An Investigation of the Trinification Scalar Sector at One Loop

Abstract: Throughout this work we investigate a trinification-based grand unification theory (GUT) with a global family symmetry, as a radiative origin of the Standard Model (SM). We show that after spontaneous symmetry breaking of the trinification gauge group, we can in theory construct an effective left-right symmetric model (LRSM) which breaks to the SM gauge group through radiative breaking induced by the running of the model’s parameters. We further argue that a low-energy limit of this effective LRSM can accommodate a realistic SM quark mass hierarchy and Cabibbo mixing. Upon close consideration, however, we show that we cannot impose a tree-level scalar mass hierarchy at the GUT scale significant enough to justify the effective LRSM as a physically viable low-energy limit of the trinification model. Thus, we compute the full one-loop scalar mass spectrum using the effective potential approach, and search for parameter space points for which such a hierarchy can be imposed at one loop. Upon implementation of a preliminary random scanning algorithm, no such parameter space points are found, and we conclude that more advanced scanning techniques are needed in future studies, and/or additional scalars should be kept in the effective theory.