Realizing vector meson dominance with transverse charge densities

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 √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∼0.5-1.5fm in the isovector density are maximally sensitive to the ρ 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 ω are comparatively more important. The dispersion approach suggests that the positive transverse charge density in the neutron at b∼1fm, found previously in a Fourier analysis of spacelike form factor data, could serve as a sensitive test of the the isoscalar strength in the ∼1GeV mass region. In terms of partonic structure, the transverse densities in the vector meson region b∼1fm support an approximate mean-field picture of the motion of valence quarks in the nucleon.