K \to \pi\pi decay amplitudes from the lattice

TL;DR

This paper presents a lattice-based finite-volume method to accurately compute K to pi pi decay amplitudes by preparing two-pion states with non-zero relative momentum, building on Lellouch and Lüscher's proposal.

Contribution

It introduces a practical approach to realize two-pion states with non-zero momentum as the lowest energy state in finite volume lattice simulations.

Findings

Enables direct calculation of physical decay amplitudes.

Provides a finite-volume technique for two-pion state preparation.

Builds on and extends Lellouch and Lüscher's theoretical framework.

Abstract

In order to directly compute physical two-pion K-decay amplitudes using lattice methods we must prepare a two-pion state with non-zero relative momentum. Building upon a proposal of Lellouch and L\"uscher, we describe a finite-volume method to realize such a state as the lowest energy state of two pions.