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

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.

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