Pure spin-3/2 propagator for use in particle and nuclear physics

TL;DR

This paper introduces a covariant pure spin-3/2 propagator for particle physics, demonstrating its application to $ riangle$ resonance in $\pi N$ scattering and addressing issues with conventional approaches.

Contribution

It proposes a new covariant pure spin-3/2 propagator using antisymmetric tensor spinor representation, improving resonance description in particle interactions.

Findings

Pure spin-3/2 propagator formulated covariantly.

Modified interaction with momentum dependence improves resonance behavior.

Hadronic form factors are essential for accurate resonance modeling.

Abstract

We propose the use of pure spin-3/2 propagator in the $(3/2,0) \oplus (0,3/2)$ representation in particle and nuclear physics. To formulate the propagator in a covariant form we use the antisymmetric tensor spinor representation and we consider the $\Delta$ resonance contribution to the elastic $\pi N$ scattering as an example. We find that the use of conventional gauge invariant interaction Lagrangian leads to a problem; the obtained scattering amplitude does not exhibit the resonance behavior. To overcome this problem we modify the interaction by adding a momentum dependence. As in the case of Rarita-Schwinger we find that a perfect resonance description could be obtained in the pure spin-3/2 formulation only if hadronic form factors were considered in the interactions.