Two bosons in a narrowly resonant trap

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.

Comments: 15 pages, 9 figures