Hidden charm-bottom structures $bc\overline{b}\overline{c}$: Axial-vector case

Mass and width of a hidden charm-bottom axial-vector structure $T$ containing $bc \overline{b}\overline{c}$ quarks are calculated in QCD sum rule framework. It is treated as a diquark-antidiquark state built of scalar diquark and axial-vector antidiquark components. The mass of $T$ is computed using the two-point sum rule method. The width of this particle is evaluated by considering eight decay modes: The decays to $\eta _{b}J/\psi $, $\eta _{c}\Upsilon (1S)$, $B_{c}^{-}B_{c}^{\ast +}$, and $B_{c}^{+}B_{c}^{\ast -}$ are dissociation processes, in which all initial quarks are distributed between the final-state particles. The decays to $DD$ and $BB$ mesons with appropriate charges and spin-parities are channels generated due to the annihilations of $b\overline{b}$ and $c\overline{c}$ quarks from $T$. Partial widths for all of these processes are obtained by employing the three-point sum rule approach necessary to find the strong couplings at relevant tetraquark-meson-meson vertices. Our results for the mass $ m=(12715\pm 90)~\mathrm{MeV}$ and width $\Gamma[T] =(140 \pm 13)~ \mathrm{MeV }$ of the tetraquark $T$, as well as its numerous decay channels explored in this article are useful for ongoing and future experimental investigations of fully heavy resonances.