Analysis of the semileptonic decays $Σ_b oΣ_clarν_l$, $Ξ'_b oΞ'_clarν_l$ and $Ω_b oΩ_clarν_l$ in QCD sum rules

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.

💡 Research Summary

In this work the authors perform a comprehensive study of the semileptonic decays Σ_b → Σ_c ℓ ν̄_ℓ, Ξ′_b → Ξ′_c ℓ ν̄_ℓ and Ω_b → Ω_c ℓ ν̄_ℓ (ℓ = e, μ, τ) using three‑point QCD sum rules (QCDSR). The motivation is twofold: (i) these transitions probe the b → c weak current in a baryonic environment, providing a testing ground for Heavy‑Quark Effective Theory (HQET) and SU(3) flavor symmetry; (ii) experimental information on the sextet bottom baryons (Σ_b, Ξ′_b, Ω_b) is still scarce, especially for their weak decays.

The paper begins by writing the effective weak Hamiltonian H_eff = (G_F/√2) V_cb \bar c γ^μ(1−γ_5) b \bar ℓ γ_μ(1−γ_5) ν_ℓ and decomposes the hadronic matrix element ⟨B_f| \bar c γ^μ(1−γ_5) b |B_i⟩ into six independent form factors: vector f_1, f_2, f_3 and axial‑vector g_1, g_2, g_3, all functions of the momentum transfer q². The authors then introduce helicity amplitudes H_{λ_f,λ_W}=H^V_{λ_f,λ_W}−H^A_{λ_f,λ_W} and express the differential decay widths for longitudinal (L) and transverse (T) W‑boson polarizations in terms of these amplitudes. Integration over q² yields the total widths Γ for each lepton flavor.

On the QCD side, a three‑point correlation function Π_μ(p′,q) is constructed with interpolating currents for the initial and final baryons and the weak current. A key methodological advance is the systematic inclusion of all possible couplings of the interpolating currents to both positive‑parity (½⁺) and negative‑parity (½⁻) states. By doing so the authors eliminate any dependence on the choice of Dirac structure, a source of ambiguity in earlier sum‑rule calculations.

The operator product expansion (OPE) is carried out up to dimension‑8 condensates, i.e. vacuum expectation values of operators such as ⟨\bar qq⟩, ⟨G²⟩, ⟨\bar q G q⟩, and four‑ and six‑quark condensates. Inclusion of these higher‑dimensional terms dramatically enlarges the set of Feynman diagrams contributing to the correlation function, improves the convergence of the OPE, and reduces the systematic uncertainty associated with truncation. After performing a double Borel transformation in the two external momenta and invoking quark–hadron duality with appropriate continuum thresholds s₀, the authors obtain sum‑rule expressions for each of the six form factors.

Numerically, the authors adopt up‑to‑date input parameters: quark masses (m_b, m_c), the CKM element V_cb, condensate values, and baryon masses from the Particle Data Group. The Borel windows are chosen as M² ∈