Abstract
It is shown that the contributions to the Adler-Weisberger sum rule (AWSR) in the simplest Veneziano model for $K\ensuremath{-}\ensuremath{\pi}$ 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 ${K}^{*}(890)$ 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 $\frac{{F}_{K}}{F\ensuremath{\pi}}$ is predicted to be 1.26, in good agreement with experiment.
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