  We calculate results for K to pi and K to 0 matrix elements to
next-to-leading order in 2+1 flavor partially quenched chiral perturbation
theory. Results are presented for both the 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 Delta I=1/2 rule, and for calculations of
epsilon'/epsilon using current lattice QCD simulations.

High Energy Physics - Lattice;High Energy Physics - Phenomenology