Compton scattering off elementary spin 3/2 particles

TL;DR

This paper compares two formalisms for calculating Compton scattering off spin 3/2 particles, revealing differences in predictions beyond the Thomson limit and analyzing their implications for scattering properties.

Contribution

It introduces a Poincare projector-based framework for high spin fields and compares its predictions with the Rarita-Schwinger formalism for Compton scattering.

Findings

Both formalisms yield the Thomson limit.

Predictions for angular distribution and cross section differ beyond the Thomson limit.

The Poincare projector formalism reproduces classical properties for spin 3/2, unlike Rarita-Schwinger.

Abstract

We calculate Compton scattering off an elementary spin 3/2 particle in a recently proposed framework for the description of elementary high spin fields based on the projection onto eigen-subspaces of the Casimir operators of the Poincare group. We also calculate this process in the conventional Rarita-Schwinger formalism. Both formalisms yield the correct Thomson limit but the predictions for the angular distribution and total cross section differ beyond this point. We point out that the average squared amplitudes in the forward direction for Compton scattering off targets with spin s = 0, 1/2, 1 are energy-independent and have the common value 4e^4. As a consequence, in the rest frame of the particle the differential cross section for Compton scattering in the forward direction is energy independent and coincides with the classical squared radius. We show that these properties are also satisfied by a spin 3/2 target in the Poincare projector formalism but not by the Rarita-Schwinger spin 3/2 particle.