The main number of free parameters in the Standard Model comes from the Higgs sector. If the many Higgs sector free parameters in SM are ultimately accidental, happening by chance, the ground of this basic modern theory looks vague despite its remarkable predicting power.
Hence, the main goal of SM phenomenology is to find a new idea for organizing the many free parameters in a physically meaningful system.
Luckily, there are hinting experimental indications that the known from geometry euclidean 3-space Metric equation may provide an organizing guide for the Higgs parameters by grouping them in hierarchical triads that appear geometric bimaximal solutions of that equation at leading approximation (arXiv:1212.1417).
This geometric organization of the Higgs sector does not increase the number of parameters; in fact it decreases it by establishing dimensionless relations between them. As result, it frees Higgs sector from the stigma of chance getting the external parameters physically organized in geometric hierarchies governed by the euclidean Metric equation at leading approximation.
Interestingly, geometric interpretation of SM hierarchies may imply new fundamental flavor physics paradigm in the simplest special case of duality between neutrino mixing angles in inner euclidean 3-space and inertially moving flavor neutrino momentum direction angles in outer euclidean 3-space. It may be similar to Einstein’s particle-wave duality in the simplest case of light that led to totally new nonclassical universal physics of quantum mechanics. It seems that the mentioned new ideas in flavor physics deserve attention.
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