Treating Top Differently from Charm and Up*

It now appears phenomenologically that the third family may be essentially different from the first two. Particularly the high value of the top quark mass suggests a special role. In the standard model all three families are treated similarly [becoming exactly the same at asymptotically high energies] so I need to extend the model to accommodate the goal of a really different third family. In this article I describe not one but two such viable extensions, quite different one from another. The first is the 331 model which predicts dileptonic gauge bosons. In the second, using as a flavor symmetry a finite nonabelian dicyclic Q2N group, I show how to derive quark mass matrices with two arrangements of symmetric texture zeros which are phenomenologically viable. Three other such acceptable textures in the recent literature are unattainable in this approach and hence disfavored. I assume massive vector-like fermions and Higgs singlets transforming as judiciously-chosen Q2N doublets and use the tree-level mass generation mechanism of Froggatt and Nielsen. In this presentation, I shall address two extensions of the standard model in which the third family is dealt with asymmetrically with respect to the lightest two. First, I shall describe the 331 Model and elaborate on its predictions including the dilepton, the neutrino masses and tests in hadronic and leptonic colliders. Second, after a review of finite nonabelian groups of order ≤ 31 and the question of their gauging and of their chiral anomalies, model building in that direction is discussed culminating in models based on the dicyclic groups Q2N . 331 Model Family symmetry is usually taken to mean a horizontal symmetry, either global or gauged, under which the three families transform under some non-trivial representation. The family symmetry is broken in order to avoid unobserved mass degeneracies. In this meaning of family symmetries, there is usually no explanation of why there are three families which are the input. Rather the hope is that the postulated family symmetry may explain the observed hierarchies: mu ≪ mc ≪ mt (1) md ≪ mc ≪ mb (2) θ13 < θ23 < θ12 (3) In the present model, the aim of family symmetry is indeed to attempt to address such hierarchies and to explain why there are three families. This may be a necessary first step to understanding hierarchies? To introduce the 331 Model[1] the following are motivating factors: