Broken Chiral Symmetry and the Veneziano Model

We investigate chiral-symmetry breaking within the $K\pi$ system when a Veneziano model is assumed for various off-mass-shell extrapolations. We derive expressions for the matrix elements of $\sigma$ terms and the divergence of the strangeness-changing current and discuss the implications to chiral-symmetry-breaking interactions. Application of our results to the $K_{l3\mathrm{}}$ form factors gives $\frac{f_K}{f_{\pi }{f}_{+}\mathrm{}\left(0\right)\mathrm{}}=1.35\mathrm{}$ and the relation ${\left(\frac{f_K}{f_{\pi }}\right)}^2=cos\left[{{\alpha }_{K^{*}}}^{\prime }\mathrm{}\right(0\left)\right({{\mu }_K}^2-{{\mu }_{\pi }}^2\left)\right]$.