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

TL;DR

This paper predicts the mass, stability, and weak decay properties of the scalar tetraquark $T_{bb;ar{u}ar{s}}^{-}$ using QCD sum rules, providing essential data for future experimental searches.

Contribution

It offers the first detailed calculation of the mass, decay channels, form factors, and lifetime of the exotic scalar tetraquark $T_{bb;ar{u}ar{s}}^{-}$ using advanced sum rule techniques.

Findings

Mass of $T_{b:ar{s}}^{-}$ is $(10250 \, ext{MeV})$ with stability against strong and electromagnetic decays.

Predicted full decay width is $(15.21 \, imes 10^{-10})$ MeV.

Estimated mean lifetime is approximately $4.33 imes 10^{-13}$ seconds.

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 $T_{b:\overline{s}}^{-} \to Z_{bc;\overline{u}\overline{s}}^{0}l\overline{ \nu }_{l}$ and nonleptonic modes $T_{b:\overline{s}}^{-} \to Z_{bc;\overline{ u}\overline{s}}^{0}\pi^{-}(K^{-}, D^{-}, D_s^{-})$, 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 $d\Gamma/dq^2$ 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 $\Gamma _{\mathrm{full}}=(15.21\pm 2.59)\times 10^{-10}~\mathrm{ MeV}$ 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.