Approximate SU(5), Fine Structure Constants

Abstract

We fit the three finestructure constants of the Standard Model with three, in first approximation theoretically estimable parameters, 1) a "unifiedscale",turning out not equal to the Planck scale and thus only estimable by a very speculative story, 2) a "number of layers" being a priori the number of families, and 3) a unified coupling related to a critical coupling on a lattice. So formally we postdict the three fine structure constants! In the philosophy of our model there is a physically lattice theory with link variables taking values in a (or in the various) "small" representations of the Standard Model Group. We argue for that these representations functio in first approximation as were the theory a genuine $SU(5)$ theory. Next we take into account fluctuation of the gauge fields in the lattice and obtain a correction to the a priori $SU(5)$ approximation, because of course the link fluctuations not corresponding any Standard model Lie algebra, but only to the SU(5), do not exist. The model is a development of our old anti-grand-unification model having as its genuine gauge group, close to fundamental scale, a cross product of the standard model group S(U(3)x U(2)) with itself, there being one Cartesian product factor for each family. In these old works we included the hypotesis of "multiple point criticallity principle" which here effectively means the coupling constants be critical on the lattice. Counted relative to the Higgs scale we suggest the in our sense "unified scale" (where the deviations between the inverse fine structure constants deviate by quantum fluctuations being only from standard model groups, not SU(5)) makes up the 2/3 th power of the Planck scale relative to the Higgs scale, or better the top quark mass scale.