Elastic and transition form factors of nucleon excited states provide vital
information about their structure and composition. They are a measurable and
physical manifestation of the nature of the hadrons constituents and the dynamics
that binds them together. In this respect, two emergent phenomena of Quantum
Chromodynamics (QCD), confinement and dynamical chiral symmetry breaking, appear to
play an important role; and Dyson-Schwinger equations (DSEs) have been established
as a nonperturbative quantum field theoretical approach for the study of continuum
strong QCD which is able to connect such emergent phenomena with the behaviour of
form factors.
In this presentation, I provide an example of the contemporary application of DSEs
to the study of elastic and transition form factors of N ∗ -states analyzing the
electromagnetic γ∗ p → ∆+ transition. This reaction has stimulated a great deal of
theoretical analysis, and speculation about: the shape deformation of involved
hadrons; the relevance of perturbative QCD to processes involving moderate momentum
transfers; and the role that experiments on resonance electroproduction can play in
exposing nonperturbative characteristics of QCD. The small-Q2 behaviour of the ∆
elastic form factors is a necessary element in computing the γ∗ N → ∆ transition
form factors. I calculate the core contributions to the ∆+ electromagnetic form
factors and compare to lattice data, both at different pion masses. The ∆ elastic
form factors appear to be very sensitive to mπ and consequently to m∆ . Hence, given
that the parameters which define extant simulations of lattice-regularised QCD
produce ∆-resonance masses that are very large, the form factors obtained therewith
are a poor guide to properties of the ∆(1232).
Finally, the measurement of form factors at high-Q2 virtualities is actually
challenging the theoretical computation techniques. This presentation is intended to
close with the description of a recently introduced method to extract parton
distribution amplitudes (PDAs) from the light-front projections of the hadron
bound-state amplitudes (BSAs). These PDAs are necessary objects in the computation
of hard exclusive processes.