Derivation of the Sum-of-Squares Relationship

Abstract

The sum-of-squares relationship connects the square of elementary particle masses to the square of the Fermi scale. It constrains the spectrum of free parameters in the Standard Model (SM) and it suggests a straightforward resolution to the hierarchy problem. Here we show that this relationship follows from the minimal fractal structure of spacetime near the Fermi scale and supports the view that Dark Matter behaves as long-range multifractal replica of the SM.