Multiple-channel generalization of Lellouch-Luscher formula

TL;DR

This paper extends the Lellouch-Luscher formula to multiple coupled decay channels, enabling more accurate lattice QCD calculations of weak decay processes involving two scalar particles.

Contribution

It provides a novel generalization of the Lellouch-Luscher formula and Luscher's quantization condition for multiple channels, including explicit formulas and derivatives for two-channel cases.

Findings

Derived a multi-channel Lellouch-Luscher formula.

Presented a field theoretic derivation of multi-channel Luscher's condition.

Applicable to arbitrary total momentum and particle degeneracy.

Abstract

We generalize the Lellouch-Luscher formula, relating weak matrix elements in finite and infinite volumes, to the case of multiple strongly-coupled decay channels into two scalar particles. This is a necessary first step on the way to a lattice QCD calculation of weak decay rates for processes such as D -> pi pi and D -> KK. We also present a field theoretic derivation of the generalization of Luscher's finite volume quantization condition to multiple two-particle channels. We give fully explicit results for the case of two channels, including a form of the generalized Lellouch-Luscher formula expressed in terms of derivatives of the energies of finite volume states with respect to the box size. Our results hold for arbitrary total momentum and for degenerate or non-degenerate particles.