Andrew Oh-Willeke suggests a new Koide triple: electron, up, down.
I consider it rather unlikely (and it depends on the up mass being zero, an old idea which features in Rivero's Koide waterfall but which is out of fashion, presumably because it is empirically disfavored). But I'll say this for Andrew's triple, that it does have a little logic; those are all the first-generation fermions except for the electron-neutrino, and the neutrino masses differ from the others by orders of magnitude.
In the Koide lore of fringe physics, we have what I call "family triples" like the original electron/muon/tauon, and "sequential triples" like top/bottom/charm; I suppose this is a "generational triple".
Andrew now needs to look at the corresponding neutrinoless triples for the other two generations. If they work well, that's really interesting; if they don't, it doesn't necessarily kill the idea; there may just be other influences dominating the masses of the second and third generations, in that case.
Although I have much more confidence in the reality of the sequential triples appearing in Alejandro's waterfall for the quark masses, it may actually be easier to build models in which Andrew's generational triple is something real (i.e. has a cause, such as a new symmetry). The sequential triples alternate between up-type and down-type quarks in a way which makes them the most difficult to accommodate.
In general this also seems a positive development simply because it rounds out the picture, regarding possible generalizations of Koide's relation to all the fermions.
Long answer in this post.
ReplyDeleteIn a nutshell, I think that the mass of a particle is a Koide-like balance of a particle and the three other particles it can transform into via weak force interactions at leading order, with Koide triples working only in cases where the omitted terms of negligble due to small CKM probabilities relative to the other possibilities and due to the omitted terms having low masses. A more accurate LO Koide formula would have quartets rather than triples. The generational triple works because beta decay is the dominant W boson interaction in mass-energy limited systems that are dominant in nature.
Also, the charged lepton family triple, the four sequential triples that work, and the generational triple that I identify all work because the included three terms have masses much greater than the omitted neutrino mass terms (in the case of the charge leptons or generational triple) or the omitted light quark term (in the case of the sequential triples).
The massless up quark could simply be an artifact of trying to approximate a proper extended Koide quartet analysis that omits a really important top or bottom quark term respectively from the quartet producing an invalid answer. Or, it could be that the omission is so small anyway because the CKM elements for t-d or u-b are so negligibly small that they don't matter even for large masses.