The spectroscopic parameters and decay channels of the axial-vector tetraquark $T_{bb;overline{u}overline{s}}^{-}$ (in what follows, $T_{b: overline{s}}^{mathrm{AV}}$) 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 $m=(10215pm 250)~ mathrm{MeV}$ 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 $T_{b:overline{s} }^{mathrm{AV}} to mathcal{Z}_{b:overline{s}}^{0}loverline{ u}_l$ and nonleptonic $T_{b:overline{s}}^{mathrm{AV}} to mathcal{Z}_{b:overline{s} }^{0}M$ decays of $T_{b:overline{s}}^{mathrm{AV}}$. In these processes, $ mathcal{Z}_{b:overline{s}}^{0}$ is a scalar tetraquark $[bc][overline{u} overline{s}]$ built of a color-triplet diquark and an antidiquark, whereas $M$ is one of the vector mesons $rho ^{-}$, $K^{ast}(892)$, $D^{ast }(2010)^{-}$, and $D_{s}^{ast -}$. To calculate the partial widths of these decays, we use the QCD three-point sum rule approach and evaluate the weak transition form factors $G_{i}$ $(i=0,1,2,3)$, which govern these processes. The full width $Gamma _{mathrm{full}} =(12.9pm 2.1)times 10^{-8}~mathrm{MeV}$ and the mean lifetime $ tau=5.1_{-0.71}^{+0.99}~mathrm{fs}$ of the tetraquark $T_{b:overline{s}}^{ mathrm{AV}}$ are computed using the aforementioned weak decays. The obtained information about the parameters of $T_{b:overline{s}}^{mathrm{AV}}$ and $ mathcal{Z}_{b:overline{s}}^{0}$ is useful for experimental investigations of these double-heavy exotic mesons.
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