Fractal Representation of Composite Elementary Fermions with Positive and Negative Mass Components

Abstract

The Fractal Rings And Composite Elementary Particles (FRACEP) Model provides an alternate view to the elementary fermion picture. FRACEP represents a dual universe where there are equal amounts of positive and negative matter (mass). Its dual universe construction allows for composite particles of mixed (positive and negative) mass with fractal-based components. The fractal dimension of these composite particles is D = ~1.55, and is consistent with other estimates of D for the elementary fermions and other fractal-based composite models. Initial efforts developed an empirically-based two-parameter fit for the mass hierarchy formula, relating the fractal dimension to the composite particle masses. The formula predicts the cross-family (first-generation particles) masses, and the intra-family masses (the three generations within each family). The mass predictions for the structure-based composite particles, as well as, the mass hierarchy are consistent with the Particle Data Group’s 2016/2020-update estimates for the elementary fermions.