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# Koide2014talk

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Slides of the talk on Koide Formula. Video should be available at http://viavca.in2p3.fr/alejandro_rivero.html
or directly al flv
http://viavca.in2p3.fr/video/alejandro_rivero.flv

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• Another errata: pm 0.87, not 0.087, in the pdg2014 top mass. See also http://arxiv.org/abs/1411.0820

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• There is a minor but interesting mistake in slide 17. It says that the solution is unique when it shoud say 'the solution has a double root' because that is the particularity of the level 4M: it is a double root and as we deform-rotate the solution, one of the roots decreases and the other increases. So this level somehow announces the bifurcation between quarks and leptons... except that there is no a 'b-level' lepton, at least no a visible one.

On other hand, the other two solutions of the quartic are the zero level and a level about 40M, which is interesting for an idea of Dave Lackey about the sin of Weinberg angle.

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### Koide2014talk

1. 1. Introduction Biblography of Koide Equation Quarks bonus worksheets
2. 2. nal Koide formula: beyond charged leptons The waterfall in the quark sector Alejandro Rivero Institute for Biocomputation and Physics of Complex Systems (BIFI) Universidad de Zaragoza October 3, 2014 arivero@unizar.es Koide Formula
3. 3. Introduction Biblography of Koide Equation Quarks bonus worksheets
4. 4. nal By Koide formula" we refer to a formula found by Y. Koide for charged leptons, exact enough to predict tau mass within experimental limits (me + m + m ) = 2 3 ( p me + p m + p m )2 exp, in MeV: 1882:99 = 1882:97 It was found in the context of composite models of quarks and leptons, but can be produced more generally. More informally, we also call Koide formula to its generalisations and look-alikes other unexplained
5. 5. ne-tuning... Compare 1882:99=1882:97 = 1:00001 with mtop=174:1 = :995 arivero@unizar.es Koide Formula
6. 6. Introduction Biblography of Koide Equation Quarks bonus worksheets
7. 7. nal potential model It is possible consider mi as a composite of two entities with charge Q0 and Qi such that mi / 1 2 Q2 0 + Q0Qi + 1 2 Q2 i and asking the matching conditions P Qi = 0 and P Q2 i = P Q2 0 . From here it is clear that p m can have a negative sign sometimes. The generalisation to more than three particles simply substitutes 3=2 by n=2. Of course, with more particles in the formula, the probability of
8. 8. nding a random coincidence increases. arivero@unizar.es Koide Formula
9. 9. Introduction Biblography of Koide Equation Quarks bonus worksheets
10. 10. nal circle model [MDS, Rosen 2007] suggested to use the notation mk = M0 1 + p 2 cos 2 3 k + 0 2 And particularly for charged leptons: Me = 313:8MeV; e = 0:222 arivero@unizar.es Koide Formula
11. 11. Introduction Biblography of Koide Equation Quarks bonus worksheets
12. 12. nal Composites and Cabibbo angle Later observations Recent Work F. Wilczek and A. Zee, Discrete Flavor Symmetries and a Formula for the Cabibbo Angle, Phys. Lett. B 70, 418 (1977) [Erratum-ibid. 72B, 504 (1978)]. tan c = r md ms H. Harari, H. Haut and J. Weyers, Quark Masses And Cabibbo Angles, Phys. Lett. B 78 (1978) 459. mu = 0; md ms = 2