Coupled-Channel-Induced $S-D$ mixing of Charmonia and Testing Possible Assignments for $Y(4260)$ and $Y(4360)$

The mass spectrum and the two-body open-charm decays of the $J^{PC}=1^{--}$ charmonium states are studied with the coupled-channel effects taken into account. The coupled-channel-induced mixing effects among the excited vector charmonia are studied. Based on our calculations of the masses and the decay widths, we find that the tension between the observed properties of $Y(4260)/Y(4360)$ and their conventional charmonia interpretations could be softened.