Current-Algebra Model ofΔI=32Effects in Nonleptonic Kaon Decay

Abstract

We construct a two-parameter semiphenomenological model for nonleptonic kaon decay under the following assumptions: (i) All single soft-$\pi$ limits are satisfied; (ii) aside from pole terms, amplitudes can be expanded as a power series in the pion momenta $q$; and (iii) in particular, we include in $〈{\pi }_q\left|{\mathcal{H}}_w\right|K_k〉$ only first-and zeroth-order terms in $q$. Our $\Delta I=\frac{1}{2}$ results are then identical to the recent work of McNamee. Because of our inclusion of $q$ dependence, nonzero $\Delta I=\frac{3}{2}$ effects are also permitted and are found to be in agreement with the model of Bouchiat and Meyer to order $\frac{m_{\pi }^{}{}_{}{}^2}{M_K^{}{}_{}{}^2}$. A theoretical estimate of the size of the first-order terms is found to agree with experiment. Uncertainties inherent in our method are discussed.