Two bosons in a narrowly resonant trap

TL;DR

This paper investigates the properties of a three-body system with two identical light bosons and a heavy particle, focusing on the technical aspects of locating three-body resonances near threshold using integral equations.

Contribution

It develops a method for constructing and analytically continuing integral equations to identify three-body resonance poles in systems with narrow inter-species resonances.

Findings

Established a framework for analyzing three-body resonances.

Demonstrated the analytic continuation technique for locating resonance poles.

Provided insights into the behavior of narrow resonances in three-body systems.

Abstract

It is rare for an $S$-wave resonance to remain narrow while approaching threshold as a result of the interaction parameters being fine tuned. Such an interaction is, however, realized by pion-charmed baryon system $\pi \Sigma_c$, which has a narrow resonance $\Lambda_c^+(2595)$ located a few MeVs above its threshold. We study the consequence of narrowly resonant inter-species interaction in a three-body system composed of two identical light bosons and an extremely heavy particle. We concern ourselves in the present paper with resonances of the three-body system, as opposed to bound states. The focus is on the technical aspects of constructing the integral equation for three-body amplitudes and of analytically continuing the integral equation to locate the "trimer" resonance pole in the unphysical sheet of the center-of-mass energy plane.