If the neutrino is a Majorana particle (i.e., the antineutrino and the neutrino are actually the same particle), and at least one type of neutrino has non-zero mass (which has been established by the neutrino oscillation experiments), then it is possible for neutrinoless double beta decay to occur. Neutrinoless double beta decay is a lepton number violating process. In the simplest theoretical treatment, known as light neutrino exchange, a nucleon absorbs the neutrino emitted by another nucleon. The exchanged neutrinos are virtual particles.
With only two electrons in the final state, the electrons' total kinetic energy would be approximately the binding energy difference of the initial and final nuclei, with the nuclear recoil accounting for the rest. Because of momentum conservation, electrons are generally emitted back-to-back. The decay rate for this process is given by
where G is the two-body phase-space factor, M is the nuclear matrix element, and m is the effective Majorana mass of the electron neutrino. In the context of light Majorana neutrino exchange, m is given by
where m are the neutrino masses and the U are elements of the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix. Therefore, observing neutrinoless double beta decay, in addition to confirming the Majorana neutrino nature, can give information on the absolute neutrino mass scale and Majorana phases in the PMNS matrix, subject to interpretation through theoretical models of the nucleus, which determine the nuclear matrix elements, and models of the decay.
The observation of neutrinoless double beta decay would require that at least one neutrino is a Majorana particle, irrespective of whether the process is engendered by neutrino exchange.