Analysis of the γNΔ and ΔNπ interactions for pion photoproduction

In this paper we analyze for the first time the γNΔ excitation vertex from the point of view of the dynamics of the Δ field, Ψμ. That is, we look for the value of the Z parameter, present in all contact invariant Δ-field interaction Lagrangians and usually regarded as redundant, and shift it to contact background non-Δ resonant amplitudes (in this sense it is called “redundant”) by imposing that the Ψ0 has no dynamics, instead of readjusting the background coupling constants. We do this within an unitarized model that comprises the Δ-direct amplitude plus background contributions including the Δ-cross term, nucleon Born and meson exchange ones, already implemented in previous works of πN scattering, photo-production and weak-π production. Also we analyze the use of a πNΔ decay vertex interaction containing both first (I1) and second (I2) order derivative contributions, as required by renormalization and power counting considerations, in building the γN→Δ→πN amplitude, in contrast with other works where only I1 or I2 is adopted. It is shown that the description of the γN→πN process, following these prescriptions, is improved. This is a first step: we plan to introduce final state interactions (FSI) in the future, following our previous work in which FCI were introduced using the I1 interaction alone.