Dispersion-theoretical analysis of the electromagnetic form factors of the nucleon: Past, present and future

TL;DR

This paper reviews dispersion-theoretical methods for analyzing nucleon electromagnetic form factors, highlighting unitarity and analyticity, presenting new results on nucleon radii, form factors, and meson couplings, with detailed uncertainty analysis.

Contribution

It introduces new extraction techniques for nucleon properties and advances the understanding of spectral functions using bootstrap and Bayesian methods.

Findings

New nucleon radii and form factor values

Quantified statistical and systematic uncertainties

Insights into time-like form factor physics

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.