A Simple Geometric Framework for Fermion Masses and Mixing

Abstract: The Standard Model (SM) of particle physics requires 19 inputs, including 9 fermion masses and 4 CKM parameters. An extension to this model adds 3 massive neutrinos and 4 PMNS parameters, for a total of 26 inputs. Using a simple geometric framework, the relative masses and mixing angles of fermions were found to arise from the same geometry. Higher fermion generations are proposed to be transformations of the first-generation particle. Masses for neutrinos are predicted via PMNS mixing angles. This framework proposes that the three generations of fermions are one-, two-, and three-dimensional particles. The embedding of lower-dimensional particles into three-dimensional space has implications for foundational physics and provides new possible answers for quantum weirdness, including wave-function collapse and double-slit interference.