On the three-particle analog of the Lellouch-L\"uscher formula

TL;DR

This paper derives a leading-order three-particle analog of the Lellouch-Luscher formula using non-relativistic effective field theory, enabling the study of three-particle decays in lattice simulations.

Contribution

It introduces a novel leading-order formula linking finite-volume and infinite-volume three-particle decay amplitudes, extending the Lellouch-Luscher framework.

Findings

Derived the three-particle Lellouch-Luscher formula at leading order

Established a method to relate finite-volume decay amplitudes to infinite-volume ones

Discussed potential extensions to higher-order corrections

Abstract

Using non-relativistic effective field theory, we derive a three-particle analog of the Lellouch-L\"uscher formula at the leading order. This formula relates the three-particle decay amplitudes in a finite volume with their infinite-volume counterparts and, hence, can be used to study the three-particle decays on the lattice. The generalization of the approach to higher orders is briefly discussed.