Electroweak bosons and gluons belong to singlet and octet of family-SU(3) and the natural assumption is that only singlet (ordinary gauge bosons) and two SU(3) neutral states of octet are light. One would have effectively 3 generations of electroweak bosons and gluons. There charge matrices would be orthogonal with respect to the inner product defined by trace so that both quark and lepton universality would be broken in the same manner. The strongest assumption is that the charge matrices in flavor space are same for all weak bosons. The CKM mixing for neutrinos complicates this picture by affecting the branching rations of charged weak bosons.
Quite recently I noticed that second generation of Z boson could explain the different values of proton charge radius determined from the hydrogen and muonium atoms as one manifestation of the violation of universality (see this). The concept of charge matrix is discussed in more detail in this post.
- There is about 4.0 σ deviation from $τ/l$ universality (l=μ,e) in b→ c transitions. In terms of branching ratios ones has:
R(D*)=Br(B→ D*→τντ)/Br(B→ D*lνl) =0.316+/- 0.016+/- 0.010 ,
R(D) =Br(B→ Dτντ)/Br(B→ lνl) =0.397+/- 0.040+/- 0.028 ,
The corresponding SM values are R(D*)|SM= 0.252+/- 0.003 and R(D)|SM=.300+/- .008. My understanding is that the normalization factor in the ratio involves total rate to D*lνl, l=μ, e involving only single neutrino in final state whereas the τν decays involve 3 neutrinos due to the neutrino pair from τ implying broad distribution for the missing mass.
The decays to τ ντ are clearly preferred as if there were an exotic W boson preferring to decay τν over lν , l=e,μ. In TGD it could be second generation W boson. Note that CKM mizing of neutrinos could also affect the branching ratios.
- Since these decays are mediated at tree level in the SM, relatively large new physics contributions are necessary to explain these deviations. Observation of 2.6 σ deviation of μ/e universality in the dilepton invariant mass bin 1 GeV2≤ q2≤ 6 GeV2 in b→ s transitions:
R(K)=Br(B→ Kμ+μ-)/Br(B→ K e+e-) =0.745+0.090/-0.074+/- 0.038
deviate from the SM prediction R(K)|SM=1.0003+/- 0.0001.
This suggests the existence of the analog of Z boson preferring to decay to e+e- rather than μ+μ- pairs.
If the charge matrices acting on dynamical family-SU(3) fermion triplet do not depend on electroweak bosons and neutrino CKM mixing is neglected for the decays of second generation W, the data for branching ratios of D bosons implies that the decays to e+e- and τ+τ- should be favored over the decays to μ+μ-. Orthogonality of the charge matrices plus the above data could allow to fix them rather precisely from data. It might be that one must take into account the CKM mixing.
- CMS recently also searched for the decay h→ τμ and found a non-zero result of Br(h→ τμ)=0.84+0.39/-0.37 , which disagrees by about 2.4 σ from 0, the SM value. I have proposed an explanation for this finding in terms of CKM mixing for leptons. h would decay to W+W- pair, which would exchange neutrino transforming to τμ pair by neutrino CKM mixing.
- According to the reference, for Z, the lower bound for the mass is 2.9 TeV, just the TGD prediction if it corresponds to Gaussian Mersenne MG,79=(1+i)79 so that the mass would be 32 times the mass of ordinary Z boson! It seem that we are at the verge of the verification of one key prediction of TGD.
For a summary of earlier postings see Latest progress in TGD.