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

TL;DR

This paper calculates the leading chiral logarithms in $ ext{Δ}S=1$ kaon decay amplitudes within effective flavor theories, aiding lattice QCD studies and understanding CP violation.

Contribution

It systematically classifies effective operators and computes their chiral logarithms, extending the analysis to new physics models like minimal left-right symmetric theories.

Findings

Derived explicit formulas for chiral logarithms of various operators.

Provided insights for lattice QCD calculations of $K o \pi ext{π}$ decays.

Applied results to models beyond the Standard Model, such as left-right symmetry.

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 $\epsilon'$. As a concrete example, we consider the new operators present in minimal left-right symmetric models.