Systematic analysis of the D-wave charmonium states with the QCD sum rules

We systematically study the 1D charmonium spin-triplet (with the $J^{PC}=1^{--},2^{--},3^{--}$) and spin-singlet (with the $J^{PC}=2^{-+}$) via the QCD sum rules in comparison with the recent experimental results. The predicted mass $M_{{\psi }_1}=3.77\pm 0.09\mathrm{G}\mathrm{e}\mathrm{V}$ supports identifying the ${\psi }_1$ as the $\psi (3770)$, the value $M_{{\psi }_2}=3.82\pm 0.09\mathrm{G}\mathrm{e}\mathrm{V}$ is consistent with the reported observation of the ${\psi }_2(3823)$, the prediction $M_{{\psi }_3}=3.84\pm 0.08\mathrm{G}\mathrm{e}\mathrm{V}$ supports identifying the ${\psi }_3$ as the ${\psi }_3(3842)$. Additionally, we estimate the unobserved ${\eta }_{c2}$ state lies at $3.83\pm 0.09\mathrm{G}\mathrm{e}\mathrm{V}$, and suggest detection prospects in the future. More experimental data will help us to unravel the mass spectrum of the charmonium states near the open-charm thresholds.