Finite-Size Scaling of Vector and Axial Current Correlators

Abstract

Using quenched chiral perturbation theory, we compute the long-distance behaviour of two-point functions of flavour non-singlet axial and vector currents in a finite volume, for small quark masses, and at a fixed gauge-field topology. We also present the corresponding predictions for the unquenched theory at fixed topology. These results can in principle be used to measure the low-energy constants of the chiral Lagrangian, from lattice simulations in volumes much smaller than one pion Compton wavelength. We show that quenching has a dramatic effect on the vector correlator, which is argued to vanish to all orders, while the axial correlator appears to be a robust observable only moderately sensitive to quenching.

version to appear in NPB

References in corpus (28)

• Exactly massless quarks on the lattice
• A Method for Simulating Chiral Fermions on the Lattice
• Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation
• Chiral Fermions from Lattice Boundaries
• More about exactly massless quarks on the lattice
• Riemannian symmetric superspaces and their origin in random matrix theory
• Chiral Determinant as an Overlap of Two Vacua
• Chiral Perturbation Theory for the Quenched Approximation of QCD
• Quenched Chiral Logarithms
• Prospects for perfect actions
• The Microscopic Spectral Density of the QCD Dirac Operator
• From chiral Random Matrix Theory to chiral Perturbation Theory
• Microscopic universality in the spectrum of the lattice Dirac operator
• Quark spectra, topology and random matrix theory
• Partially Quenched Chiral Perturbation Theory and the Replica Method
• A variant approach to the overlap action
• Finite-size scaling of the quark condensate in quenched lattice QCD
• Replica field theories, Painleve transcendents, and exact correlation functions
• Non-perturbative renormalization of the quark condensate in Ginsparg-Wilson regularizations
• Finite-size Scaling of Meson Propagators
• Microscopic Spectral Density of the Dirac Operator in Quenched QCD
• Quenched Finite Volume Logarithms
• Spectral Sum Rules of the Dirac operator and Partially Quenched Chiral Condensates
• Universal Scaling of the Chiral Condensate in Finite-Volume Gauge Theories
• Statistical properties of the spectrum of the QCD Dirac operator at low energy
• Partially Quenched Chiral Condensates from the Replica Method
• The Replica Limit of Unitary Matrix Integrals
• Chiral measurements with the Fixed-Point Dirac operator and construction of chiral currents

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• FLAG Review 2019
• Review of lattice results concerning low energy particle physics
• Theta dependence of SU(N) gauge theories in the presence of a topological term
• Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops
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• Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
• Deconfinement in Matrix Models about the Gross--Witten Point
• Matrix Models and QCD with Chemical Potential
• Actions for dynamical fermion simulations: are we ready to go?
• Axial Correlation Functions in the epsilon-Regime: a Numerical Study with Overlap Fermions
• A New Method for Determining $F_{\pi }$ on the Lattice
• Spectral Properties of the Overlap Dirac Operator in QCD
• Lattice study of meson correlators in the epsilon-regime of two-flavor QCD
• Low-energy couplings of QCD from topological zero-mode wave functions
• Parameters of the lowest order chiral Lagrangian from fermion eigenvalues
• The epsilon regime with Wilson fermions
• Overlap Hypercube Fermions in QCD Simulations Near the Chiral Limit
• A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule
• Quarks with Twisted Boundary Conditions in the Epsilon Regime
• Finite size scaling of meson propagators with isospin chemical potential
• Exploring Topology Conserving Gauge Actions for Lattice QCD
• Partially quenched chiral perturbation theory in the epsilon-regime
• Finite-volume Correction to the Pion Decay Constant in the Epsilon-Regime
• Interpolation between the epsilon and p regimes
• Finite-size scaling for the left-current correlator with non-degenerate quark masses
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Probing the chiral weak Hamiltonian at finite volumes
• Individual Eigenvalue Distributions of Chiral Random Two-Matrix Theory and the Determination of F_pi
• Testing chiral effective theory with quenched lattice QCD
• Optimised Dirac Operators on the Lattice: Construction, Properties and Applications
• Quenched and Unquenched Chiral Perturbation Theory in the ε-Regime
• Meson Correlation Functions in the epsilon-Regime
• Overlap Hypercube Fermions in QCD
• Vector and Axial-Vector Propagators in the ε-Regime of QCD
• Exploring the Aoki regime
• Simulations in the epsilon-Regime of Chiral Perturbation Theory