# Two-photon interactions with Majorana fermions

## TL;DR

This paper investigates the electromagnetic properties of Majorana fermions, showing that their self-conjugate nature constrains induced dipole moments and polarizabilities, with implications for their annihilation cross-sections.

## Contribution

It provides a detailed analysis of how Majorana fermions' symmetry properties restrict their electromagnetic interactions and calculates their polarizabilities and annihilation cross-sections.

## Key findings

- Induced dipole moments are constrained by symmetry considerations.
- Polarizabilities are explicitly calculated using a simple model.
- The annihilation cross-section into photons is larger than naive estimates.

## Abstract

Because Majorana fermions are their own antiparticles, their electric and magnetic dipole moments must vanish, leaving the anapole moment as their only static electromagnetic property. But the existence of induced dipole moments is not necessarily prohibited. Through a study real Compton scattering, we explore the constraints that the Majorana fermion's self-conjugate nature has on induced moments. In terms of the Compton amplitude, we find no constraints if the interactions are separately invariant under charge conjugation, parity, and time reversal. However, if the interactions are odd under parity and even under time reversal, then these contributions to the Compton amplitude must vanish. We employ a simple model to confirm these general findings via explicit calculation of the Majorana fermion's polarizabilities. We then use these polarizabilities to estimate the cross-section for $s$-wave annihilation of two Majorana fermions into photons. The cross-section is larger than a na\"ive estimate might suggest.