Consistency of Hard-Pion Theorems inKl3Decays

The $K_{l3\mathrm{}}$ scalar form factor is studied by the hard-pion method in the framework of a (3,$3^{*}$)+($3^{*}$,3)-symmetry-breaking model using a modified pole-dominance approximation. A set of consistency relations is found which provides a test of the reliability of the quadratic-smoothness assumption as well as of the symmetry-breaking model. In particular, we find that the solution for the symmetry-breaking parameters which fit the data is inconsistent with the quadratic-smoothness assumption. In addition, the status of other theoretical models is briefly reviewed.