Society of Mathematicians, Physicists and Astronomers of Slovenia Organizing Committee

We fit the three fine structure constants in the Standard Model (SM) from the assumptions of what we call “Multiple Point Principle” (MPP) [1,2] and “AntiGUT” [3], three fine structure constants with only one essential parameter. By the first assumption wemean that we require coupling constants and mass parameters of the SM to be adjusted by our MPP: to be just so as to make several vacua have the same (zero or approximately zero) cosmological constants. By AntiGUT we refer to our assumption of a more fundamental precursor to the usual Standard Model Group (SMG) consisting of the (Ngen = 3) fold Cartesian product of the usual SMG such that each of the three families of quarks and leptons has its own set of gauge fields. The usual SMG comes about when SMG breaks down to the diagonal subgroup at roughly a factor 10 below the Planck scale. Up to this scale μdiag ≡ μG we assume the absence of new physics of relevance for our results (except heavy right-handed neutrinos). Relative to earlier works where the MPP was used to get predictions for the gauge couplings independently of one another, the point here is to increase accuracy by considering relations between all the gauge couplings (i.e., for U(1), and SU(N) with N=2 or 3) as a function of a N-dependent parameter dN that is characteristic of U(1) and SU(N) groups. In doing this, the parameter dN that initially only takes discrete values corresponding to the N in SU(N) is promoted to being a continuous variable corresponding to fantasy groups for N / ∈ Z. By an appropriate extrapolation in the variable dN to a fantasy group, we consider the β-function for the magnetic coupling squared g̃ which vanishes thereby avoiding the problem of our ignorance of the ratio of the monopole mass scale to the fundamental scale. Compared to the earlier work of this series [4], in the present paper we add a couple of extra assumptions of a rather reasonable technical character. We thereby get one more prediction meaning that we now fit the three couplings with one “slope” parameter. We may interpret our results as being very supportive of the MPP and AntiGUT. 1.