arXiv:1503.01612v1 [nucl-th] 5 Mar 2015 About consistence between πN ∆ spin-3/2 gauge couplings and electromagnetic gauge invariance D. Badagnani ∗ , C. Barbero ∗∗ and A. Mariano ∗∗ 1 ∗ Departamento de F´ ısica, Universidad Nacional de La Plata, C. C. 67, 1900 La Plata, Argentina ∗∗ Instituto de F´ ısica La Plata, CONICET, 1900 La Plata, Argentina Abstract We analyze the consistence between the recently proposed “spin 3/2 gauge” interaction for the ∆ resonance with nucleons (N ) and pions (π), and the fundamental electromag- netic gauge invariance in any radiative amplitude. Chiral symmetric π-derivative πN ∆ couplings can be substituted through a linear transformation to get ∆-derivative ones, which have the property of decoupling the 1/2 field components of the ∆ propagator. Nevertheless, the electromagnetic gauge invariance introduced through minimal substitu- tion in all derivatives, can only be fulfilled at a given order n without destroying the spin 3/2 one by dropping n+1 order terms within an effective field theory (EFT) framework with a defined power counting. In addition, we show that the Ward identity for the ∆γ ∆ vertex cannot be fulfilled with a trimmed 3/2 propagator, which should be necessary in order to keep the “spin 3/2 gauge” symmetry in the radiative case for the ∆γ ∆ amplitude. Finally, it is shown that radiative corrections of the spin 3/2 gauge strong vertexes at one loop, reintroduce the conventional interaction. Keywords: ∆ resonance; spin 3/2 symmetry ; radiative pion-nucleon scattering Pacs: 13.75.Gx; 14.20.Gk; 13.40.Em 1 corresponding author:mariano@fisica.unlp.edu.ar