Zero-Energy Limits and NonleptonicKDecays

Abstract

A dynamical model is proposed that reproduces all the zero-energy limits predicted by the algebra of currents for the ${K}_{2\ensuremath{\pi}}$ and ${K}_{3\ensuremath{\pi}}$ 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 ${K}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$ rate and other violations of the $\ensuremath{\Delta}T=\frac{1}{2}$ rule. Mass-shell corrections to the current-algebra relations between ${K}_{3\ensuremath{\pi}}$ and ${K}_{2\ensuremath{\pi}}$ are given by the model in good agreement with experiment.