#### arivero

Gold Member

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I am detaching this to BSM because it is already getting too much parameters in the bag.

What has happened this year is that Werner Rodejohann and He Zhang, from the MPI in Heidelberg, proposed that the quark sector did not need to match triplets following weak isospin, and then empirically found that it was possible to build triplets choosing either the massive or the massless quarks. This was preprint http://arxiv.org/abs/1101.5525 and it is already published in Physics Letters B.

Later, two weeks ago, another researcher from the same institute veifyed the previous assertion and proposed a six quarks generalisation, in http://arxiv.org/abs/1111.0480

Then myself, answering to https://www.physicsforums.com/showthread.php?t=485458", checked that there was also a Koide triplet for the quarks of intermediate mass. I have not tried to find a link between this and the whole six quarks generalisation, but I found other interesting thing: that the mass constant AND the phase for the intermediate quarks is three times the one of the charged leptons. This seems to be a reflect of the limit when the mass of electron is zero, jointly with an orthogonality between the triplets of quarks and leptons in this limit: it implies a phase of 15 degrees for leptons and 45 degrees for quarks, so that 45+120+15=280. If besides orthogonality of Koide-Foot vectors we ask for equality of the masses (charm equal to tau, strange equal muon), the mass constant needs to be three too.

So,

with the premises

And the input

The sum rules allow to calculate the following masses.

(Errors are just from the extreme plus and minus, actually they would be a bit smaller; most probably any fundamental theory for the sum rules should propose greater second order corrections.).

Furthermore, the mass unit for leptons is 0.313,856,4 GeV and then for intermediate quarks is 0.941,569 GeV. Very typical QCD masses.

Plus, some of the sum rules of the Heidelberg group(s) can be used to give diffrent estimates for up and down. Or it can be tryed from other triplets (eg, Marrni with top-up-down).

What has happened this year is that Werner Rodejohann and He Zhang, from the MPI in Heidelberg, proposed that the quark sector did not need to match triplets following weak isospin, and then empirically found that it was possible to build triplets choosing either the massive or the massless quarks. This was preprint http://arxiv.org/abs/1101.5525 and it is already published in Physics Letters B.

Later, two weeks ago, another researcher from the same institute veifyed the previous assertion and proposed a six quarks generalisation, in http://arxiv.org/abs/1111.0480

Then myself, answering to https://www.physicsforums.com/showthread.php?t=485458", checked that there was also a Koide triplet for the quarks of intermediate mass. I have not tried to find a link between this and the whole six quarks generalisation, but I found other interesting thing: that the mass constant AND the phase for the intermediate quarks is three times the one of the charged leptons. This seems to be a reflect of the limit when the mass of electron is zero, jointly with an orthogonality between the triplets of quarks and leptons in this limit: it implies a phase of 15 degrees for leptons and 45 degrees for quarks, so that 45+120+15=280. If besides orthogonality of Koide-Foot vectors we ask for equality of the masses (charm equal to tau, strange equal muon), the mass constant needs to be three too.

So,

with the premises

- Top, Bottom, Charm have a Koide sum rule
- Strange, Charm, Bottom have a Koide sum rule
- Electron, Muon, Tau have a Koide sum rule
- phase and mass of S-C-B are three times the phase and mass of e-mu-tau

And the input

- electron=0.510998910 \pm 0.000000013
- muon=105.6583668 \pm 0.0000038

The sum rules allow to calculate the following masses.

- tau=1776.96894(7) MeV
- strange=92.274758(3) MeV
- charm=1359.56428(5) MeV
- bottom=4197.57589(15) MeV
- top=173.263947(6) GeV

(Errors are just from the extreme plus and minus, actually they would be a bit smaller; most probably any fundamental theory for the sum rules should propose greater second order corrections.).

Furthermore, the mass unit for leptons is 0.313,856,4 GeV and then for intermediate quarks is 0.941,569 GeV. Very typical QCD masses.

Plus, some of the sum rules of the Heidelberg group(s) can be used to give diffrent estimates for up and down. Or it can be tryed from other triplets (eg, Marrni with top-up-down).

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