Electromagnetic excitation of the -resonance

We review the description of the lowest-energy nucleon excitation—the Δ ( 1232 ) -resonance. Much of the recent experimental effort has been focused on the precision measurements of the nucleon-to- Δ transition by means of electromagnetic probes. We confront the results of these measurements with the state-of-the-art calculations based on chiral effective-field theories (EFT), lattice Quantum Chromodynamics (QCD), large- N c relations, perturbative QCD, and QCD-inspired models. We also discuss the link of the nucleon-to- Δ form factors to generalized parton distributions (GPDs). Some of the theoretical approaches are reviewed in detail, in particular, recent dynamical and unitary-isobar models of pion electroproduction, which are extensively used in the interpretation of experiments. A novel extension of chiral EFTs to the energy domain of the Δ -resonance is reviewed. The two-photon exchange effects in the electroexcitation of the Δ -resonance are addressed.