Article

Few-Body Systems

, Volume 55, Issue 1, pp 1-33

Elastic and Transition Form Factors of the Δ(1232)

  • Jorge SegoviaAffiliated withPhysics Division, Argonne National Laboratory
  • , Chen ChenAffiliated withHefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of ChinaDepartment of Modern Physics, Institute for Theoretical Physics, University of Science and Technology of China
  • , Ian C. CloëtAffiliated withPhysics Division, Argonne National Laboratory
  • , Craig D. RobertsAffiliated withPhysics Division, Argonne National Laboratory Email author 
  • , Sebastian M. SchmidtAffiliated withInstitute for Advanced Simulation, Forschungszentrum Jülich and JARA
  • , Shaolong WanAffiliated withDepartment of Modern Physics, Institute for Theoretical Physics, University of Science and Technology of China

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Abstract

Predictions obtained with a confining, symmetry-preserving treatment of a vector ⊗ vector contact interaction at leading-order in a widely used truncation of QCD’s Dyson–Schwinger equations are presented for Δ and Ω baryon elastic form factors and the γN → Δ 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 Δ elastic form factors are very sensitive to m Δ. Hence, given that the parameters which define extant simulations of lattice-regularised QCD produce Δ-resonance masses that are very large, the form factors obtained therewith are a poor guide to properties of the Δ(1232). Considering the Δ-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 Δ-baryon’s deformation in the infinite momentum frame. Results for analogous properties of the Ω baryon are less contentious. In connection with the N → Δ 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 Δ; and, furthermore, these quadrupole ratios do slowly approach their anticipated asymptotic limits.