Empirical Transverse Charge Densities in the Nucleon and the Nucleon-to-$\Delta$ Transition

Using only the current empirical information on the nucleon electromagnetic form factors we map out the transverse charge density in proton and neutron as viewed from a light front moving towards a transversely polarized nucleon. These charge densities are characterized by a dipole pattern, in addition to the monopole field corresponding with the unpolarized density. Furthermore, we use the latest empirical information on the $N\to \Delta$ transition form factors to map out the transition charge density which induces the $N\to \Delta$ excitation. This transition charge density in a transversely polarized $N$ and $\Delta$ contains both monopole, dipole and quadrupole patterns, the latter corresponding with a deformation of the $N$ and $\Delta$ charge distribution.

Figure 1

Quark transverse charge densities in the proton. The upper panel shows the density in the transverse plane for a proton polarized along the $x$ axis. The light (dark) regions correspond with largest (smallest) values of the density. The lower panel compares the density along the $y$ axis for an unpolarized proton (dashed curve), and for a proton polarized along the $x$ axis (solid curve). For the proton e.m. FFs, we use the empirical parameterization of Arrington et al. [15].

Figure 2

Same as Fig. 1 for the quark transverse charge densities in the neutron. For the neutron e.m. FFs, we use the empirical parameterization of Bradford et al. [18].

Figure 3

Quark transverse transition charge density corresponding with the $p\to {\Delta }^{+}$ transition. Upper panel: when $N$ and $\Delta$ are unpolarized (${\rho }_0^{N\Delta }$). Middle panel: when $N$ and $\Delta$ are polarized along the $x$-axis (${\rho }_T^{N\Delta }$). Lower panel: quadrupole contribution to ${\rho }_T^{N\Delta }$. For the $N\to \Delta$ e.m. FFs, we use the empirical parameterization of MAID2007 [20].