Finite-volume effects in the evaluation of the K_L - K_S mass difference

TL;DR

This paper discusses the calculation of finite-volume corrections necessary for accurately determining the K_L-K_S mass difference in lattice QCD, extending existing techniques to more general volumes.

Contribution

It proposes a new approach to compute finite-volume corrections for the K_L-K_S mass difference, generalizing previous methods used for decay amplitudes.

Findings

Suggested form of finite-volume corrections for general volumes

Strategy for taking the infinite-volume limit

Reduction to known corrections in special degenerate volume case

Abstract

The RBC and UKQCD collaborations have recently proposed a procedure for computing the K_L-K_S mass difference. A necessary ingredient of this procedure is the calculation of the (non-exponential) finite-volume corrections relating the results obtained on a finite lattice to the physical values. This requires a significant extension of the techniques which were used to obtain the Lellouch-Luscher factor, which contains the finite-volume corrections in the evaluation of non-leptonic kaon decay amplitudes. We review the status of our study of this issue and, although a complete proof is still being developed, suggest the form of these corrections for general volumes and a strategy for taking the infinite-volume limit. The general result reduces to the known corrections in the special case when the volume is tuned so that there is a two-pion state degenerate with the kaon.