Tensor hybrid charmonia

Abstract

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 $D^{(\pm )}{D}^{\ast (\mp )}$, $D^0{\overline{D}}^{\ast 0}$, and $D_s^{(\pm )}{D}_s^{\ast (\mp )}$ mesons are taken into account. The processes ${\tilde{H}}_{\mathrm{c}}\to D^{(\ast )+}{D}^{(\ast )-}$, $D^{(\ast )0}{\overline{D}}^{(\ast )0}$, and $D_s^{(\ast )+}{D}_s^{(\ast )-}$ are employed to estimate the full width of the hybrid charmonium ${\tilde{H}}_{\mathrm{c}}$. 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 $m=(4.16\pm 0.14)\mathrm{GeV}$ , and $\tilde{m}=(4.5\pm 0.1)\mathrm{GeV}$ for the masses and $\hat{I}“\left[H_{\mathrm{c}}\right]=(160\pm 30)\mathrm{MeV}$, and $\hat{I}“\left[{\tilde{H}}_{\mathrm{c}}\right]=(206\pm 33)\mathrm{MeV}$ 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.

12 Pages, 4 Figures and 1 Table