Tensor hybrid charmonia

The mass and current coupling of the tensor hybrid charmonia $H_{\mathrm{c}} $ and $\widetilde{H}_{\mathrm{c}}$ 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 \langle g_{s}^{3}G^{3}\rangle ^{2} $. The full decay widths of the charmonia $H_{\mathrm{c}}$ and $\widetilde{H}_{\mathrm{c}}$ are evaluated by considering their kinematically allowed decay channels. In the case of the hybrid state $H_{\mathrm{c}} $ decays to $D^{(\pm )}D^{\ast (\mp )}$, $D^{0} \overline{D}^{\ast 0}$, and $D_{s}^{(\pm )}D_{s}^{\ast (\mp )} $ mesons are taken into account. The processes $\widetilde{H}_{\mathrm{c}} \to D^{(\ast)+}D^{(\ast )-}$, $D^{(\ast) 0}\overline{D}^{(\ast) 0}$, and $ D_{s}^{(\ast)+}D_{s}^{(\ast) -} $ are employed to estimate the full width of the hybrid charmonium $\widetilde{H}_{\mathrm{c}}$. 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 $m=(4.16\pm 0.14)~\mathrm{GeV}$ , and $\widetilde{m}=(4.5\pm 0.1)~\mathrm{GeV}$ for the masses and $\Gamma \left[ H_{\mathrm{c}}\right] =(160\pm 30)~\mathrm{MeV}$, and $\Gamma \left[ \widetilde{H }_{\mathrm{c}}\right] =(206\pm 33)~\mathrm{MeV}$ for the full width of these hybrid charmonia can be useful to study and interpret various resonances in the $4-5~\mathrm{GeV}$ mass range.