Different vertex parameterizations and propagators for the Δ contribution in π-photoproduction

We evaluate the total cross section for the π-photoproduction process and analyze the behavior of the $\Delta \left(1232\right)$ resonance contribution when the photon energy is increased from threshold up to 0.7 GeV. Within this energy range we compare two different parameterizations for the $\gamma N\Delta$ vertex: the normal parity and the covariant multipole decomposition ones. For completeness, we also compare different versions for the Δ propagator: the first is the dressed propagator obtained including one-loop self-energy contributions (EXACT), the second is the complex mass scheme which consists in replacing $m_{\Delta }\to m_{\Delta }-i{\Gamma }_{\Delta }/2$ in the bare propagator, and the third is an intermediate approximation between the two previous ones (EXCMS). We conclude that, in order to extend the present calculation to include more energetic resonances in the future and to obtain non-divergent results for the total cross section we will need to use the MD parametrization and the EXCMS propagator. (paper)