Gauge- and point-invariant vertices of nucleon-to-resonance interactions

Abstract

We construct interactions of nucleons $N$ with higher-spin resonances $R$ invariant under point and gauge transformations of the Rarita-Schwinger field. It is found for arbitrarily high spin of a resonance that the requirement of point and gauge invariance uniquely determines a Lagrangian of $NR$ interactions with pions, photons, and vector mesons, which might reduce model ambiguity in effective-field calculations involving such vertices. Considering the $NR$ interactions with photons and vector mesons, the symmetry provides a classification of three $NR$ vertices in terms of their differential order. The ${Q}^{2}$ dependencies of the point- and gauge-invariant form factors are considered in a vector-meson--dominance model. The model is in good agreement with experimental data. In addition, we point out some empirical patterns in the ${Q}^{2}$ dependencies of the form factors: low-${Q}^{2}$ scaling of the $N\ensuremath{\Delta}(1232)$ form factor ratios and relations between form factors for $NN(1520)$ and $NN(1680)$ transitions.