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Geometric
Contrast of Quark and Neutrino Mixing Hierarchies
‘Geometric interpretation of Standard Model
hierarchies’ is a prolific research theme in SM semi-empirical phenomenology
arXiv:1212.1417 (updated in ResearchGate). At decisive leading geometric approximation
(benchmark) it confronts particle mixing-angle triads with cube-geometry in
Euclidean 3-space. It
starts a new semi-empirical approach to unification of quark and lepton mixing
hierarchies by including in SM weak interaction phenomenology the distinctive
quark feature of color degree of freedom (formally independent of QCD - just
three symmetric quark colors). Bimaximal neutrino mixing angles are geometrically
represented in the Euclidean 3-space by one edge of a cube as factual particular
solution of the Euclidean Geometry Metric Equation. That is factually an empirically
indicated spontaneous violation of neutrino mixing geometric symmetry. It should be noted that realistic
neutrino mixing angles are small deviations from that benchmark approximation.
At benchmark approximation, the mixing angles
of one color quark are represented by a symmetric superposition of all three
cube edges (cube diagonal) since there is no empirical indications on violation
of quark mixing-angle symmetry at that approximation. This geometric quark symmetry
is needed indeed to get zero mixing benchmark approximation for quark mixing
angles after necessary sum of three quark colors. It should be underlined that that
sum leads to low energy ‘white color’ quark zero mixing angles at benchmark
approximation. Thus
there is a geometric type contrast between one color quark and neutrino mixing
phenomena at the decisive leading approximation – neutrino mixing is related to
violation of geometric cube-symmetry in Euclidean 3-space (represented by one
cube-edge), while one-color quark mixing is related to exact geometric
cube-symmetry in that 3-space represented by cube-diagonal). A particular fundamental paradigm is
lurking behind the experimental data -- flavor-geometric interpretation of the
SM hierarchies 1) connects quark 3-color symmetry in weak interactions with
Euclidean 3-spase geometric symmetry, and 2) unites color quark and neutrino
mixing at the fundamental level and contrast them at the observational level.
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