K to pi and K to 0 in 2+1 Flavor Partially Quenched Chiral Perturbation Theory

TL;DR

This paper provides next-to-leading order calculations of K to pi and K to 0 matrix elements in 2+1 flavor partially quenched chiral perturbation theory, aiding lattice QCD studies of kaon decays and CP violation.

Contribution

It offers new formulas for matrix elements in partially quenched chiral perturbation theory applicable to lattice QCD analyses of kaon decays.

Findings

Formulas for K to pi and K to 0 matrix elements at NLO

Results applicable to Delta I=1/2 and 3/2 channels

Facilitates determination of low energy constants from lattice QCD

Abstract

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.