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Current Conservation in the Covariant Quark-Diquark Model of the Nucleon

The description of baryons as fully relativistic bound states of quark and glue reduces to an effective Bethe-Salpeter equation with quark-exchange interaction when irreducible 3-quark interactions are neglected and separable 2-quark (diquark) correlations are assumed. This covariant quark-diquark model of baryons is studied with the inclusion of the quark substructure of the diquark correlations. In order to maintain electromagnetic current conservation it is then necessary to go beyond the impulse approximation. A conserved current is obtained by including the coupling of the photon to the exchanged quark and direct ``seagull'' couplings to the diquark structure. Adopting a simple dynamical model of constituent quarks and exploring various parametrisations of scalar diquark correlations, the nucleon Bethe-Salpeter equation is solved and the proton and neutron electromagnetic form factors are calculated numerically. The resulting magnetic moments are still about 50% too small, the improvements necessary to remedy this are discussed. The results obtained in this framework provide an excellent description of the electric form factors (and charge radii) of the proton, up to a photon momentum transfer of 3.5GeV^2, and the neutron.