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.

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

References in corpus (23)

• Big-Bang Nucleosynthesis
• 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
• The Proton Radius Puzzle
• Dispersion analysis of the nucleon form factors including meson continua
• Model independent extraction of the proton charge radius from electron scattering
• The size of the proton - closing in on the radius puzzle
• 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
• New Parity-Violating Muonic Forces
• Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors
• Proton size anomaly
• Model independent extraction of the proton magnetic radius from electron scattering
• 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
• Pionic deuterium
• Isospin violation in the vector form factors of the nucleon
• Isospin breaking in the pion-nucleon scattering lengths
• Reduction of the proton radius discrepancy by 3 sigma
• Hadronic shift in pionic hydrogen

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• Radiative resonance couplings in $\gamma \pi \to \pi \pi$
• 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
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• 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
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• Chiral extrapolation of hadronic vacuum polarization
• 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
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• 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
• 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
• Differential Cross Section Predictions for PRad-II from Dispersion Theory
• Method for measuring the charge radii of charged hyperons from the time-like region
• 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
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• Baryon Form Factors