Quark transverse charge densities in the Δ (1232) from lattice QCD

We extend the formalism relating electromagnetic form factors to transverse quark charge densities in the light-front frame to the case of a spin-3/2 baryon and calculate these transverse densities for the Δ (1232) isobar using lattice QCD. The transverse charge densities for a transversely polarized spin-3/2 particle are characterized by monopole, dipole, quadrupole, and octupole patterns representing the structure beyond that of a pure point-like spin-3/2 particle. We present lattice QCD results for the Δ-isobar electromagnetic form factors for pion masses down to approximatively 350 MeV for three cases: quenched QCD, two-degenerate flavors of dynamical Wilson quarks, and three flavors of quarks using a mixed action that combines domain wall valence quarks and dynamical staggered sea quarks. We extract transverse quark charge densities from these lattice results and find that the Δ is prolately deformed, as indicated by the fact that the quadrupole moment G_{E 2} (0) is larger than the value -3 characterizing a point particle and the fact that the transverse charge density in a Δ⁺ of maximal transverse spin projection is elongated along the axis of the spin.