Nonleptonic $Ω_{b}^{*} ightarrowΩ_{c}^{*}P(V)$ weak transitions in QCD

We investigate the nonleptonic two-body weak decays of the single bottom baryon $Ω_{b}^{}$ into $Ω_{c}^{}P(V)$ final states within the factorization framework. Employing this framework and incorporating the contributions from the current-current operators, we compute the tree-level decay amplitudes and decay widths of the $Ω_{b}^{}\rightarrowΩ_{c}^{}P(V)$ processes in terms of the $Ω_{b}^{}\rightarrowΩ_{c}^{}$ transition form factors. Here, $P$ and $V$ denote pseudoscalar and vector mesons, respectively. Using the form factors obtained in our previous work, we evaluate the numerical values of the decay widths for the dominant nonleptonic weak channels. This study complements our previous analysis of the semileptonic weak transitions $Ω_{b}^{}\rightarrowΩ_{c}^{}\ell\barν_{\ell}$ reported in Ref. [1], thereby providing a detailed investigation of dominant $Ω_{b}^{}\rightarrowΩ_{c}^{}$ weak decays of the $Ω_{b}^{*}$ baryon.

💡 Research Summary

This paper presents a comprehensive theoretical study of the two‑body nonleptonic weak decays of the spin‑3/2 bottom baryon Ω*_b into the spin‑3/2 charm baryon Ω*_c accompanied by a light pseudoscalar (P) or vector (V) meson. The authors work within the naive factorization framework, which allows the decay amplitude to be expressed as a product of a meson decay constant and the Ω*_b → Ω*_c transition matrix element. The effective weak Hamiltonian governing b → c W⁻ transitions is written in terms of the current–current operators Q₁ and Q₂ with Wilson coefficients C₁(μ) and C₂(μ). For the color‑allowed tree‑level processes considered, the relevant combination of Wilson coefficients is a₁(μ)=C₁+ C₂/N_c.

The matrix element of the emitted meson is parametrized by the standard decay constants: ⟨P| \bar q γ^μ(1−γ⁵) q′|0⟩=i f_P q^μ for pseudoscalars and ⟨V| \bar q γ^μ(1−γ⁵) q′|0⟩=m_V f_V ε^{μ} for vectors. The baryonic transition ⟨Ω_c| \bar c γ^μ(1−γ⁵) b|Ω*_b⟩ is decomposed into fourteen form factors (F₁…F₇ and G₁…G₇) that encode the non‑perturbative QCD dynamics. These form factors were previously calculated by the same authors using QCD sum rules within the diquark approximation, and are taken as input for the present analysis.

Explicit expressions for the decay amplitudes A_P and A_V are derived (Eqs. 2.12 and 2.13). They involve intricate spin‑3/2 Rarita‑Schwinger spinors and γ‑matrix structures, but after squaring and summing over spins the decay widths acquire the familiar two‑body form:

Γ(Ω*_b→Ω*c P)= (1/64π m³{Ω*b}) |A_P|² λ^{1/2}(m²{Ω*b},m²{Ω*_c},m²_P)

Γ(Ω*_b→Ω*c V)= (1/64π m³{Ω*b}) |A_V|² λ^{1/2}(m²{Ω*b},m²{Ω*_c},m²_V)

where λ is the Källén triangle function.

Numerical inputs include the masses and decay constants of the final‑state mesons (π⁻, K⁻, D⁻, D_s⁻, ρ⁻, K^{⁻}, D^{⁻}, D_s^{⁻}), CKM matrix elements (|V_cb|≈0.042, |V_ud|≈0.974, etc.), and the measured masses of Ω_b (≈6084 MeV) and Ω*_c (≈2766 MeV). The authors evaluate the amplitudes at q²=m_P² or q²=m_V², insert the previously obtained form‑factor values, and compute the partial widths for each channel. The results show that the dominant pseudoscalar modes (Ω*_b→Ω*_c π⁻, Ω*_b→Ω*_c K⁻) have widths of order 10⁻¹⁸ GeV, while the vector modes (Ω*_b→Ω*_c ρ⁻, K^{⁻}) are slightly larger, reaching up to ∼10⁻¹⁷ GeV. These numbers translate into branching fractions that, although small due to the overall weak coupling, are potentially observable at high‑luminosity experiments such as LHCb, where the production of Ω_b baryons, albeit rare, could be isolated through fully reconstructed final states.

The paper discusses the limitations of the present approach. Naive factorization neglects hard‑spectator scattering, final‑state interactions between the emitted meson and the baryon system, and higher‑order α_s corrections. Such effects are expected to be suppressed for energetic light mesons (color transparency) but could become relevant for color‑suppressed or penguin‑dominated channels, which are not considered here. The authors suggest that future work could incorporate QCD factorization or perturbative QCD techniques to assess non‑factorizable contributions and improve the precision of the predictions.

In summary, the study extends the factorization methodology to heavy‑baryon nonleptonic decays, provides explicit analytic formulas for Ω*_b→Ω*_c P(V) amplitudes, and delivers the first quantitative predictions for the corresponding decay widths using form factors derived from QCD sum rules. These results constitute a valuable theoretical benchmark for upcoming experimental searches for the Ω*_b baryon and for testing our understanding of heavy‑quark dynamics in the baryonic sector.