Chiral Perturbation Theory for the Quenched Approximation of QCD

Abstract

[This version is a minor revision of a previously submitted preprint. Only references have been changed.] We describe a technique for constructing the effective chiral theory for quenched QCD. The effective theory which results is a lagrangian one, with a graded symmetry group which mixes Goldstone bosons and fermions, and with a definite (though slightly peculiar) set of Feynman rules. The straightforward application of these rules gives automatic cancellation of diagrams which would arise from virtual quark loops. The techniques are used to calculate chiral logarithms in $f_K/f_{\pi }$, $m_{\pi }$, $m_K$, and the ratio of $⟨\bar{s}s⟩$ to $⟨\bar{u}u⟩$. The leading finite-volume corrections to these quantities are also computed. Problems for future study are described.

14 pages

Cited by in corpus (276)

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• The QCD spectrum with three quark flavors
• Physical Results from 2+1 Flavor Domain Wall QCD and SU(2) Chiral Perturbation Theory
• Quenched Chiral Logarithms
• Recent Developments in Chiral Perturbation Theory
• Partially Quenched Gauge Theories and a Application to Staggered Fermions
• Pion and Kaon masses in Staggered Chiral Perturbation Theory
• Hadron Scattering Lengths in Lattice QCD
• Up, down, strange and charm quark masses with Nf = 2+1+1 twisted mass lattice QCD
• Quenched Light Hadron Spectrum
• Physical Results from Unphysical Simulations
• The Microscopic Spectral Density of the QCD Dirac Operator
• From chiral Random Matrix Theory to chiral Perturbation Theory
• QED in finite volume and finite size scaling effect on electromagnetic properties of hadrons
• Partially quenched chiral perturbation theory without ${\Phi }_0$
• Lattice QCD at the physical point: light quark masses
• Quenched Lattice QCD with Domain Wall Fermions and the Chiral Limit
• Quenched Chiral Perturbation Theory for Baryons
• Quenched lattice QCD at finite isospin density and related theories
• Chiral Perturbation Theory Beyond One Loop
• Enhanced chiral logarithms in partially quenched QCD
• Chiral Analysis of Quenched Baryon Masses
• Pseudoscalar Decay Constants in Staggered Chiral Perturbation Theory
• Quenched Chiral Perturbation Theory for Heavy-light Mesons
• Meson masses in electromagnetic fields with Wilson fermions
• Leptonic decay constants fK, fD and fDs with Nf = 2+1+1 twisted-mass lattice QCD
• Hadron Masses from the Valence Approximation to Lattice QCD
• Non-perturbatively Improved Heavy-Light Mesons: Masses and Decay Constants
• Precision computation of the strange quark's mass in quenched QCD
• Kaon Matrix Elements and CP-violation from Quenched Lattice QCD: (I) the 3-flavor case
• 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
• Testing the fixed-point QCD action and the construction of chiral currents
• Partially Quenched Chiral Perturbation Theory and the Replica Method
• Light Hadron Spectrum and Quark Masses from Quenched Lattice QCD
• Sp(4) gauge theory on the lattice: towards SU(4)/Sp(4) composite Higgs (and beyond)
• Nucleon Magnetic Moments Beyond the Perturbative Chiral Regime
• Quenched spectroscopy with fixed-point and chirally improved fermions
• The K -> pi vector form factor at zero momentum transfer on the lattice
• Nucleon Masses and Magnetic Moments in a Finite Volume
• Probing Unquenching Effects in the Gluon Polarisation in Light Mesons
• Padé - Z${}_2$ Estimator of Determinants
• Staggered Chiral Perturbation Theory and the Fourth-Root Trick
• Applications of Partially Quenched Chiral Perturbation Theory
• Chiral Logs in the Presence of Staggered Flavor Symmetry Breaking
• Domain wall fermions with improved gauge actions
• The QCD Chiral Condensate from the Lattice
• A Lattice Computation of the Decay Constants of $B$ and $D$ Mesons
• Localization in Lattice QCD
• Baryons in Partially Quenched Chiral Perturbation Theory
• The nucleon's strange electromagnetic and scalar matrix elements
• Chiral Loops and Ghost States in the Quenched Scalar Propagator
• Heavy meson chiral perturbation theory in finite volume
• Lattice Calculation of Heavy-Light Decay Constants with Two Flavors of Dynamical Quarks
• Effective Chiral Lagrangians and Lattice QCD
• Nucleons in Two-Flavor Partially-Quenched Chiral Perturbation Theory
• Order a improved renormalization constants
• BB Potentials in Quenched Lattice QCD
• Light quark masses, chiral condensate and quark-gluon condensate in quenched lattice QCD with exact chiral symmetry
• Effects of Quenching and Partial Quenching on Penguin Matrix Elements
• Standard Model Matrix Elements for Neutral B-Meson Mixing and Associated Decay Constants
• Twist-two matrix elements at finite and infinite volume
• K^0-\bar K^0 mixing beyond the standard model and CP-violating electroweak penguins in quenched QCD with exact chiral symmetry
• Leading Quenching Effects in the Proton Magnetic Moment
• Moments of Isovector Quark Distributions from Lattice QCD
• Quenched QCD with O(a) improvement: I. The spectrum of light hadrons
