Chiral perturbation theory for the Wilson lattice action

Abstract

We extend chiral perturbation theory to include linear dependence on the lattice spacing a for the Wilson action. The perturbation theory is written as a double expansion in the small quark mass ${m}_{q}$ and lattice spacing a. We present formulas for the mass and decay constant of a flavor-nonsinglet meson in this scheme to order a and ${m}_{q}^{2}.$ The extension to the partially quenched theory is also described.