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Naively, I'd just think of considering them as any other massive fermions (but without electric charge), including the appropriate chiralities (and neutrino-higgs coupling when necessary). Nevertheless something tells me it is not that simple. People talk about sterile neutrinos and things like that.

Would consider massive neutrinos bring extra complications to the SM? Would it require changes in the way we describe the weak interactions? What exactly would it conflict with?

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Neutrino mass is not in conflict with electroweak theory. One can introduce neutrino masses by modifying the Higgs or lepton sector of the Standard Model.

The simplest method, that which you propose, is introducing a right handed neutrino with a Yukawa coupling with the left handed neutrino (extending the lepton sector). The right handed neutrino, however, is permitted a bare Majorana mass, because no e.g. U(1) symmetries forbid it, which results in a richer phenomenology; see e.g. the seesaw mechanism.

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Is it to say that we need extra fields? Is it because right-handed neutrinos haven't been seen? I thought we could accommodate that on the theory in a more "minimal" way. If you could elaborate a little bit more, I'd be pleased to accept your answer. –  user34134 Nov 21 '13 at 17:35
    
Gotta dash. Quickly: SM does not include RH neutrinos. RH neutrinos would be sterile as only have Yukawa interaction, and haven't been observed. –  innisfree Nov 21 '13 at 17:44
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