Electromagnetic annihilation into charged leptons and scattering off nucleons of spin-3/2 Majorana particles

TL;DR

This paper calculates electromagnetic annihilation and scattering cross sections for spin-3/2 Majorana particles, revealing similarities and differences with spin-1/2 cases, with implications for dark matter and nucleosynthesis.

Contribution

It provides the first detailed derivation of electromagnetic cross sections for spin-3/2 Majorana particles, incorporating specific vertex function restrictions.

Findings

Derived formulas for annihilation and scattering cross sections

Identified key differences from spin-1/2 Majorana particles

Potential applications in dark matter and nucleosynthesis contexts

Abstract

We compute the cross section for the electromagnetic annihilation into charged leptons, and the electromagnetic scattering off nucleons, of spin-3/2 self-conjugate (Majorana) particles using the general form of the electromagnetic vertex function that was obtained previously for such particles. In addition to the restrictions imposed by common principles such as electromagnetic gauge invariance and hermiticity, the vertex function incorporates the restriction due to the Majorana condition as well as the particular properties related to the spinors in the Rarita-Schwinger representation, and is the counterpart of the so-called anapole interaction of spin-1/2 Majorana particles. The formulas obtained for the cross sections share certain similarities with the corresponding results in the spin-1/2 case, but they also reveal some important differences which are pointed out and discussed. The results given here can be useful for applications involving the electromagnetic interactions of spin-3/2 or spin-1/2 Majorana particles in several contexts that have been of interest in the recent literature such as nucleosynthesis and dark matter.