Weinberg angle, current coupling constant, and mass of particles as properties of culminating-point filters - consequences for particle astrophysics

TL;DR

This paper introduces a novel filter-based geometric framework for particles, deriving fundamental constants and particle properties, and explores implications for particle astrophysics, including dark matter and confinement phenomena.

Contribution

It presents a new culminating-point filter approach uniting particle construction with conformal mappings, deriving key physical constants and predicting new particle classes.

Findings

Calculated Weinberg angle and coupling constants from filter properties.

Restricted the spectrum of massive particles due to model instability.

Predicted new particles such as dark matter candidates and confinons.

Abstract

Culminating-point filter construction for particle points is distinguished from torus construction for wave functions in the tangent objects of their neighborhoods. Both constructions are not united by a general manifold diffeomorphism, but are united by a map of a hidden conformal $S^{1}\times S^{3}$ charge with harmonic (Maxwell) potentials into a physical space formed by culminating points, tangent objects, and Feynman connections. The particles are obtained from three classes of eigensolutions of the homogeneous potential equations on $S^{1}\times S^{3}$. The map of the $u(2)$ invariant vector fields into the Dirac phase factors of the connections yields the electro-weak Lagrangian with explicit mass operators for the massive leptons. The spectrum of massive particles is restricted by the small, manageable number of eigensolution classes and an instability of the model for higher mass values. This instability also defines the huge numbers of filter elements needed for the culminating points. Weinberg angle, current coupling constant, and lepton masses are calculated or estimated from the renormalization of filter properties. Consequences for particle astrophysics follow, on the one hand, from the restriction of particle classes and, on the other hand, from the suggestion of new particles from the three classes e.g. of dark matter, of a confinon for the hadrons, and of a prebaryon. Definitely excluded are e.g. SUSY constructions, Higgs particles, and a quark gluon plasma: three-piece phenoma from the confinons are always present.