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We perform a unified description of the experimental data of the $\pi^+\pi^-$and $J/\psi\pi^\pm$ invariant mass spectra for $e^+e^- \rightarrow J/\psi\pi^+\pi^-$ and the $D^0 D^{\ast-}$ mass spectrum for $e^+e^- \rightarrow D^0D^{\ast-} \pi^+$ at $e^+e^-$ center-of-mass energies 4.23 and 4.26 GeV. Theanalysis takes into account open-charm meson loops that contain trianglesingularities, the $J/\psi\pi$-$D\bar D^*$ coupled-channel interactionrespecting unitarity, and the strong $\pi\pi$-$K\bar K$ final state interactionusing dispersion relations. The analysis leads to a precise determination ofthe $Z_c(3900)$ pole with the pole mass and width $(3880.5 \pm 2.6)$ MeV and$(25.5 \pm 2.5)$ MeV, respectively, and hints at that the $D\bar D^*$ molecularand non-molecular components are of similar importance in the $Z_c(3900)$formation.

Precise determination of the pole position of the exotic $Z_c(3900)$