Kl3-Decay Form Factors, Current Algebra, and Subtracted Dispersion Relations. II

Once-subtracted dispersion relations are used together with the algebra of currents and soft-pion techniques to investigate the form factors $f_{\pm }\mathrm{}\left(t\right)\mathrm{}$ which describe $K_{l3\mathrm{}}$ decays. Particular attention is paid to the influence of $S$-wave $K\pi$ states, and results are obtained which depend explicitly on the $S$-wave phase shift. Various parametrizations of this phase shift are made in an effort to clarify the interdependence of the $K\pi$ scattering amplitude and the $K_{l3\mathrm{}}$ form factors. It is found to be difficult to obtain a value for $\xi \equiv \frac{f_{-}\mathrm{}\left(0\right)\mathrm{}}{f_{+}\mathrm{}\left(0\right)\mathrm{}}$ which is not small and negative, while the momentum dependence of $f_{-}\mathrm{}\left(t\right)\mathrm{}$ may be quite rapid in some cases.