$Y(4260)$ as the first $S$-wave open charm vector molecular state?

Since its first observation in 2005, the vector charmonium $Y(4260)$ has turned out to be one of the prime candidates for an exotic state in the charmonium spectrum. It was recently proposed that the $Y(4260)$ should have a prominent $D_1\overline{D}+\mathrm{c}.\mathrm{c}.$ molecular component that is strongly correlated with the production of the charged $Z_c(3900)$. In this paper we demonstrate that the nontrivial cross section line shapes of $e^{+}{e}^{-}\to J/\psi \pi \pi$ and $h_c\pi \pi$ can be naturally explained by the molecular scenario. As a consequence we find a significantly smaller mass for the $Y(4260)$ than previously studied. In the $e^{+}{e}^{-}\to \overline{D}{D}^{*}\pi +\mathrm{c}.\mathrm{c}.$ process, with the inclusion of an additional $S$-wave ${\overline{D}}^{*}\pi$ contribution constrained from data on the $D{\overline{D}}^{*}$ invariant mass distribution, we obtain a good agreement with the data of the angular distributions. We also predict an unusual line shape of $Y(4260)$ in this channel that may serve as a smoking gun for a predominantly molecular nature of $Y(4260)$. Improved measurements of these observables are therefore crucial for a better understanding of the structure of this famous resonance.

Figure 1

Feynman diagrams for the $e^{+}{e}^{-}\to Y(4260)\to D{\overline{D}}^{*}\pi$ via (a) the tree diagram and (b) an intermediate $Z_c$.

Figure 2

The cross sections for the $e^{+}{e}^{-}\to J/\psi {\pi }^{+}{\pi }^{-}$ and $e^{+}{e}^{-}\to h_c{\pi }^{+}{\pi }^{-}$ around the $Y(4260)$ mass region. The long-dashed, short-dashed, dotted, and solid lines are the contributions from the $D_1\overline{D}$ box diagrams, the $Z_c(3900)$ pole, the $S$-wave background and the sum of them, respectively. The data in (a) are from Belle [35] and those in (b) from BESIII [7], respectively.

Figure 3

The $D^0{\pi }^{+}$, $D^{*-}{\pi }^{+}$, and $D^0{D}^{*-}$ invariant mass distributions for $Y(4260)\to D^0{D}^{*-}{\pi }^{+}$. The brown dotted, green dashed, and red solid lines are the contributions from the $S$-wave, the $D$-wave, and the sum of them, respectively.

Figure 4

Predictions for the cross section of $e^{+}{e}^{-}\to D{\overline{D}}^{*}\pi$ with the dashed, dotted, and solid lines denoting the contributions from $D$-wave, $S$-wave, and the sum of them, respectively. Here the $D$-wave contribution is from our model due to the $D$-wave behavior between ${\overline{D}}^{*}$ and $\pi$. Meanwhile the $S$-wave contribution means the background contribution with the ${\overline{D}}^{*}$ and $\pi$ in $S$-wave. The data are from Belle [39].

Figure 5

Angular distribution of the pion in the rest frame of the $Y(4260)$ with respect to the beam axis (Jackson angle). The legends are the same as that in Fig. 3. The experimental data are from Ref. [37].

Figure 6

The partial width of $Y(4260)\to D^0{D}^{*-}{\pi }^{+}$ is shown in terms of the relative angle between the ${\pi }^{+}$ and the $D^0$ in the $D^0{D}^{*-}$ rest frame. The legends are the same as that in Fig. 3. Left panel: using the whole Dalitz plot; right panel: with a cut on small $D{\overline{D}}^{*}$ invariant masses imposed, i.e. using the events from the $D{\overline{D}}^{*}$ threshold to 3.92 GeV.

Figure 7

Left panel: Pion angular distribution from the general amplitude of Eq. (a1). The green dashed, brown dotted, and red solid lines are the contributions from $D$-wave, $S$-wave, and the sum of them. The experimental data are from Ref. [37]. Right panel: ${\chi }^2$ in terms of the $S$-wave strength parameter $C_S$—for each value of $C_S$ the parameter $C_D$ is refitted.