Chiral perturbation theory for the Wilson lattice action

TL;DR

This paper extends chiral perturbation theory to include linear lattice spacing effects for Wilson fermions, providing formulas for meson masses and decay constants to order a and m_q^2, applicable to partially quenched theories.

Contribution

It introduces a systematic extension of chiral perturbation theory incorporating lattice spacing effects for Wilson fermions, including partially quenched cases.

Findings

Derived formulas for meson mass and decay constant at order a and m_q^2.

Extended chiral perturbation theory to Wilson lattice action with linear lattice spacing dependence.

Applicable to partially quenched lattice QCD simulations.

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 formulae for the mass and decay constant of a flavor-non-singlet meson in this scheme to order $a$ and $m_q^2$. The extension to the partially quenched theory is also described.