Electromagnetic transition form factors of baryon resonances

Recent experimental and theoretical advancements have led to significant progress in our understanding of the electromagnetic structure of nucleons ($N$), nucleon excitations ($N^{\ast }$), and other baryons. These breakthroughs have been made possible by the capabilities of modern facilities, enabling the induction of photo- and electro-excitation of nucleon resonances. These experiments have specifically probed the evolution of their electromagnetic structure across a range of squared momentum transfer scales, from $Q^2=0-0.01{\mathrm{GeV}}^2$ up to $Q^2=5$ or $8{\mathrm{GeV}}^2$. These experimental advances have sparked notable developments in theoretical approaches. New theoretical methods have been tested and proven to be robust, marking the beginning of a new era in our understanding on baryons. This includes the study of newly discovered exotic hadrons with various multiquark components. We present a comprehensive review of progress in experimental data on ${\gamma }^{\ast }N\to N^{\ast }$ reactions. Additionally, we discuss various analyses and theoretical results, such as quark models in combination (or not) with meson cloud excitations of the baryon quark cores, lattice QCD, Dyson–Schwinger equations, chiral effective field theory, the large $N_c$ limit, and AdS/CFT correspondence, among others. Some of these methods have matured in their predictive power, offering new perspectives on exotic hadrons with multiquark components. We place special emphasis on both the low-$Q^2$ and large-$Q^2$ regions to reinforce crucial physical constraints on observables that hold in these limits. Furthermore, we illustrate that the combination of lattice QCD with chiral effective field theory and quark models, respectively, proves beneficial in interpreting data and applying constraints within those different regimes. As a practical contribution and for future reference, we review the formulas for helicity amplitudes, multipole form factors and the relations between these two sets of functions for transitions to resonances with general spin $J\ge \frac{1}{2}$. These formulas are ubiquitous and play a pivotal role in experimental and theoretical studies on baryon structure. Notably, the multipole transition form factors for $J⩾\frac{3}{2}$ resonances momentum serve as valuable tools to test perturbative QCD results in the large-$Q^2$ region, thanks to the correlations between electric and magnetic transition form factors.