Phenomenological Model for Unified Representation of Fundamental Particle Masses

A geometric representation of the (N = 279) masses of quarks, leptons, hadrons and gauge bosons was introduced by employing a Riemann Sphere facilitating the interpretation of the N masses in terms of a single particle, the Masson, which might be in one of the N eigen-states. Geometrically, its mass is the radius of the Riemann Sphere. Dynamically, its derived mass is near the mass of the nucleon regardless of whether it is determined from all N particles or only the hadrons, the mesons or the baryons separately. Ignoring all the other properties of these particles, it is shown that the eigen-values, the polar representation (θν) of the masses on the Sphere, satisfy the symmetry θν + θN+1−ν = π within less that 1% relative error. These pair correlations include the pairs θγ +θtop ' π and θgluon+θH ' π as well as pairing the weak gauge bosons with the three neutrinos. The eigen-values form 6 clusters that are reflective of a ”Periodic” Chart of the Particles. A function was established whose zeros were a good approximation to the masses (θν). A Regge analysis for missing masses was carried out and some uses for particle fusion reactions were considered including energy production. It was shown that there are very few particles with spin (J) larger than 1 + θ.