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Chiral Logarithms in $ΔS=1$ Kaon Decay Amplitudes in General Effective Flavor Theories

We study the chiral logarithms in $ΔS=1$ 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 $K\to ππ$ decay necessary, for example, to understand the physical origin of the direct CP violation parameter $ε'$. As a concrete example, we consider the new operators present in minimal left-right symmetric models.