Spectroscopy of hidden-heavy tetraquark states with $J^{PC}=0^{--}$ in a color-octet configuration

Within the framework of QCD sum rules, we investigate hidden-heavy tetraquark states with the exotic quantum number $J^{PC}=0^{--}$ in color-octet configurations, namely $[Q\bar{q}{]}_{8_c}\otimes [q\bar{Q}{]}_{8_c}$ and $[Q\bar{Q}{]}_{8_c}\otimes [\bar{q}q{]}_{8_c}$ with $Q=c,b$. Since the $0^{--}$ quantum number cannot be realized by conventional $q\bar{q}$ mesons, the observation of such a state would provide a particularly clean signal for exotic hadronic structures. We construct four color-octet interpolating currents for the hidden-heavy systems and carry out the operator product expansion up to dimension-eight condensates. Our numerical analysis indicates that the hidden-bottom sector exhibits the clearest sum-rule stability, with flatter Borel platforms than the corresponding hidden-charm sector. We obtain four $0^{--}$ hidden-bottom tetraquark candidates in the mass range $10.8$–$11.1\mathrm{G}\mathrm{e}\mathrm{V}$, while their hidden-charm partners are predicted around $4.3$–$4.6\mathrm{G}\mathrm{e}\mathrm{V}$. The extracted masses suggest a compact spectral pattern with a mild dependence on the underlying color-octet clustering structure. We also discuss possible decay patterns and emphasize that the absence of the lowest pseudoscalar–pseudoscalar heavy-meson channels is a distinctive consequence of the exotic $0^{--}$ assignment. These results provide useful theoretical guidance for future searches for hidden-heavy exotic states at Belle II and LHCb, with complementary probes of the hidden-charm partners at BESIII.