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

TL;DR

This paper introduces a novel lattice QCD method using twisted boundary conditions to accurately determine the decay amplitude for $K o\pi\pi$ processes, improving the connection between finite-volume calculations and physical decay rates.

Contribution

The paper presents a new approach employing partially twisted boundary conditions to evaluate the Lellouch-L"uscher factor, enabling more precise extraction of decay amplitudes from lattice simulations.

Findings

Feasibility demonstrated through exploratory computation.

Allows continuous variation of the $\pi\pi$ phase shift with momentum.

Provides a new tool for lattice QCD studies of weak decays.

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.