# A coupled-channel lattice study on the resonance-like structure $Z_c(3900)$

## TL;DR

This lattice QCD study investigates the $Z_c(3900)$ resonance-like structure through coupled-channel scattering analysis of $D$ and $ar{D}^*$ mesons, providing insights into its nature and challenging the resonance interpretation.

## Contribution

First lattice QCD analysis using coupled-channel formalism to study the $Z_c(3900)$ structure, combining finite-volume energy levels with Ross-Shaw theory to extract scattering parameters.

## Key findings

- No peak behavior in elastic scattering cross section near threshold.
- Disfavors a narrow resonance scenario for $Z_c(3900)$ beyond 3 sigma.
- Scattering parameters suggest the $Z_c(3900)$ may not be a conventional resonance.

## Abstract

In this exploratory study, near-threshold scattering of $D$ and $\bar{D}^*$ meson is investigated using lattice QCD with $N_f=2+1+1$ twisted mass fermion configurations. The calculation is performed within the coupled-channel L\"uscher's finite-size formalism. The study focuses on the channel with $I^G(J^{PC})=1^+(1^{+-})$ where the resonance-like structure $Z_c(3900)$ was discovered. We first identify the most relevant two channels of the problem and the lattice study is performed within the two-channel scattering model. Combined with a two-channel Ross-Shaw theory, scattering parameters are extracted from the energy levels by solving the generalized eigenvalue problem. Our results on the scattering length parameters suggest that, at the particular lattice parameters that we studied, the best fitted parameters do not correspond to a peak behavior in the elastic scattering cross section near the threshold. Furthermore, within the zero-range Ross-Shaw theory, the scenario of a narrow resonance close to the threshold is disfavored beyond $3\sigma$ level.