(Kπ) Phase Shifts from a Current-Algebra Model

An earlier model for ($\pi \pi$) $S$-wave phase shifts from current algebra and partially conserved axial-vector current is extended to the ($K\pi$) $S$-wave phase shifts in the isospin-½ channel. The solutions depend on a cutoff parameter and give the scattering length in the range $\frac{0.12}{m_{\pi }}-\frac{0.18}{m_{\pi }}$, a broad maximum of the phase shift in the range 1200-1500 MeV, and a slow decrease to zero at higher energies. The height of the maximum is cutoff-dependent; its value has been estimated by requiring saturation of the ($K\pi$) Adler-Weisberger relation. The results are applied to give information on the form factors of $K_{\mu 3}$ decay. In particular, we find $\xi \approx -0.15\mathrm{}$.