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

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