Pure spin-3/2 representation with consistent interactions

TL;DR

This paper develops a formalism using pure spin-3/2 propagators with consistent interactions, ensuring correct degrees of freedom, and validates it through pion scattering and photoproduction calculations.

Contribution

It introduces a consistent interaction framework for pure spin-3/2 resonances using antisymmetric tensor spinor representation, verified by phenomenological calculations.

Findings

The formalism correctly describes spin-3/2 resonances in scattering processes.

Calculated amplitudes match the expected resonance properties.

The approach is suitable for nuclear and particle physics phenomenology.

Abstract

We have investigated the use of pure spin-3/2 propagator with consistent interaction Lagrangians to describe the property of spin-3/2 resonance. For this purpose we use the antisymmetric tensor spinor representation. By using the primary and secondary constraints we obtain the interaction fields that have the correct degrees of freedom. To visualize the result we calculate the contribution of spin-3/2 $\Delta$ resonance to the total cross section of pion scattering and pion photoproduction off the nucleon. The result confirms that the scattering and photoproduction amplitudes obtained from the pure spin-3/2 representation with consistent interaction Lagrangians exhibit the required property of a resonance. Therefore, the formalism can be used for phenomenological investigations in the realm of nuclear and particle physics.