Zero-Energy Limits and NonleptonicKDecays

A dynamical model is proposed that reproduces all the zero-energy limits predicted by the algebra of currents for the $K_{2\pi }$ and $K_{3\pi }$ amplitudes. The nonlinearities predicted by the algebra as two pions are brought to zero four-momentum in different order are related to a gauge condition on the weak interactions of vector mesons. Over-all numerical agreement is good including prediction of the $K^{+}\to {\pi }^{+}{\pi }^0$ rate and other violations of the $\Delta T=\frac{1}{2}$ rule. Mass-shell corrections to the current-algebra relations between $K_{3\pi }$ and $K_{2\pi }$ are given by the model in good agreement with experiment.