> neutrinos have mass and this in itself is a problem because the Higgs mechanism doesn't provide mass to them ...
The Higgs mechanism doesn't provide all mass, even of the things that it provides mass for. They each have a "bare" mass, that is, a mass without any Higgs interactions. They just have a much greater mass because of the Higgs interaction. (And maybe that's why neutrinos have so little mass...)
The Higgs mechanism doesn't provide all mass, even of the things that it provides mass for. They each have a "bare" mass, that is, a mass without any Higgs interactions. They just have a much greater mass because of the Higgs interaction. (And maybe that's why neutrinos have so little mass...)