Which symmetry protects the yukawa couplings?

[arivero]

I asked this in a thread on string theory, but the answer could well be in the standard model, so here I ask the same from the traditional point of view.

Naturalness tells us, roughly, that if there is a quantity near zero, it is because a slightly broken symmetry protects it.

Of the 24 yukawa couplings of the standard model, 21 of them are almost zero. The only three ones different of zero are the ones for the three colours of the top quark.

Se we need a group protecting them, and such group should ideally have a multiplet covering all the massless fermions. It could be and 84 then, or a 42 (if looking at Weyl fermions), or a 21 (if looking at Diract fermions), or something smaller (if we apply SU(3) colour to reduce the number of yukawas from 21 to 11, but the rationale for this is unclear to me).

Groups as SO(9), SU(6) or SU(4) could provide a 84 multiplet, but under which justification could we invoke such groups?

Also, I am nor sure if we have confirmation about the protection of the neutrino mass, it could be they, or some of they, are unprotected and then of the same mass than the top quark.

Enough food for thinking? Any idea about the answer to the question, or at least about the current state of the art?

 

[Evalesco]

I am interested in this topic as well and it is certainly a lot of food for thought. At this point, I don't think there is a definitive answer, but I am curious to see what other people think about it. It is interesting that you mention the possibility of reducing the number of Yukawa couplings by applying SU(3) color. Do you think this would have any impact on the protection of the massless fermions? Also, have there been any attempts to explain the protection of neutrino masses within the standard model?