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 is the definition of the proton radius.
- Received 20 December 2018
DOI:https://doi.org/10.1103/PhysRevC.99.035202
©2019 American Physical Society
Physics Subject Headings (PhySH)
Synopsis
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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