The nucleon isovector electromagnetic form factors are calculated up to next-to-next-to-leading order by combining relativistic chiral perturbation theory (ChPT) of pion, nucleon, and Δ(1232) with dispersion theory. We specifically address the light-quark mass dependence of the form factors, achieving a good description of recent lattice QCD results over a range of Q²≲0.6  GeV² and M_π≲350  MeV. For the Dirac form factor, the combination of ChPT and dispersion theory outperforms the pure dispersive and pure ChPT descriptions. For the Pauli form factor, the combined calculation leads to results comparable to the purely dispersive ones. The anomalous magnetic moment and the Dirac and Pauli radii are extracted.

The transition form factors of N*(1520) have been formulated and computed at low energies (|q²| < 1 GeV²) using dispersion theory for the first time. Utilizing hadronic data from N*(1520) -> N π, N*(1520) -> Δπ, and N*(1520) -> N ρ processes, we have calculated both space-like and time-like transition form factors. Our results demonstrate agreement with the existing space-like form factor data. The predicted time-like form factors can be experimentally tested by the HADES experiment.

Dispersion theory is used to provide a model-independent low-energy representation of the three electromagnetic isovector transition form factors N^∗(1520)→N. At low energies the virtual photon couples dominantly to a pion pair. Taking the very well understood pion vector form factor and pion re-scattering into consideration, the determination of the transition form factors is traced back to the determination of pion-baryon scattering amplitudes. Their low-energy aspects are parametrized by baryon exchange, accounting for the main decay channels of the N^∗(1520). Short-distance physics is encoded in subtraction constants that are fitted to data on space-like form factors and hadronic decays. It is shown that a limitation in the determination of the subtraction constants lies in the fact that isovector form factors require sufficient information about the differences between protons and neutrons. In particular, this calls for improvements in the form factor extraction from the electroproduction of the N^∗(1520) on the neutron. Via the dispersion relations, space- and time-like regions are naturally connected from first principles. This allows to predict the time-like form factors that enter the Dalitz decays N^∗(1520)→Ne⁻e⁺ and N^∗(1520)→Nμ⁻μ⁺. Under the assumption of the dominance of the isovector over the isoscalar channel, the Dalitz decay distributions are predicted.