It’s discussed in this thread. The Koide formula is the prototype; Alejandro Rivero, who opened the thread, found its generalization. The barrier to the original formula’s credibility, as explained in the Wikipedia article (I added this section just yesterday), and also in Motl’s post, is that that sort of relation “shouldn’t” hold for that sort of quantity. The physicist Yukinari Sumino devised a mechanism to protect the original Koide relation from quantum corrections, but his paper has received very little attention, even from the people who work on generalizing the Koide relation. We don’t know that the Sumino mechanism is the only way to protect a Koide relation, but it’s natural to think about extending it to Rivero’s new relations. That’s actually a highly conservative response; one of the peculiarities of these formulas is the appearance of mass scales also found in QCD, which is suggestive of something really deep going on, like a supersymmetric QCD dual to the whole standard model. As far as Sumino’s paper goes, later in the thread “fzero”, who is evidently a working particle physicist, gives it some critical scrutiny, but we didn’t yet come to any conclusions.
So other people are paying serious attention to this already? Have you considered seeing if Rivero considers your ideas strong enough to help you put a paper on the arxiv?
So other people are paying serious attention to this already?
To explain the situation I have to describe the sociology of theoretical attention to Koide’s relation. Koide first discovered it in a model 30 years ago. Dozens of people have written papers about it. But as Lubos mentioned, the relation “shouldn’t” be as accurate as it is, because of RG flow (which is why Lubos dismisses it as a coincidence). A much smaller number of papers have been written about the behavior of Koide relations under RG flow. Sumino’s papers are the only ones describing a mechanism capable of making the Koide relation exact, and they haven’t received much attention.
Alejandro’s generalization of the Koide relation was found in a theoretical milieu where the RG issue hasn’t been discussed very much. The bare facts are a set of numbers, the fermion masses. The people looking for Koide-type relations have included mainstream physicists, “alternative” physicists, and ex-physicists. (Alejandro is in the last category; he has a physics PhD, but works in IT now, but participates vigorously in these online discussions.) The mainstream theorists who have in recent years proposed extended Koide relations do sometimes consider how they would be affected by RG flow, but it’s a rather peremptory discussion, and you don’t even get that much from the others.
So I’m the only one publicly talking about “Rivero + Sumino”, but who knows what’s going on in Germany, Japan, and elsewhere. There are a few things which might inhibit consideration of Alejandro’s paper: it involves an unfamiliar parametrization of the Koide relation, and it may sound odd to have quarks from different weak doublets in such a relationship. However, the paper actually describes a chain of Koide relations encompassing all the quark masses… Anyway, without going into the details, the relationships he found are a little peculiar from the vantage of theoretical expectations, which is an extra issue on top of the RG issue for physicists not already involved in these investigations; but in my opinion these peculiarities are actually mighty clues to the cause of the relationship.
If I ever do manage to make a Rivero-Sumino model, getting on the arxiv won’t be a problem. The challenge is just to make the model.
It’s discussed in this thread. The Koide formula is the prototype; Alejandro Rivero, who opened the thread, found its generalization. The barrier to the original formula’s credibility, as explained in the Wikipedia article (I added this section just yesterday), and also in Motl’s post, is that that sort of relation “shouldn’t” hold for that sort of quantity. The physicist Yukinari Sumino devised a mechanism to protect the original Koide relation from quantum corrections, but his paper has received very little attention, even from the people who work on generalizing the Koide relation. We don’t know that the Sumino mechanism is the only way to protect a Koide relation, but it’s natural to think about extending it to Rivero’s new relations. That’s actually a highly conservative response; one of the peculiarities of these formulas is the appearance of mass scales also found in QCD, which is suggestive of something really deep going on, like a supersymmetric QCD dual to the whole standard model. As far as Sumino’s paper goes, later in the thread “fzero”, who is evidently a working particle physicist, gives it some critical scrutiny, but we didn’t yet come to any conclusions.
So other people are paying serious attention to this already? Have you considered seeing if Rivero considers your ideas strong enough to help you put a paper on the arxiv?
To explain the situation I have to describe the sociology of theoretical attention to Koide’s relation. Koide first discovered it in a model 30 years ago. Dozens of people have written papers about it. But as Lubos mentioned, the relation “shouldn’t” be as accurate as it is, because of RG flow (which is why Lubos dismisses it as a coincidence). A much smaller number of papers have been written about the behavior of Koide relations under RG flow. Sumino’s papers are the only ones describing a mechanism capable of making the Koide relation exact, and they haven’t received much attention.
Alejandro’s generalization of the Koide relation was found in a theoretical milieu where the RG issue hasn’t been discussed very much. The bare facts are a set of numbers, the fermion masses. The people looking for Koide-type relations have included mainstream physicists, “alternative” physicists, and ex-physicists. (Alejandro is in the last category; he has a physics PhD, but works in IT now, but participates vigorously in these online discussions.) The mainstream theorists who have in recent years proposed extended Koide relations do sometimes consider how they would be affected by RG flow, but it’s a rather peremptory discussion, and you don’t even get that much from the others.
So I’m the only one publicly talking about “Rivero + Sumino”, but who knows what’s going on in Germany, Japan, and elsewhere. There are a few things which might inhibit consideration of Alejandro’s paper: it involves an unfamiliar parametrization of the Koide relation, and it may sound odd to have quarks from different weak doublets in such a relationship. However, the paper actually describes a chain of Koide relations encompassing all the quark masses… Anyway, without going into the details, the relationships he found are a little peculiar from the vantage of theoretical expectations, which is an extra issue on top of the RG issue for physicists not already involved in these investigations; but in my opinion these peculiarities are actually mighty clues to the cause of the relationship.
If I ever do manage to make a Rivero-Sumino model, getting on the arxiv won’t be a problem. The challenge is just to make the model.