Unification and low-energy supersymmetry at one and two-loop orders

The status of coupling constant unification--assuming the validity of the standard model or of its minimal supersymmetric extension at high energies--and of relations between various Yukawa couplings (assuming the supersymmetric extension) which are implied in certain grand-unified theories, are studied in detail. Theoretical uncertainties in the calculations are emphasized, and low-energy constraints and predictions are derived. In particular, we find that bottom-tau unification favors a Higgs boson lighter than 110 GeV. The structure of the vacuum in the model studied is also discussed. Implications of embedding supersymmetric models in grand-unified theories are further explored and are shown to affect the soft supersymmetry breaking mass parameters of the models, and thus the spectrum at low-energy