Spectral density of the Hermitean Wilson Dirac operator: a NLO computation in chiral perturbation theory

TL;DR

This paper calculates the next-to-leading order lattice spacing corrections to the spectral density of the Hermitean Wilson Dirac operator using Wilson Chiral Perturbation Theory, providing insights into discretisation effects and the phase diagram of Wilson fermions.

Contribution

It introduces a NLO computation of spectral density corrections in Wilson Chiral Perturbation Theory considering a specific quark mass and lattice spacing regime.

Findings

Discretisation effects can be treated as perturbations in the specified regime.

The framework helps understand spectral properties away from the threshold.

Implications for the phase diagram of Wilson fermions are discussed.

Abstract

We compute the lattice spacing corrections to the spectral density of the Hermitean Wilson Dirac operator using Wilson Chiral Perturbation Theory at NLO. We consider a regime where the quark mass $m$ and the lattice spacing $a$ obey the relative power counting $m\sim a \Lambda_{\rm QCD}^2$: in this situation discretisation effects can be treated as perturbation of the continuum behaviour. While this framework fails to describe lattice spectral density close to the threshold, it allows nevertheless to investigate important properties of the spectrum of the Wilson Dirac operator. We discuss the range of validity of our results and the possible implications in understanding the phase diagram of Wilson fermions.