We present the first lattice QCD determination of the $\mathrm{\Lambda }\to N$ vector and axial-vector form factors, which are essential inputs for studying the semileptonic decay $\mathrm{\Lambda }\to p\ell {\overline{\nu }}_{\ell }$. This channel provides a clean, theoretically controlled avenue for extracting the Cabibbo-Kobayashi-Maskawa matrix element $|V_{us}|$ from the baryon sector. Our analysis uses a gauge ensemble with physical light, strange, and charm quark masses and yields the most precise determination to date of the full set of transition form factors—including second-class contributions—as well as the associated couplings, radii, and the ratio of muon-to-electron decay rates, an observable sensitive to possible nonstandard scalar and tensor interactions. We compare our nonperturbative results with next-to-next-to-leading order expansions in the small parameter $\delta =(m_{\mathrm{\Lambda }}-m_N)/m_{\mathrm{\Lambda }}\approx 0.16$. We find that the common phenomenological approximation of neglecting the $q^2$ dependence of the form factors leads to a $\sim 4\%$ deviation in the decay rate. This underscores the critical importance of precise, fully nonperturbative form factor inputs for achieving the subpercent precision targets of upcoming experimental programs.

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• Beta decay
• Cabibbo–Kobayashi–Maskawa matrix
• Leptonic, semileptonic & radiative decays
• Nuclear transition rates
• Baryons
• Form factors
• Lattice QCD
• Lattice gauge theory
• Nuclear structure & decays