E-eight exceptional Lie groups, Fibonacci lattices and the standard model

This short paper is intended to disclose a most interesting connection between the roots system of the exceptional Lie groups family and the standard model. First an accurate correspondence is found between the roots number of the different groups and the various sections of the mass-spectrum of the standard model and beyond. Second it is shown that the exact gauging of the renormalization group equation is not a logarithmic but rather a fractal scaling related to the geometrical mean of exceptional Lie group family or a Fibonacci line describing the extended standard model. This family may be approximated by (α¯0)(φ3)=32.3606399 as an average where α¯0=137.082033989 is the E-infinity exact value for the inverse fine structure constant and φ=(5-1)/2.