Three-particle Lellouch-L\"uscher formalism in moving frames

TL;DR

This paper develops a relativistically invariant formalism for three-particle decays in moving frames, extending previous approaches by incorporating higher-order effects and ensuring Lorentz invariance.

Contribution

It introduces a new Lellouch-Lüscher formalism that maintains manifest Lorentz invariance and systematically includes higher-order couplings and partial waves.

Findings

Formalism guarantees relativistic invariance.

Inclusion of higher-order derivative couplings.

Framework applicable to three-particle decay studies.

Abstract

A manifestly relativistic-invariant Lellouch-L\"uscher formalism for the three-particle decays is proposed. Similarly to ref.[1], the formalism is based on the use of the non-relativistic effective Lagrangians. Manifest Lorentz invariance is guaranteed, as in ref.[2], by choosing the quantization axis along the total four-momentum of the three-particle system. A systematic inclusion of the higher-order derivative couplings, as well as higher partial waves is addressed.