Solving the PCAC puzzle for nucleon axial and pseudoscalar form factors

Abstract

It has been observed in multiple lattice determinations of isovector axial and pseudoscalar nucleon form factors, that, despite the fact that the partial conservation of the axialvector current is fulfilled on the level of correlation functions, the corresponding relation for form factors (sometimes called the generalized Goldberger-Treiman relation in the literature) is broken rather badly. In this work we trace this difference back to excited state contributions and propose a new projection method that resolves this problem. We demonstrate the efficacy of this method by computing the axial and pseudoscalar form factors as well as related quantities on ensembles with two flavors of improved Wilson fermions using pion masses down to 150 MeV. To this end, we perform the $z$-expansion with analytically enforced asymptotic behaviour and extrapolate to the physical point.

References in corpus (62)

• A New Way to Set the Energy Scale in Lattice Gauge Theories and its Application to the Static Force and ${\alpha }_s$ in SU(2) Yang--Mills Theory
• A General Method for Non-Perturbative Renormalization of Lattice Operators
• Impact Parameter Space Interpretation for Generalized Parton Distributions
• Axial structure of the nucleon
• First Measurement of the Muon Neutrino Charged Current Quasielastic Double Differential Cross Section
• Simulation of QCD with N_f=2+1 flavors of non-perturbatively improved Wilson fermions
• Nucleon structure from mixed action calculations using 2+1 flavors of asqtad sea and domain wall valence fermions
• A percent-level determination of the nucleon axial coupling from Quantum Chromodynamics
• Further results on O(a) improved lattice QCD to one-loop order of perturbation theory
• Deuterium target data for precision neutrino-nucleus cross sections
• Model independent extraction of the proton charge radius from electron scattering
• Nucleon Form Factors in QCD
• Axial, Scalar and Tensor Charges of the Nucleon from 2+1+1-flavor Lattice QCD
• The nucleon axial charge from lattice QCD with controlled errors
• Nucleon Charges and Electromagnetic Form Factors from 2+1+1-Flavor Lattice QCD
• Nucleon isovector couplings from $N_f=2$ lattice QCD
• Nucleon form factors with 2+1 flavor dynamical domain-wall fermions
• Axial Vector Form Factors of the Nucleon from Lattice QCD
• Nucleon axial charge in 2+1 flavor dynamical lattice QCD with domain wall fermions
• Model independent determination of the axial mass parameter in quasielastic neutrino-nucleon scattering
• Nucleon mass and sigma term from lattice QCD with two light fermion flavors
• A measurement of the axial form factor of the nucleon by the p(e,e'pi+)n reaction at W=1125 MeV
• Nucleon axial form factors using lattice QCD simulations with a physical value of the pion mass
• Axial Nucleon form factors from lattice QCD
• Quark spins and Anomalous Ward Identity
• Axial, induced pseudoscalar, and pion-nucleon form factors in manifestly Lorentz-invariant chiral perturbation theory
• Up, down, and strange nucleon axial form factors from lattice QCD
• Model independent extraction of the proton magnetic radius from electron scattering
• Nucleon Structure from Lattice QCD Using a Nearly Physical Pion Mass
• Nucleon Axial Radius and Muonic Hydrogen - A New Analysis and Review
• Iso-vector axial form factors of the nucleon in two-flavour lattice QCD
• Perturbative and Nonperturbative Renormalization in Lattice QCD
• Nucleon form factors on a large volume lattice near the physical point in 2+1 flavor QCD
• Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation
• Lattice simulations with $N_f=2+1$ improved Wilson fermions at a fixed strange quark mass
• On the Feynman-Hellmann Theorem in Quantum Field Theory and the Calculation of Matrix Elements
• Nucleon axial charge and pion decay constant from two-flavor lattice QCD
• Measurement of Muon Capture on the Proton to 1% Precision and Determination of the Pseudoscalar Coupling g_P
• Cross sections for neutrino and antineutrino induced pion production on hydrocarbon in the few-GeV region using MINERvA
• Non-perturbative improvement of the axial current for dynamical Wilson fermions
• Isovector charges of the nucleon from 2+1-flavor QCD with clover fermions
• The moment $⟨x{⟩}_{u-d}$ of the nucleon from $N_f=2$ lattice QCD down to nearly physical quark masses
• A Feynman-Hellmann approach to the spin structure of hadrons
• Perturbative calculation of improvement coefficients to O(g^2a) for bilinear quark operators in lattice QCD
• Extraction of nucleon axial charge and radius from lattice QCD results using baryon chiral perturbation theory
• Lattice Calculation of Nucleon Isovector Axial Charge with Improved Currents
• Extraction of the Axial Nucleon Form Factor from Neutrino Experiments on Deuterium
• An accurate calculation of the nucleon axial charge with lattice QCD
• Pion electroproduction, PCAC, chiral Ward identities, and the axial form factor revisited
• Axial form factor of the nucleon at large momentum transfers
• Chiral Corrections to Nucleon Two- and Three-Point Correlation Functions
• Chiral perturbation theory and nucleon-pion-state contaminations in lattice QCD
• Nucleon matrix elements from lattice QCD with all-mode-averaging and a domain-decomposed solver: an exploratory study
• Chiral extrapolation of nucleon wave function normalization constants
• Multi-hadron-state contamination in nucleon observables from chiral perturbation theory
• Nucleon Axial and Electromagnetic Form Factors
• QPACE -- a QCD parallel computer based on Cell processors
• Nucleon structure from 2+1 flavor lattice QCD near the physical point
• Nucleon-pion-state contamination in lattice calculations of the axial form factors of the nucleon
• Connected and disconnected contributions to nucleon axial form factors using $N_f=2$ twisted mass fermions at the physical point
• Muon Capture on the Proton
• Nucleon electromagnetic and axial form factors with N${}_f$=2 twisted mass fermions at the physical point

