Tensor hybrid charmonia

The mass and current coupling of the tensor hybrid charmonia $ {H}_{\mathrm{c}}$ and $ {\tilde{H}}_{\mathrm{c}}$ with quantum numbers $ {J}^{\mathrm{PC}}={2}^{-+}$ and $ {2}^{++}$, as well as their full widths, are calculated in the context of the QCD sum rule method. The spectral parameters of these states are computed using the QCD two-point sum rule approach including dimension-12 terms $ \sim ⟨{g}_{s}^{3}{G}^{3}{⟩}^{2}$. The full decay widths of the charmonia $ {H}_{\mathrm{c}}$ and $ {\tilde{H}}_{\mathrm{c}}$ are evaluated by considering their kinematically allowed decay channels. In the case of the hybrid state $ {H}_{\mathrm{c}}$, decays to $ {D}^{(\pm )}{D}^{*(\mp )}$, $ {D}^{0}{\overline{D}}^{*0}$, and $ {D}_{s}^{(\pm )}{D}_{s}^{*(\mp )}$ mesons are taken into account. The processes $ {\tilde{H}}_{\mathrm{c}}\to {D}^{(*)+}{D}^{(*)-}$, $ {D}^{(*)0}{\overline{D}}^{(*)0}$, and $ {D}_{s}^{(*)+}{D}_{s}^{(*)-}$ are employed to estimate the full width of the hybrid charmonium $ {\tilde{H}}_{\mathrm{c}}$. The partial widths of these decays are computed by means of the QCD three-point sum rule method, which is necessary to calculate strong couplings at the relevant hybrid-meson-meson vertices. Our predictions $ m=(4.16\pm 0.14)\text{}\text{}\mathrm{GeV}$ and $ \tilde{m}=(4.5\pm 0.1)\text{}\text{}\mathrm{GeV}$ for the masses and $ \mathrm{\Gamma }[{H}_{\mathrm{c}}]=(160\pm 30)\text{}\text{}\mathrm{MeV}$ and $ \mathrm{\Gamma }[{\tilde{H}}_{\mathrm{c}}]=(206\pm 33)\text{}\text{}\mathrm{MeV}$ for the full width of these hybrid charmonia can be useful to study and interpret various resonances in the 4–5 GeV mass range.