Chiral perturbation theory at O(a^2) for lattice QCD

TL;DR

This paper extends chiral perturbation theory to lattice QCD with Wilson fermions and with a mixed Wilson/Ginsparg-Wilson setup by deriving Symanzik effective actions through ${O(a^2)}$ and constructing the corresponding chiral Lagrangians. It shows that only a small number of new ${O(a^2)}$ operators appear, and that discretization effects shift continuum low-energy constants at this order while ${O(4)}$-breaking effects contribute at ${O(a^2 p^4)}$ and are thus subleading. The authors provide explicit ${O(a^2)}$ terms in the chiral Lagrangian for both Wilson and mixed-action theories via spurion analysis, and compute pseudoscalar meson masses at NLO, finding no ${O(a^2)}$ corrections to valence-valence masses in the mixed theory due to enhanced chiral symmetry in the valence sector. These results inform chiral extrapolations of lattice data, highlighting when ${O(a^2)}$ effects must be included and how they enter observables, thereby improving the connection between lattice simulations and continuum QCD.

Abstract

We construct the chiral effective Lagrangian for two lattice theories: one with Wilson fermions and the other with Wilson sea fermions and Ginsparg-Wilson valence fermions. For each of these theories we construct the Symanzik action through order $a^2$. The chiral Lagrangian is then derived, including terms of order $a^2$, which have not been calculated before. We find that there are only few new terms at this order. Corrections to existing coefficients in the continuum chiral Lagrangian are proportional to $a^2$, and appear in the Lagrangian at order $a^2 p^2$ or higher. Similarly, O(4) symmetry breaking terms enter the Symanzik action at order $a^2$, but contribute to the chiral Lagrangian at order $a^2 p^4$ or higher. We calculate the light meson masses in chiral perturbation theory for both lattice theories. At next-to-leading order, we find that there are no order $a^2$ corrections to the valence-valence meson mass in the mixed theory due to the enhanced chiral symmetry of the valence sector.