Semileptonic Kaon Decays

We present the matrix elements for the semileptonic kaon decays $K_{l2\gamma }$ , $K_{l2l^{+}{l}^{-}}$, $K_{l2l^{\mathrm{\prime }+}{l}^{\mathrm{\prime }-}}$,$K_{l3}$, $K_{l3\gamma }$ and $K_{l4}$ at next-to-leading order, and $K_{e5}$ at leading order in Chiral Perturbation Theory and compare the predictions with experimental data. For $K_{l4}$ decays we estimate yet higher orders in order to reduce theoretical uncertainties in the comparison with the data. Monte Carlo event generators are used to calculate the corresponding rates at DA$\mathrm{\Phi }$NE. We discuss the possibilities to improve our knowledge of the low-energy structure of the Standard Model at this and similar machines.