On a gauge-invariant interaction of spin-$\fth$ resonances

TL;DR

This paper investigates gauge-invariant couplings for spin-5/2 resonances, showing how to remove non-pole terms and discussing the implications of free parameters on physical observables.

Contribution

It demonstrates that gauge-invariant couplings can be refined to eliminate non-pole terms and explores the role of free parameters in the Lagrangian affecting off-shell content.

Findings

Gauge-invariant coupling removes non-pole terms only for specific parameters.

Including higher derivatives or modifying couplings can resolve the problem.

Physical observables remain unaffected by off-shell parameters.

Abstract

We show that the gauge-invariant coupling suggested by Pascalutsa removes non-pole terms from a spin-$\fth$ propagator only for a specific choice of free parameter. For the general case the problem can be solved by including higher order derivatives of spin-$\fth$ fields or by modifying the original coupling. In the latter case the obtained Lagrangian depends on one free parameter pointing to the freedom in choosing an 'off-shell' content of the theory. However, the physical observables must not be affected by the 'off-shell' contributions and should not depend on the free parameter of the Lagrangian.