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

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 $m\sim a{\Lambda }_{\mathrm{QCD}}^2$: 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.

27 pages, 4 figures; few typos corrected, added footnote, published version

References in corpus (5)

• Accelerating Dynamical Fermion Computations using the Rational Hybrid Monte Carlo (RHMC) Algorithm with Multiple Pseudofermion Fields
• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• Local coherence and deflation of the low quark modes in lattice QCD
• The epsilon regime with Wilson fermions
• Observations on the Wilson fermions in the epsilon regime

Cited by in corpus (15)

• Symmetries of hadrons after unbreaking the chiral symmetry
• Unbreaking chiral symmetry
• Chiral condensate from the twisted mass Dirac operator spectrum
• Eigenvalue Density of the non-Hermitian Wilson Dirac Operator
• Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
• Spectral density of the Dirac operator in two-flavour QCD
• The Wilson Dirac Spectrum for QCD with Dynamical Quarks
• Spectral properties of the Wilson Dirac operator in the $\epsilon$-regime
• Determination of Low-Energy Constants of Wilson Chiral Perturbation Theory
• Spectral Properties of the Wilson Dirac Operator and random matrix theory
• Constraint on the Low Energy Constants of Wilson Chiral Perturbation Theory
• The Realization of the Sharpe-Singleton Scenario
• New Ways to Determine Low-Energy Constants with Wilson Fermions
• Individual Eigenvalue Distributions for the Wilson Dirac Operator
• Exploring the Aoki regime