Effective range expansion for narrow near-threshold resonances

TL;DR

This paper examines the effective range expansion's features and parameters, especially for near-threshold states like $ ext{X}(3872)$ and $T_{cc}^+$, highlighting their likely molecular nature.

Contribution

It provides a detailed analysis of the effective range expansion for near-threshold states, including modifications for coupled channels and isospin violations, with applications to exotic hadrons.

Findings

$ ext{X}(3872)$ and $T_{cc}^+$ are predominantly molecular states.

Effective range expansion parameters reveal the nature of near-threshold states.

Modifications are necessary for coupled channels and isospin violations.

Abstract

We discuss some general features of the effective range expansion, the content of its parameters with respect to the nature of the pertinent near-threshold states and the necessary modifications in the presence of coupled channels, isospin violations and unstable constituents. As illustrative examples, we analyse the properties of the $\chi_{c1}(3872)$ and $T_{cc}^+$ states supporting the claim that these exotic states have a predominantly molecular nature.