A COMPREHENSIVE MECHANISM REPRODUCING THE MASS AND MIXING PARAMETERS OF QUARKS AND LEPTONS

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 θ12, θ13, θ23 in ν-oscillation, and the masses mc, mμ, me) agree well with experiment, mostly to within experimental errors; four others (ms, mu, md, mν2), the experimental values for which can only be inferred, agree reasonably well; while two others (mν1, δ CP for leptons), not yet measured experimentally, remain as predictions. In addition, one gets as bonuses, estimates for (i) the right-handed neutrino mass mνR and (ii) the strong CP angle θ inherent in QCD. One notes in particular that the output value for sin 2 2 θ13 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 θ23 must depart from its "maximal" value: sin 2 2 θ23 ~ 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 | sin δ CP | ≤ 0.31 if not vanishing altogether.