Status of Lattice QCD Determination of Nucleon Form Factors and their Relevance for the Few-GeV Neutrino Program

Abstract

Calculations of neutrino-nucleus cross sections begin with the neutrino-nucleon interaction, making the latter critically important to flagship neutrino oscillation experiments, despite limited measurements with poor statistics. Alternatively, lattice QCD (LQCD) can be used to determine these interactions from the Standard Model with quantifiable theoretical uncertainties. Recent LQCD results of $g_{\mathrm{A}}$ are in excellent agreement with data, and results for the (quasi-)elastic nucleon form factors with full uncertainty budgets are expected within a few years. We review the status of the field and LQCD results for the nucleon axial form factor, $F_{\mathrm{A}}(Q^2)$, a major source of uncertainty in modeling sub-GeV neutrino-nucleon interactions. Results from different LQCD calculations are consistent, but collectively disagree with existing models, with potential implications for current and future neutrino oscillation experiments. We describe a road map to solidify confidence in the LQCD results and discuss future calculations of more complicated processes, important to few-GeV neutrino oscillation experiments.

arXiv comment29 pages, 5 figures. Review article for Ann. Rev. Nucl. Part., comments from the community are welcome. v2: consistent with version to be published in Annual Reviews of Nuclear and Particle Science with updates reflecting referee and community comments

References in corpus (106)

