Abstract
We calculate results for $K\ensuremath{\rightarrow}\ensuremath{\pi}$ and $K\ensuremath{\rightarrow}0$ matrix elements to next-to-leading order in $2+1$ flavor partially quenched chiral perturbation theory. Results are presented for both the $\ensuremath{\Delta}I=1/2$ and $3/2$ channels, for chiral operators corresponding to current-current, gluonic penguin, and electroweak penguin 4-quark operators. These formulas are useful for studying the chiral behavior of currently available $2+1$ flavor lattice QCD results, from which the low-energy constants of the chiral effective theory can be determined. The low-energy constants of these matrix elements are necessary for an understanding of the $\ensuremath{\Delta}I=1/2$ rule, and for calculations of ${ϵ}^{\ensuremath{'}}/ϵ$ using current lattice QCD simulations.
Published Version
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