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

TL;DR

This paper develops a unique, symmetry-invariant framework for modeling nucleon-resonance interactions, reducing ambiguity in effective-field theories and aligning well with experimental data.

Contribution

It introduces a point- and gauge-invariant Lagrangian for high-spin nucleon-resonance interactions, providing a systematic classification and form factor analysis.

Findings

Unique Lagrangian determined by symmetry constraints

Classification of interaction vertices by differential order

Model agrees with experimental Q^2 dependencies

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-Delta(1232) form factor ratios and relations between form factors for N-N(1520) and N-N(1680) transitions.