Algebra of Currents and Vector-Meson Dominance of LeptonicKDecays

The algebra of currents is applied to a simple vector-meson-dominance model of leptonic $K$ decays. The algebra predicts different limits for the $K_{l4\mathrm{}}$ current as the various pseudoscalar mesons are brought to zero four-momentum in different order. It is found that this nonlinear behavior can be reproduced by requiring gauge invariance at the vector-meson weak vertices. The model provides immediate mass-shell corrections to the predictions of the current algebra. Reasonable numerical agreement is found for all the weak form factors of mesons.