Timelike and spacelike electromagnetic form factors of nucleons, a unified description

Abstract

The extended Lomon-Gari-Krümpelmann model of nucleon electromagnetic form factors, which embodies ρ, ρ ′ , ω, ω ′ and φ 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-Krümpelmann 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 − ↔ N N 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.

Measurement of the Neutron Electric to Magnetic Form Factor Ratio atQ2=1.58 GeV2Using the Reaction

“…The uncertainties shown are the statistical and the systematic errors added in quadrature. Also shown are the results of recent calculations based on general parton distributions [32] (solid line), dispersion analysis [33] (gray band), a quark-diquark model with a pion cloud [34] (dashed line) and the extended Lomon-Gari-Krümpelmann model of nucleon electromagnetic FF [35] (dotted lines, for two different parametrizations of resonance widths, timelike proton form factor data from BABAR included).…”

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

“…Here, A = 8.79 14) suggested in [44,54] with the 3-pole (green dashed-dotted curve and band) and oscillation (magenta dotted curve and band) contributions; (b) residuals of the proton |G eff |, after subtraction of the smooth function described by Equation (12), as a function of the relative momentum p(s) = s( s 4m 2 p − 1) with a fit of the oscillation according to Equation (13) (magenta solid curve and band). The shown data are the published measurements from BESIII [36,37,45,46], BABAR [47][48][49], CMD3 [34,35], CLEO [33], BES [32], FENICE [20][21][22], E835 [30,31], E760 [29], PS170 [26][27][28], DM2 [24,25], DM1 [23], M. S. T [19], and ADONE [18].…”

“…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.…”

Analytic continuation of nucleon electromagnetic form factors in the time-like region

“…Various techniques and procedures have been proposed to develop such an SL-TL unified description of nucleon FFs. Many of them make use of dispersion relations-see for example references [14][15][16]-while others suggest new models (for instance, in reference [17], a semiphenomenological microscopic model is proposed), and some others use analytic continuation methods to extend, to all values of q 2 , parametrizations usually defined only in the SL or TL region [18].…”