Exploratory study of the coupled-channel scattering in finite volume and the $Z_c(3900)$ resonance

TL;DR

This paper develops a theoretical framework for coupled-channel scattering in finite volume and applies it to analyze the $Z_c(3900)$ resonance, comparing predictions with recent lattice QCD spectra.

Contribution

It introduces a formalism for unitarized coupled-channel scattering in finite volume and applies it to the $Z_c(3900)$ resonance, bridging theory and lattice data.

Findings

Predicted finite-volume spectra for $Z_c(3900)$

Compared theoretical predictions with lattice QCD results

Provided insights into the nature of the $Z_c(3900)$ resonance

Abstract

In this note we first introduce the theoretical formalism of the unitarization of the two-body scattering both in the infinite and finite volumes. Then we apply this formalism to the study of the $Z_c(3900)$ resonance in the $J/\psi\,\pi$ and $D\bar{D}^{*}$ coupled-channel scattering. The recent lattice finite-volume spectra are confronted with our predictions.