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Physics
Beyond the Standard Models
What is new with Koide sum rules?
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[QUOTE="CarlB, post: 6502785, member: 26624"] The Koide formula is a relation among changes in generation. It works for the charged leptons where the triplet is (e,mu,tau), one from each generation. It doesn't work for either of the quark sets (d,s,b) and (u,c,t) so it would be a huge miracle to me if it worked for mesons that differ only in their valence quark content. (That said, for the quark Koide equations see the Piotr ̇Zenczykowski papers i.e. [URL]https://arxiv.org/abs/1301.4143[/URL] There the coincidence that is applied to the quarks is about the phase 2/9 used for the charged leptons changing into 2/3 and 1/3 that when used for the two quark sets. Accordingly, I'd be more interested in coincidences involving that phase and I don't think anyone has looked for them.) A triplet of mesons that differ by generation would be a triplet that is different from having d, s or b valence quark(s) or (u,c,t), that is, something like a triplet (d/d, s/s, b/b) if we transform both of the quarks or (d/d, d/s, d/b) if we keep the first constant at d. The whole problem is made more difficult by the fact that the mesons do not have precise quark composition but instead are superpositions. For example, pi0 is partly d/d and partly u/u. It would help me if you gave the quark composition, with superpositions, of the mesons that the Koide equation relates. Of course the problem with looking for coincidences among a list of states without a restriction of this sort is that the statistics have to be adjusted for the fact that any list of random numbers will have coincidences and the longer the list the more and better coincidences. This contributes to why the particle people like 5 sigma statistics but that's after the theoretical justification for the coincidence search not before they put every known meson into the hopper of the woodchipper. [/QUOTE]
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What is new with Koide sum rules?
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