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

Abstract: We propose a new method to evaluate the Lellouch-L\"uscher 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.