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Abstract
We review the dispersion-theoretical analysis of the electromagnetic form factors of the nucleon. We emphasize in particular the role of unitarity and analyticity in the construction of the isoscalar and isovector spectral functions. We present new results on the extraction of the nucleon radii, the electric and magnetic form factors and the extraction of omega -meson couplings. All this is supplemented by a detailed calculation of the theoretical uncertainties, using bootstrap and Bayesian methods to pin down the statistical errors, while systematic errors are determined from variations of the spectral functions. We also discuss the physics of the time-like form factors and point out further issues to be addressed in this framework.
Highlights
While electron scattering was the method of choice to refine the proton radius in the decades following these pioneering experiments, the Lamb shift in electronic hydrogen and muonic hydrogen is sensitive to the proton radius [8]
The error analysis was improved compared to earlier dispersion relation (DR) work, the bootstrap method was used to determine the “statistical” error, while the “systematic” error was obtained from varying the number of effective poles, e.g. in the combined analysis the range from (2+2) to (7+7) isoscalar + isovector poles was covered
We have reviewed the dispersion-theoretical approach to the electromagnetic form factors of the nucleon, with particular emphasis on the constraints posed by unitarity and analyticity on the spectral functions
Summary
A new twist was recently added to this picture by measurements of the proton charge radius in muonic hydrogen. The electronic Lamb shift measurements as well as most electron scattering experiments gave the socalled large radius, r. At about the same time, a highprecision electron-proton scattering experiment performed at the Mainz Microtron (MAMI) reinforced the large radius [11]. This glaring discrepancy in such a fundamental quantity, which was believed to be understood since long, became known as the “proton radius puzzle”. Recent experiments on the electronic Lamb shift [12,13,14] and a novel measurement of electron-proton scattering at unprecedented small momentum transfer [15]. We collect the various parameters of our best fit discussed in the main text
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