Magnetic moment and radius of the nucleon in a nonlocal model of meson-nucleon interaction

Magnetic moment and radius of the nucleon are calculated in a nonlocal extension of the chiral linear $\sigma$-model. Properties of the nonlocal model under the vector and axial transformations are considered. The conserved electromagnetic and vector currents, and partially conserved axial vector current are obtained. In the calculation of the nucleon electromagnetic vertex the $\pi$- and $\sigma$-loop diagrams are included. Contribution from vector mesons is added in the vector meson dominance model with a gauge-invariant photon-meson coupling. The nonlocality parameter associated with the $\pi N$ interaction is fixed from the experimental magnetic moment of the neutron. Other parameters (nonlocality parameter for the $\sigma N$ interaction and the mass of the $\sigma$-meson) are constrained by the magnetic moment of the proton. The calculated electric and magnetic mean-square radii of the proton and neutron are in satisfactory agreement with experiment