Defining the Proton Radius: a Unified Treatment

Abstract

Background: There is significant current interest in knowing the value of the proton radius and also its proper definition. Purpose: Combine the disparate literatures of hydrogen spectroscopy and diverse modern parton distributions to show that the quantity $r_p^2\equiv -6G_E^{\prime }(0)$ is the relativistically proper definition that originates from the separate bodies of work. Methods: Use perturbation theory, light-front dynamics and elementary techniques to find relativistically correct definitions of the proton radius and charge density. Results: It is found that the very same proton radius is accessed by measurements of hydrogen spectroscopy and elastic lepton scattering. The derivation of the mean-square radius as a moment of a spherically symmetric three-dimensional density is shown to be incorrect. A relativistically-correct, two-dimensional charge density is related to the diverse modern literature of various parton distributions. Relativistically invariant moments thereof are derived in a new moment expansion, the RME.

18 pages, two figures. Replacement involves improving the language and adding a reference

References in corpus (9)

• Generalized parton correlation functions for a spin-1/2 hadron
• The Proton Radius Puzzle
• Quark Wigner Distributions and Orbital Angular Momentum
• Nucleon electromagnetic form factors
• Proton and neutron electromagnetic form factors and uncertainties
• Empirical transverse charge densities in the nucleon and the nucleon-to-$\Delta$ transition
• Electromagnetic Form Factors and Charge Densities From Hadrons to Nuclei
• Singular Charge Density at the Center of the Pion?
• Densities, Parton Distributions, and Measuring the Non-Spherical Shape of the Nucleon

Cited by in corpus (10)

• Ambiguities in the definition of local spatial densities in light hadrons
• The proton radius (puzzle?) and its relatives
• An accurate evaluation of electron (anti-)neutrino scattering on nucleons
• Nucleon relativistic polarization and magnetization distributions
• Optimal Settings For Amplification And Estimation Of Small Effects In Postselected Ensembles
• Light-front dynamic analysis of the longitudinal charge density using the solvable scalar field model in (1+1) dimensions
• Connecting spatial moments and momentum densities
• Quantum stress and torsion distributions in the deuteron
• GTMD model predictions for diffractive dijet production at EIC
• Transverse energy-momentum tensor distributions in polarized nucleons