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Defining the proton radius: A unified treatment

Gerald A. Miller
Phys. Rev. C 99, 035202 – Published 7 March 2019
Physics logo See Synopsis: Putting the Proton Radius in Its Proper Place

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 understand the meaning of the proton radius in a manner consistent with 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 relativistic moment expansion, the RME.

Conclusion: The equation rp26GE(0) is the definition of the proton radius.

  • Figure
  • Figure
  • Received 20 December 2018

DOI:https://doi.org/10.1103/PhysRevC.99.035202

©2019 American Physical Society

Physics Subject Headings (PhySH)

  1. Physical Systems
  1. Properties
Particles & FieldsNuclear Physics

Synopsis

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Putting the Proton Radius in Its Proper Place

Published 7 March 2019

An analysis of the proton radius puzzle helps to define what the proton radius really means.

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Authors & Affiliations

Gerald A. Miller

  • Department of Physics, University of Washington, Seattle, Washington 98195-1560, USA

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Issue

Vol. 99, Iss. 3 — March 2019

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