Study of the semileptonic decay $\Lambda \to p\,\ell\,\bar{\nu}_{\ell}$ in QCD

We conduct a comprehensive study of the semileptonic decay process $\Lambda \to p\,\ell\,\bar{\nu}_{\ell}$, 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 $R^{\mu e} \equiv \frac{\Gamma(\Lambda \to p\,\mu\,\bar{\nu}_{\mu})}{\Gamma(\Lambda \to p\,e\,\bar{\nu}_{e})}$ obtaining $R^{\mu e} = 0.196^{+0.009}_{-0.012}$ from the polynomial fit and $R^{\mu e} = 0.174^{+0.002}_{-0.005}$ 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.