In neutrinoless double-$\beta$ decay, the contributions of two virtual Majorana neutrinos with opposite $\mathrm{CP}$ parity will interfere destructively. This makes it evident that the amplitudes for reactions involving Majorana particles contain significant new phase factors, reflecting the special discrete-symmetry properties of these particles. To study this phenomenon, we derive and examine the $\mathrm{CPT}$, $\mathrm{CP}$, and $C$ properties of Majorana particles. We then apply these properties, especially to the study of neutrinoless double-$\beta$ decay, and to the neutral weak and electromagnetic interactions of Majorana particles. We show how the new phase factors in the Feynman amplitudes for Majorana-particle processes arise, and see that their precise form and location within these amplitudes depends on one's choice of formalism.

• Received 3 April 1984

DOI:https://doi.org/10.1103/PhysRevD.30.1023