Structure of Near-Threshold s-Wave Resonances

TL;DR

This paper analyzes the structure of near-threshold s-wave resonances and bound states, revealing constraints on their properties, and applies the findings to the Lambda_c(2595) resonance, suggesting it is not a simple molecule.

Contribution

It introduces a new understanding of resonance properties constrained by pole positions and discusses the compositeness of resonances through analytic continuation.

Findings

Resonance properties are constrained by pole positions within the effective range expansion.

The compositeness of resonances is purely imaginary and normalized.

Lambda_c(2595) likely not a pi Sigma_c molecule due to large effective range.

Abstract

We study the structure of two-body s-wave bound states as well as resonances in the threshold energy region. We focus on the single-channel scattering where the scattering length and the effective range are given by real numbers. It is shown that, in the energy region where the effective range expansion is valid, the properties of resonances are constrained only by the position of the pole. We find that the compositeness defined through the analytic continuation of the field renormalization constant is pure imaginary and normalized for resonances. We discuss the interpretation of this quantity by examining the structure of the hadron resonance Lambda_c(2595) in the pi Sigma_c scattering. We show that the Lambda_c(2595) resonance requires an unnaturally large effective range and hence it is not likely a pi Sigma_c molecule.