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 $\sqrt{t}\lesssim 1/b$, 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 $b\sim 0.5–1.5\text{fm}$ in the isovector density are maximally sensitive to the $\rho$ meson region, with only a $\sim 10\%$ 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 $b\sim 1\text{fm}$, found previously in a Fourier analysis of spacelike form factor data, could serve as a sensitive test of the the isoscalar strength in the $\sim 1\text{GeV}$ mass region. In terms of partonic structure, the transverse densities in the vector meson region $b\sim 1\text{fm}$ support an approximate mean-field picture of the motion of valence quarks in the nucleon.

• Received 8 June 2011

DOI:https://doi.org/10.1103/PhysRevC.84.045205