Heavy exotic scalar meson Tbb;u¯s¯−

Abstract

The spectroscopic parameters and decay channels of the scalar tetraquark ${T}_{bb;\overline{u}\overline{s}}^{\ensuremath{-}}$ (in what follows ${T}_{b:\overline{s}}^{\ensuremath{-}}$) are investigated in the framework of the QCD sum rule method. The mass and coupling of the ${T}_{b:s}^{\ensuremath{-}}$ 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 $m=(10250\ifmmode\pm\else\textpm\fi{}270)\text{ }\text{ }\mathrm{MeV}$ demonstrates that ${T}_{b:\overline{s}}^{\ensuremath{-}}$ is stable against the strong and electromagnetic decays. Therefore to find the width and mean lifetime of the ${T}_{b:\overline{s}}^{\ensuremath{-}}$, we explore its dominant weak decays generated by the transition $b\ensuremath{\rightarrow}{W}^{\ensuremath{-}}c$. These channels embrace the semileptonic decay ${T}_{b:\overline{s}}^{\ensuremath{-}}\ensuremath{\rightarrow}{Z}_{bc;\overline{u}\overline{s}}^{0}l{\overline{\ensuremath{\nu}}}_{l}$ and nonleptonic modes ${T}_{b:\overline{s}}^{\ensuremath{-}}\ensuremath{\rightarrow}{Z}_{bc;\overline{u}\overline{s}}^{0}{\ensuremath{\pi}}^{\ensuremath{-}}({K}^{\ensuremath{-}},{D}^{\ensuremath{-}},{D}_{s}^{\ensuremath{-}})$, 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 $d\mathrm{\ensuremath{\Gamma}}/d{q}^{2}$ 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 ${m}_{l}^{2}\ensuremath{\le}q2\ensuremath{\le}(m\ensuremath{-}\stackrel{\texttildelow{}}{m}{)}^{2}$, where $\stackrel{\texttildelow{}}{m}$ is the mass of ${Z}_{bc;\overline{u}\overline{s}}^{0}$. Predictions for the full width ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{full}}=(15.21\ifmmode\pm\else\textpm\fi{}2.59)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\text{ }\text{ }\mathrm{MeV}$ and mean lifetime ${4.33}_{\ensuremath{-}0.63}^{+0.89}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\text{ }\text{ }\mathrm{s}$ of the ${T}_{b:s}^{\ensuremath{-}}$ are useful for experimental and theoretical investigations of this exotic meson.