Semileptonic $Ω_{b}^{*}\rightarrowΩ_{c}^{*} \ell \barν_{\ell}$ transition in QCD

TL;DR

The study addresses the semileptonic decay $\Omega_{b}^{*}\to\Omega_{c}^{*}\ell\bar{\nu}_{\ell}$ in a $3/2\to3/2$ transition using three‑point QCD sum rules. It computes the correlator on both the hadronic and quark–gluon sides, including perturbative and nonperturbative contributions up to dimension six, to extract the fourteen form factors $F_i(q^2)$ and $G_i(q^2)$ and fits their $q^2$ dependence for full kinematic coverage. Using these form factors, the authors calculate decay widths for all lepton channels and provide a tau-to-light-lepton width ratio $R \approx 0.29$, enabling tests of SM expectations. The results furnish nonperturbative QCD benchmarks for heavy baryon weak decays and offer predictions to guide and interpret upcoming measurements at facilities such as LHCb.

Abstract

We employ the QCD sum rule method to study the semileptonic weak decay of the single bottom baryon $Ω_{b}^{*}$ with spin $\frac{3}{2}$ into the single charmed baryon $Ω_{c}^{*}$ 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 $Ω_{b}^{*}\rightarrowΩ_{c}^{*} \ell \barν_{\ell}$ 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 $Ω_{b}^{*}\rightarrowΩ_{c}^{*} \ell \barν_{\ell}$ weak decay.

Figures (4)

• Figure 1: Dependence of the form factors, $F_i$ and $G_i$, on the auxiliary parameters $M^2$ and $s_0$ at $q^2 = 0$, with the other auxiliary parameters fixed at their central values, for the first set of selected structures.
• Figure 2: Dependence of the form factors, $F_i$ and $G_i$, on the auxiliary parameters $M'^2$ and $s'_0$ at $q^2 = 0$, with the other auxiliary parameters fixed at their central values, for the first set of selected structures.
• Figure 3: The behavior of the form factors, $F_i$ and $G_i$, as functions of $q^2$ at the central values of the auxiliary parameters for the first set of selected structures.
• Figure 4: The behavior of the form factors, $F_i$ and $G_i$, as functions of $q^2$ at the central values of the auxiliary parameters, using the fitted functions with their corresponding errors from Tables \ref{['VecF']} and \ref{['AVecF']}.