It is shown that the contributions to the Adler-Weisberger sum rule (AWSR) in the simplest Veneziano model for $K-\pi$ scattering are too large by a factor of 2. A modification of the simplest Veneziano amplitude is proposed which satisfies (i) the Adler self-consistency condition, (ii) the AWSR, and (iii) the $K^{*}\mathrm{}\left(890\right)\mathrm{}$ having the experimentally observed width of 50 MeV. If this modified Veneziano amplitude is required to satisfy the Adler-Weisberger-type sum rule for zero-mass $K$ mesons scattering from physical pions, the ratio $\frac{F_K}{F\pi }$ is predicted to be 1.26, in good agreement with experiment.

• Received 7 August 1969

DOI:https://doi.org/10.1103/PhysRev.188.2465