Wilson fermions in the epsilon regime

TL;DR

This paper extends chiral perturbation theory to include lattice spacing effects for Wilson fermions, analyzing how lattice artifacts influence low-energy observables in the epsilon regime.

Contribution

It introduces Wilson Chiral Perturbation Theory in the epsilon regime, detailing the regimes of quark mass and lattice spacing, and computes corrections to correlation functions.

Findings

Lattice spacing effects are suppressed at m ~ a Lambda^2_QCD.

Corrections become significant at smaller quark masses.

Lattice data fits show these corrections are small.

Abstract

We extend the epsilon-expansion of continuum chiral perturbation theory to nonzero lattice spacing in the framework of Wilson Chiral Perturbation Theory. We distinguish various regimes by defining the relative power counting of the quark mass m and the lattice spacing a. We observe that for m ~ a Lambda^2_QCD, the explicit breaking of chiral symmetry in Wilson fermions is still driven by the quark mass and lattice corrections are highly suppressed. The lattice spacing effects become more pronounced for smaller quark masses and may lead to non-trivial corrections of the continuum results at next-to-leading order. We compute these corrections for standard current and density correlation functions. A fit to lattice data shows that these corrections are small, as expected.