The Realization of the Sharpe-Singleton Scenario

Abstract

The microscopic spectral density of the Wilson Dirac operator for two flavor lattice QCD is analyzed. The computation includes the leading order a^2 corrections of the chiral Lagrangian in the microscopic limit. The result is used to demonstrate how the Sharpe-Singleton first order scenario is realized in terms of the eigenvalues of the Wilson Dirac operator. We show that the Sharpe-Singleton scenario only takes place in the theory with dynamical fermions whereas the Aoki phase can be realized in the quenched as well as the unquenched theory. Moreover, we give constraints imposed by gamma_5-Hermiticity on the additional low energy constants of Wilson chiral perturbation theory.

33 pages, 4 figures, version to appear in PRD

References in corpus (7)

• Chiral symmetry breaking and the Banks--Casher relation in lattice QCD with Wilson quarks
• A numerical reinvestigation of the Aoki phase with N_f=2 Wilson fermions at zero temperature
• Discretization errors in the spectrum of the Hermitian Wilson-Dirac operator
• The epsilon regime with Wilson fermions
• Observations on the Wilson fermions in the epsilon regime
• Phase Diagram of the Dirac Spectrum at Nonzero Chemical Potential
• Determining low-energy constants in partially quenched Wilson chiral perturbation theory

Cited by in corpus (17)

• Lattice QCD with open boundary conditions and twisted-mass reweighting
• Phase Diagram of Dynamical Twisted Mass Wilson Fermions at Finite Isospin Chemical Potential
• Determination of Low-Energy Constants of Wilson Chiral Perturbation Theory
• The Dirac spectrum in Complex Langevin Simulations of QCD
• Spectral Properties of the Wilson Dirac Operator and random matrix theory
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• New Ways to Determine Low-Energy Constants with Wilson Fermions
• Random Matrix Theory and Quantum Chromodynamics
• Dirac Spectrum of the Wilson Dirac Operator for QCD with Two Colors
• The $\epsilon$-regime of dilaton chiral perturbation theory
• Kondo effect with Wilson fermions
• Elucidating the Vacuum Structure of the Aoki Phase
• Phase structure of a generalized Nambu Jona-Lasinio model with Wilson fermions in the mean field or large $N$-expansion
• Random Matrix Models for the Hermitian Wilson-Dirac operator of QCD-like theories
• Wilson chiral perturbation theory, Wilson-Dirac operator eigenvalues and clover improvement
• Wilson chiral perturbation theory for dynamical twisted mass fermions vs lattice data - a case study
• New term in effective field theory at fixed topology