Few-Body Systems

, Volume 55, Issue 1, pp 1–33

Elastic and Transition Form Factors of the Δ(1232)


  • Jorge Segovia
    • Physics DivisionArgonne National Laboratory
  • Chen Chen
    • Hefei National Laboratory for Physical Sciences at MicroscaleUniversity of Science and Technology of China
    • Department of Modern Physics, Institute for Theoretical PhysicsUniversity of Science and Technology of China
  • Ian C. Cloët
    • Physics DivisionArgonne National Laboratory
    • Physics DivisionArgonne National Laboratory
  • Sebastian M. Schmidt
    • Institute for Advanced SimulationForschungszentrum Jülich and JARA
  • Shaolong Wan
    • Department of Modern Physics, Institute for Theoretical PhysicsUniversity of Science and Technology of China

DOI: 10.1007/s00601-013-0734-x

Cite this article as:
Segovia, J., Chen, C., Cloët, I.C. et al. Few-Body Syst (2014) 55: 1. doi:10.1007/s00601-013-0734-x


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 mΔ. 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.

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© Springer-Verlag Wien (outside the USA) 2013