Bounds on the number of possible Higgs particles using grand unification and exceptional Lie groups

Abstract

The total sum of dimensions of a magnum exceptional Lie symmetry groups hierarchy is 4 α ¯ o = ( 4 ) ( 137 + k o ) ≃ 548 . Dividing this value among the various quantum fields leads to the possibility of an eight degrees of freedom Higgs field. However analyzing the same situation using sub groups of the largest exceptional Lie group leads to the conclusion that we are likely to find three Higgs particles only at the energy scale of the standard model. Consequently five of the eight degrees of freedom are unlikely to materialize as particles at this particular energy scale. This conclusion is reinforced by an entirely different approach based on grand unification analysis which excludes any grand unification using 4HD, i.e. four Higgs doublets. This leaves us with one, two and three Higgs doublets. Noting that a super symmetric standard model with two Higgs doublets gives almost perfect grand unification and that the result agrees with our exceptional Lie symmetry groups analysis, we exclude everything else. The final result is that we expect to find at least three more Higgs particles leading to a total of 66 elementary particles while at a somewhat higher energy, the expected number of 69 particles found using E-infinity theory is obtained.