Analytical Unified Particle and Interaction Model

Abstract

The derivation of the Standard Model of Particle Physics (SM) and its validation by intensive experiments is one of the key achievements in physics of the last decades.                                                
However, despite the prediction and discovery of more and more elementary particles, still no analytical particle model describing their energy values, nor a unified interaction model, has been found. Such models could be expected to lead to a next level in understanding and unification in description of Nature.           
As of now, particle energy values for the fermions: leptons, quarks and hadrons, as well as for the bosons, are the result of measurements and stand for themselves isolated. Next to this, there are separate electroweak, strong and gravitation interaction models, while for the latter one still no coherent quantum theory has been found.

In this treatise from deriving a vacuum energy in the Universe and accepted laws for the fundamental interactions, a generic formula with the aim to unify description of interactions is derived. Along with this the Universe appears with a Schwarzschild radius and the Weyl and Dirac Large Number Hypotheses (LNHs) are found to become valid. Moreover, an elementary quantum gravity model is derived, and it is shown that Coulombian/electro interaction can be understood to emerge from quantum gravity.

This is used to build a first version of an analytical Unified Particle and Interaction Model (UPIM) to describe and explore basic particle interaction processes quantitatively based on canonic vacuum energies. Applying the model, I do find a complete match within the current given precision of measured quantities for the fundamental fermions, bosons and interaction processes observed in Nature in line with current data from the Particle Data Group (PDG).

From this, simple formulas for the basic particle energy values are discovered and discussed:                               
First generation quark energies appear as powers of three from canonic vacuum energies.                                 
Rational powers of the ratio between proton and electron mass are found to be related to ratios between these particles and the W-boson mass.  
For the Higgs boson energy canonic vacuum energies in multiples of the number of fundamental fermions are found, as well as a vector-based formula including the W- and Z-boson.                          
Finally, simple formulas linking the natural Planck mass and the mass of the Universe with the canonic vacuum energies for the electroweak, the residual strong and the gravitational interactions are found.