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 $(2878\pm 128)\mathrm{MeV}$ 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 ${\mathrm{\Gamma }}_{\mathrm{full}}=(3.28\pm 0.60)\times {10}^{-10}\mathrm{MeV}$ 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.

Figure 1

The mass $m_T$ of the tetraquark $T_{cs}^0$ as a function of the Borel and continuum threshold parameters.

Figure 2

The same as in Fig. 1, but for the coupling $f_T$.

Figure 3

The strong coupling $|g_{T{D}^0{\overline{K}}^0}|$ as a function of the Borel and continuum threshold parameters.

Figure 4

Dependence of the weak form factor $G_1(q^2)$ on $q^2$: the QCD sum rule predictions and the fit function ${\mathcal{G}}_1(q^2)$. The solid line corresponds to the central values of the parameters ${\mathcal{G}}_1^0$, $g_1^1$, $g_2^1$, for the upper dashed curve ${\mathcal{G}}_1^0=1.126$, $g_1^1=1.792$, $g_2^1=-0.875$, whereas for the lower dashed line ${\mathcal{G}}_1^0=0.901$, $g_1^1=1.255$, $g_2^1=1.106$.

Figure 5

The form factor $|G_2(q^2)|$. The solid line describes the central function. Parameters of the upper and lower dashed curves are ${\mathcal{G}}_1^0=-0.982$, $g_1^1=1.771$, $g_2^1=-0.545$, and ${\mathcal{G}}_1^0=-0.790$, $g_1^1=1.039$, $g_2^1=2.414$, respectively.

Figure 6

Some of the decay modes of the tetraquark $T_{bb;\overline{u}\overline{d}}^{-}$.