Weak transition matrix elements from finite-volume correlation functions

TL;DR

This paper demonstrates how to extract weak decay transition matrix elements from finite-volume lattice QCD calculations, enabling direct numerical study of non-leptonic decays like K -> pi pi without analytic continuation.

Contribution

It provides a method to obtain finite-volume transition matrix elements directly from Euclidean correlation functions, facilitating lattice QCD studies of weak decay processes.

Findings

Finite-volume transition matrix elements can be extracted without analytic continuation.

The method applies to K -> pi pi and similar non-leptonic decays.

Decay rates are proportional to the square of these matrix elements.

Abstract

The two-body decay rate of a weakly decaying particle (such as the kaon) is shown to be proportional to the square of a well-defined transition matrix element in finite volume. Contrary to the physical amplitude, the latter can be extracted from finite-volume correlation functions in euclidean space without analytic continuation. The K -> pi pi transitions and other non-leptonic decays thus become accessible to established numerical techniques in lattice QCD.