Analysis of the semileptonic decays $Σ_b\toΣ_cl\barν_l$, $Ξ'_b\toΞ'_cl\barν_l$ and $Ω_b\toΩ_cl\barν_l$ in QCD sum rules

TL;DR

This work analyzes the vector and axial-vector transition form factors governing the semileptonic decays of single heavy baryons $\Sigma_b\to\Sigma_c$, $\Xi'_b\to\Xi'_c$, and $\Omega_b\to\Omega_c$ within three-point QCD sum rules. By constructing a comprehensive three-point correlator and including perturbative and condensate contributions up to dimension $8$, the authors obtain twenty-four form factors in the $++$ parity sector and fit their $q^2$-dependence via a $z$-series expansion. Using these form factors, they predict differential and total decay widths, branching ratios (notably $\mathcal B(\Omega_b\to\Omega_c l\nu)$ in the percent range), lepton-universality ratios $R_{\mathcal B_f}$, and helicity asymmetries $A_{FB}$ and $\alpha$, observing approximate $SU(3)$ flavor symmetry in the widths. The results provide a consistent, Dirac-structure–independent set of hadronic inputs for heavy-baryon weak decays and offer benchmarks for upcoming experimental tests and new-physics studies.

Abstract

In this article, the electroweak transition form factors of $Σ_b\toΣ_c$, $Ξ'_b\toΞ'_c$ and $Ω_b\toΩ_c$ are analyzed within the framework of three-point QCD sum rules. In phenomenological side, all possible couplings of interpolating current to hadronic states are considered, and the Dirac structure dependence on the form factors is systematically eliminated. In QCD side, our calculation incorporates both the perturbative part and the contributions from vacuum condensates up to dimension 8. This systematic inclusion of higher-dimensional terms accounts for a broader set of Feynman diagrams, thereby enhancing the comprehensiveness and reliability of the operator product expansion. Using the obtained form factors, we study the partial widths of semileptonic decays $Σ_b\toΣ_cl\barν_l$, $Ξ'_b\toΞ'_cl\barν_l$ and $Ω_b\toΩ_cl\barν_l$ ($l=e$, $μ$ and $τ$). The results indicate that these decay widths approximately satisfy SU(3) flavor symmetry. Next, we calculate the branching ratios for the decay process $Ω_b\toΩ_cl\barν_l$ and compare them with the results from other collaborations. Furthermore, the lepton universality ratios and some asymmetry parameters of these decay processes are also analyzed, which provide information for the study of new physics. We hope that these results will serve as a useful reference for future theoretical and experimental studies of weak decays involving heavy flavor baryons.

Figures (6)

• Figure 1: The Feynman diagram for semileptonic decays $\Sigma_b\to\Sigma_cl\bar{\nu}_l$, $\Xi'_b\to\Xi'_cl\bar{\nu}_l$ and $\Omega_b\to\Omega_cl\bar{\nu}_l$.
• Figure 2: The Feynman diagrams for the perturbative part and vacuum condensate terms in quark level, where the blue, red, green and black solid lines denote the $b$, $c$, $q_1$ and $q_2$ quark lines, respectively. The black loop lines are the gluon lines.
• Figure 3: The pole contributions (a) and the contributions of perturbative term and different vacuum condensates (b) of formfactors $F_1$ for $\Sigma_b\to\Sigma_c$ transition. The grey bound represent Borel platform.
• Figure 4: The fitting results of vector (a-c) and axial vector (d-f) form factors for $\Sigma_b\to\Sigma_c$ transition.
• Figure 5: It is the same as Fig. \ref{['FFS']}, but for $\Xi'_b\to\Xi'_c$ transition.