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The weak decays of the axial-vector tetraquark $T_{bb;\bar{u} \bar{d}}^{-}$to the scalar state $Z_{bc;\bar{u} \bar{d}}^{0}$ are investigated using the QCDthree-point sum rule approach. In order to explore the process $T_{bb; \bar{u}\bar{d}}^{-} \to Z_{bc;\bar{u} \bar{d}}^{0}l \bar{\nu_l}$, we recalculate thespectroscopic parameters of the tetraquark $T_{bb;\bar{u} \bar{d}}^{-}$ andfind the mass and coupling of the scalar four-quark system $Z_{bc;\bar{u}\bar{d}}^{0}$, which are important ingredients of calculations. Thespectroscopic parameters of these tetraquarks are computed in the framework ofthe QCD two-point sum rule method by taking into account various condensates upto dimension ten. The mass of the $T_{bb;\bar{u} \bar{ d}}^{-}$ state is foundto be $m=(10035~\pm 260)~\mathrm{MeV}$, which demonstrates that it is stableagainst the strong and electromagnetic decays. The full width $\Gamma$ and meanlifetime $\tau$ of $T_{bb;\bar{u} \bar{d} }^{-}$ are evaluated using itssemileptonic decay channels $T_{bb; \bar{u} \bar{d}}^{-} \to Z_{bc;\bar{u}\bar{d}}^{0}l \bar{\nu_l}$, $l=e,\mu$ and $\tau$. The obtained results,$\Gamma=(7.17\pm 1.23)\times 10^{-8\ \ } \mathrm{MeV}$ and $\tau=9.18_{-1.34}^{+1.90}~\mathrm{fs}$, can be useful for experimentalinvestigations of the doubly-heavy tetraquarks.

Weak decays of the axial-vector tetraquark $T_{bb;\bar{u} \bar{d}}^{-}$