$Y(4260)$ 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 $D_1\bar{D}+c.c.$ 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 previous studied. In the $e^+e^-\to \bar D D^*\pi+c.c.$ process, with the inclusion of an additional $S$-wave $\bar D^*\pi$ contribution constrained from data on the $D\bar D^*$ 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.