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arXiv:2403.18696v1 Announce Type: cross
Abstract: We revisit the masses of heavy quarkonium double-gluon hybrid mesons with $J^{PC}=1^{-+}$ and $2^{+-}$ in the framework of the QCD sum rules. Considering the $\bar QGGQ$ operators in the $(\mathbf{8}_{[\bar{Q}Q]} \otimes \mathbf{8}_{[GG]})$ color structure, we have constructed two independent interpolating currents with $J^{PC}=1^{-+}$ and five independent currents with $J^{PC}=2^{+-}$, in which the glueball operators can be symmetric $d^{rst}G^{s}_{\mu\nu}G^{t}_{\alpha\beta}$ or antisymmetric $f^{rst}G^{s}_{\mu\nu}G^{t}_{\alpha\beta}$. For the interpolating currents with antisymmetric glueball operator $f^{rst}G^{s}_{\mu\nu}G^{t}_{\alpha\beta}$, there exist non-local divergences in one kind of additional Feynman diagrams of tri-gluon condensate, which will give important contributions to the sum rule stabilities and mass predictions. We use the diagrammatic operator renormalization to cancel out such divergences. At the leading order of $\alpha_s$, the two-point correlation functions and spectral densities can be expressed in the analytic form of the generalized hypergeometric functions and Meijer's G-functions. After performing the numerical analysis, we predict the masses of the $1^{-+}$ and $2^{+-}$ charmonium double-gluon hybrid mesons to be around $6.1-7.2$ GeV and $6.3-6.4$ GeV, respectively. For the bottomonium systems, their masses are predicted to be $13.7-14.3$ GeV and $12.6-13.3$ GeV for the $1^{-+}$ and $2^{+-}$ channels, respectively. Besides, it is possible to hunt for these charmonium $\bar{c}GGc$ hybrids in the radiative decays of $\Upsilon (nS)$ and $\chi_{bJ}$ mesons in BelleII experiment. Further investigations on these hybrid states in various theoretical and phenomenological methods are also anticipated in the future.