The shape of the $\Delta$ baryon in a covariant spectator quark model

Abstract

Using a covariant spectator quark model that describes the recent lattice QCD data for the $\Delta$ electromagnetic form factors and all available experimental data on $\gamma N\to \Delta$ transitions, we analyze the charge and magnetic dipole distributions of the $\Delta$ baryon and discuss its shape. We conclude that the quadrupole moment of the $\Delta$ is a good indicator of the deformation and that the ${\Delta }^{+}$ charge distribution has an oblate shape. We also calculate transverse moments and find that they do not lead to unambiguous conclusions about the underlying shape.

Comments: Extended introduction, references added, other small modifications. To appear in Phys. Rev. D. 14 pages, 8 figures