Properties of the tensor state $ bc\overline{b}\overline{c}$

Spectroscopic parameters and decays of the exotic tensor meson $ T$ with content $ bc\overline{b}\overline{c}$ are explored in the context of the diquark-antidiquark model. We treat it as a state built of axial-vector diquark $ {b}^{T}C{\gamma }_{\mu }c$ and antidiquark $ \overline{b}{\gamma }_{\nu }C{\overline{c}}^{T}$, where $ C$ is the charge conjugation matrix. The mass $ m$ and current coupling $ \mathrm{\Lambda }$ of this tetraquark are extracted from two-point sum rules. Our result for $ m=(12.70\pm 0.09)\text{}\text{}\mathrm{GeV}$ proves that $ T$ is unstable against strong dissociations to two-meson final states. Its dominant decay channels are processes $ T\to J/\psi \mathrm{\Upsilon }$, $ {\eta }_{b}{\eta }_{c}$, and $ {B}_{c}^{(*)+}{B}_{c}^{(*)-}$. Kinematically allowed transformations of $ T$ include also decays $ T\to {D}^{(*)+}{D}^{(*)-}$ and $ {D}^{(*)0}{\overline{D}}^{(*)0}$, which are generated by $ b\overline{b}$ annihilation inside of $ T$. The full width of $ T$ is estimated by considering all of these channels. Their partial widths are calculated by invoking methods of three-point sum rule approach, which are required to evaluate strong couplings at corresponding tetraquark-meson-meson vertices. Our predictions for the mass and width $ {\mathrm{\Gamma }}_{T}=(117.4\pm 15.9)\text{}\text{}\mathrm{MeV}$ of the tensor state $ T$ provide useful information for experimental studies of fully heavy four-quark exotic structures.