I took a postgraduate course in "Unification" during my MSc Physics degree. The lecture notes have things like "neutrinos are predicted to be massless" and "neutrino mass signals physics beyond the standard model".
However, aren't right handed neutrinos not included in the Standard Model because nobody ever observed them for sure? There's no neutrino mass term analogous to quarks or electrons because only left handed ones are in the SM, but if right handed ones were not included on purpose, how is this even a prediction? Isn't it a direct consequence of not including right handed ones...?
If there are right handed sterile neutrinos (that don't feel the weak force), can't we just add an analogous right handed singlet neutrino term, just like for the electron? Then we just "extend" the standard model - that's not new physics beyond it.
I understand that if they are Majorana particles, and if there's a Majorana mass term, then e.g. the Higgs field needs to be a triplet, or if we add both a Majorana & Dirac mass term there's the seesaw mechanism which predicts some new particles, but even then, that doesn't feel like "new Physics", and it feels like the extension of the SM, not something "beyond" it.
Based on trying to find similar questions to mine here, it really appears to me neutrinos aren't predicted to be massless, I guess I'm just looking for confirmation. So my real question is, do any of the extension of the SM to add neutrino mass signal new physics? What does even count as new physics? I think it would be something like a fifth force. Not sure what the general agreement is on "new physics".