The theoretical description of the Standard Model of Particle Physics (SM) is based on a product of three symmetry group factors, SU(3) × SU(2) × U(1), corresponding to three of the four fundamental interactions. These are the weak, the strong and the electromagnetic interactions. Gravity is not included in the SM. In addition, it describes the elementary fermionic matter in terms of five different representations of that group. For large energies, it can be embedded in a single group with fewer representations for the SM particles in the context of Grand Unified Theories (GUT) like SO(10). Moreover, in the SM the five fermion representations each come in three flavours which differ only by their masses. These as well as the mixing between the different flavours are parametrised by the Yukawa matrices.
In this thesis we present models based on a Pati-Salam (PS) symmetric GUT which generate the Yukawa matrices dynamically. The PS group is only a semi-simple group and thus it does not achieve complete unification. Still, it can be embedded in SO(10). The breaking of PS down to the SM allows for multiple intermediate symmetries at various scales. In the first class of models, we assume complete unification of all three gauge couplings at the GUT scale. Moreover, we restrict ourselves to a setup where all additional fields can be embedded in small representations of SO(10). Finally, we allow all of these fields to appear in three copies similar to the SM fermions. We then study the possible ranges for the intermediate scales.
In the second class of models we focus on the flavour aspects and present two approaches to generate the Yukawa matrices dynamically. In both cases we consider gauged flavour symmetries which are broken by vacuum expectation values of additional scalar flavon’ fields.
In the first approach, the Yukawa matrices are generated using non-renormalisable terms, i.e. allowing for multiple insertions of these flavons. Here, we consider the special case that the SM Higgs field exists in three generations and transforms similarly to the SM fermions under the flavour gauge group. This motivates us to consider also flavon representations being larger than the commonly used fundamental one. We present particular models containing flavons which transform solely in the decuplet or triplet representation, respectively.
In the second approach we introduce additional fermionic fields that communicate the breaking of the flavour symmetry to the SM fermions. These extra fermions violate fundamental properties of the SM such as the pure left-chiral couplings of the weak gauge bosons. We study how large such effects can be and to what extent they may be observable in current or future experiments.