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

Abstract

The $Z_c^{\pm }(3900)/Z_c^{\pm }(3885)$ 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 ${\bar{D}}^{\ast }D$ $S$-wave interaction. In the first one, the $Z_c$ peak is due to a resonance with a mass around the $D{\bar{D}}^{\ast }$ 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, $Z_c^{\pm }(3900)$ and $Z_c^{\pm }(3885)$, are shown to have the same common origin, and a ${\bar{D}}^{\ast }D$ bound state solution is not allowed. Precise measurements of the line shapes around the $D{\bar{D}}^{\ast }$ threshold are called for in order to understand the nature of this state.

6 pages, 6 figures

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