Defining the proton radius: A unified treatment

2018/12/11 by Gerald A. Miller · 2 citations
Physics and Astronomy · #Charge radius #Classical electron radius #High-Energy Particle Collisions Research #Moment (physics) #Nuclear physics #Particle physics #Particle physics theoretical and experimental studies #Parton #Physics #Proton #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quark #RADIUS #Scattering #hep-ph #nucl-ex #nucl-th #physics.atom-ph

paper · pdf · doi:10.1103/physrevc.99.035202

published as Phys. Rev. C 99, 035202 (2019) · 18 pages, two figures. Replacement involves improving the language and adding a reference

arxiv created 2018/12/11 · openalex publication_date 2019/03/07 · arxiv updated 2019/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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_p²≡ -6 G_E'(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.

Citations

• Generalized parton distributions
• Densities, parton distributions, and measuring the nonspherical shape of the nucleon
• Viewing the Proton through “Color” Filters
• Parton distribution and decay functions
• Proton Structure from the Measurement of 2S-2P Transition Frequencies of Muonic Hydrogen
• Empirical Transverse Charge Densities in the Nucleon and the Nucleon-to-ΔTransition
• Theory of Light Hydrogenlike Atoms
• The size of the proton
• The Proton Radius Puzzle
• On the Quantum Correction For Thermodynamic Equilibrium

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