Partially Quenched Chiral Perturbation Theory and the Replica Method

Abstract

We describe a novel framework for partially quenched chiral perturbation theory based on the replica method. The computational rules are exceedingly simple. We illustrate these rules by computing the partially quenched chiral condensate to one-loop order. By considering arbitrary chiral $k$-point functions we show explicitly to one-loop order the equivalence between this method and the one based on supersymmetry. It is possible to go smoothly from the conventional replica method to a supersymmetric variant by choosing the number of valence quarks to be negative.

arXiv commentLaTeX, 11 pages. Minor changes. Version accepted by PRD

References in corpus (26)

• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• Chiral Perturbation Theory for the Quenched Approximation of QCD
• Quenched Chiral Logarithms
• Partially Quenched Gauge Theories and a Application to Staggered Fermions
• Renormalization of chiral perturbation theory to order p^6
• Universality of random matrices in the microscopic limit and the Dirac operator spectrum
• The Microscopic Spectral Density of the QCD Dirac Operator
• From chiral Random Matrix Theory to chiral Perturbation Theory
• Chiral Effective Lagrangian in the large-Nc limit: the nonet case
• Enhanced chiral logarithms in partially quenched QCD
• Quenched Chiral Perturbation Theory for Heavy-light Mesons
• Applications of Partially Quenched Chiral Perturbation Theory
• Universal scaling of the valence quark mass dependence of the chiral condensate
• Finite-size scaling of the quark condensate in quenched lattice QCD
• Multicritical Microscopic Spectral Correlators of Hermitian and Complex Matrices
• Finite-volume two-pion energies and scattering in the quenched approximation
• Dirac Operator Spectra from Finite-Volume Partition Functions
• The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking
• Quenched Chiral Perturbation Theory to one loop
• Consistency Conditions for Finite-Volume Partition Functions
• Universal Scaling of the Chiral Condensate in Finite-Volume Gauge Theories
• Spectral Sum Rules of the Dirac operator and Partially Quenched Chiral Condensates
• Partially Quenched Chiral Condensates from the Replica Method
• On Finite-Volume Gauge Theory Partition Functions

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• Lattice study of meson correlators in the epsilon-regime of two-flavor QCD
• Mixed Meson Masses with Domain-Wall Valence and Staggered Sea Fermions
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• Distributions of the Phase Angle of the Fermion Determinant in QCD
• A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule
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• Supersymmetric Quenching of the Toda Lattice Equation
• The Pseudoscalar Meson Mass to Two Loops in Three-Flavor Partially Quenched $\chi$PT
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• Effects of non-equilibrated topological charge distributions on pseudoscalar meson masses and decay constants
• Masses and Decay Constants of Pseudoscalar Mesons to Two Loops in Two-Flavor Partially Quenched Chiral Perturbation Theory
• Lattice extraction of $K\to \pi \pi$ amplitudes to NLO in partially quenched and in full chiral perturbation theory
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• On the foundations of partially quenched chiral perturbation theory
• Doubly Heavy Baryons and Quark-Diquark Symmetry in Quenched and Partially Quenched Chiral Perturbation Theory
• Applications of Chiral Perturbation theory to lattice QCD
• Heavy-light mesons in the epsilon-regime
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• 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
• Baryon Number Dirac Spectrum in QCD
• Systematic effects of the quenched approximation on the strong penguin contribution to epsilon'/epsilon
• Chiral Random Matrix Theory and Chiral Perturbation Theory
• Probing the chiral weak Hamiltonian at finite volumes
• Semileptonic Kaon Decay in Staggered Chiral Perturbation Theory
• Microscopic Encoding of Macroscopic Universality: Scaling Properties of Dirac Eigenspectra near QCD Chiral Phase Transition
• Staggered Heavy Baryon Chiral Perturbation Theory
• Testing chiral effective theory with quenched lattice QCD
• The Replica Method and Toda Lattice Equations for QCD_3
• Lattice calculation of $\kappa$ meson
• Divergent chiral condensate in the quenched Schwinger model
• Twisted finite-volume corrections to $K_{l3}$ decays with partially-quenched and rooted-staggered quarks
• Quenched and Unquenched Chiral Perturbation Theory in the ε-Regime
• Determination of the $\Delta S=1$ weak Hamiltonian in the SU(4) chiral limit through topological zero-mode wave functions
• Taste non-Goldstone, flavor-charged pseudo-Goldstone boson masses in staggered chiral perturbation theory
• Staggered chiral perturbation theory in the two-flavor case
• Electromagnetic Corrections in Staggered Chiral Perturbation Theory
• Studying $\kappa$ meson with a MILC fine lattice
• The Fluctuations of the Quark Number and of the Chiral Condensate
• Topics in Effective Field Theory for Lattice QCD
• The gradient flow of the Dirac spectrum
• Finite Volume Chiral Partition Functions and the Replica Method
• Finite Volume for Three-Flavour Partially Quenched Chiral Perturbation Theory through NNLO in the Meson Sector
• Taste non-Goldstone, flavor-charged pseudo-Goldstone boson decay constants in staggered chiral perturbation theory
• Vector and Axial-Vector Propagators in the ε-Regime of QCD
• Masses and decay constants of pions and kaons in mixed-action staggered chiral perturbation theory
• Finite-volume meson propagators in quenched chiral perturbation theory