Decay modes of the scalar exotic meson ${T}_{bs;\overline{u}\overline{d}}^{-}$

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 $b\to cl{\overline{\nu }}_{l}$. 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 $\left(2878±128\right)\text{}\text{}\mathrm{MeV}$ 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 ${G}_{1}\left({q}^{2}\right)$ and ${G}_{2}\left({q}^{2}\right)$, 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 ${\Gamma }_{\mathrm{full}}=\left(3.28±0.60\right)×{10}^{-10}\text{}\text{}\mathrm{MeV}$ and mean lifetime $\tau =2.0{1}_{-0.31}^{+0.44}\text{}\text{}\mathrm{ps}$ 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.