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

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 $$\omega $$ ω -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.

Dispersion relation analysis of the radiative corrections to gA in the neutron β-decay

“…Different parameterizations of these form factors [76][77][78][79][80][81] all give consistent results within their respective error bars. In particular, the parametrization of ref.…”

Proton charge radius from a dispersive analysis of the experimental data over the space- and time-like regions

“…Thus, the vector meson dominance (VMD) model is introduced to get the high energy part of the nucleon FFs in our dispersion theoretical parametrization, see Ref. [10] for more details. Here, we summarize the ingredients in the spectral functions,…”

“…Secondly, one can relate the time-like physics to the space-like ones by means of the crossing symmetry in the dispersion theory. And finally, when specific to the nucleon form factors, it is convenient to include the strictures from perturbative QCD at very large momentum transfer (see the recent review [10] for more details). Here, we extend the previous applications of the dispersion theory in the extraction of nucleon form factors from the space-like scattering data [10,11] to include the time-like annihilation data.…”

“…And finally, when specific to the nucleon form factors, it is convenient to include the strictures from perturbative QCD at very large momentum transfer (see the recent review [10] for more details). Here, we extend the previous applications of the dispersion theory in the extraction of nucleon form factors from the space-like scattering data [10,11] to include the time-like annihilation data. It leads us to the best phenomenological nucleon form factors which incorporate all the physical knowledge we have so far in the theoretical aspect and are consistent with all existing scattering and annihilation data in the experimental aspect.…”

Proton Electromagnetic Form Factors in the Time-like Region through the Scan Technique

“…Various approaches to providing a theoretical description of the proton EM FFs exist, among them approaches based on modified versions of the old, yet still relevant, vector meson dominance (VMD) model [12], models based on the unitarity and analyticity of the proton FFs using dispersion theoretical approaches [13], descriptions based on a relativistic constituent quark model [14], and more. A comprehensive review of all these approaches is outside the scope of this article.…”