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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.      Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman",serif;}