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

We propose a new method to evaluate the Lellouch-Lüscher factor which relates the $ΔI=3/2$ $K\toππ$ 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 $ππ$ 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.

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