[Sniffnoy]

I wouldn't say that we have no experimental data which contradicts them. Rather, we do have experimental data which contradicts them, but no experimental data that points us in the direction of a solution (and whenever we go looking for the latter, we fail).

Consider e.g. neutrino masses. We have plenty of experimental data indicating that neutrinos oscillate and therefore have mass. This poses a problem for the standard model (because there are problems unless the mass comes from the Higgs mechanism, but in the standard model neutrinos can't participate in the Higgs mechanism due to always being left-handed). But whenever we do experiments to attempt to verify one of the ways of fixing this problem -- are there separate right-handed neutrinos we didn't know about, or maybe instead the right-handed neutrinos were just antineutrinos all along? -- we turn up nothing.

[T-A]

> the standard model neutrinos can't participate in the Higgs mechanism due to always being left-handed

This again? It's only true if you insist on sticking with the original form of Weinberg's "model of leptons" from 1967 [1], which was written when massless neutrinos were consistent with available experimental data. Adding quark-style (i.e. Dirac) neutrino mass terms to the Standard Model is a trivial exercise. If doing so offends some prejudice of yours that right-handed neutrino can not exist because they have no electric and weak charge (in which case you must really hate photons too, not to mention gravity) you can resort to a Majorana mass term [2] instead.

That question (are neutrinos Dirac or Majorana?) is not a "contradiction", it's an uncertainty caused by how difficult it is to experimentally rule out either option. It is most certainly not "a problem for the standard model".

[1] https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.19.1264

[2] https://en.wikipedia.org/wiki/Majorana_equation#Mass_term

[Sniffnoy]

So, I'm not actually a particle physicist. My understanding had been (based on something I'd read somewhere -- should try to find it again) that there is some problem caused by just declaring "neutrinos just have innate masses, they're not from the Higgs mechanism", but I could be mistaken. Obviously, if that is mistaken, then as you say it merely a question rather than a contradiction. Should try to dig that up though.

Edit: Doing some quick searching seems to indicate that giving neutrinos a bare mass term would violate electroweak gauge invariance? I don't know enough to evaluate that claim, or TBH really even to understand it. But I believe that's what I was thinking of, so maybe you can say how true and/or pertinent that is.

[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?

[TheOtherHobbes]

It's trivial to add a matrix to account for neutrino masses, but that doesn't explain their origin.

That is not a trivial problem at all. It certainly has not been solved, and it's possible experiments will say "Both the current ideas are wrong."

[T-A]

> It's trivial to add a matrix to account for neutrino masses

The matrix you are thinking of is presumably the PMNS matrix [1]. It's equivalent to the CKM matrix for quarks [2]. The purpose of both is to parametrize the mismatch between flavor [3] and mass eigenstates, not "to account for neutrino masses" or "explain their origin".

As far as the standard model is concerned, neutrino masses and quark masses all originate from Yukawa couplings [4] with the Higgs field. Adding such terms to Weinberg's original model of leptons is very much a trivial exercise, and was done already well before there was solid evidence for non-zero neutrino masses.

> it's possible experiments will say "Both the current ideas are wrong."

Assuming that by "Both current ideas" you mean Dirac vs Majorana mass, those are the only available relativistic invariants. For both to be wrong, special relativity would have to be wrong. Hopefully I don't need to explain how extraordinarily unlikely that is.

[1] https://en.wikipedia.org/wiki/Pontecorvo%E2%80%93Maki%E2%80%...

[2] https://en.wikipedia.org/wiki/Cabibbo%E2%80%93Kobayashi%E2%8...

[3] https://en.wikipedia.org/wiki/Flavour_(particle_physics)

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

[Yossarrian22]

Thanks Lord Kelvin

[T-A]

Poor Lord Kelvin gets maligned a lot:

https://arxiv.org/abs/2106.16033

That aside, a distinction should be made between

1) claiming that physics is pretty much done (what he's often accused of) and

2) pointing out factual errors in claims about the current state of knowledge (what I am doing).

If you absolutely must make flattering comparisons, may I suggest Feynman instead, especially on lying to laymen?

https://calteches.library.caltech.edu/51/2/CargoCult.htm

I should add that I am not in complete agreement with what he said in that speech: calling it "not essential to the science" strikes me as naive. Once you start juggling two standards of communication, you are on a slippery slope. If it's OK to lie to the funding public at large, what about politicians, funding bodies, colleagues in other disciplines competing for the same funding, journal editors asking you to review a rival's work in your own field? Where do you draw the line? Do you draw a line, or do you descend into a state of generalized charlatanry?