Unified Fano-like interference picture for charmonium-like states $Y(4008)$, $Y(4260)$ and $Y(4360)$

We propose that the unified Fano-like interference picture applies to $e^+e^-\to \pi^+\pi^- J/\psi$ and $e^+e^-\to \pi^+\pi^- \psi(3686)$, where $Y(4260)$ and $Y(4360)$ are observed, respectively, to provide a reasonable interpretation of the asymmetric lines hapes of $Y(4260)$ and $Y(4360)$ structures. Moreover, the Fano-like interference induces an extra broad structure $Y(4008)$ in $e^+e^-\to \pi^+\pi^- J/\psi$ as a companion peak to $Y(4260)$. Three charmonium-like states $Y(4008)$, $Y(4260)$ and $Y(4360)$ observed in $e^+e^-$ annihilation processes are not genuine resonances. Under this scenario, it is well explained why $Y(4008)$, $Y(4260)$ and $Y(4360)$ are absent in the experimental data of the $R$ value scan and missing in open-charm decay channels. Although the present work presents a typical application of the Fano-like interference in particle physics at the lower energy region, we have reason to believe that the Fano-like phenomena may exist in other processes such as $e^+e^-\to \pi^+\pi^-\psi(3770)$ and $e^+e^-\to K^+K^- J/\psi$, which will be accessible at BESIII and forthcoming BelleII.