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Description
This work presents a non-perturbative lattice-QCD study of the semileptonic decay (\Lambda \to p\ell\bar{\nu}_{\ell}), where (\ell=e,\mu). The main objective is to calculate the hadronic transition matrix element
$$ \langle p|\bar{u}\gamma^\mu(1-\gamma_5)s|\Lambda\rangle $$ and extract the corresponding vector and axial-vector form factors. Two-point and three-point correlation functions are constructed on the lattice. Excited-state contamination is reduced using the summation method, correlated global fits, and jackknife resampling. The momentum-transfer dependence of the form factors is described using a model-independent \(z\)-expansion with the appropriate kinematic constraints. The extracted form factors are then used to calculate the differential and total decay rates, $$ \Gamma_\ell = \int_{m_\ell^2}^{(m_\Lambda-m_N)^2} dq^2\, \frac{d\Gamma_\ell}{dq^2}, $$ and to determine the CKM matrix element \(\lvert V_{us}\rvert\). Using experimental baryon masses, the resulting muon-to-electron decay-rate ratio is $$ R_{\mu/e}=0.16464(18), $$ while the extracted values of \(\lvert V_{us}\rvert\) are $$ V_{us,e}=0.2438(21), V_{us,\mu}=0.2557(161). $$
The study demonstrates the feasibility of determining (\Lambda)-baryon semileptonic form factors from lattice QCD. Further calculations with multiple lattice spacings, improved mass tuning, and continuum extrapolation are required for a precision determination of (\lvert V_{us}\rvert).
\langle p|\bar{u}\gamma^\mu(1-\gamma_5)s|\Lambda\rangle
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