Aligning a Majorana fermion's anapole moment with an external current through photon emission mediated by the fermion's generalized polarizabilities

TL;DR

This paper investigates how Majorana fermions with only an anapole moment can become polarized in a background current through photon emission processes involving their polarizabilities, with implications for dark matter models.

Contribution

It introduces a detailed analysis of Majorana fermion spin-flip processes mediated by photon emission via polarizabilities, a novel approach to understanding their polarization in background currents.

Findings

Two-photon emission rates are negligible during thermal decoupling.

Partial polarization of dark matter can occur via virtual Compton scattering if currents are present.

The study provides a framework for polarization mechanisms of Majorana fermions in cosmological contexts.

Abstract

The sole static electromagnetic property of a spin-$\frac{1}{2}$ Majorana fermion is its anapole moment. Though they cannot couple to single real photons, these particles can interact with electric currents through virtual photons. If a Majorana fermion is immersed in a background current, there is an energy difference between the spin states of the fermion; the higher energy state has its anapole moment antialigned with the current. In this paper, we address the ability of a system of initially unpolarized Majorana fermions to achieve some degree of polarization relative to a static background current. In considering processes that allow the Majorana fermion's spin to flip to the lower-energy state, we focus upon two irreversible processes: the spontaneous emission of two real photons and the emission of a single real photon emitted in virtual Compton scattering. Both of these processes involve coupling to photons via the fermion's polarizaibilities. We compute the spin-flip transition rates for these processes using a low-energy expansion of the Hamiltonian and construct a toy model to showcase how these rates depend upon the underlying parameters within a model. Applying these ideas to a thermal dark matter (DM) model, we find that when the DM thermally decouples from the Standard Model plasma in the early universe, two-photon emission is negligible but partial polarization for the DM medium can proceed via virtual Compton scattering if sufficient currents exist.