Elastic and Transition Form Factors of the Δ(1232)

Predictions obtained with a confining, symmetry-preserving treatment of a vector aSu vector contact interaction at leading-order in a widely used truncation of QCD's Dyson-Schwinger equations are presented for Delta and Omega baryon elastic form factors and the gamma N -> Delta transition form factors. This simple framework produces results that are practically indistinguishable from the best otherwise available, an outcome which highlights that the key to describing many features of baryons and unifying them with the properties of mesons is a veracious expression of dynamical chiral symmetry breaking in the hadron bound-state problem. The following specific results are of particular interest. The Delta elastic form factors are very sensitive to m (Delta). Hence, given that the parameters which define extant simulations of lattice-regularised QCD produce Delta-resonance masses that are very large, the form factors obtained therewith are a poor guide to properties of the Delta(1232). Considering the Delta-baryon's quadrupole moment, whilst all computations produce a negative value, the conflict between theoretical predictions entails that it is currently impossible to reach a sound conclusion on the nature of the Delta-baryon's deformation in the infinite momentum frame. Results for analogous properties of the Omega baryon are less contentious. In connection with the N -> Delta transition, the Ash-convention magnetic transition form factor falls faster than the neutron's magnetic form factor and nonzero values for the associated quadrupole ratios reveal the impact of quark orbital angular momentum within the nucleon and Delta; and, furthermore, these quadrupole ratios do slowly approach their anticipated asymptotic limits.