Majorana neutrinos and their electromagnetic properties

To help develop a picture of Majorana neutrinos, we study their electromagnetic properties. We show that $\mathrm{CPT}$ invariance forbids a Majorana neutrino from having a magnetic or electric dipole moment. Then, by considering the process $\gamma \to \nu \overline{\nu }$, we find the most general expression for the matrix element of the electromagnetic current of a Majorana neutrino. The result is verified in a way which leads us to explore the behavior under parity of such a particle. Next, we see how electromagnetic properties which follow from one-loop diagrams conform to our general results. Finally, we show how the striking electromagnetic differences between Majorana and Dirac neutrinos can become invisible as the neutrino mass goes to zero.