Inclusion of Resonances from the Second and Third Region in Π-Photoproduction on Nucleons Within the Effective Lagrangian Approach

Abstract

We develop a formalism based on the effective Lagrangian approach (ELA) to evaluate the Chew-Goldberger-Low-Nambu(CGLN)amplitudesfortheπ-photoproductionprocessonnucleons,γN →πN′. This formalism allows us systematically include any spin 1/2-isospin 1/2, spin 1/2-isospin 3/2, spin 3/2-isospin 1/2, and spin 3/2-isospin 3/2 resonance, with both positive and negative parities. In particular, we analyze the effect of the P33(1232) resonance, the second region four-star N∗ resonancesP11(1440), D13(1520), S11(1535), P33(1600), and also the third region S11(1650) and P11(1710) resonances on total cross-cross-sections for both proton-induced γ p → nπ+ and γ p → pπ0 processes, we describe the strategy for performing the fitting, highlighting the region where each model parameter will be varied, consistently with existing literature information on the same. We have established a reliable set of parameters for the model in accordance with experimental data, which include the coupling constants, the magnetic moments, masses, and widths of the nucleon resonances. With the fitted parameters, we have evaluated the electric and magnetic multipoles, which have shown an excellent agreement with the experimental data, after incorporating the effects of unitarity. Additionally, we have predicted a value for the electric to magnetic ratio of the P33(1600) resonance, RE M = −0.115, not yet reported in the literature.Keywords Pion photoproduction · Resonances · Effective Lagrangian approachsections and simultaneously on the E 3/2 and M 3/2 electromagnetic multipoles. To reproduce the experimental data of the totalcross-sections for both proton-induced γ p → nπ+ and γ p → pπ0 processes, we describe the strategy for performing the fitting, highlighting the region where each model parameter will be varied, consistently with existing literature information on the same. We have established a reliable set of parameters for the model in accordance with experimental data, which include the coupling constants, the magnetic moments, masses, and widths of the nucleon resonances. With the fitted parameters, we have evaluated the electric and magnetic multipoles, which have shown an excellent agreement with the experimental data, after incorporating the effects of unitarity. Additionally, we have predicted a value for the electric to magnetic ratio of the P33(1600) resonance, RE M = −0.115, not yet reported in the literature.