If the neutrinos have enough energy, then they can just produce a lepton-anti-lepton pair. But for low energies the simplest process is creation of a virtual W

If the neutrinos have enough energy, then they can just produce a lepton-anti-lepton pair. But for low energies the simplest process is creation of a virtual W pair, that annihilates to two photons. Trying to explain a bit, because of the uncertainty principle you can borrow energy from the vacuum, as long as the resulting particles are destroyed quickly enough. So for intermediate stage in a process you do not need to exactly satisfy energy conservation, but instead the resulting cross section is suppressed and the reaction becomes more unlikely. But the neutrino less double beta decay works somewhat differently. In a normal beta decay, a nucleus transmutes to a daughter nucleus, a electron and a anti-neutrino. ( X, X' are the nuclei, nubar the anti neutrino, e- the electron.) X -> X' + nubar + e- In a neutrino less double beta decay, this is what the article is talking about, the anti-neutrino then reacts with the daughter nucleus to produce yet another nucleus and an additional electron. Here the energy to create the two electrons comes from the mass difference between the initial nucleus and the final nucleus. X' + nubar + e- -> X'' + 2 e- But it is only possible if the anti-neutrino is actually a normal neutrino, since otherwise the second reaction would need to create a positron, which would mean that the initial and final nucleus are identical, which means that there is no mass difference to create the electron positron pair. So detection of a neutrino less double beta decay is immediate proof that the neutrino is its own anti particle.