Decoding the riddle of Y(4260) and $Z_c(3900)$

Abstract

The observation of $Z_c(3900)$ by the BESIII collaboration in the invariant mass spectrum of $J/\ddot{I}ˆ\ddot{I}{€}^{\pm }$ in $e^{+}{e}^{-}\to J/\ddot{I}ˆ\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ at the center of mass 4.260 GeV suggests the existence of a charged $\bar{D}{D}^{\ast }+D{\bar{D}}^{\ast }$ molecular state with $I(J^P)=1(1^{+})$, which could be an isovector brother of the famous X(3872) and an analogue of $Z_b(10610)$ claimed by the Belle Collaboration. We demonstrate that this observation provides strong evidence that the mysterious Y(4260) is a $\bar{D}{D}_1(2420)+D{\bar{D}}_1(2420)$ molecular state. Especially, we show that the decay of this molecule naturally populates low momentum $\bar{D}{D}^{\ast }$ pairs and leads unavoidably to a cusp at the $\bar{D}{D}^{\ast }$ threshold. We discuss the signatures that distinguish such a $\bar{D}{D}^{\ast }$ cusp from the presence of a true resonance.

Version to appear in Phys. Rev. Letters