The three-particle system on a torus

TL;DR

This paper develops a theoretical framework using the Lippmann-Schwinger equation to connect finite-volume energy spectra with scattering amplitudes for a three-particle system on a torus, focusing on narrow resonances.

Contribution

It introduces a set of equations relating finite-volume energies to scattering amplitudes specifically for three-particle systems with narrow resonances, under the isobar model approximation.

Findings

Derived equations linking finite-volume energies to scattering amplitudes.

Applicable to systems with narrow two- and three-body resonances.

Provides a theoretical basis for analyzing three-particle systems in lattice simulations.

Abstract

Based on Lippmann-Schwinger equation approach, we discuss a three-particle system in finite volume. A set of equations which relate the discrete finite-volume energies to the scattering amplitudes are derived under the approximation of the isobar model relevant for the case of narrow two- and three-body resonances.