UC Santa Cruz

In this thesis, we study supersymmetric extensions of the Standard Model and particularly the phenomenological implications arising from discrete and flavor symmetries. Symmetries are frequently added to theories in order to simplify the treatment and to reach phenomenologically viable regions of the parameter space.

At the beginning of the dissertation, an introduction is given on topics that will form the main body of the thesis: we introduce anomalies and instantons, discuss the supersymmetric flavor problem and flavor symmetries, illustrate gravitino interactions and review inflationary cosmology.

After this introductory material, we discuss how imposing constraints such as anomaly freedom or anomaly universality on discrete R-symmetries relies on non-generic assumptions about the high-energy theory. We give examples of string theoretic models where the low-energy anomalies are non-universal and consider the implications of gauge coupling unification.

We then use this insight to reconsider Abelian flavor symmetries that can account for the large hierarchies of the fermion masses and mixings. We describe in detail models without R-parity and determine textures for the R-parity-violating couplings; the consequences for LHC phenomenology are analyzed next. It is concluded that collider bounds are relaxed, especially for squarks.

We continue the study of model of R-parity violation (RPV) by considering Dark Matter candidates in this framework, in particular gravitinos. If lighter than all other superpartners, the gravitino is an unstable, long-lived dark matter candidate. Additionally, this solves some problems with gravitinos interfering with Big Bang Nucleosynthesis.

We study the decay of gravitinos to antideuterons because of the low astrophysical background that this channel offers, and cast upper limits on RPV couplings. Specifically, we explore the consequences of flavor symmetries that set specific RPV textures and are able to constrain the gravitino mass, which is related to the scale of SUSY breaking.

We terminate this dissertation with the study of inflation, in particular hybrid inflation, and show discrete symmetry corrections to the hybrid potential. We are able to set the scale of inflation and all the parameters of the theory depend on the order of the discrete symmetry group.