On the pi pi continuum in the nucleon form factors and the proton radius puzzle

Abstract

We present an improved determination of the $\pi \pi$ continuum contribution to the isovector spectral functions of the nucleon electromagnetic form factors. Our analysis includes the most up-to-date results for the $\pi \pi \to \bar{N}N$ partial waves extracted from Roy-Steiner equations, consistent input for the pion vector form factor, and a thorough discussion of isospin-violating effects and uncertainty estimates. As an application, we consider the $\pi \pi$ contribution to the isovector electric and magnetic radii by means of sum rules, which, in combination with the accurately known neutron electric radius, are found to slightly prefer a small proton charge radius.

arXiv comment10 pages, 3 figures, spectral functions included as supplementary material; journal version

References in corpus (62)

• Big-Bang Nucleosynthesis
• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• ππscattering
• High-precision determination of the electric and magnetic form factors of the proton
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Dispersion-Theoretical Analysis of the Nucleon Electromagnetic Formfactors
• Muonic hydrogen and the proton radius puzzle
• The electric and magnetic form factors of the proton
• Pion-nucleon scattering in chiral perturbation theory I: Isospin-symmetric case
• Precise measurement of the e+ e- to pi+ pi- (gamma) cross section with the Initial State Radiation method at BABAR
• The Proton Radius Puzzle
• Measurement of the ${\mathrm{e}}^{+}{\mathrm{e}}^{-}\to {\pi }^{+}{\pi }^{-}$ Cross Section between 600 and 900 MeV Using Initial State Radiation
• High-precision determination of the pion-nucleon $\sigma$-term from Roy-Steiner equations
• Roy-Steiner-equation analysis of pion-nucleon scattering
• Dispersion analysis of the nucleon form factors including meson continua
• Matching pion-nucleon Roy-Steiner equations to chiral perturbation theory
• High-Statistics Study of the tau^- -> pi^- pi^0 nu_tau Decay
• Model independent extraction of the proton charge radius from electron scattering
• Precision measurement of $\sigma (e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma )/\sigma (e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\gamma )$ and determination of the ${\pi }^{+}{\pi }^{-}$ contribution to the muon anomaly with the KLOE detector
• Extraction of the proton radius from electron-proton scattering data
• Regge analysis of the pi pi scattering amplitude
• The size of the proton - closing in on the radius puzzle
• Precision calculation of threshold pi^- d scattering, pi N scattering lengths, and the GMO sum rule
• Ground-state energy of pionic hydrogen to one loop
• Muonic hydrogen and MeV forces
• Light dark matter in neutrino beams: production modelling and scattering signatures at MiniBooNE, T2K and SHiP
• Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering
• omega --> pi0 gamma* and phi --> pi0 gamma* Transition form factors in dispersion theory
• New Parity-Violating Muonic Forces
• Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors
• Reconciling threshold and subthreshold expansions for pion-nucleon scattering
• Proton size anomaly
• A new Parameterization for the Pion Vector Form Factor
• Model independent extraction of the proton magnetic radius from electron scattering
• Low-energy expansion of the pion-nucleon Lagrangian
• Roy-Steiner equations for pion-nucleon scattering
• Dispersive analysis of the scalar form factor of the nucleon
• Atomic Precision Tests and Light Scalar Couplings
• Updated dispersion-theoretical analysis of the nucleon electromagnetic form factors
• Are Electron Scattering Data Consistent with a Small Proton Radius?
• New Physics and the Proton Radius Problem
• Constraints on muon-specific dark forces
• Constraint on parity-violating muonic forces
• Pionic deuterium
• Electrophobic Scalar Boson and Muonic Puzzles
• Remarks on the pion-nucleon sigma-term
• Isospin violation in the vector form factors of the nucleon
• Isospin violation in low-energy pion-nucleon scattering revisited
• Isospin breaking in the pion-nucleon scattering lengths
• Reduction of the proton radius discrepancy by 3 sigma
• Hadronic shift in pionic hydrogen
• Precise Determination of Charge Dependent Pion-Nucleon-Nucleon Coupling Constants
• Effective field theory for large logarithms in radiative corrections to electron proton scattering
• Novel evaluation of the two-pion contribution to the nucleon isovector form factors
• Proton radius puzzle and large extra dimensions
• Proton radius puzzle and quantum gravity at the Fermi scale
• Pion Form Factor Phase, PIon Pion Elasticity and New Electron-Positron Data
• Realizing vector meson dominance with transverse charge densities
• Extending theories on muon-specific interactions
• Charge Symmetry Breaking and Parity Violating Electron-Proton Scattering
• Avoiding common pitfalls and misconceptions in extractions of the proton radius
• Charge Symmetry Breaking and Parity Violating Electron Scattering

Cited by in corpus (70)

