Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors

Abstract

We calculate the two-photon exchange corrections to electron-proton scattering with nucleon and $\Delta$ intermediate states. The results show a dependence on the elastic nucleon and nucleon-$\Delta$-transition form factors used as input which leads to significant changes compared to previous calculations. We discuss the relevance of these corrections and apply them to the most recent and precise data set and world data from electron-proton scattering. Using this, we show how the form factor extraction from these data is influenced by the subsequent inclusion of physical constraints. The determination of the proton charge radius from scattering data is shown to be dominated by the enforcement of a realistic spectral function. Additionally, the third Zemach moment from the resulting form factors is calculated. The obtained radius and Zemach moment are shown to be consistent with Lamb shift measurements in muonic hydrogen.

minor changes, added references, version to appear in PRD

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Cited by in corpus (74)

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• Joint lattice QCD - dispersion theory analysis confirms the quark-mixing top-row unitarity deficit
• Two-photon exchange in elastic electron-proton scattering
• On the pi pi continuum in the nucleon form factors and the proton radius puzzle
• Nucleon Polarizabilities: from Compton Scattering to Hydrogen Atom
• The Proton Radius from Electron Scattering Data
• Are Electron Scattering Data Consistent with a Small Proton Radius?
• Extraction of the neutron charge radius from a precision calculation of the deuteron structure radius
• Parameterization and applications of the low-$Q^2$ nucleon vector form factors
• Determining the leading-order contact term in neutrinoless double $\mathbf{\beta }$ decay
• The proton structure in and out of muonic hydrogen
• A dispersive approach to two-photon exchange in elastic electron-proton scattering
• Nuclear Currents in Chiral Effective Field Theory
• High-accuracy calculation of the deuteron charge and quadrupole form factors in chiral effective field theory
• High-precision determination of the electric and magnetic radius of the proton
• Comprehensive theory of the Lamb shift in light muonic atoms
• Dispersion-theoretical analysis of the electromagnetic form factors of the nucleon: Past, present and future
• Two-photon exchange correction in elastic unpolarized electron-proton scattering at small momentum transfer
• Precise determination of proton magnetic radius from electron scattering data
• Dispersion relation analysis of the radiative corrections to $g_A$ in the neutron $\beta$-decay
• The proton radius: From a puzzle to precision
• Evaluation of the strength of electron-proton scattering data for determining the proton charge radius
• Proton radius from electron-proton scattering and chiral perturbation theory
• New structures in the proton-antiproton system
• Effective field theory for large logarithms in radiative corrections to electron proton scattering
• Two-photon exchange contribution to elastic $e^{-}$-proton scattering: Full dispersive treatment of $\pi N$ states and comparison with data
• Robust extraction of proton charge radius from electron-proton scattering data
• Two-loop analysis of the pion-mass dependence of the $\rho$ meson
• Nucleon matrix elements of the antisymmetric quark tensor
• Review of experimental and theoretical status of the proton radius puzzle
• The Lamb shift in muonic hydrogen and the proton radius from effective field theories
• Electromagnetic Transition Form Factors of Baryon Resonances
• Dispersion relation formalism for the two-photon exchange correction to elastic muon-proton scattering: elastic intermediate state
• Nuclear structure corrections to the Lamb shift in ${\mu }^3$He${}^{+}$ and ${\mu }^3$H
• Model-independent determination of the axial mass parameter in quasielastic antineutrino-nucleon scattering
• Model-independent determination of the nucleon charge radius from lattice QCD
• Light- and strange-quark mass dependence of the $\rho (770)$ meson revisited
• Two-photon exchange corrections to elastic $e^{-}$-proton scattering: Full dispersive treatment of $\pi N$ states at low momentum transfers
• Charge radii of the nucleon from its flavor dependent Dirac form factors
• How Analytic Choices Can Affect the Extraction of Electromagnetic Form Factors from Elastic Electron Scattering Cross Section Data
• Experiments towards resolving the proton charge radius puzzle
• Radiative corrections to semileptonic beta decays: Progress and challenges
• Precision calculation of the electromagnetic radii of the proton and neutron from lattice QCD
• Superallowed nuclear beta decays and precision tests of the Standard Model
• Electromagnetic form factors of the nucleon from $N_f=2+1$ lattice QCD
• Model independent determination of the muonic hydrogen Lamb shift and proton radius
• The Standard Model theory of neutron beta decay
• Phenomenological extraction of two-photon exchange amplitudes from elastic electron-proton scattering cross section data
• New insights into the oscillation of the nucleon electromagnetic form factors
• Spectral functions of nucleon form factors: Three-pion continua at low energies
• Leading order corrections to the Bethe-Heitler process in the $\gamma p\to l^{+}{l}^{-}p$ reaction
• Soft-photon corrections to the Bethe-Heitler process in the $\gamma p\to l^{+}{l}^{-}p$ reaction
• Elements of QED-NRQED Effective Field Theory: I. NLO scattering at leading power
• Breakdown of the expansion of finite-size corrections to the hydrogen Lamb shift in moments of charge distribution
• Radiative and chiral corrections to elastic lepton-proton scattering in chiral perturbation theory
• Sensitivity of the elastic electron-proton cross section to the proton radius
• The electromagnetic Sigma-to-Lambda transition form factors with coupled-channel effects in the space-like region
• Elements of QED-NRQED Effective Field Theory: II. Matching of Contact Interactions
• Radiative Correction to Lepton Proton Scatterings in Manifestly Lorentz-Invariant Chiral Perturbation Theory
• Lower bound on the proton charge radius from electron scattering data
• Properties of the Sachs electric form factor of the proton on the basis of recent $e-p$ scattering experiments and hydrogen spectroscopy
• The Structure of the Nucleon: Elastic Electromagnetic Form Factors
• Hybrid analysis of radiative corrections to neutron decay with current algebra and effective field theory
• Radiative corrections to elastic muon-proton scattering at low momentum transfers
• Radiative corrections to elastic proton-electron scattering measured in coincidence
• Chiral constraints on the isoscalar electromagnetic spectral functions of the nucleon from leading order vector meson couplings
• Differential Cross Section Predictions for PRad-II from Dispersion Theory
• Radiative corrections to the magnetic moments of the proton and the neutron
• Resonance Contributions to Radiative Corrections in Charged-Current Elastic (Anti)Neutrino-Nucleon Scattering at GeV Energies
• Exact Relations for Two-Photon-Exchange Effect in Elastic $ep$ Scattering by Dispersion Relation and Hadronic Model
• Nuclear deformation effects on charge radius measurements of the proton and deuteron
• Baryon Form Factors