A CRITICAL STUDY OF TWO PATI-SALAM MODELS

Abstract

One of the open questions in the Standard Model (SM) is what the origin for the mass hierarchy and mixing of fermions is. This is the so called "flavor problem", it arises because in the lagrangian of the Standard Model the masses and mixing angles of fermions are completely arbitrary, their values are explained by ad hoc Yukawa couplings to fit the experimental data without giving a theoretical motivation that makes us able to understand such numbers. A possible way to solve this problem is to use flavour symmetries and/or symmetries like GUT and/or of partial unification, like Pati-Salam models, in order to decrease the number of free parameters in the models. This thesis is dedicated to the analytical study of two Pati-Salam models of partial unification based on the gauge group SU(4) ⊗ SU(2)L ⊗ SU(2)R, where the leptons and quarks belong to the same representations (4, 2, 1) and (4, 1, 2). The target of this study is to see whether these two models are able to reproduce the recent values of the masses of the fermions and their mixings (CKM and PMNS matrices), or they have to be ruled out. The two models, considered in this work, differ from each other because of the choice of the scalar multiplets, therefore also the scalar potentials and the Yukawa interactions in the Lagrangians will differ. As first consequence of this we will have that: while in the first model the only existing tree level fermion masses are those for some Beyond SM neutrinos, the second model provides, a tree level mass for each fermion. Beside this difference, in order to compare in a fair way these two models, we demand, for both, the existence of massive sterile neutrinos and the equality, at the partial-unification scale, of the gauge couplings of the groups SU(2)L and SU(2)R. The common features of the two models is the fact that the hierarchy between the fermion masses will come from loop corrections. Therefore we will study how these corrections come out and in which form, trying to understand, by means of computer analysis, which is the best model to describe the current experimental data. The final result are: the first model is able to generate all the quark and charged lepton masses with a good agreement with the experimental values, but not for the neutrino masses and the mixings of the CKM and PMNS matrices; the second model, although it can generates a good mass spectrum for the up-type quarks by means of the one-loop corrections, mantains approximately valid the tree-level identity me = md, for all the three fermion families.