We investigate the semileptonic decay of the scalar tetraquark $T_{ bs; \overline{ u}\overline{ d}}^{ -}$ to final state $T_{ cs;\overline{ u}\overline{ d} }^{ 0} l \overline{ \nu}_l$, which proceeds due to the weak transition $b \to c l \overline{ \nu}_l$. For these purposes, we calculate the spectroscopic parameters of the final-state scalar tetraquark $T_{ cs;\overline{ u}\overline{ d}}^{ 0}$. In calculations we use the QCD sum rule method by taking into account the quark, gluon, and mixed condensates up to dimension 10. The mass of the $T_{ cs;\overline{ u}\overline{ d}}^{ 0}$ obtained in the present work $( 2878 \pm 128 )~\mathrm{ MeV}$ indicates that it is unstable against the strong interactions, and can decay to the mesons $D^{ 0}\overline{ K}^{ 0}$ and $D^{ +}K^{ -}$. Partial widths of these $S$-wave modes as well as the full width of the tetraquark $T_{ cs;\overline{ u}\overline{ d}}^{ 0}$ are found by means of the QCD light-cone sum rule method and technical tools of the soft-meson approximation. The partial widths of the main semileptonic processes $T_{ bs;\overline{ u}\overline{ d}}^{ -} \to T_{ cs;\overline{ u} \overline{ d}}^{ 0}l\overline{ \nu}_l$, $l=e, \mu$, and $\tau$ are computed by employing the weak form factors $G_{ 1}(q^2)$ and $G_{ 2}(q^2)$, which are extracted from the QCD three-point sum rules. We also trace back the weak transformations of the stable tetraquark $T_{ bb;\overline{ u}\overline{ d} }^{ -} $ to conventional mesons. The obtained results for the full width $ \Gamma_{ \mathrm{ full}}=(3.28\pm 0.60) \times 10^{ -10}~\mathrm{ MeV} $ and mean lifetime $\tau=2.01_{ -0.31}^{ +0.44}~\mathrm{ ps}$ of $T_{ bs;\overline{ u} \overline{ d}}^{ -}$, as well as predictions for decay channels of the tetraquark $T_{ bb;\overline{ u}\overline{ d}}^{ -}$ can be used in experimental studies of these exotic states. \end{ abstract}
Categories: hep-ph hep-ex hep-lat