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

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

2011-01-10

arxiv.org/abs/1101.1778v2

Physics

High Energy Physics

High Energy Physics - Lattice

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

Scientific paper

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.

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