• Chiral Dynamics in Nucleons and Nuclei
• The fate of hints: updated global analysis of three-flavor neutrino oscillations
• A Method for Simulating Chiral Fermions on the Lattice
• The GENIE Neutrino Monte Carlo Generator
• Chiral Fermions from Lattice Boundaries
• From eV to EeV: Neutrino Cross Sections Across Energy Scales
• Chiral symmetry and O(a) improvement in lattice QCD
• Axial symmetries in lattice QCD with Kaplan fermions
• Solving Lattice QCD systems of equations using mixed precision solvers on GPUs
• Non-perturbative O(a) improvement of lattice QCD
• Axial structure of the nucleon
• Chirally improving Wilson fermions - I. O(a) improvement
• Constraint on the Matter-Antimatter Symmetry-Violating Phase in Neutrino Oscillations
• A novel quark-field creation operator construction for hadronic physics in lattice QCD
• Non-perturbative quark mass renormalization in quenched lattice QCD
• Lattice QCD ensembles with four flavors of highly improved staggered quarks
• NuSTEC White Paper: Status and Challenges of Neutrino-Nucleus Scattering
• Spontaneous Flavor and Parity Breaking with Wilson Fermions
• Non-perturbative determination of the axial current normalization constant in O(a) improved lattice QCD
• A new parameterization of the nucleon elastic form factors
• The T2K Neutrino Flux Prediction
• Energy dependence of the ρ resonance in ππ elastic scattering from lattice QCD
• A percent-level determination of the nucleon axial coupling from Quantum Chromodynamics
• Updated MiniBooNE Neutrino Oscillation Results with Increased Data and New Background Studies
• Novel quark smearing for hadrons with high momenta in lattice QCD
• Decay width of light quark hybrid meson from the lattice
• Deuterium target data for precision neutrino-nucleus cross sections
• Light hadron spectroscopy using domain wall valence quarks on an Asqtad sea
• Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD
• Origin of Difference between $\overline{d}$ and $\overline{u}$ Partons in the Nucleon
• Isovector Charges of the Nucleon from 2+1+1-flavor Lattice QCD
• The nucleon axial charge from lattice QCD with controlled errors
• Measurement of neutrino and antineutrino oscillations by the T2K experiment including a new additional sample of ${\nu }_e$ interactions at the far detector
• Progress and open questions in the physics of neutrino cross sections
• Nucleon isovector couplings from $N_f=2$ lattice QCD
• Axial Vector Form Factors of the Nucleon from Lattice QCD
• Model independent determination of the axial mass parameter in quasielastic neutrino-nucleon scattering
• Improved constraints on neutrino mixing from the T2K experiment with $3.13\times 10^{21}$ protons on target
• Scattering in the pion-nucleon negative parity channel in lattice QCD
• Axial Vector Form Factors from Lattice QCD that Satisfy the PCAC Relation
• Nucleon axial, tensor and scalar charges and $\sigma$-terms in lattice QCD
• From deep inelastic scattering to heavy-flavor semi-leptonic decays: Total rates into multi-hadron final states from lattice QCD
• Neutrino Interactions with Nucleons and Nuclei: Importance for Long-Baseline Experiments
• Quark mass dependence of hadron masses from lattice QCD
• Quark spins and Anomalous Ward Identity
• Chiral Perturbation Theory for Staggered Sea Quarks and Ginsparg-Wilson Valence Quarks
• Nucleon electromagnetic form factors from lattice QCD using a nearly physical pion mass
• Recent highlights from GENIE v3
• Precision Nucleon Charges and Form Factors Using 2+1-flavor Lattice QCD
• Proton-proton fusion and tritium $\beta$-decay from lattice quantum chromodynamics
• Simulations with different lattice Dirac operators for valence and sea quarks
• Neutrino-Nucleon Cross-Section Model Tuning in GENIE v3
• Lattice QCD study of the $H$ dibaryon using hexaquark and two-baryon interpolators
• Nucleon axial structure from lattice QCD
• Threshold Pion Electroproduction in Chiral Perturbation Theory
• Nucleon Axial Radius and Muonic Hydrogen - A New Analysis and Review
• Towards grounding nuclear physics in QCD
• Hadronic physics with domain-wall valence and improved staggered sea quarks
• Inclusive semi-leptonic decays from 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 lattice QCD at the physical point
• Nucleon isovector charges and twist-2 matrix elements with $N_f=2+1$ dynamical Wilson quarks
• Weakly bound $H$ dibaryon from SU(3)-flavor-symmetric QCD
• On the Feynman-Hellmann Theorem in Quantum Field Theory and the Calculation of Matrix Elements
• Nuclear matrix elements from lattice QCD for electroweak and beyond-Standard-Model processes
• Parameterization and applications of the low-$Q^2$ nucleon vector form factors
• Two-nucleon S-wave interactions at the $SU(3)$ flavor-symmetric point with $m_{ud}\simeq m_s^{\mathrm{phys}}$: a first lattice QCD calculation with the stochastic Laplacian Heaviside method
• Nucleon axial, scalar, and tensor charges using lattice QCD at the physical pion mass
• Domain decomposition, multi-level integration and exponential noise reduction in lattice QCD
• Lattice QCD and Neutrino-Nucleus Scattering
• Computing the nucleon charge and axial radii directly at $Q^2=0$ in lattice QCD
• $N\pi$-state contamination in lattice calculations of the nucleon axial form factors
• Towards the nucleon hadronic tensor from lattice QCD
• In Search of the Chiral Regime
• Nuclear modification of scalar, axial and tensor charges from lattice QCD
• Baryons with Ginsparg-Wilson quarks in a staggered sea
• The puzzle of apparent linear lattice artifacts in the 2d non-linear sigma-model and Symanzik's solution
• Reconstruction of Energy Spectra of Neutrino Beams Independent of Nuclear Effects
• Solving the PCAC puzzle for nucleon axial and pseudoscalar form factors
• On the extraction of zero momentum form factors on the lattice
• New Ideas in Constraining Nuclear Forces
• A new method for an improved anti-neutrino energy reconstruction with charged-current interactions in next-generation detectors
• A Feynman-Hellmann approach to the spin structure of hadrons
• The pion-nucleon sigma term from lattice QCD
• Asymptotic behavior of cutoff effects in Yang-Mills theory and in Wilson's lattice QCD
• Universality of Mixed Action Extrapolation Formulae
• Nucleon-pion-state contribution in lattice calculations of the nucleon charges $g_A,g_T$ and $g_S$
• Logarithmic corrections to O(a^2) lattice artifacts
• Nucleon form factors from quenched lattice QCD with domain wall fermions
• Precise Measurements of the Decay of Free Neutrons
• Chiral perturbation theory and nucleon-pion-state contaminations in lattice QCD
• Recent Advances and Open Questions in Neutrino-induced Quasi-elastic Scattering and Single Photon Production
• Elastic Form Factors of Nucleon Excitations in Lattice QCD
• A Stochastic Method for Computing Hadronic Matrix Elements
• Variations on the Maiani-Testa approach and the inverse problem
• Neutrino-hydrogen interactions with a high-pressure time projection chamber
• Controlling Excited-State Contributions with Distillation in Lattice QCD Calculations of Nucleon Isovector Charges $g_S^{u-d}$, $g_A^{u-d}$, $g_T^{u-d}$
• Parity-expanded variational analysis for non-zero momentum
• Staggered Baryon Operators with Flavor SU(3) Quantum Numbers
• Excited states in nucleon structure calculations
• Opposite-Parity Contaminations in Lattice Nucleon Form Factors
• Towards fully non-perturbative computation of inelastic $\ell N$ scattering cross sections from lattice QCD
• Nucleon mass and isovector couplings in 2+1-flavor dynamical domain-wall lattice QCD near physical mass
• Multigrid for Chiral Lattice Fermions: Domain Wall
• Simulating the weak death of the neutron in a femtoscale universe with near-Exascale computing
• Nucleon Mass with Highly Improved Staggered Quarks

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