Standard Model Couplings with $α^{-1}=137 \pm 9$ from Multiple Point Criticality and 3 Generations of Gauge Bosons: No GUT, No SUSY

Abstract

We consider the application of the Multiple Point Criticality Principle to the Standard Model and its extension to the anti-grand gauge group $SMG^3 \otimes U(1)_f$ at the Planck scale. In particular we discuss the predictions for the fine structure constants: $α^{-1}(0) = 137 \pm 9$, $α^{-1}_{1}(M_Z) =99 \pm 5$, $α^{-1}_{2}(M_Z) =29 \pm 6$, $α^{-1}_{3}(M_Z) =12 \pm 6$. We also present our Standard Model predictions for the top quark and Higgs masses and a $SMG^3 \otimes U(1)_f$ fit of the quark-lepton masses and mixing angles. We characterise $SMG^3 \otimes U(1)_f$ as the largest possible extension of the Standard Model gauge group satisfying some relatively simple assumptions. The resolution of some other fine-tuning problems ($Λ_{cosmological}$, $Θ_{QCD}$, $M_{Higgs}$) by the multiple point requirement of degenerate vacua is briefly discussed.