K→π and K→0 in 2+1 flavor partially quenched chiral perturbation theory

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