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.

• Received 22 January 2009

DOI:https://doi.org/10.1103/PhysRevD.80.014018