• Finite-volume two-pion energies and scattering in the quenched approximation
• The Magnetic Moments of the Octet Baryons in Quenched Chiral Perturbation Theory
• Two Meson Systems with Ginsparg-Wilson Valence Quarks
• Quark Contributions to Baryon Magnetic Moments in Full, Quenched and Partially Quenched QCD
• Lattice QCD with Ginsparg-Wilson fermions
• The $B_K$ Parameter in the $1/N_c$ Expansion
• An Introduction to Chiral Symmetry on the Lattice
• Decuplet Baryon Masses in Partially Quenched Chiral Perturbation Theory
• Nambu-Goldstone mesons in strong magnetic field
• Effective Field Theory of the Random Flux Model
• Short distance current correlators: Comparing lattice simulations to the instanton liquid
• Finite-size Scaling of Meson Propagators
• Chiral Symmetry, Quark Mass, and Scaling of the Overlap Fermions
• Quenched Chiral Perturbation Theory for Heavy-Light Mesons
• Hadron Spectrum with Wilson fermions
• Impact of the finite volume effects on the chiral behavior of fK and BK
• The Spectral Density of the QCD Dirac Operator and Patterns of Chiral Symmetry Breaking
• Is the Quenched Spectrum in agreement with Experiment?
• Chiral symmetry breaking at large N_c
• Axial Correlation Functions in the epsilon-Regime: a Numerical Study with Overlap Fermions
• Quenched Chiral Perturbation Theory to one loop
• Kaon B Parameter in Quenched QCD
• Improved Analysis of J/psi Decays into a Vector Meson and Two Pseudoscalars
• Chiral Logs in Quenched QCD
• Heavy--light decay constants in the continuum limit of quenched lattice QCD
• Finite-Size Scaling of Vector and Axial Current Correlators
• Nucleon-Nucleon Interactions on the Lattice
• Influence of quark boundary conditions on the pion mass in finite volume
• Charge Radii of the Meson and Baryon Octets in Quenched and Partially Quenched Chiral Perturbation Theory
• Spontaneous $CP$ breaking in QCD and the axion potential: an effective Lagrangian approach
• Spectral Properties of the Overlap Dirac Operator in QCD
• Spectrum of quenched twisted mass lattice QCD at maximal twist
• Model Independent Results for SU(3) Violation in Light-Cone Distribution Functions
• Nucleons Properties at Finite Lattice Spacing in Chiral Perturbation Theory
• Quenched Chiral Perturbation Theory for Vector Mesons
• The Kaon B-parameter from Quenched Domain-Wall QCD
• Witten-Veneziano Relation, Quenched QCD, and Overlap Fermions
• The role of the double pole in lattice QCD with mixed actions
• Anomalous Chiral Behavior in Quenched Lattice QCD
• SU(3) Flavor Breaking in Hadronic Matrix Elements for $B-\bar{B}$ Oscillations
• Quenched Finite Volume Logarithms
• Electromagnetic Corrections in Partially Quenched Chiral Perturbation Theory
• Low-energy couplings of QCD from topological zero-mode wave functions
• Strange quarks in quenched twisted mass lattice QCD
• Three-Flavor Partially Quenched Chiral Perturbation Theory at NNLO for Meson Masses and Decay Constants
• Order of the Chiral and Continuum Limits in Staggered Chiral Perturbation Theory
• Baryon Decuplet to Octet Electromagnetic Transitions in Quenched and Partially Quenched Chiral Perturbation Theory
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• Hadronic Parity-Violation on the Lattice
• Electromagnetic Properties of the Baryon Decuplet in Quenched and Partially Quenched Chiral Perturbation Theory
• An Efficient Algorithm for QCD with Light Dynamical Quarks
• Extrapolations of Lattice Meson Form Factors
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• Recent Results from the CP-PACS Collaboration
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• Testing m(up)=0 on the Lattice
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• On the Determination of Nonleptonic Kaon Decays from $K\to \pi$ Matrix Elements
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• Effective theory for quenched lattice QCD and the Aoki phase
• Chiral Lagrangian Parameters for Scalar and Pseudoscalar Mesons
• Lattice study of large $N_c$ QCD
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• Chiral Random Matrix Model for Critical Statistics
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• Microscopic Spectrum of the QCD Dirac Operator in Three Dimensions
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• Lattice calculation of low energy constants with Ginsparg-Wilson type fermions
• Light hadron and diquark spectroscopy in quenched QCD with overlap quarks on a large lattice
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• Scale setting the Möbius Domain Wall Fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales $t_0$ and $w_0$
• Large N meson masses from a matrix model
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• Hadron Masses and Decay Constants with Wilson Quarks at $\beta =5.85$ and 6.0
• Continuum limit of lattice QCD with staggered quarks in the quenched approximation - a critical role for the chiral extrapolation
• QCD with Bosonic Quarks at Nonzero Chemical Potential
• Methods for Pseudoscalar Flavour-Singlet Mesons with Staggered Fermions
