We present a lattice-QCD determination of the $\Lambda \to p$ vector and axial-vector form factors, providing theoretical input for studies of the semileptonic decay $\Lambda \to p\ell\bar{\nu}_\ell$.
The calculation is carried out on a single gauge ensemble with physical light, strange, and charm quark masses and delivers a precise determination of the complete set of transition form factors, including second-class contributions.

Using these form factors, we compute decay rates for both the electronic and muonic channels, as well as their ratio, which offers a sensitive test of lepton-flavor universality and possible non-standard scalar or tensor interactions.

This decay mode provides a theoretically well-controlled avenue for extracting the CKM matrix element $|V_{us}|$ from the baryon sector.

Our estimate of $|V_{us}|$ is obtained by combining our recent lattice-QCD results with recent measurements of the relevant branching fraction reported by BESIII and LHCb.