Theory of two-meson photo- and electroproduction off the nucleon

Using the reaction gamma N -> pi pi N as the paradigmatic topological framework, a field-theoretical description of the electromagnetic production of two pseudoscalar mesons off the nucleon is derived and applied to photo- and electroproduction processes, assuming only one-photon exchange for the latter. The dynamics of all explicit three-point interaction mechanisms of the iurN system is accounted for by the Faddeev-type ordering structure of thc Alt-Grassberger-Sandhas equations. The modifications necessary for incorporating n-meson vertices for n > 4 are discussed. The formulation is valid for hadronic two-point and threepoint functions dressed by arbitrary (even nonlinear) internal mechanisms provided all associated electromagnetic currents are constructed to satisfy their respective (generalized) Wiird-Takahashi identities. Coupling thc photon to the Faddeev structure of the underlying hadronic two-pion production mechanisms results in a natural expansion of the full two-pion photoproduction current in terms of multiple dressed loops involving two-body subsystem scattering amplitudes of the irirN system that preserves gauge invariance as a matter of course order by order in the number of (dressed) loops. A closed-form expression is presented for the entire gauge-invariant current /14',, with complete three-body dynamics. Individually gauge-invariant truncations of the full dynamics most relevant for practical applications at the no-loop, one loop, and two-loop levels are discussed in detail. An approximation scheme to the full two-meson amplitude for calculational purposes is also presented. It approximates, systematically, the full amplitude to any desired order of expansion in the underlying hadronic two-body amplitude. Moreover, it allows for the approximate incorporation of all neglected higher-order mechanisms in terms of a locally gauge-invariant phenomenological remainder current.