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Beyond the Standard Models
What is new with Koide sum rules?
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[QUOTE="mitchell porter, post: 3709955, member: 103130"] Since we have another thread discussing E6 grand unification, I will point out the work of [URL="http://arxiv.org/find/hep-ph/1/au:+Stech_B/0/1/0/all/0/1"]Berthold Stech[/URL]. In my comment #14, I said that an "obvious" way to make a model for these extended Koide relations, would be to extend the standard model with a new scalar sector of "flavons", whose VEVs-squared determine the Yukawa couplings, and with a gauged family symmetry that protects the Koide relations, as suggested by [URL="http://arxiv.org/abs/0812.2090"]Yukinari Sumino[/URL]. (The Koide relations among the flavon VEVs would result from a flavon potential.) So it's very interesting that Stech's E6 models more or less resemble this picture. The Yukawas come from flavon VEVs, and there's a flavor symmetry. Especially interesting is that his lightest Higgs is at about 123 GeV! Stech's models definitely do not produce Koide relations at present. In particular, I can't think of any model ever that implies the peculiar e-mu-tau/s-c-b relation that Alejandro found. Though let's note that that relation also resembles the u-s-c/s-c-b relation in the "zeroth-order" or "primordial" version of the extended Koide relations, as described in his paper; so there may be something more complicated than a Georgi-Jarlskog "multiplication by three" at work here. (Another quantitative issue to investigate is whether all six lepton masses, neutrinos as well as charged leptons, can be arranged into a set of four chained Koide triplets like the quarks, or whether the leptons naturally fall into two disjoint triplets, this being an aspect of how they [I]differ[/I] from the quarks.) But the "peculiar" relation should be seen simply as a challenge: come up with a flavon potential and a new symmetry which produces it. And Stech's E6 framework looks worth investigating, though the minimal way to proceed would be just to add flavons (and maybe more Higgses) to the standard model until the extended Koide relations (and quark-lepton complementarity for the mixing angles, see comment #16) are obtained. [/QUOTE]
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What is new with Koide sum rules?
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