# Why Majorana neutrinos is a solution for the existence of only LH neutrinos?

At lesson my teacher stated that the possible reason for why only LH neutrinos are observed are that either: neutrinos are Dirac fermion but the RH neutrinos are not interacting weakly or that they are Majorana fermion ($\Psi=\Psi^{\star}$) but he didn't explain why this second solution solves the issue, he only wrote $\Psi=(\Psi_L, i\sigma_2\Psi_L^\star)$ but not how to reach this (if this is true I understand why we do not find RH neutrinos). Can anybody help me clarify this point?

## 1 Answer

If the neutrino is Majorana in nature, it means that the "RH neutrinos" are actually just the anti-neutrinos which we do see in nature. Majorana particles are those Fermions whose antiparticle is itself (kind of like how photons are their own anti-particles, except photons are Bosons). If neutrinos are Dirac in nature, the "RH neutrinos" would be sterile states that we don't observe. Either way, we will never see a "RH neutrino" because either it's sterile (Dirac) or it's actually just the antineutrino (Majorana).

• I'm failing to see why this statement is true though: "If the neutrino is Majorana in nature, it means that the "RH neutrinos" are actually just the anti-neutrinos". Could you explain this? – Ringo_00 Sep 15 '18 at 14:15
• @Ringo_00 sure, that statement is arises merely from the definition of Majorana vs Dirac. A Dirac spinor is 4 components. In some basis, one could label those 4 components as (LH Neutrino, RH Neutrino, LH Anti-Neutrino, RH Anti-Neutrino). In contrast, a Majorana spinor has only 2 components. And so one could associate with those 2 components the states (LH Neutrino, RH Anti-neutrino). Those would be the only 2 states possible. Of course one could also just label the states (Neutrino, AntiNeutrino) or (LH, RH) then. – enumaris Sep 16 '18 at 18:25