Spin-5/2 fields in hadron physics

TL;DR

This paper analyzes the free spin-5/2 field's Lagrangian in the spinor-tensor form, deriving its propagator with auxiliary fields and discussing how to eliminate lower spin components through higher derivative couplings.

Contribution

It provides a detailed derivation of the spin-5/2 propagator including auxiliary fields and explores methods to remove lower spin contributions via higher order derivatives.

Findings

Derived the spin-5/2 propagator with auxiliary fields.

Identified non-pole contributions from lower spin sectors.

Showed how to eliminate lower spin degrees of freedom.

Abstract

We show that the Lagrangian of the free spin-5/2 field in the spinor-tensor representation with the auxiliary spinor field depends on the three arbitrary parameters. The first two parameters are associated with the spin-3/2 and -1/2 sector of the theory while the latter one is related to the auxiliary degrees of freedom. We derive a corresponding propagator of the system which represents (2 x 2) matrix in the $(\psi_{\mu\nu},\xi)$ space. The diagonal terms stand for the propagation of the spin-5/2 and auxiliary fields whereas the non-diagonal ones correspond to the $\psi_{\mu\nu}-\xi$ mixing. The resulting spin-5/2 propagator contains non-pole contributions coming from the spin-3/2 and -1/2 sector of the spinor-tensor representation. A general form of the interaction vertex involving spin-5/2 field is discussed on the example of the $\pi N N^*_{5/2}$ coupling. It is demonstrated that lower spin degrees of freedom can be removed from the theory by using higher order derivative coupling.