[T-A]

> giving neutrinos a bare mass term would violate electroweak gauge invariance?

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]

Huh. Why do other sources seem to say that's only the case for bosons? Or am I conflating two distinct problems? Sorry, once again, not a physicist.

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]

> the mass should come from the Higgs mechanism,

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...

[Sniffnoy]

OK, so the actual disagreement here seems to be whether adding same-mass right-handed neutrinos counts as a significant modification to the Standard Model. I have generally seen adding any sort of right-handed neutrinos to be considered a significant modification. I agree that certainly adding same-mass ones, like all othe fermions have, makes everything simpler and more symmetric! And in an alternate history of physics, that would have been considered the Standard Model, the baseline. But as best I've seen, in the history of physics that actually happened, "no right-handed neutrinos" got codified as the baseline, so changing over to this alternate one would to my mind be a significant change from what people mean by "the Standard Model".

But that doesn't exactly seem like something it makes a lot of sense to argue over, now that we've identified the disagreement.

> 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].

Hm, is that true? I know these experiments can only detect certain mass ranges and IIRC you're right that they were looking for heavier ones, but my understanding was that they were not getting it from physics beyond "standard model plus right-handed neutrinos" (technically beyond the standard model but only a way that is necessary to even discuss the subject!), rather they were just getting it via the ordinary Higgs mechanism? (The bit you linked regarding this doesn't appear to contradict this?) Unless by "beyond the standard model" you just mean that the right-handed mass is different from the left-handed mass, in which case, well, see above, now we're just talking about what "the standard model" normally means.

I mean you say you're a particle physicist, so I guess you'd know -- when you talk to your colleagues, what do they think "the standard model" means with regard to neutrinos? That right-handed ones don't exist? Or that they do exist and have the same mass as their left-handed counterparts? At the very least all the popularizations I've seen (generally written by particle physicists) have said it means the former... you're really sure other particle physicists mean the latter? This may sound a little silly, but have you tried taking like a quick poll or anything to make sure?

[T-A]

> so the actual disagreement here seems to be whether adding same-mass right-handed neutrinos counts as a significant modification to the Standard Model

I disagree. That has been the working definition of Standard Model for decades. All quarks and all charged leptons are known to have Dirac masses, which require both left- and right-handed components, so once it became clear that neutrinos have mass too, extending that pattern to them too was the obvious thing to do.

> in the history of physics that actually happened, "no right-handed neutrinos" got codified as the baseline

Again, I disagree. Weinberg introduced what you insist on calling "standard model" in a three-page letter, at a time when there was no evidence for neutrino masses. He correctly designed it as a minimal proof of concept, knowing full well that extending it would be trivial. For the same reason, his "model of leptons" did not even mention quarks; those were also not an established thing in 1967.

I can't imagine anyone seriously claiming that quarks are not part of the standard model. And yet, here I am having to explain for the umpteenth time that neutrinos working like all other standard model particles are part of what everybody competent means by standard model.

>> Plain vanilla standard model fermions have the same mass whether they are left- or right-handed, so quite small for neutrinos > > Hm, is that true?

Yes. A Dirac fermion has a left-handed component and a right-handed one. The Dirac mass term is what binds them together and makes them behave like a single particle with one mass. Set that mass to zero and you have two massless Weyl fermions. [1]

> Unless by "beyond the standard model" you just mean that the right-handed mass is different from the left-handed mass

Of course. Different masses for left- and right-handed components of a Dirac fermion is a contradiction in terms.

> I mean you say you're a particle physicist

Do I?

> the popularizations I've seen (generally written by particle physicists) have said it means the former

There is an unfortunate tendency in popularization to blur the lines between established knowledge and speculation (see Feynman's "Cargo cult science", linked elsewhere in this thread), and an understandable desire to make one's own subject look particularly exciting. If you are neutrino physicist (an intrinsically soporific activity which mainly involves staring for years or decades on end at large quantities of a transparent mass hoping to see a rare interesting event [2]) your best bet to achieve that is to push the "window into Beyond the Standard Model (BSM) physics" narrative. So you bring up the fact that neutrino masses are very small, point to the seesaw mechanism [3] as a possible explanation, and emphasize that massive right-handed neutrinos could be cold dark matter [4]. That's fine, although it's getting old and not looking as promising as it once did. What is not fine is stretching the truth to the point of breaking it by claiming that right-handed neutrinos are, by themselves, BSM. That is abject nonsense.

[1] https://en.wikipedia.org/wiki/Dirac_equation#Weyl_and_Majora...

[2] https://en.wikipedia.org/wiki/List_of_neutrino_experiments

[3] https://en.wikipedia.org/wiki/Seesaw_mechanism

[4] https://en.wikipedia.org/wiki/Cold_dark_matter