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

Abstract

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 $(2878\pm 128)\mathrm{MeV}$ 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}

9 Pages, 6 Figures and 2 Tables

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