## Thursday, November 17, 2011

### Koide Quarks

These new quark Koide triplets of Alejandro Rivero's are super cool! So instead of the original charge based triplets, we split the six quarks into two triplets in other ways. Alejandro notes that the $(b,c,s)$ triplet works for Koide parameters

$r = \sqrt{2}$ (the basic lepton parameter)
$\theta = 0.66642$

at a scale of $939.65$ MeV (roughly the proton mass). This gives the mass set ($4189.9$,$92.01$,$1356.0$) MeV. The strange quark eigenvalue comes with a minus sign. Now to check the $(t,u,d)$ triplet ...

1. When six or seven years ago, Yuri Danoyan wrote me about his "18 degrees" parametrization of mesons, I criticized him by using a baryon mass as base unit... Here the same criticism comes back against myself! It can be argued that what is important is the constituent mass of the quark, or even the eta' mass.

Ah yes, and perhaps at the end Koide triplets and Yuri "18 degrees" are the same phenomena, the later coming from empirical observation, the former rooted in theoretical models.

2. Alejandro, the Koide rule has also always been related to theoretical models.

3. Observe also that the $(t,c,u)$ triplet has a scale around $24$ times the $939$ MeV.

4. For the $(t,u,d)$ triplet, with a minus sign at the up quark, I get acceptable masses at

$r = 1.997$, $\theta = 0.008$, $M = 19100$ MeV

5. So for $(t,u,d)$ the integer ansatz gives something like $\theta = 1/128$ (the seven qubit space). And we can write $r = 2 - 0.0035$, where the $0.0035$ needs to be near the small CKM parameter.

6. Interesting that this new r is so near of 2, yep. And intriguing that a particle can be in various triplets; but even this year there was an article in the arxiv proposing generalisations beyond the triplet, so we are in the conservative side :-D.

About the phases, it is good to see the six combinations (changing sign, and adding 2pi/3 or 4/pi3). In this way it is possible to set bcs at 170 degrees from electrons.

And it is interesting to look at the limits where the small parameters go to zero. For instance if we set bcs at 180 degrees from electron, this amounts to set the electron phase equal to 15 degrees (the infamous pi/12), and the b,c,s phase to 120+3*15. If, besides, we set the mass of electrons to 313 and the one of b,c,s to 939, we have strange=muon and charm=tau, restoring some kind of symmetry. Hat tip 't Hoft.

This is the only symmetry I have found involving two triplets. Of course with a single triplet we have, if we set phase=0 in your t,u,d, that up=down. And same if we do it with t,b,c, it should exhibit bottom=charm symmetry.

7. Alejandro,

I encountered and answered an email from Yuri last year. This idea is another example of the universal patterns of the new physics and the numbers come up such as the 128 in Kea's comment above.

Kea,

Might the idea of 14 "qubit" space be a good view here?

Yuri when I saw his later stuff on line had much to say about tetrahedrons. But I was seeing it as a simple one but something more fundamental so I did not look that deeply into his ideas. How wise to consider the imaginary mass.

BTW if my comment is true then we could expect more like 48 protons- yes?

ThePeSla

8. Quite possible, The Pe Sla, but we are still sorting out the lower dimensions!

9. Older posts on the quark triplets.

10. I think that Kartavtsev person is a scoundrel. Nothing in that paper is original. He doesn't cite Dave, or me, or a number of others. And he doesn't even understand about the minus signs. It's just disgusting.

11. Kea, I was just thinking he was just no careful to check references... I have seen my own work (instantons, susy QM) repeated each five years by different teams, not knowing each from other. So I was not surprised he has missed us, nor that he has missed the french guy who did the summatory for six quarks in his PhD thesis (although I have only need two days to find it). But it is a bit strange he is not collaborating with the other two guys from the same institution.

12. By the way, it is a bit depressing... with two inputs, now we are getting five perfect, beyond discussion, outputs (tau,s,c,b,t), plus two acceptable ones (u,d), plus good hints, independent of the inputs, for neutrinos (pi/12 fases etc). And we can even reduce one of the inputs, arguing that the scale is from QCD.

This should deserve some attention.

13. Alejandro, try being a woman. My work, although much of it unpublished, has been deserving of attention since the late '90s. With the advent of the internet, many people (including from leading research institutions, and including people who have listened to many of my seminars) have been reading my work and ideas. They regularly rediscover them. I have yet to receive one decent citation, let alone a postdoc, even though some of my coauthors are highly respected, with much, much less knowledge about physics and maths. Even Carl doesn't cite me, for a paper that I should have been coauthor on.

Yes, of course it deserves attention. Just like the lack of fairies, zombies, GWs, FTL neutrinos, LHCb results, and a long list of other things that I predicted correctly. It will get attention when some hotshot decides that He invented it.

14. Ok, if this is the method, then Koide sum rules deserve that some hotshot decides that He invented it. I have no problem for my theories to be discovered by others. Well, Koide is not mine, but lets say the sBootstrap or the Z0/pi0 coincidence.

If by lecturing or speaking to others you have got some of your ideas to go rediscovered as mainstream, I envy you. I have never got such success. The most I have found is some others rediscovering techniques that I had also rediscovered unknowingly.

15. Alejandro, there was a great deal of (now wasted) talent and hard work involved. Envy usually manifests itself as hatred.

16. Well, then delete "envy", for sure I am not having a condition of hate with anybody. Actually I had preferred if someone had discovered the strange triplet and the orthogonal condition to leptons, and that either Carl or yourself had put more detail on the descritption of delta (the 0.2222) as a small perturbation and its limit. I can put effort in other places then.

As for wasted talent, the history of continous repeating small works in mathphys is horrible. I can tell you of two or three lines I had suffered. There is dirac delta potentials, where a mistake in a mainstream book causes people to retake the topic each five or six years. There is eigenstate removal in 1D potentials (aka SUSY QM, also repeated from time to time when someone rediscovers that Witten was a kind of genius. There is a topic related to the two previous ones: the dynamics of the poles of the S matrix for scattering in 1D potentials, as you move the coupling. Lot of papers done here, some very ancient by famous hotshots, some early by youngsters. Ah, and I enjoy this one, asymmetric tunneling, I did it in the nineties, I saw it repeated online, then I uploaded to the ArXiV to claim some merit, I got some good citations... and then later I found that the same kind of work was already in a Phys Rev from 1992, about two years before mine!

17. Alejandro, this blog does not exist for you to promote your work. Please stop. As for the $2/9$ ... I have spent a great deal of effort trying to understand how it fits into the heavy math phys picture. From this perspective, Koide formulae are kindergarten stuff.

18. Hmm, that was not the point. More on the contrary. It was about work that needs promotion (such as Koide) and work that doesn't -except perhaps to avoid people wasting years on the same topic again and again-, such as the examples I cited. I did explicit citations because I don't like to speak without concrete reference, that was all. Not that I do not like alchemical alegory, but I prefer IUPAC formulation.

Well, enough detour. Back to work. Ah, just to say that if sometimes you read some paper from me and you think that I have failed to quote something from you, it is enough that you send me the reference and I will ack gladly.