Dispersion analysis of the nucleon form factors including meson continua

Abstract

Dispersion relations provide a powerful tool to analyse the electromagnetic form factors of the nucleon for all momentum transfers. Constraints from meson-nucleon scattering data, unitarity, and perturbative QCD can be included in a straightforward way. In particular, we include the 2pi, rho-pi, and KKbar continua as independent input in our analysis and provide an error band for our results. Moreover, we discuss two different methods to include the asymptotic constraints from perturbative QCD. We simultaneously analyze the world data for all four form factors in both the space-like and time-like regions and generally find good agreement with the data. We also extract the nucleon radii and the omega-NN coupling constants. For the radii, we generally find good agreement with other determinations with the exception of the electric charge radius of the proton which comes out smaller. The omega-NN vector coupling constant is determined relatively well by the fits, but for the tensor coupling constant even the sign can not be determined.Comment: 24 pages, 9 figure

Model independent extraction of the proton magnetic radius from electron scattering

“…(5) model (2) group fm [85]. This value is considerably lower than r p M = 0.876 ± 0.010 ± 0.016 fm extracted in [86] or 0.854 ± 0.005 fm extracted in [87], the two other extractions cited by the Particle Data Group (PDG) [88]. Are we facing also a magnetic radius puzzle?…”

“…The imaginary part of G (1) M close to the cut can be described by the pion form factor F π (t) (normalized to F π (0) = 1) and f 1 − (t), a partial ππ → NN amplitude [95,96,87]:…”

Nucleon electromagnetic form factors

“…Using such an analysis, a good description of most FF data with the exception of the G Ep /G M p polarization data at Q 2 > 3 GeV 2 , was obtained in [Ham04]. The dispersion relation analysis of nucleon e.m. FFs has been further improved by Belushkin et al [Bel07]. In addition to the 2π continuum present in the isovector spectral functions of the previous DR analyses, also the ρπ and KK continua were included as independent input in the isoscalar spectral functions.…”

“…In Ref. [Bel07], the 2π continuum was reevaluated using the latest experimental data for the pion FFs in the time-like region [Bel06]. The KK continuum was obtained from an analytic continuation of KN scattering data [Ham99].…”

“…It will be interesting to confront the most recent and sophisticated DR fit of [Bel07] with upcoming data for G Ep /G M p out to 8.5 GeV 2 [Bra04]. In all discussed VMD and DR fits starting with Gari-Krümpelmann [Gar85] the asymptotic pQCD limit F 2 /F 1 ∼ 1/Q 2 was built in, although the data do not support this limit at available momentum transfers, see Fig.…”