Geometric Interpretation of Standard Model Hierarchies and Zero Neutrino Mass Scale

TL;DR

This paper proposes a geometric interpretation of Standard Model hierarchies, linking particle masses and mixing angles to Euclidean 3-space geometry, and explores the zero neutrino mass scale hypothesis with specific mass values.

Contribution

It introduces a novel geometric framework connecting SM hierarchies to Euclidean 3-space and discusses implications for neutrino masses and mixing angles.

Findings

Hierarchies linked to Euclidean 3-space geometry

Explanation of large and small SM particle masses

Analysis supporting zero neutrino mass scale hypothesis

Abstract

Numerous confirmations may indicate that, besides the problem of Higgs sector many external parameters, the Standard Model is a complete low energy particle interaction theory not crying for new physics. But there are serious problems with understanding flavor in SM phenomenology. Firstly, equal number 3 of SM particle generations coincide with the dimension number of outer euclidean 3-space and secondly, the factual SM particle mass and mixing hierarchies at leading approximation appear solutions of the Metric equation for unit vector direction angles in euclidean 3-space geometry. The power of the Metric equation in hierarchy phenomenology is visualized by explanation of the outstanding in the SM large empirical Tau-lepton, Top-quark, Bottom-quark masses and small neutrino Reactor mixing angle. New in the SM weak interactions particle color degree of freedom (3 quark colors and 1 lepton color) appears appropriate for representing quark and neutrino mixing angle unity at basic level and substantial difference at the observational level. Based on suggested by data idea of zero neutrino mass scale, absolute neutrino masses m1 = 0, m2 = 0.009 eV, m3 = 0.05 eV are analyzed. They are related to the neutrino mixing angles and are of the same hierarchy type that the known Dirac mass patterns of charged leptons and quarks.