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st1\:*{behavior:url(#ieooui) } /* 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-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";}              Flavor-Inertia Hierarchy Hypothesis Relates 3 Generations of the SM

                                             to 3 Euclidean Space Dimensions        

    Major problem of the Standard Model of elementary particles is the origin, interrelations and understanding of the many mass and mixing hierarchies still described by free empirical parameters. We observed a semi-empirical universal feature – bimaximal ‘hierarchy-angle’ structure (90, 90, 0)deg at leading approximation of the experimental free flavor parameters - that unites all known mass and mixing hierarchies in the SM. It appears in close analogy with the hierarchy of momentum vector direction angles of an inertial moving particle in Newton mechanics first law. We emphasize that this model independent leading approximation phenomenological analogy requires three generations of elementary particles in the SM. 


    The SM empirical regularities appear simple. At leading approximations (no external parameters) all known SM mass hierarchies turn out to be united by basic universal bimaximal form fi = (90, 90, 0)deg of the ‘mass hierarchy angles fi’ that are naturally defined as cos^2 fi = mi /(m1 + m2 + m3), m3 >> (m1, m2) for all three Dirac particle flavor mass triads - charged leptons and up- and down-quarks. The singled out ‘0’ in those hierarchy-angle triads corresponds to the mentioned three large masses and also the neutrino reactor angle in the SM, on the one hand. On the other hand, at approximation of Newton inertia principle (no external forces, i.e. no free parameters) the direction angles of an inertial moving particle are also of the singled out basic bimaximal form (90, 90, 0) in an inertial frame of reference and physically preferred orthogonal coordinate system with Z-axis parallel to particle momentum vector (the residual symmetry of rotations about the momentum vector is represented by symmetry of the two ‘90’ in the triad of angles). Note that the considered bimaximal triad is an inner solution without free parameters of the euclidean geometry Pythagorean equation for direction-angle cosines and so is trivially fulfilled for an arbitrary translational moving constant vector in an inertial frame of reference. But only particle phenomena, not geometry of solid vectors, may be in analogy with SM hierarchies. In fact, the mechanical inertial particle motion with constant momentum vector in an inertial frame of reference appears the physically meaningful particle phenomenon that is described by proper bimaximal solution for direction angles and is in close analogy with the known SM hierarchies.     

     Essential contents of flavor-inertia hypothesis is that at the outlined leading approximation every known SM flavor hierarchy can be represented in a euclidean 3-space by an inertial moving particle direction angle hierarchy in an inertial frame and orthogonal coordinate system. Expressing in visual form, the singled out large masses of Tau-lepton, Top-quark, Down-quark and neutrino Reactor angle in the SM are in conformity with the singled out by the inertial momentum vector direction in 3-space (zero angle), while the two lower masses in each SM mass triad and the two large neutrino mixing angles are in conformity with the two equal direction angles (90deg angles) in the orthogonal to momentum vector plane. Such conformity is possible only in case of three SM generations.