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

Understand

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.