Study of the semileptonic decay $Λ\to p\,\ell\,\barν_{\ell}$ in QCD

TL;DR

This study determines the full set of vector and axial-vector form factors for the semileptonic decay $\Lambda \to p\ell\bar{\nu}$ using QCD sum rules applied to a three-point correlator. The authors compute the form factors $F_1,F_2,F_3,G_1,G_2,G_3$ via the hadronic and QCD representations, employing a double Borel transform and quark-hadron duality to suppress excited states. They model the $q^{2}$-dependence with both a polynomial fit and a $z$-expansion to extrapolate across the physical region, then use these form factors to obtain decay widths, branching ratios, and the ratio $R^{\mu e}$ for $\mu$ versus $e$ channels. The results are in good agreement with PDG and lattice QCD, with the $z$-expansion offering higher precision and strong compatibility with experimental averages, highlighting the viability of hyperon semileptonic decays as probes of SM dynamics and CKM elements such as $|V_{us}|$.

Abstract

We conduct a comprehensive study of the semileptonic decay process \(Λ\to p\,\ell\,\barν_{\ell}\), focusing on the determination of all six vector and axial-vector form factors that govern the low-energy hadronic matrix elements of the underlying theory. These invariant form factors constitute the essential inputs for describing the decay, and their dependence on the momentum transfer \(q^{2}\) is analyzed across the entire physical kinematic region. To parametrize the \(q^{2}\)dependence, we adopt both the \(z\)-expansion formalism and a polynomial fitting approach. Utilizing parametrizations, we compute the exclusive decay widths for both the electron and muon channels, and subsequently extract the corresponding branching ratios. Furthermore, we evaluate the ratio of decay widths between the muon and electron channels defined as $R^{μe} \equiv \frac{Γ(Λ\to p\,μ\,\barν_μ)}{Γ(Λ\to p\,e\,\barν_{e})}$ obtaining \(R^{μe} = 0.196^{+0.009}_{-0.012}\) from the polynomial fit and \(R^{μe} = 0.174^{+0.002}_{-0.005}\) from the \(z\) expansion. While both ratios are compatible with previously reported values in the literature, the result from the \(z\) expansion exhibits particularly strong agreement with the averages reported by the Particle Data Group.

Figures (8)

• Figure 1: Illustration of the semileptonic decay $\Lambda \rightarrow p ~{\ell}\bar{\nu}_{\ell}$.
• Figure 2: The dependence of the form factor $F_3$ associated with the structure $p'_{\mu}\slashed {p}$ on $\cos\theta$ evaluated at the central values of $s_0$, $s'_0$, $M^2$, $M'^2$ and at $q^2=0$.
• Figure 3: Dependence of the form factors on the Borel parameter $M^2$ for various $s_0$, evaluated at $q^2=0$ and the mean values of other auxiliary parameters.
• Figure 4: Dependence of the form factors on the Borel parameter $M'^2$ for various $s_0$, evaluated at $q^2=0$ and the mean values of other auxiliary parameters.
• Figure 5: Dependence of the form factors on the Borel parameter $M^2$ for various $s'_0$, evaluated at $q^2=0$ and the mean values of other auxiliary parameters.