Defining the proton radius: A unified treatment Article Swipe
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· 2019
· Open Access
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· DOI: https://doi.org/10.1103/physrevc.99.035202
· OA: W2902823003
There is significant current interest in knowing the value of the proton radius and also its proper definition. 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. Use perturbation theory, light-front dynamics, and elementary techniques to find relativistically correct definitions of the proton radius and charge density. As a result, 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. The equation $r$ $^{2}_{p}$ ≡ – 6G'<sub>E</sub>(0) is the definition of the proton radius.