Cited by in corpus (30)

• Parton distributions and lattice QCD calculations: toward 3D structure
• Axial Vector Form Factors from Lattice QCD that Satisfy the PCAC Relation
• Nucleon axial structure from lattice QCD
• Towards grounding nuclear physics in QCD
• Precision Studies of QCD in the Low Energy Domain of the EIC
• Nucleon axial and pseudoscalar form factors from lattice QCD at the physical point
• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks
• Nucleon Helicity Generalized Parton Distribution at Physical Pion Mass from Lattice QCD
• Lattice QCD and Neutrino-Nucleus Scattering
• $N\pi$-state contamination in lattice calculations of the nucleon axial form factors
• Status of Lattice QCD Determination of Nucleon Form Factors and their Relevance for the Few-GeV Neutrino Program
• Moments of proton GPDs from the OPE of nonlocal quark bilinears up to NNLO
• Nucleon axial-vector and pseudoscalar form factors, and PCAC relations
• $N\pi$-state contamination in lattice calculations of the nucleon pseudoscalar form factor
• Toward $N$ to $N\pi$ matrix elements from lattice QCD
• On the axial-vector form factor of the nucleon and chiral symmetry
• $N\pi$-states and the projection method for the nucleon axial and pseudoscalar form factors
• Moments of Axial-Vector GPD from Lattice QCD: Quark Helicity, Orbital Angular Momentum, and Spin-Orbit Correlation
• $N\pi$-state contamination in lattice calculations of the nucleon electromagnetic form factors
• Excited states in nucleon structure calculations
• Axial and pseudoscalar form factors from charged current quasielastic neutrino-nucleon scattering
• Axial-vector form factors of the baryon octet and chiral symmetry
• Unified model of nucleon elastic form factors and implications for neutrino-oscillation experiments
• Mapping Parton Distributions of Hadrons with Lattice QCD
• Method for high-precision determination of the nucleon axial structure using lattice QCD: Removing $\pi N$-state contamination
• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks at Nonzero Skewness
• Recent results of nucleon structure & matrix element calculations
• The axial-vector form factor of the nucleon in a finite box
• Symmetry breaking effects in pion couplings to constituent quark currents
• Theory of QED radiative corrections to neutrino scattering at accelerator energies