Realizing vector meson dominance with transverse charge densities

TL;DR

This paper uses dispersion integrals of the nucleon form factor's imaginary part to analyze transverse charge densities, revealing dominance of vector mesons like rho and omega at specific distances, and connecting to partonic structures.

Contribution

It introduces a dispersion-based method to connect transverse charge densities with specific spectral regions, highlighting vector meson dominance and partonic interpretations.

Findings

Transverse densities at 0.5-1.5 fm are sensitive to rho meson contributions.

Higher-mass states beyond omega are significant in the isoscalar density.

The neutron's positive transverse charge density at 1 fm can test isoscalar strength.

Abstract

The transverse charge density in a fast-moving nucleon is represented as a dispersion integral of the imaginary part of the Dirac form factor in the timelike region (spectral function). At a given transverse distance b the integration effectively extends over energies in a range sqrt{t} ~< 1/b, with exponential suppression of larger values. The transverse charge density at peripheral distances thus acts as a low-pass filter for the spectral function and allows one to select energy regions dominated by specific t-channel states, corresponding to definite exchange mechanisms in the spacelike form factor. We show that distances b ~ 0.5 - 1.5 fm in the isovector density are maximally sensitive to the rho meson region, with only a ~10% contribution from higher-mass states. Soft-pion exchange governed by chiral dynamics becomes relevant only at larger distances. In the isoscalar density higher-mass states beyond the omega are comparatively more important. The dispersion approach suggests that the positive transverse charge density in the neutron at b ~ 1 fm, found previously in a Fourier analysis of spacelike form factor data, could serve as a sensitive test of the the isoscalar strength in the ~1 GeV mass region. In terms of partonic structure, the transverse densities in the vector meson region b ~ 1 fm support an approximate mean-field picture of the motion of valence quarks in the nucleon.