Determination of the Kobayashi-Maskawa-Cabibbo matrix element $V_{us}$ under various flavor-symmetry breaking models in hyperon semileptonic decays

We study the success to describe hyperon semileptonic decays of four models that incorporate second-order $SU(3)$ symmetry breaking corrections. The criteria to assess their successs is by determining $V_{us}$ in each of the three relevant hyperon semileptonic decays and comparing the values obtained with one another and also with the one that comes from $K_{l3}$ decays. In the context of chiral perturbation theory, only the model whose corrections are $O(m_s)$ and $O(m_s^{3/2})$ is successful. Using its predictions for the $f_1$ form factors one can quote a value of $V_{us}$ from hyperon semileptonic decays, namely, $V_{us} = 0.2176 \pm 0.0026$, which is in excellent agreement with the $K_{l3}$ one.