• The Pseudoscalar Meson Mass to Two Loops in Three-Flavor Partially Quenched $\chi$PT
• Matrix elements of the complete set of ΔB = 2 and ΔC = 2 operators in heavy meson chiral perturbation theory
• Electromagnetic Structure of Light Baryons in Lattice QCD
• Finite volume effects in chiral perturbation theory
• Baryon masses at O(a^2) in chiral perturbation theory
• Baryon Masses in Partially Quenched Heavy Hadron Chiral Perturbation Theory
• 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
• Spontaneous chiral symmetry breaking in QCD:a finite-size scaling study on the lattice
• Finite Volume Scaling of Pseudo Nambu-Goldstone Bosons in QCD
• Finite-Volume Two-Pion Amplitudes in the I=0 Channel
• Instantons in QCD with Many Colors
• Doubly Heavy Baryons and Quark-Diquark Symmetry in Quenched and Partially Quenched Chiral Perturbation Theory
• Quenched QCD at finite temperature with chiral Fermions
• Realisation of chiral symmetry in the domain model of QCD
• Quenched QCD with fixed-point and chirally improved fermion
• Chiral Perturbation Theory and the $\bar{B}\bar{B}$ Strong Interaction
• The Chiral Extrapolation of Strange Matrix Elements in the Nucleon
• B --> pi and B --> K transitions in partially quenched chiral perturbation theory
• Applications of Chiral Perturbation theory to lattice QCD
• K-->pipi amplitudes from lattice QCD with a light charm quark
• Pion Polarizabilities and Volume Effects in Lattice QCD
• Matrix Elements of Twist-2 Operators in Quenched Chiral Perturbation Theory
• Hadron spectrum, quark masses and decay constants from light overlap fermions on large lattices
• Model-Independent Results for SU(3) Violation in Twist-3 Light-Cone Distribution Functions
• Heavy-light mesons in the epsilon-regime
• Testing improved staggered fermions with $m_s$ and $B_K$
• Chiral Corrections to Hyperon Axial Form Factors
• Finite-volume Correction to the Pion Decay Constant in the Epsilon-Regime
• Recent results from systematic parameterizations of Ginsparg-Wilson fermions
• Recent results on light hadron and quark masses
• On the effects of (partial) quenching on penguin contributions to K-> pi pi
• Quenched Light Hadron Spectrum with the Wilson Quark Action: Final Results from CP-PACS
• Ginsparg-Wilson Fermions: A study in the Schwinger Model
• Topology and Low Lying Fermion Modes
• Chiral corrections to the axial charges of the octet baryons from quenched QCD
• A Mixed Action Analysis of $\eta$ and ${\eta }^{\prime }$ Mesons
• Quenched and Partially Quenched Chiral Perturbation Theory for Vector and Tensor Mesons
• The Ademollo-Gatto theorem for lattice semileptonic decays
• On Lattice Computations of K+ --> pi+ pi0 Decay at m_K =2m_pi
• $Z_3$ Twisted Chiral Condensates in QCD at Finite Temperatures
• Chiral condensate in the quenched Schwinger model
• Decay constants with Wilson fermions at $\beta =6.0$
• Light Hadron Spectrum in Quenched Lattice QCD with Staggered Quarks
• Strongly coupled compact lattice QED with staggered fermions
• New results on cut-off effects in spectroscopy with the fixed point action
• Finite-size scaling for the left-current correlator with non-degenerate quark masses
• Hadronic Electromagnetic Properties at Finite Lattice Spacing
• Quenched Chiral Perturbation Theory for Baryons
• Analytic estimates for penguin operators in quenched QCD
• Quenched chiral logarithms in lattice QCD with exact chiral symmetry
• Moments of Isovector Quark Distributions in Lattice QCD
• Quenched chiral perturbation theory for baryon form factors
• Connecting the Quenched and Unquenched Worlds via the Large N_c World
• Systematic effects of the quenched approximation on the strong penguin contribution to epsilon'/epsilon
• Nucleon form factors and parton distributions in nonlocal chiral effective theory
• Probing the chiral weak Hamiltonian at finite volumes
• Testing chiral effective theory with quenched lattice QCD
• Quenched divergences in the deconfined phase of SU(2) gauge theory
• Divergent chiral condensate in the quenched Schwinger model
• Light quark masses in quenched QCD with exact chiral symmetry
• Chiral extrapolation of the charged-pion magnetic polarizability with Padé approximant
• Quenched Supersymmetry
• Dynamical Wilson fermions and the problem of the chiral limit in compact lattice QED
• Finite Volume Gauge Theory Partition Functions in Three Dimensions
• Quenched penguins and the Delta I=1/2 rule
• Quenched Chiral Perturbation Theory for Heavy Baryons
• Quenched and Unquenched Chiral Perturbation Theory in the ε-Regime
• Comparison of Lattice and Chiral Perturbation Theory calculations of pion scattering lengths
• Determination of the $\Delta S=1$ weak Hamiltonian in the SU(4) chiral limit through topological zero-mode wave functions
• K to pi and K to 0 in 2+1 Flavor Partially Quenched Chiral Perturbation Theory
• Chiral 1/M^2 corrections to B^(*) -> D^(*) at Zero Recoil in Quenched Chiral Perturbation Theory
• Dynamical Generation of Elementary Fermion Mass: First Lattice Evidence
• Is there an Aoki phase in quenched QCD?
