Lepton flavour violation, Yukawa unification and neutrino masses in supersymmetric unified models

We explore some phenomenological consequences of models based on supersymmetric extensions of the Standard Model. In particular, we focus on the Minimal Supersymmetric Standard Model supplemented by right-handed neutrinos in the context of the Pati-Salam SU(4) x SU(2)L x SU(2)R Grand Unified Theory. We start by analysing the possibility of using Lepton Flavour Violation as a probe of physics beyond the Standard Model. We show that the μ → eγ and τ → μγ decays impose important constraints to the soft supersymmetry breaking parameters of the Pati-Salam model that already allow the formulation of lower bounds for the masses of the lighter supersymmetric particles. Secondly, we investigate how third family Yukawa unification can be used to provide a window into the soft supersymmetry breaking Lagrangian. We show that, a successful top quark mass prediction requires that the supersymmetric corrections to the bottom quark mass are small which, in turn, imposes a distinct hierarchy between the soft breaking parameters. Finally, we explicitly construct a realistic model of quark, charged lepton and neutrino masses and mixing angles, based on the Pati-Salam. gauge group supplemented by an abelian flavour symmetry, that can explain the large atmospheric neutrino mixing angle, suggested by the Super-Kamiokande data, and account for the large mixing angle Mikheyev-Smirnov-Wolfenstein solution to the solar neutrino problem. (author)