[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...

[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