  The baryon electromagnetic form factors are expressed in terms of
two-dimensional densities describing the distribution of charge and
magnetization in transverse space at fixed light-front time. We calculate the
transverse densities of the spin-1/2 flavor-octet baryons at peripheral
distances b = O(M_\pi^{-1}) using methods of relativistic chiral effective
field theory (\chi EFT) and dispersion analysis. The densities are represented
as dispersive integrals over the imaginary parts of the form factors in the
timelike region (spectral functions). The isovector spectral functions on the
two-pion cut t > 4 M_\pi^2 are calculated using relativistic \chi EFT including
octet and decuplet baryons. The \chi EFT calculations are extended into the
\rho meson mass region using an N/D method that incorporates the pion
electromagnetic form factor data. The isoscalar spectral functions are modeled
by vector meson poles. We compute the peripheral charge and magnetization
densities in the octet baryon states, estimate the uncertainties, and determine
the quark flavor decomposition. The approach can be extended to baryon form
factors of other operators and the moments of generalized parton distributions.
