On effective range expansion in a multichannel system and compositeness of near-threshold resonance

We discuss effective range expansion in a two-channel system and establishing the nature of a near-threshold hadronic resonance with the help of parameters obtained from a fit to experimental data. In particular, the situation of two strong thresholds located close to each other and a hadronic resonance residing at the lower of them is considered. For the case of a bound state, simple expressions are derived that allow one to estimate the probability of finding the given resonance in each hadronic channel and as a compact quark state if the resonance wave function contains such a component.