Abstract: It is shown that if, from the starting point of a universal rank-one mass matrix long favored by phenomenologists, one adds the assumption that it rotates (changes its orientation in generation space) with changing scale, one can reproduce, in terms of only six real parameters, all the 16 mass ratios and mixing parameters of quarks and leptons. Of these 16 quantities so reproduced, 10 for which data exist for direct comparison (i.e. the CKM elements including the CP-violating phase, the angles theta(12), theta(13), theta(23) in nu-oscillation, and the masses m(c), m(mu), m(e)) agree well with experiment, mostly to within experimental errors; four others (m(s), m(u), m(d), m(nu 2)), the experimental values for which can only be inferred, agree reasonably well; while two others (m(nu 1), delta(CP) for leptons), not yet measured experimentally, remain as predictions. In addition, one gets as bonuses, estimates for (i) the right-handed neutrino mass m(nu R) and (ii) the strong CP angle theta inherent in QCD. One notes in particular that the output value for sin(2) 2 theta(13) from the fit agrees very well with recent experiments. By inputting the current experimental value with its error, one obtains further from the fit two new testable constraints: (i) that theta(23) must depart from its “maximal” value: sin(2) 2 theta(23) similar to 0.935 +/- 0.021, (ii) that the CP-violating (Dirac) phase in the PMNS would be smaller than in the CKM matrix: of order only vertical bar sin delta(CP)vertical bar <= 0.31 if not vanishing altogether.

Abstract: The framed standard model (FSM) is obtained from the standard model by incorporating, as field variables, the frame vectors (vielbeins) in internal symmetry space. It gives the standard Higgs boson and 3 generations of quarks and leptons as immediate consequences. It gives moreover a fermion mass matrix of the form: m = mT alpha alpha dagger, where alpha is a vector in generation space independent of the fermion species and rotating with changing scale, which has already been shown to lead, generically, to up-down mixing, neutrino oscillations and mass hierarchy. In this paper, pushing the FSM further, one first derives to 1-loop order the RGE for the rotation of alpha, and then applies it to fit mass and mixing data as a first test of the model. With 7 real adjustable parameters, 18 measured quantities are fitted, most (12) to within experimental error or to better than 0.5 percent, and the rest (6) not far off. (A summary of this fit can be found in Table 2 of this paper.) Two notable features, both generic to FSM, not just specific to the fit, are: (i) that a theta-angle of order unity in the instanton term in QCD would translate via rotation into a Kobayashi-Maskawa phase in the CKM matrix of about the observed magnitude (J similar to 10(-5)), (ii) that it would come out correctly that m(u) < m(d), despite the fact that m(t) >> m(b), m(c) >> m(s). Of the 18 quantities fitted, 12 are deemed independent in the usual formulation of the standard model. In fact, the fit gives a total of 17 independent parameters of the standard model, but 5 of these have not been measured by experiment.