Why do Majorana particles occur?
For example, why is the antiparticle of photon itself?
They don't. The photon is its own antiparticle but is not a Majorana particle. A Majorana particle is a hypothesized type of fermion that is its own antiparticle. There are no Majorana particles known.
I think thats an overstatement. There are no particles we KNOW FOR SURE are majorana. However, we suspect neutrinos might be. The neutrinoless-double-beta-decay experiments will have to decide the question.
My understanding is that none of the known neutrinos can be Majorana. Only an as yet undiscovered sterile neutrino might have a Majorana mass, since all of its quantum numbers are zero. Isn't that right?
No. The physical neutrinos may, in fact, be Majorana particles. Certainly, the neutrino states that appear in the SM before EW symmetry breaking can't be Majorana, as they carry both SU(2)_L and U(1)_Y charges. However, after EWSB, those charges are no longer conserved and the neutrinos don't carry those that are. So, there's nothing to stop the physical neutrinos from being Majorana particles. It simply becomes a matter of whether the neutrino mass-generating mechanism allows it or not.
The known neutrinos don't carry any unbroken charges. The typical neutrino mass parameters added to the lagrangian are majorana. If there are no right-handed neutrinos, you have to have a majorana mass.
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