Approximate Minimal SU(5), Several Fundamental Scales, Fluctuating Lattice

TL;DR

This paper proposes a model where fluctuating lattice link sizes in a grand unified SU(5) framework produce various physical energy scales, explaining their relationships and small deviations in magnetic moments.

Contribution

It introduces a fluctuating lattice model with a log-normal distribution to explain the emergence and relations of multiple fundamental energy scales in SU(5) GUT.

Findings

Good agreement with experimental magnetic moment deviations

Different energy scales arise from lattice link size powers

Log-normal distribution explains scale relationships

Abstract

Having shortly reviewed our idea of the grand unified SU(5) being only exact in a classical limit, in a truly existing lattice, an ontological lattice, we go over to putting a series of different physical energy scales such the approximate unification scale for the SU(5)(without any SUSY), the Planck scale, and e.g. the scale of see-saw neutrino masses into a certain plot showing the energy scales on a straight line. This straight line of this plot supposed to result from such an ontological lattice, that fluctuates in link size a and lattice density in a very strong way according to a log normal distribution. The point is that different energy scales result from the link size of the lattice to different powers, like the averages a to the n th , where the power n depends on the type of scale considered. Since the n th root of the average of the n th power of the link size in the fluctuating lattice is very strongly dependent on the power n, because of very huge fluctuations, the different types of physical energy scales can get very different. With a Galton i.e. log normal distribution of the link size the various energy scales have their logarithms fall into a nice straight line versus the power of the link size, on which they depend. Our model gives a surprisingly good number for the small deviations of the experimental electron-and muon-anomalous magnetic moment from the pure Standard Model value.