A New Method for Determining $F_{\pi }$ on the Lattice

Abstract

We derive the two-point spectral correlation function of the Dirac operator with a specific external source in the $\epsilon$-regime of QCD. This correlation function has a unique and strong dependence on $F_{\pi }$, and thus provides an novel way to extract $F_{\pi }$ from lattice simulations. We test the method in a quenched lattice simulation with staggered fermions.

5 pages, 3 figures

References in corpus (34)

• QCD at finite isospin density
• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• Light pseudoscalar decay constants, quark masses, and low energy constants from three-flavor lattice QCD
• On two-color QCD with baryon chemical potential
• Universal results from an alternate random matrix model for QCD with a baryon chemical potential
• An Accelerated Conjugate Gradient Algorithm to Compute Low-Lying Eigenvalues --- a Study for the Dirac Operator in SU(2) Lattice QCD
• Microscopic universality in the spectrum of the lattice Dirac operator
• Staggered eigenvalue mimicry
• Low-energy couplings of QCD from current correlators near the chiral limit
• Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
• Distribution of the k-th smallest Dirac operator eigenvalue
• Unquenched QCD Dirac Operator Spectra at Nonzero Baryon Chemical Potential
• Partially Quenched Chiral Perturbation Theory and the Replica Method
• Diquark Condensate in QCD with Two Colors at Next-to-Leading Order
• The Index Theorem and Universality Properties of the Low-lying Eigenvalues of Improved Staggered Quarks
• Chiral Symmetry Breaking and the Dirac Spectrum at Nonzero Chemical Potential
• Thermodynamics of chiral symmetry at low densities
• Replica Limit of the Toda Lattice Equation
• Replica field theories, Painleve transcendents, and exact correlation functions
• Finite-size Scaling of Meson Propagators
• The Low-Lying Dirac Spectrum of Staggered Quarks
• Microscopic Spectral Density of the Dirac Operator in Quenched QCD
• Axial Correlation Functions in the epsilon-Regime: a Numerical Study with Overlap Fermions
• Distributions of Dirac Operator Eigenvalues
• Finite-Size Scaling of Vector and Axial Current Correlators
• Effective Low Energy Theories and QCD Dirac Spectra
• Quenched Finite Volume Logarithms
• Statistical properties of the spectrum of the QCD Dirac operator at low energy
• Staggered Fermions and Gauge Field Topology
• Low-lying mode contribution to the quenched meson correlators in the epsilon-regime
• Systematics of Staggered Fermion Spectral Properties and Topology
• Supersymmetric Quenching of the Toda Lattice Equation
• Quarks with Twisted Boundary Conditions in the Epsilon Regime
• Random-matrix universality in the small-eigenvalue spectrum of the lattice Dirac operator

Cited by in corpus (41)

• Phase of the Fermion Determinant at Nonzero Chemical Potential
• Spectrum of the Wilson Dirac Operator at Finite Lattice Spacings
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Matrix Models and QCD with Chemical Potential
• A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential
• Equivalence of QCD in the epsilon-regime and chiral Random Matrix Theory with or without chemical potential
• Parameters of the lowest order chiral Lagrangian from fermion eigenvalues
• Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential
• Extracting $F_{\pi }$ from small lattices: unquenched results
• Overlap Hypercube Fermions in QCD Simulations Near the Chiral Limit
• Are Bosonic Replicas Faulty?
• Lattice calculation of low energy constants with Ginsparg-Wilson type fermions
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• Finite Volume Scaling of Pseudo Nambu-Goldstone Bosons in QCD
• Unquenched complex Dirac spectra at nonzero chemical potential: two-colour QCD lattice data versus matrix model
• Finite size scaling of meson propagators with isospin chemical potential
• New Ways to Determine Low-Energy Constants with Wilson Fermions
• The epsilon expansion at next-to-next-to-leading order with small imaginary chemical potential
• Individual complex Dirac eigenvalue distributions from random matrix theory and comparison to quenched lattice QCD with a quark chemical potential
• Staggered chiral random matrix theory
• Finite-volume Correction to the Pion Decay Constant in the Epsilon-Regime
• Geometry dependence of RMT-based methods to extract the low-energy constants Sigma and F
• Finite-size scaling for the left-current correlator with non-degenerate quark masses
• Determining F_pi from spectral sum rules
• Probing the chiral weak Hamiltonian at finite volumes
• Handbook Article on Applications of Random Matrix Theory to QCD
• The Sign Problem via Imaginary Chemical Potential
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Individual Eigenvalue Distributions of Chiral Random Two-Matrix Theory and the Determination of F_pi
• Lessons from Random Matrix Theory for QCD at Finite Density
• Partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order
• Universality crossover between chiral random matrix ensembles and twisted SU(2) lattice Dirac spectra
• Lattice QCD with fixed topology
• Universality and critical behavior in the chiral two-matrix model
• The Fluctuations of the Quark Number and of the Chiral Condensate
• Meson-Baryon Scattering Parameters from Lattice QCD with an Isospin Chemical Potential
• The gradient flow of the Dirac spectrum
• The k-th Smallest Dirac Operator Eigenvalue and the Pion Decay Constant
• Triage of the Sign Problem
• New term in effective field theory at fixed topology
• Low energy constants from the chirally improved Dirac operator D_CI