# Why a neutrinoless double beta decay implies a massive neutrino?

I know neutrinos have mass thanks to the observation of the neutrino oscillations between one type to another (that cannot happen if they are massless particles because the mixing matrix will not contain any non-zero elements but in the diagonal, if I'm not wrong). I know about experiments trying to perform direct measurements as KATRIN but I read that you can reach lower limits measuring neutrinoless double beta decay. Apparently, if this process takes place, it will imply that neutrinos are massive particles, so I was wondering what is the proof that the existence of a neutrinoless double beta decay implies that neutrinos must have mass?

• Neutrino flavor oscillations imply that neutrinos have mass. Neutrinoless double beta decay would imply that the neutrino is its own antiparticle (in more formal terms, it would be a Majorana fermion rather than a Dirac fermion). Based on how the Majorana fermion works, this would give a natural explanation for the neutrino's tiny mass, but it's not why we know neutrinos to have mass in the first place. – probably_someone May 2 '18 at 4:31
• – anna v May 2 '18 at 4:33
• I think Schechter and Valle were the first to show that double beta decay implies a non-zero mass for the electron neutrino. – John Rennie May 2 '18 at 5:02
• The correct answer is that of the paper of Schechter and Valle, thanks! Anyways I do not get yet why a violation of the leptonic number implies that the mass of the particle needs to be different from 0 – Juanjo May 3 '18 at 12:01
• possible duplicate of physics.stackexchange.com/q/118932/84967 – AccidentalFourierTransform May 3 '18 at 20:15