Yifan Cheng, Otto C. W. Kong
This is a review on structure of the fermion mass terms of the Standard Model extended with the so-called "right-handed neutrinos" or "sterile neutrinos". The review is meant to be pedagogical, with detailed mathematics presented beyond the level one can find any easily in the literature. The discussions, however, bring up important subtleties and ambiguities about the subject that may be less than well appreciated. In fact, the naive perspective of the nature and masses of fermions as one would easily drawn from the presentations of fermion fields and their equations of motion from a typical textbook on quantum field theory leads to some confusing or even wrong statements which we clarify here. In particular, we illustrate clearly that a Dirac fermion mass eigenstate is mathematically equivalent to two degenerated Majorana fermion mass eigenstates at least so long as the mass terms are concerned. There are further ambiguities and subtleties in the exact description of the eigenstate(s). For the case of the neutrinos, especially, the use of the Dirac or Majorana terminology may be mostly a matter a choice.
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http://arxiv.org/abs/1305.5772
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