Heavy exotic scalar meson $T_{bb;\bar{u}\bar{s}}^{-}$

Abstract

The spectroscopic parameters and decay channels of the scalar tetraquark $ T_{bb;\overline{u}\overline{s}}^{-}$ (in what follows $T_{b:\overline{s} }^{-} $) are investigated. The mass and coupling of the $T_{b:s}^{-}$ are calculated using the two-point sum rules by taking into account quark, gluon and mixed vacuum condensates up to dimension 10. Our result for its mass $m=(10250 \pm 270)~\mathrm{MeV}$ demonstrates that $T_{b:\overline{s}}^{-} $ is stable against the strong and electromagnetic decays. Therefore to find the width and mean lifetime of the $T_{b:\overline{s}}^{-}$, we explore its dominant weak decays generated by the transition $b \to W^{-}c$. These channels embrace the semileptonic decay $T_{b:\overline{s}}^{-} \to Z_{bc;\overline{u}\overline{s}}^{0}l\overline{ ν}_{l}$ and nonleptonic modes $T_{b:\overline{s}}^{-} \to Z_{bc;\overline{ u}\overline{s}}^{0}π^{-}(K^{-}, D^{-}, D_s^{-})$, which at the final state contain the scalar tetraquark $Z_{bc;\overline{u}\overline{s}}^{0}$. Key quantities to compute partial widths of the weak decays are the form factors $G_1(q^2)$ and $G_2(q^2)$: they determine differential rate $dΓ/dq^2$ of the semileptonic and partial widths of the nonleptonic processes, respectively. These form factors are extracted from relevant three-point sum rules at momentum transfers $q^2$ accessible for such analysis. By means of the fit functions $F_{1(2)}(q^2)$ they are extrapolated to cover the whole integration region $m_l^{2}\leq q2\leq(m-\widetilde m)^2$, where $\widetilde m$ is the mass of $Z_{bc;\overline{u}\overline{s}}^{0}$. Predictions for the full width $Γ_{\mathrm{full}}=(15.21\pm 2.59)\times 10^{-10}~\mathrm{ MeV}$ and mean lifetime $4.33_{-0.63}^{+0.89}\times 10^{-13}~\mathrm{s}$ of the $T_{b:s}^{-} $ are useful for experimental and theoretical investigations of this exotic meson.