  While the standard model is the most successfully theory to describe all
interactions and constituents in elementary particle physics, it has been
constantly examined for over four decades. Weak decays of charm quarks can
measure the coupling strength of quarks in different families and serve as an
ideal probe for CP violation. As the lowest charm-strange baryons with three
different flavors, $\Xi_c$ baryons (made of $csu$ or $csd$) have been
extensively studied in experiments at the large hadron collider and in
electron-positron collision. However the lack of reliable knowledge in theory
becomes the unavoidable obstacle in the way. In this work, we use the
state-of-the-art Lattice QCD techniques, and generate 2+1 clover fermion
ensembles with two lattice spacings, $a=(0.108{\rm fm},0.080{\rm fm})$. We then
present the first {\it ab-initio} lattice QCD determination of form factors
governing $\Xi_{c}\to \Xi \ell^+\nu_{\ell}$, analogous with the notable
$\beta$-decay of nuclei. Our theoretical results for decay widths are
consistent with and about two times more precise than the latest measurements
by ALICE and Belle collaborations. Together with experimental measurements, we
independently determine the quark-mixing matrix element $|V_{cs}|$, which is
found in good agreement with other determinations.
