Phenomenological Constraints on Supersymmetric Grand Unification

The a.im of this thesis is the study of Supersymmetric Grand Unified models (SUSY GUT) from the phenomenologica.l point of view. The present Introduction is an overvievv of the subjects studied, in which the lines of a.pproach followed a.re explained. In the first Chapter the basic theory of supersymmetric models is reviewed. Particula.r attention is devoted to settle a. formalism suited for studying the general supersymmetric theory: derivation of la.grangia.ns, analysis of the qua.ntum structure, renormalisation group equations. This pa.rt can be considered a. sort of ""opera.ting system" for the study of the phenomenology. Then I pass to define the :Minimal Supersymmetric Extension of the Sta.nda.rd l\fodel ( MSSM). I believe tha.t some ea.re is needed to a.How rea.da.bility of the results, a.nd also to a.void misunderstandings. Important formulae for the masses of supersymmetric particles and for their interactions with the standard ones are derived. The third Chapter is devoted to the study of possibility of embedding the MSSlVI in a SUSY GUT, or in other vvords to spelling out the most direct predictions of this kind of models. In this discussion virtues and Yices of the model become apparent. It is noticeable the possibility to predict correctly 0: 8 ~ to address successfully b- T unification (with some proviso), to have a consistent picture of CP violation a.ncl a beautiful mechanism to explain the electroweak breaking; but the difficulty to predict for sure the observation of supersymmetric particles-except for the lightest higgs-in large regions of the parameter space is surely not a. virtue of the model. In fact the key point is how to probe the space of supersymmetric parameters. Important technical tools needed for this aim are discussed. The last Chapter ca.n be considered a. partial answer to the problem of the exploration of the para.meter space, that uses interesting theoretical means and it is in a sense complementary to supersymmetric particle searches. Tvvo processes that a.re forbidden a.t the tree-level in the Standard l\Iodel a.re studied in the context of SUSY GUT: the first (the electric dipole of the neutron) is related to the CP viola.ting sector, the second (the b -+ S/ cleca.y) to the Flavour-Changing Neutral Currents (FCNC) of the theory. vVhile the first test is passed for what matter present da.y phenomenology, the latter is not a.utoma.tically; in fact experimental observations require strong restrictions to the para.meter space of the model, whereas SM, even if with large theoretical uncertainties, fits the data. This is clearly not a failure of the MSSM models, even if the question of a natural explanation of such constraints is in my opinion important. Future theoretical progresses, restricting the para.meter space or giving reasons of the elusiveness of SUSY world, or hopefully experimental findings are eagerly awaited.