Chiral Logarithms in $\Delta S=1$ Kaon Decay Amplitudes in General Effective Flavor Theories

Abstract

We study the chiral logarithms in $\Delta S=1$ kaon decay amplitudes from new flavor physics in beyond-standard-model theories. We systematically classify the chiral structures of dimension-5, 6 and 7 effective QCD operators constructed out of light-quark (up, down and strange) and gluon fields. Using the standard chiral perturbation theory, we calculate the leading chiral-logarithms associated with these operators. The result is useful for lattice calculations of the QCD matrix elements in $K\to \pi \pi$ decay necessary, for example, to understand the physical origin of the direct CP violation parameter ${ϵ}^{\prime }$. As a concrete example, we consider the new operators present in minimal left-right symmetric models.