Büyük birleştirme E6 modelinde yüksüz fermiyonların kütle ve karışımları

The modern theory of elementary particle physics is based on the Standard Model and the symmetry groups in question are Lie groups as far as continous symmetries are considered. The strong, weak and electromagnetic interactions among the elementary particles are associated with the Lie algebras of SU(3)C, SU(2) and U(1) in the Standard Model. There are many reasons not to believe that the Standard Model is a final theory. New physics on which we will concentrate in this thesis is based on the idea of uni fication where three types of known gauge interactions are uni fied at the same very high energy scale by linking the three of the four forces in nature by combining strong and electroweak forces, called the Grand Uni fied Theory (GUT). We here ground on the exceptional E6 group for Grand Uni fication to give the masses and mixing of neutral leptons. We start by giving some algebraic foundations of exceptional groups including division algebras, octonions and quaternions. Then, we focus on E6 model where the fundamental representation 27 include the fermionic content of the model. Then a brief review of the assignment of elementary fermions and bosons to irreducible multiplets in E6 models is followed by a discussion of di fferent, hierarchical symmetry breaking chains from E6 down to SU(3)C x U(1)EM. We fi rst discuss the symmetry breaking pattern for the E6-> SO(10) ->SU(5) x U(2)EW x SU(3)C ->U(1)QED x SU(3)C chain that involves Georgi and Glashow's SU(5) Model. Next we concentrate on the symmetry breaking chain E6 -> SO(10) -> SU(2)L x SU(2)R x SU(4)C -> U(2)EW x SU(3)C -> U(1)EM x SU(3)C with an intermediate Pati-Salam symmetry for which (B - L) is conserved. In particular, the mass/mixing matrix of electrically neutral fermions (i.e.neutrinos) that would be derived from Yukawa couplings is constructed. The pattern of neutrino masses and some bounds on mixing parameters are discussed.