A family of double-beauty tetraquarks: Axial-vector state \begin{document}${{T}^{{-}}_{{bb};\overline{{u}}\overline{{s}}}}}$\end{document}

The spectroscopic parameters and decay channels of the axial-vector tetraquark \begin{document}$ T_{bb;\overline{u}\overline{s}}^{-} $\end{document} (in what follows, \begin{document}$ T_{b:\overline{s}}^{\mathrm{AV}} $\end{document} ) are explored using the quantum chromodynamics (QCD) sum rule method. The mass and coupling of this state are calculated using two-point sum rules by taking into account various vacuum condensates, up to 10 dimensions. Our prediction for the mass of this state \begin{document}$ m = (10215\pm 250)\; \mathrm{MeV} $\end{document} confirms that it is stable with respect to strong and electromagnetic decays and can dissociate to conventional mesons only via weak transformations. We investigate the dominant semileptonic \begin{document}$ T_{b:\overline{s}}^{\mathrm{AV}} \to {\cal{Z}}_{b:\overline{s}}^{0}l\overline{\nu}_l $\end{document} and nonleptonic \begin{document}$ T_{b:\overline{s}}^{\mathrm{AV}} \to {\cal{Z}}_{b:\overline{s}}^{0}M $\end{document} decays of \begin{document}$ T_{b:\overline{s}}^{\mathrm{AV}} $\end{document} . In these processes, \begin{document}$ {\cal{Z}}_{b:\overline{s}}^{0} $\end{document} is a scalar tetraquark \begin{document}$ [bc][\overline{u}\overline{s}] $\end{document} built of a color-triplet diquark and an antidiquark, whereas M is one of the vector mesons \begin{document}$ \rho ^{-} $\end{document} , \begin{document}$ K^{\ast}(892) $\end{document} , \begin{document}$ D^{\ast }(2010)^{-} $\end{document} , and \begin{document}$ D_{s}^{\ast -} $\end{document} . To calculate the partial widths of these decays, we use the QCD three-point sum rule approach and evaluate the weak transition form factors \begin{document}$ G_{i} $\end{document} ( \begin{document}$ i = 0.1,2,3 $\end{document} ), which govern these processes. The full width \begin{document}$ \Gamma _{\mathrm{full}} = (12.9\pm 2.1)\times 10^{-8}\; \mathrm{MeV} $\end{document} and the mean lifetime \begin{document}$ \tau = 5.1_{-0.71}^{+0.99}\; \mathrm{fs} $\end{document} of the tetraquark \begin{document}$ T_{b:\overline{s}}^{\mathrm{AV}} $\end{document} are computed using the aforementioned weak decays. The obtained information about the parameters of \begin{document}$ T_{b:\overline{s}}^{\mathrm{AV}} $\end{document} and \begin{document}$ {\cal{Z}}_{b:\overline{s}}^{0} $\end{document} is useful for experimental investigations of these double-heavy exotic mesons.