Wilson chiral perturbation theory, Wilson-Dirac operator eigenvalues and clover improvement

TL;DR

This paper extends chiral perturbation theory to include lattice effects for Wilson fermions, tests predictions against eigenvalue data, and shows clover improvement reduces lattice artifacts, enabling extraction of low-energy constants from spectral data.

Contribution

It introduces a method to incorporate lattice effects into chiral perturbation theory for Wilson fermions and demonstrates how clover improvement mitigates lattice artifacts for better parameter extraction.

Findings

Lattice effects are reduced with clover improvement.

Spectral data can determine Wilson low-energy constants.

Predictions match eigenvalue distributions from quenched ensembles.

Abstract

Chiral perturbation theory for eigenvalue distributions, and equivalently random matrix theory, has recently been extended to include lattice effects for Wilson fermions. We test the predictions by comparison to eigenvalue distributions of the Hermitian Wilson-Dirac operator from pure gauge (quenched) ensembles. We show that the lattice effects are diminished when using clover improvement for the Dirac operator. We demonstrate that the leading Wilson low-energy constants associated with Wilson (clover) fermions can be determined using spectral information of the respective Dirac operator at finite volume.