Two-photon interactions with Majorana fermions

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 of 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 naive estimate might suggest.

Figure 1

Interaction vertex between an on-shell fermion and an off-shell photon of momentum $q$.

Figure 2

Two-photon interaction with a fermion. The photons are assumed to be real and transverse, and the fermion is on mass shell.

Figure 3

Leading order contributions to the anapole moment for the Majorana fermion.

Figure 4

Leading order contributions to Compton scattering via a Majorana fermion.