Reconciling experimental and lattice data of $Z_c(3900)$ in a $J/\psi\pi$-$D\bar{D}^*$ coupled-channel analysis

TL;DR

This paper presents a coupled-channel analysis of the $Z_c(3900)$ state, fitting experimental and lattice data to predict scattering properties and identify poles associated with the state.

Contribution

It introduces a covariant coupled-channel framework that simultaneously fits experimental invariant-mass distributions and lattice QCD energy levels for the $Z_c(3900)$.

Findings

Poles corresponding to $Z_c(3900)$ are identified in the complex energy plane.

The analysis predicts phase shifts and inelasticities consistent with experimental data.

Current lattice data do not exclude the existence of a physical $Z_c(3900)$ state.

Abstract

We study the $J/\psi \pi$ and $D\bar{D}^*$ coupled-channel system within a covariant framework. The $J/\psi \pi$ and $D\bar{D}^*$ invariant-mass distributions measured at 4.23~GeV and 4.26~GeV by BESIII and the finite-volume energy levels from recent lattice QCD simulations are simultaneously fitted. Phase shifts and inelasticities of the $J/\psi \pi$ and $D\bar{D}^*$ scattering are predicted using the resulting amplitudes. Poles corresponding to the $Z_c(3900)$ state are found in the complex energy plane and their couplings with $J/\psi \pi$ and $D\bar{D}^*$ are determined. Our results indicate that the current lattice data do not preclude the existence of a physical $Z_c(3900)$ state.