$D$ wave charmonia

Inspired by the recent observations of the vector charmonium-like states at BES III Collaboration and $\psi(3842)$ at LHCb Collaboration, we comb the $D$ wave charmonium state in the present work. We first evaluate the possibility of $Y(4320)$ as $\psi(3^3D_1)$ by investigating its open charm decays in quark-pair creation model and we find the width of $Y(4320)$ can be reproduced in a reasonable parameter range. Moreover, we take $\psi(3770)$, $\psi(4160)$ and $Y(4320)$ as the scale of $1D$, $2D$ and $3D$ charmonia to estimate the open charm decays of other $D$ wave charmonia. The total and partial widths of $D$ wave charmonium states have been predicted, which could be tested by further measurements at LHCb and Belle II Collaborations.