The Wilson Dirac Spectrum for QCD with Dynamical Quarks

Abstract

All microscopic correlation functions of the spectrum of the Hermitian Wilson Dirac operator with any number of flavors with equal masses are computed. In particular, we give explicit results for the spectral density in the physical case with two light quark flavors. The results include the leading effect in the discretization error and are given for fixed index of the Wilson Dirac operator. They have been obtained starting from chiral Lagrangians for the generating function of the Dirac spectrum. Microscopic correlation functions of the real eigenvalues of the Wilson Dirac operator are computed following the same approach.

26 pages, 5 figures

References in corpus (7)

• 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
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• Spectral density of the Hermitean Wilson Dirac operator: a NLO computation in chiral perturbation theory
• On the Efetov-Wegner terms by diagonalizing a Hermitian supermatrix
• Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor

Cited by in corpus (24)

• Lattice QCD with open boundary conditions and twisted-mass reweighting
• Symmetries of hadrons after unbreaking the chiral symmetry
• Unbreaking chiral symmetry
• Eigenvalue Density of the non-Hermitian Wilson Dirac Operator
• Random Matrix Theory for the Hermitian Wilson Dirac Operator and the chGUE-GUE Transition
• Finite-Volume Scaling of the Wilson-Dirac Operator Spectrum
• 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
• QED with external field: Hamiltonian treatment for anisotropic medium formed by the Lorentz-non-invariant vacuum
• The Realization of the Sharpe-Singleton Scenario
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• The Microscopic Twisted Mass Dirac Spectrum
• 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
• Baryon Number Dirac Spectrum in QCD
• Chiral Dynamics With Wilson Fermions
• Microscopic Spectral Density of the Wilson Dirac Operator for One Flavor
• Non-Hermitian CP-Symmetric Dirac Hamiltonians with Real Energy Eigenvalues
• Progress on the Microscopic Spectrum of the Dirac Operator for QCD with Wilson Fermions
• Surprising Pfaffian factorizations in Random Matrix Theory with Dyson index $\beta =2$
• Random Matrix Models for the Hermitian Wilson-Dirac operator of QCD-like theories
• Wilson chiral perturbation theory for dynamical twisted mass fermions vs lattice data - a case study