$K\to (\pi \pi {)}_{I=2}$ decays and twisted boundary conditions

Abstract

We propose a new method to evaluate the Lellouch-Lüscher factor which relates the $\Delta I=3/2$ $K\to \pi \pi$ matrix elements computed on a finite lattice to the physical (infinite-volume) decay amplitudes. The method relies on the use of partially twisted boundary conditions, which allow the s-wave $\pi \pi$ phase shift to be computed as an almost continuous function of the centre-of-mass relative momentum and hence for its derivative to be evaluated. We successfully demonstrate the feasibility of the technique in an exploratory computation.

Comments: 19 pages, 7 figures