Title:

Fermion masses and partially conserved chiral symmetries

This thesis addresses one of the outstanding questions of modern theoretical particle physics: what underlies the fermion mass and quark mixing hierarchies? All fermions (except the top quark) have masses which are suppressed to varying degrees relative to their natural scale, which is set by electroweak symmetry breaking. Most models, including the Standard Model (SM), attribute this to a hierarchy amongst fundamental Yukawa couplings. Here, the view is taken that partially conserved chiral symmetries provide a much more satisfactory rationale for suppressed fermion masses, and the fermion mass sector of promising models is analysed. Firstly, Chapter 1 discusses relevant aspects of the SM and some popular Standard Model Group (SMG) extensions. In Chapter 2, a classification scheme is introduced for SMG extensions which possess no nonSM fermions in the low energy regime. This classification is based on the manner in which fermion irreducible representations (IRs) of the SM are collected to form IRs of these extensions. It is argued that the class of extensions whose members' IRs are identical to those of the SM show most promise of naturally generating the fermion mass hierarchy. The SMG is seen to be embedded within these extensions as a diagonal subgroup and, consequently, the nonabehan part of each extension must be gauged. Assuming that all abelian symmetries are also gauged, the anomalyfree members of this favoured class are discussed. They are seen to be closely related to the antigrand unified group SMG X SMG X SMG. For this group, corresponding Weyl fermions in different generations belong to inequivalent IRs. Chapter 3 begins by taking some time out to emphasise that the whole approach to fermion masses and quark mixing angles in this thesis is geared towards accounting for them order of magnitudewise. It then becomes more quantitative in specifying how various approximately conserved symmetries suppress fermion mass matrix elements, and several plausible ansatze for constructing these elements are introduced. Finally, the existence of the large intergeneration mass gaps points towards particular candidate symmetries before the intrageneration gaps are seen to lead in two quite different directions. One of these directions is examined in Chapter 4, where the candidate symmetries of the previous chapter are extended to include a partially conserved and gauged abelian flavoiir symmetry. This is done in order to directly account for mass splitting within the generations, assuming that the heavy generation mass eigenstates are approximately equal to the corresponding gauge eigenstates (a welldefined concept for the type of groups under consideration). Unfortunately, the full symmetry group cannot then include SMG X SMG X SMG, but only a subgroup of it. Several anomalyfree flavour charge sets are found for each model, subject to some basic constraints. The resulting models are then analysed using the ansatze of Chapter 3, following a general discussion of how the ansatze parameters are chosen to fit the known data on fermion masses and quark mixing angles. Finally, Chapter 5 examines the alternative method of obtaining intrageneration mass splitting. This is based on the hope that the abelian subgroup of the antigrand unified group SMG x SMG X SMG might itself be responsible for such splitting, providing the assumption of Chapter 4 regarding the heavy generation mass eigenstates is explicitly violated. The mass gaps thus generated turn out to be unrealistic, however, and again a gauged abelian flavour symmetry is introduced in an effort to rescue the antigrand unified model. The resulting SMG X SMG X SMG X U(1) model is then analysed in exactly the same way as the models of Chapter 4.
