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T-A | 16 days ago
Giving any standard model fermion a bare mass term would violate electroweak gauge invariance. That was one of the problems with Glashow's electroweak model from 1961 [1]: he had the right symmetry group, but all particles had to be massless in order not to break it. Weinberg's contribution was to combine Glashow's proposal with Higgs' mass generation mechanism. It is done exactly the same way for any electroweak fermion doublet (as long as you are happy with the default choice of Dirac mass terms for all of them), be it up quark and down quark or neutrino and electron.
[1] https://www2.physik.uni-muenchen.de/lehre/vorlesungen/sose_2...
Sniffnoy|16 days ago
But if that's correct then I'm confused what your objection is to what I said earlier. If a bare mass would violate electroweak gauge invariance, then instead the mass should come from the Higgs mechanism, but that has the problem of, where are all the right-handed neutrinos, then? Am I missing something here? If you can't just give the neutrinos a bare mass and call it a day (at least not w/o causing significant problems), but do in fact have to make a more significant modification like inventing sterile neutrinos or making them Majorana particles, I'd call that a "contradiction" rather than merely a "question", because no hypothesis so far is a good fit for all of what we see (searches for sterile neutrinos have come up empty, neutrinoless double beta decay remains undetected, and I assume nobody's ever observed violations of electroweak gauge invariance!). Or I guess there are more out-there hypotheses that are consistent with what we see in that they've yet to really be tested, but, y'know, nothing that's been really tested AFAIK.
T-A|16 days ago
Correct. That's the pattern we see in quarks, and also applying it to leptons works just fine. In practice, if you are a particle physicist doing calculations which happen to involve neutrinos, and you are not explicitly analyzing the effects of alternative mass generation mechanisms, you use Dirac masses for all fermions.
> but that has the problem of, where are all the right-handed neutrinos, then?
One of the patterns of the standard model is that only left-handed fermions have weak isospin [1] (the charge of the "weak" nuclear force). Their right-handed counterparts have all the same properties but zero weak isospin; they do not interact via the weak nuclear force.
If you take a left-handed neutrino, which only interacts via the weak nuclear force (and gravity), and apply that pattern to get the properties of a right-handed neutrino, what you're left with is a particle with the same mass and no other interactions than gravity. That makes it pretty hard to detect.
This is not a "significant modification" of the standard model: it's what you get if you apply the pattern followed by all other fermions.
It is sometimes argued that making neutrinos Majorana is more minimalistic, since it reduces the number of particles by eliminating right-handed neutrinos, but that ignores the cost of deviating from the default pattern. In information terms, it would take more bits to encode "use Dirac masses for all fermions except neutrinos, those are Majorana and there are no right-handed ones" than just "use Dirac masses for all fermions".
> searches for sterile neutrinos have come up empty
Those would be heavy neutrinos which get their mass from physics beyond the standard model. Plain vanilla standard model fermions have the same mass whether they are left- or right-handed, so quite small for neutrinos [2].
> neutrinoless double beta decay remains undetected
Those would be a signature of Majorana neutrinos.
Both your "contradictions" support the plain vanilla standard model, with all fermions following the same pattern.
[1] https://en.wikipedia.org/wiki/Weak_isospin
[2] https://en.wikipedia.org/wiki/Neutrino#Properties_and_reacti...