Kaon decays and a determination of the scale of chiral symmetry

Abstract

Using effective chiral Lagrangians, we consider the occurrence of quadratic terms in the $\Delta I=\frac{1}{2}$ $K\to 3\pi$ matrix element. The inclusion of higher-derivative Lagrangians leads to a significant improvement over the usual current-algebra analysis. This allows an extraction directly from experimental data of ${\Lambda }_{\chi }$, a measure of the scale of chiral symmetry. We give an operational definition of the chiral scale, and find ${\Lambda }_{\chi }\approx 1$ GeV. The issue of uncertainty in the phenomenological determination of the $B$ parameter is clarified.