Quark transverse charge densities in the Delta(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 $\Delta (1232)$ 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 $\Delta$-isobar electromagnetic form
factors for pion masses down to approximatively 350 MeV for three cases: quenched QCD, two-degenerate flavors of dynamicalWilson 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 $Delta$ is prolately deformed, as indicated by the fact that the quadrupole moment $G_{E2}(0)$ is larger than the value −3 characterizing a point particle and the fact that the transverse charge density in a $\Delta^+$ of maximal transverse spin projection is elongated along the axis of the spin.