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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 reasonableinterpretation of the asymmetric lines hapes of $Y(4260)$ and $Y(4360)$structures. Moreover, the Fano-like interference induces an extra broadstructure $Y(4008)$ 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. Underthis scenario, it is well explained why $Y(4008)$, $Y(4260)$ and $Y(4360)$ areabsent in the experimental data of the $R$ value scan and missing in open-charmdecay channels. Although the present work presents a typical application of theFano-like interference in particle physics at the lower energy region, we havereason to believe that the Fano-like phenomena may exist in other processessuch as $e^+e^-\to \pi^+\pi^-\psi(3770)$ and $e^+e^-\to K^+K^- J/\psi$, whichwill be accessible at BESIII and forthcoming BelleII.

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