Finite-volume effects in the evaluation of the Kₗ - Kₛ mass difference

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The RBC and UKQCD collaborations have recently proposed a procedure for computing the Kₗ-Kₛ 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.