Semileptonic $\Omega_{b}^{*}\rightarrow\Omega_{c}^{*} \ell \bar{\nu}_{\ell}$ transition in QCD

Abstract

We employ the QCD sum rule method to study the semileptonic weak decay of the single bottom baryon $\Omega_{b}^{*}$ with spin $\frac{3}{2}$ into the single charmed baryon $\Omega_{c}^{*}$ with spin $\frac{3}{2}$, corresponding to a $\frac{3}{2}\rightarrow\frac{3}{2}$ weak transition. A three-point correlation function is calculated in both the physical and theoretical sides to derive the sum rules for the form factors of the transition. The analysis incorporates both the perturbative and non-perturbative contributions up to mass dimension six. After determining the working regions of the auxiliary parameters and performing numerical calculations of the sum rules of the form factors, we extract the $q^2$-dependent fit functions for the form factors. The obtained fit functions are then applied to compute the decay widths of the $\Omega_{b}^{*}\rightarrow\Omega_{c}^{*} \ell \bar{\nu}_{\ell}$ transition in all lepton channels. Our results, when compared with the future experimental data, can test the Standard Model predictions and probe potential deviations from the theoretical expectations in the $\Omega_{b}^{*}\rightarrow\Omega_{c}^{*} \ell \bar{\nu}_{\ell}$ weak decay.