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

The observation of $Z_c(3900)$ by the BESIII Collaboration in the invariant mass spectrum of $J/\psi {\pi }^{\pm }$ in $e^{+}{e}^{-}\to J/\psi {\pi }^{+}{\pi }^{-}$ at the center of mass 4.260 GeV suggests the existence of a charged $\overline{D}{D}^{*}+D{\overline{D}}^{*}$ 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 $\overline{D}{D}_1(2420)+D{\overline{D}}_1(2420)$ molecular state. Especially, we show that the decay of this molecule naturally populates low momentum $\overline{D}{D}^{*}$ pairs and leads unavoidably to a cusp at the $\overline{D}{D}^{*}$ threshold. We discuss the signatures that distinguish such a $\overline{D}{D}^{*}$ cusp from the presence of a true resonance.

Figure 1

The Feynman diagrams for $Y(4260)\to \overline{D}{D}_1+\mathrm{c}.\mathrm{c}.\to J/\psi \pi \pi$ and $h_c\pi \pi$ considered in this work.

Figure 2

The invariant mass spectra for (a) $J/\psi \pi$ and (b) $\pi \pi$ in $Y(4260)\to J/\psi \pi \pi$. The solid, dashed, and dotted lines stand for the results of the full calculation, box diagrams, and triangle diagram with the $Z_c(3900)$ pole, respectively.

Figure 3

The invariant mass spectra for (a) $h_c\pi$ and (b) $\pi \pi$ in $Y(4260)\to h_c\pi \pi$. The notations are the same as in Fig. 2.