systematic errors in rare decay simulations.

Abstract

In Ref. [1], a method was proposed 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 $K^+\to\pi^+\nu\bar\nu$ from a lattice quantum chromodynamics computation with only exponentially small finite-volume corrections.