$Z_c(3900)$: what has been really seen?

Abstract

The $Z^\pm_c(3900)/Z^\pm_c(3885)$ resonant structure has been experimentally observed in the $Y(4260) \to J/\psi \pi\pi$ and $Y(4260) \to \bar{D}^\ast D \pi$ decays. This structure is intriguing since it is a prominent candidate of an exotic hadron. Yet, its nature is unclear so far. In this work, we simultaneously describe the $\bar{D}^\ast D$ and $J/\psi \pi$ invariant mass distributions in which the $Z_c$ peak is seen using amplitudes with exact unitarity. Two different scenarios are statistically acceptable, where the origin of the $Z_c$ state is different. They correspond to using energy dependent or independent $\bar D^* D$ $S$-wave interaction. In the first one, the $Z_c$ peak is due to a resonance with a mass around the $D\bar D^*$ threshold. In the second one, the $Z_c$ peak is produced by a virtual state which must have a hadronic molecular nature. In both cases the two observations, $Z^\pm_c(3900)$ and $Z^\pm_c(3885)$, are shown to have the same common origin, and a $\bar D^* D$ bound state solution is not allowed. Precise measurements of the line shapes around the $D\bar D^*$ threshold are called for in order to understand the nature of this state.