Photons are self-conjugate but neutrinos may or may not: why is that?

Question

Caution: This may be a very naive question but I find it confusing. Moreover, I believe this question is based on potential misconception. I would like it to be clarified.

Although the neutrinos are electrically neutral and colorless they have non-zero weak hypercharge $Y=-1$ (for left-chiral neutrinos), and lepton number $L=1$. So how can the possibility that neutrino being its own antiparticle be entertained? Even if we assign $L=0$, there is still the non-zero hypercharge fixed by the relation $Y=2(Q-I_3)$. So why can't we surely tell that there are antineutrinos, distinct from neutrinos, and charecterized by $Y=+1$?

If we assign, $L=+1$ for right-handed sterile neutrinos $N_R$, can I any longer entertain the possibility that $(N_R)^c$ to be same as $N_R$?

As far as I know, photons are their own antiparticles, that is clear. But particle physicists are not sure whether neutrinos are self-conjugate or not. They often treat neutrinos are Majorana particles and often as Dirac particles. Why is this ambiguity not there for photons?

Answer 1

• Because we have observed processes where the photon number is not conserved. For example positronium can decay into 2 or 3 (or more) photons. This means that it is not possible to assign a global conserved charge to photons.
• For neutrinos we can assign lepton number and so far we have not observed a process that would violate total lepton number (lepton number conservation means that to total number of charged leptons and neutrinos is conserved not separately the number of neutrinos or charged leptons).
• Concerning the hypercharge - it is not a conserved quantity. It is broken by the Higgs mechanism. To be precise: in the space of hypercharge and weak isospin there is a direction that is conserved and this is the electric charge. Symmetry in other directions is broken by the vacuum state.