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.
Highlights
We explore its dominant weak decays generated by the transition b
Investigation of exotic mesons that are composed of four quarks is among the interesting topics of the high energy physics
Our analysis has proved that the exotic meson
Summary
Investigation of exotic mesons that are composed of four quarks (tetraquarks) is among the interesting topics of the high energy physics. Masses of these four-quark compounds are above the Dþs DÃs0þð2317Þ and DþDÃs0þð2317Þ thresholds, and they can decay to these conventional mesons The widths of these strong decays, evaluated in Ref. In accordance with results of this work the mass of the isoscalar axial-vector state equals to m 1⁄4 ð10389 Æ 12Þ MeV which is 215 MeV below the This means that the tetraquark is stable against the strong and electromagnetic decays and transforms to ordinary mesons only through weak processes. For these purposes, we derive two-point sum rules from analysis of corresponding correlation functions and include into calculations the quark, gluon and mixed condensates up to dimension ten. Appendix contains explicit expressions of quark propagators, and the correlation function used to evaluate parameters of the tetraquark T−b∶s
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