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We demonstrate that the recent measurement of the cross section line shapesof $e^+e^-\to \chi_{c0}\omega$ can be naturally explained by the molecularpicture for $Y(4260)$ where the $Y(4260)$ is treated as a hadronic moleculedominated by $\bar{D}D_1(2420)+c.c.$ This result is consistent with propertiesextracted for $Y(4260)$ as the $\bar{D}D_1(2420)+c.c.$ molecular state in otherreactions such as $e^+e^-\to J/\psi\pi\pi$, $h_c\pi\pi$, $\bar D D^*\pi +c.c.$,and $\gamma X(3872)$.

Cross section line shape of $e^+e^-\to\chi_{c0}\omega$ around the $Y(4260)$ mass region