Bound states in the B-matrix formalism for the three-body scattering

TL;DR

This paper analyzes a relativistic three-body scattering model with bound states, identifying nonphysical singularities in the B-matrix parametrization and proposing methods to eliminate them and ensure unitarity.

Contribution

It introduces a method to remove nonphysical singularities in the B-matrix formalism for three-body scattering using dispersion relations and channel considerations.

Findings

Identified nonphysical singularities in the B-matrix parametrization.

Proposed a dispersion relation-based method to eliminate these singularities.

Demonstrated how to maintain unitarity by including all relevant channels.

Abstract

We consider a model of relativistic three-body scattering with a bound state in the two-body sub-channel. We show that the na\"ive K-matrix type parametrization, here referred to as the B-matrix, has nonphysical singularities near the physical region. We show how to eliminate such singularities by using dispersion relations and also show how to reproduce unitarity relations by taking into account all relevant open channels.