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

Abstract

We perform a unified description of the experimental data of the ${\pi }^{+}{\pi }^{-}$ and $J/\psi {\pi }^{\pm }$ invariant mass spectra for $e^{+}{e}^{-}\to J/\psi {\pi }^{+}{\pi }^{-}$ and the $D^0{D}^{\ast -}$ mass spectrum for $e^{+}{e}^{-}\to D^0{D}^{\ast -}{\pi }^{+}$ at $e^{+}{e}^{-}$ center-of-mass energies 4.23 and 4.26 GeV. The analysis takes into account open-charm meson loops that contain triangle singularities, the $J/\psi \pi$-$D{\bar{D}}^{\ast }$ coupled-channel interaction respecting unitarity, and the strong $\pi \pi$-$K\bar{K}$ final state interaction using dispersion relations. The analysis leads to a precise determination of the $Z_c(3900)$ pole with the pole mass and width $(3880.7\pm 1.7_{\text{stat}}\pm 22.4_{\text{syst}})$ MeV and $(35.9\pm 1.4_{\text{stat}}\pm 15.3_{\text{syst}})$ MeV, respectively, and hints at that the $D{\bar{D}}^{\ast }$ molecular and non-molecular components are of similar importance in the $Z_c(3900)$ formation.

Comments: 15 pages, 4 figures, systematic uncertainties provided, more discussions added. Version to be published in SCPMA