Theory of Higher-Order Weak Interactions and $\mathrm{CP}$-Invariance Violation. II. The Neutral $K$ System

Continuing our exposition of a nonpolynomial theory of higher-order weak interactions, we examine the neutral $K$ system, with particular emphasis on the $\mathrm{CP}$-invariance-violating amplitudes. These first appear in second order in the weak interactions. We use the free-quark model to estimate the short-distance singularity of products of hadronic currents, and we find that with appropriate choices of the minor coupling constants our theory is consistent with the known experimental results. In particular, we find $\left|\epsilon \right|\approx {10}^{-3\mathrm{}}$, and we give an argument leading to ${\eta }_{+-}\approx {\eta }_{00}$. The neutron dipole moment is a third-order weak effect in our theory and is estimated to be about ${10}^{-27\mathrm{}}$ e cm. We calculate the production cross section for the superprop-agating particles, and find it to be too small for the particles to have yet been observed.