• The anomalous magnetic moment of the muon in the Standard Model
• Two-pion contribution to hadronic vacuum polarization
• Dispersion relation for hadronic light-by-light scattering: two-pion contributions
• Three-pion contribution to hadronic vacuum polarization
• Coherent elastic neutrino-nucleus scattering: EFT analysis and nuclear responses
• Constraints on the two-pion contribution to hadronic vacuum polarization
• Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon
• The proton charge radius
• Reconciling threshold and subthreshold expansions for pion-nucleon scattering
• Improved limits for Higgs-portal dark matter from LHC searches
• Precision Nucleon Charges and Form Factors Using 2+1-flavor Lattice QCD
• New insights into the nucleon's electromagnetic structure
• Extracting the sigma-term from low-energy pion-nucleon scattering
• Kaon electromagnetic form factors in dispersion theory
• Nuclear structure factors for general spin-independent WIMP-nucleus scattering
• Hadrons and Nuclei
• Determining the leading-order contact term in neutrinoless double $\mathbf{\beta }$ decay
• Isospin-breaking effects in the two-pion contribution to hadronic vacuum polarization
• Radiative resonance couplings in $\gamma \pi \to \pi \pi$
• Proton charge radius extraction from electron scattering data using dispersively improved chiral effective field theory
• The electromagnetic Sigma-to-Lambda hyperon transition form factors at low energies
• Isovector electromagnetic form factors of the nucleon from lattice QCD and the proton radius puzzle
• High-precision determination of the electric and magnetic radius of the proton
• Dispersion-theoretical analysis of the electromagnetic form factors of the nucleon: Past, present and future
• The branching ratio $\omega \to {\pi }^{+}{\pi }^{-}$ revisited
• The pion-nucleon sigma term from lattice QCD
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Proton radius from electron-proton scattering and chiral perturbation theory
• The proton radius: From a puzzle to precision
• Ab initio calculation of nuclear structure corrections in muonic atoms
• Dispersive $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ amplitudes from scattering data, threshold parameters and the lightest strange resonance $\kappa$ or $K_0^{\ast }(700)$
• Nucleon matrix elements of the antisymmetric quark tensor
• Two-loop analysis of the pion-mass dependence of the $\rho$ meson
• The nucleon as a test case to calculate vector-isovector form factors at low energies
• Review of experimental and theoretical status of the proton radius puzzle
• The Triton Charge Radius to Next-to-next-to-leading order in Pionless Effective Field Theory
• On the role of isospin violation in the pion-nucleon $\sigma$-term
• Nucleon form factors in dispersively improved Chiral Effective Field Theory I: Scalar form factor
• Nucleon resonance parameters from Roy-Steiner equations
• Nucleon form factors in dispersively improved Chiral Effective Field Theory II: Electromagnetic form factors
• Light- and strange-quark mass dependence of the $\rho (770)$ meson revisited
• Chiral extrapolation of hadronic vacuum polarization
• Accurate nucleon electromagnetic form factors from dispersively improved chiral effective field theory
• Peripheral transverse densities of the baryon octet from chiral effective field theory and dispersion analysis
• What can we learn about light-meson interactions at electron-positron colliders?
• Precision calculation of the electromagnetic radii of the proton and neutron from lattice QCD
• A bound on the nucleon Druck-term from chiral EFT in curved space-time and mechanical stability conditions
• Electromagnetic form factors of the nucleon from $N_f=2+1$ lattice QCD
• Lepton-Proton Two-Photon Exchange in Chiral Perturbation Theory
• The electromagnetic form factors of the transition from the spin-3/2 Sigma to the Lambda hyperon
• Rescattering effects in nucleon-to-meson form factors and application to tau-lepton-induced proton decay
• Dispersive Determination of Nucleon Gravitational Form Factors
• Precision calculation of the recoil--finite-size correction for the hyperfine splitting in muonic and electronic hydrogen
• Spectral functions of nucleon form factors: Three-pion continua at low energies
• Improved Standard-Model prediction for $K_L\to {\ell }^{+}{\ell }^{-}$
• Transverse charge and current densities in the nucleon from dispersively improved chiral effective field theory
• The electromagnetic Sigma-to-Lambda transition form factors with coupled-channel effects in the space-like region
• Pauli form factor contributions to the inelastic proton bremsstrahlung and dark photon production
• Lower bound on the proton charge radius from electron scattering data
• Chiral constraints on the isoscalar electromagnetic spectral functions of the nucleon from leading order vector meson couplings
• Gravitational form factors of pions, kaons and nucleons from dispersion relations
• Hadronic light-by-light contribution to $(g-2{)}_{\mu }$: a dispersive approach
• Method for measuring the charge radii of charged hyperons from the time-like region
• Differential Cross Section Predictions for PRad-II from Dispersion Theory
• Transverse densities of octet baryons from chiral effective field theory
• Dispersive analysis of the $J/\psi \to {\pi }^0{\gamma }^{\ast }$ transition form factor with $\rho$-$\omega$ mixing effects
• Muonic Lithium atoms: nuclear structure corrections to the Lamb shift
• Baryon Form Factors
• Structure-dependent radiative corrections to $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma$ in the GVMD approach
• Nucleon mass: trace anomaly and $\sigma$-terms