Effective-range-expansion study of near threshold heavy-flavor resonances

Abstract

In this work we study the resonances near the thresholds of the open heavy-flavor hadrons using the effective-range-expansion method. The unitarity, analyticity and compositeness coefficient are also taken into account in our theoretical formalism. We consider the $Z_c(3900)$, $X(4020)$, $χ_{c1}(4140)$, $ψ(4260)$ and $ψ(4660)$. The scattering lengths and effective ranges from the relevant elastic $S$-wave scattering amplitudes are determined. Tentative discussions on the inner structures of the aforementioned resonances are given.

10 pages. Comparisons with other ways to define the compositeness are included. To match the published version