Multiple-channel generalization of Lellouch-L\"uscher formula: Lattice 2012 conference proceedings

TL;DR

This paper generalizes the Lellouch-L"uscher formula to multiple coupled decay channels, enabling more accurate lattice QCD calculations of weak decay rates involving two scalar particles.

Contribution

It extends the original formula to handle multiple channels, arbitrary couplings, and various decay operators, broadening its applicability for lattice QCD studies.

Findings

Derived a relation between finite and infinite volume weak matrix elements for multiple channels.

Applicable to energies below the three- or four-particle thresholds.

Supports arbitrary total momentum and particle degeneracy.

Abstract

We describe a generalization of the Lellouch-L\"uscher formula to the case of multiple strongly-coupled decay channels. As in the original formula, our final result is a relation between weak matrix elements in finite and infinite volumes. Our extension is limited to final states with two scalar particles, with center of mass energies below the lowest three- or four-particle threshold. Otherwise the extension is general, accommodating any number of channels, arbitrary strong coupling between channels, as well as any form of weak decay operators in the matrix elements. Among many possible applications, we emphasize that this is a necessary first step on the way to a lattice-QCD calculation of weak decay rates for D -> pi pi and D -> K K-bar. Our results allow for arbitrary total momentum and hold for degenerate or non-degenerate particles.