Prospects of $|V_{us}|$ and axial vector form factors in $\Lambda\to pe^{-}{\bar\nu}_{e}$ decay at STCF

We report a feasibility study of the semileptonic decay $\Lambda\to pe^{-} {\bar\nu}_{e}$ by using a fast simulation software package at STCF. With an anticipated integrated luminosity of 3.4 trillion $J/\psi$ per year at a center-of-mass energy at 3.097 GeV, the statistical sensitivity of the branching fraction is determined to be 0.15\%. The statistical sensitivities of form factors $g_{av}$ and $g_w$ are determined to be 0.4\% and 2.15\%, respectively. Combining this result with $g_1(0)$ from Lattice QCD, we can obtain the projected sensitivity of $|V_{us}|$, to be 0.9\%, which is comparable to the precision obtained through meson decay measurements. The precise measurement to be obtained at STCF will provide a rigorous test of Standard Model.