• Staggered chiral perturbation theory in the two-flavor case
• The eta mass and NNLO Three-Flavor Partially Quenched Chiral Perturbation Theory
• Pion loops in quenched Quantum Chromodynamics
• Taste non-Goldstone, flavor-charged pseudo-Goldstone boson masses in staggered chiral perturbation theory
• Evidence for quenched chiral logs
• Chiral extrapolation of the magnetic polarizability of the neutral pion
• Testing the mechanism of lepton compositness
• Proposal for Topologically Unquenched QCD
• Analytic estimates of quenched penguins
• IR-Divergence and Anomalous Temperature Dependence of the Condensate in the Quenched Schwinger Model
• Quenched Chiral Behavior of Hadrons with Overlap Fermions
• Aspects of Quenched Chiral Perturbation Theory for Matter Fields
• Mass dependence of the hairpin vertex in quenched QCD
• Taste non-Goldstone, flavor-charged pseudo-Goldstone boson decay constants in staggered chiral perturbation theory
• K* vector and tensor couplings from Nf = 2 tmQCD
• Do we understand the unquenched value of fB?
• Quenched Supersymmetry
• Pseudoscalar flavor-singlets and staggered fermions
• Finite Volume Chiral Partition Functions and the Replica Method
• Topologically Unquenched QCD: Prospects from an explorative study in 2-flavour QED(2)
• How good is the quenched approximation of QCD?
• Chiral limit of light hadron mass in quenched staggered QCD
• Chiral Perturbation Theory on the Lattice and its Applications
• Determining the low energy parameters of Wilson Chiral Perturbation Theory
• Vector and Axial-Vector Propagators in the ε-Regime of QCD
• Phase ambiguity of the measure for continuum Majorana fermions
• Sea quark contributions to nucleon electromagnetic form factors with the nonlocal chiral effective Lagrangian
• Quenched Chiral Log and Light Quark Mass from Overlap Fermions
• Current Physics Results from Staggered Chiral Perturbation Theory
• Finite-volume meson propagators in quenched chiral perturbation theory
• Simulating the vacuum properties of QCD with dynamical quarks
• Towards measuring the eta' mass with N_f=2+1 staggered fermions
• Kaon weak interactions in powers of 1/Nc
• Quark mass dependence of the pseudoscalar hairpin vertex
• Low Energy Constants from the zero mode contribution to the pseudo-scalar correlator
• Beyond the Thouless energy
• Comment on the "Coupling Constant and Quark Loop Expansion for Corrections to the Valence Appeoximation" by Lee and Weingarten
• Quenched chiral logarithms in lattice QCD with overlap Dirac quarks
• Quenched Chiral Perturbation Theory to one loop
• Miscellanies of $K^0-{\bar{K}}^0$ mixing and $B_K$
• Sea quark contributions to the electromagnetic form factors of $\Sigma$ hyperons
• Chiral Logarithms in $\Delta S=1$ Kaon Decay Amplitudes in General Effective Flavor Theories
• On the phase diagram of quenched QCD with Wilson fermions
• Towards a quantitative understanding of the Delta I=1/2 rule
• Axial U(1) and spontaneous chiral symmetry breaking within a confining model of the QCD vacuum
• Quark disconnected diagrams in chiral perturbation theory - the scalar form factor
• Meson masses and decay constants at large $N$
• The quenched generating functional for hadronic weak interactions