Determination of the Kobayashi-Maskawa-Cabibbo matrix elementVusunder 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 success is by determining $V_{\mathrm{us}}$ in each of the three relevant hyperon semileptonic decays and comparing the values so obtained with one another and also with the one that comes from $K_{l3\mathrm{}}$ decays. A strong dependence on the particular symmetry-breaking model is observed. Values of $V_{\mathrm{us}}$ which do not agree with the one of $K_{l3\mathrm{}}$ are generally obtained. However, in the context of chiral perturbation theory, only the model whose corrections are $O\left(m_s\right)$ and $O\left(m_s^{\frac{3}{2}}\right)$ is successful. Using its predictions for the $f_1$ form factors one can quote a value of $V_{\mathrm{us}}$ from this model, namely, $V_{\mathrm{us}}=0.2176\mathrm{}\pm 0.0026$, which is in excellent agreement with the $K_{l3\mathrm{}}$ one.