Can Koide's yukawaon models explain the neglected clue in particle physics?

[mitchell porter]

http://arxiv.org/abs/1106.0971" .

I regard Koide's relation for the charged lepton masses as the most neglected clue in particle physics. It's amazing that it isn't routinely discussed when people talk about BSM physics. The inherent difficulty of explaining it ought to be attracting attention from ambitious theorists.

A while back, Yukinari Sumino produced a http://arxiv.org/abs/0903.3640" for it. As a model, I don't think it fit anyone's agenda very well - a new symmetry, nine new scalar fields, a new hierarchy problem - but at least it was trying to explain some neglected data.

Now Koide himself has taken it a little further by combining Sumino's model with a GUT. Perhaps the model-building mainstream will now get involved?

 

[mitchell porter]

There's a preprint today announcing http://arxiv.org/abs/1106.2822" modeling quark and lepton mixing matrices. That paper states

Our numerical conclusions from the present systematical study is summarized in Figs. 2-7. Especially, as seen in Fig.7, the results sin² 2θ_atm ≃ 1 and |U₁₃|² ≤ 0.005 are insensitive to the value of the parameter ξ_ν . In other words, if |U₁₃|² ∼ 0.01 (the possibility was pointed out by Fogli, et al...) is established experimentally, the present model will be ruled out, or it will need a drastic revision.

and, if I am reading the notation correctly, the experimentally preferred value of |U₁₃|² is now "about 0.15 plus minus 0.1 or so" (Lubos). The uncertainties are large because the number of events is so small, 6 out of 88. This surely won't put Koide's "yukawaon" models out of commission, he'll just need to change the superpotential in his theory.

It's a little eccentric to say so - since they are so unknown - but it could be argued that Koide's yukawaon models are empirically the best models we have, because they do explain something - http://en.wikipedia.org/wiki/Koide_formula" that Koide himself discovered thirty years ago - that most other work in high-energy physics is just ignoring. These models are complicated, but until such time as we have a theory of everything that derives all observed quantities from some ultimate postulate, this is what physics is about, making models that fit the data, and the data includes the existence of this relation, even though it's slightly problematic from the perspective of conventional theory.

Readers may find Koide's preprint a little impenetrable, so let me direct them to page 8, table 2, where the fields and their transformation properties are enumerated. This is a SUSY-GUT model with symmetry group SU(5) x U(3) x O(3), where SU(5) is the GUT group, and U(3) and O(3) are family symmetries. A lot of fields, a lot of groups, but if Koide has done his homework, then it fits all the data we have, including the neglected datum mentioned above. Well, maybe it doesn't fit this new neutrino measurement, but I'm sure he can add a new epicycle to accommodate it!