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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.
