Time-like and space-like electromagnetic form factors of nucleons, a unified description

TL;DR

This paper extends a nucleon electromagnetic form factor model to the time-like region, ensuring it satisfies physical constraints and fits all available data, enabling predictions of form factors at higher momentum transfers.

Contribution

The paper introduces an analytic extension of the Lomon-Gari-Kr"umpelmann model to the time-like region, incorporating broad resonances with momentum-dependent widths for a unified description.

Findings

Successful fit to all space-like and time-like form factor data

Predictions for form factors at higher momentum transfers

Insights into the phase and ratio of electric to magnetic form factors

Abstract

The extended Lomon-Gari-Kr\"umpelmann model of nucleon electromagnetic form factors, which embodies \rho, \rho', \omega, \omega' and \phi vector meson contributions and the perturbative QCD high momentum transfer behavior has been extended to the time-like region. Breit-Wigner formulae with momentum-dependent widths have been considered for broad resonances in order to have a parametrization for the electromagnetic form factors that fulfills, in the time-like region, constraints from causality, analyticity, and unitarity. This analytic extension of the Lomon-Gari-Kr\"umpelmann model has been used to perform a unified fit to all the nucleon electromagnetic form factor data, in the space-like and time-like region (where form factor values are extracted from e+e- <-> nucleon-antinucleon cross sections data). The knowledge of the complete analytic structure of form factors enables predictions at extended momentum transfer, and also of time-like observables such as the ratio between electric and magnetic form factors and their relative phase.