  The mass and coupling of the scalar tetraquark $T_{bb;\overline{u}\overline{d
}}^{-}$ (hereafter $T_{b:\overline{d}}^{-} $) are calculated in the context of
the QCD two-point sum rule method. In computations we take into account effects
of various quark, gluon and mixed condensates up to dimension ten. The result
obtained for the mass of this state $m=(10135\pm 240)~\mathrm{MeV} $
demonstrates that it is stable against the strong and electromagnetic decays.
We also explore the dominant semileptonic $T_{b:\overline{d}}^{-} \to
\widetilde{Z}_{bc;\bar{u}\bar{d}}^{0}l\overline{\nu }_{l}$ and nonleptonic
decays $T_{b:\overline{d}}^{-} \to \widetilde{Z}_{bc;\bar{u}\bar{ d}}^{0}M$,
where $\widetilde{Z}_{bc;\bar{u}\bar{d}}^{0}$ is the scalar tetraquark composed
of color-sextet diquark and antidiquark, and $M$ is one of the final-state
pseudoscalar mesons $\pi^{-}, K^{-}, D^{-}$ and $D_s^{-}$ , respectively. The
partial widths of these processes are calculated in terms of the weak form
factors $G_{1(2)}(q^2)$, which are determined from the QCD three-point sum
rules. Predictions for the mass, full width $\Gamma _{\mathrm{full}} =(10.88\pm
1.88)\times 10^{-10}~\mathrm{MeV}$, and mean lifetime
$\tau=0.61_{-0.09}^{+0.13}~\mathrm{ps}$ of the $T_{b:\overline{d} }^{-}$
obtained in the present work can be used in theoretical and experimental
studies of this exotic state.
