Quantum Numbers of AGUT Higgs Fields from the Quark-Lepton Spectrum

Abstract

A series of Higgs field quantum numbers in the anti-grand unification model, based on the gauge group $SMG^3 \times U(1)_f$, is tested against the spectrum of quark and lepton masses and mixing angles. A more precise formulation of the statement that the couplings are assumed of order unity is given. It is found that the corrections coming from this more precise assumption do not contain factors of order of the number of colours, $N_c= 3$, as one could have feared. We also include a combinatorial correction factor, taking account of the distinct internal orderings within the chain Feynman diagrams in our statistical estimates. Strictly speaking our model predicts that the uncertainty in its predictions and thus the accuracy of our fits should be $\pm 60\%$. Many of the best fitting quantum numbers give a higher accuracy fit to the masses and mixing angles, although within the expected fluctuations in a $χ^2$. This means that our fit is as good as it can possibly be.