# Semileptonic decays of the scalar tetraquark $Z_{bc;\overline{u} \overline{d}}^{0}$

## TL;DR

This paper calculates the decay properties and lifetime of the scalar tetraquark $Z_{bc;ar{u}ar{d}}^{0}$ using QCD sum rules, providing theoretical predictions for its semileptonic and nonleptonic decay widths.

## Contribution

It introduces a comprehensive QCD sum rule analysis of the $Z_{bc;ar{u}ar{d}}^{0}$ tetraquark's decay channels and lifetime, including new calculations of form factors and decay widths.

## Key findings

- Predicted full decay width of (3.18 ± 0.39) × 10^{-11} MeV.
- Estimated mean lifetime of approximately 20.7 ps.
- Provided form factors for semileptonic decays across the entire kinematic range.

## Abstract

We study semileptonic decays of the scalar tetraquark $Z_{bc;\overline{u} \overline{d}}^{0}$ to final states $T_{bs;\overline{u}\overline{d} }^{-}e^{+}\nu_{e}$ and $T_{bs;\overline{u}\overline{d}}^{-}\mu^{+}\nu_{\mu}$ , which run through the weak transitions $c\to se^{+}\nu_{e}$ and $c\to s\mu^{+}\nu_{\mu}$, respectively. To this end, we calculate the mass and coupling of the final-state scalar tetraquark $T_{bs;\overline{u}\overline{d} }^{-} $ by means of the QCD two-point sum rule method: these spectroscopic parameters are used in our following investigations. In calculations we take into account the vacuum expectation values of the quark, gluon, and mixed operators up to dimension ten. We use also three-point sum rules to evaluate the weak form factors $G_{i}(q^2)$ ($i=1,~2$) that describe these decays. The sum rule predictions for $G_{i}(q^2)$ are employed to construct fit functions $F_{i}(q^2)$, which allow us to extrapolate the form factors to the whole region of kinematically accessible $q^2$. These functions are required to get partial widths of the semileptonic decays $\Gamma \left( Z_{bc}^{0}\rightarrow Te^{+}\nu_{e}\right) $ and $\Gamma \left( Z_{bc}^{0}\rightarrow T\mu ^{+}\nu_{\mu }\right)$ by integrating corresponding differential rates. We analyze also the two-body nonleptonic decays $Z_{bc;\overline{u}\overline{d}}^{0} \to T_{bs;\overline{u}\overline{d }}^{-}\pi^{+}$ and $Z_{bc;\overline{u}\overline{d}}^{0} \to T_{bs;\overline{u }\overline{d}}^{-}K^{+}$, which are necessary to evaluate the full width of the $Z_{bc;\overline{u}\overline{d}}^{0}$. The obtained results for $\Gamma_{ \mathrm{full}}=(3.18\pm 0.39)\times 10^{-11}~\mathrm{MeV}$ and mean lifetime $20.7_{-2.3}^{+2.9}~\mathrm{ps}$ of the tetraquark $Z_{bc;\overline{u} \overline{d}}^{0}$ can be used in experimental investigations of this exotic state.