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Abstract
The present work study the role of the discrete symmetries to explain the
mixing in the standard model by assuming discrete symmetries as extension
for the standard model.
Chapter 1 :
It is a review of the basic principles of the standard model, Higgs mechanism
of spontaneous symmetry breaking which is the most familiar way to generate
the masses for the fundamental particles, and a brief description for the
supersymmetry theory in the nature.
Chapter 2 :
In this chapter, the experimental results for the fermion mixing in the stan-
. dard model is presented . The experimental data showed that the mixing in
the lepton sector is maximal mixing while it is very small in the quark sector,
that might stimulate future theoretical investigations.
Chapter 9 :
It is a review of discrete symmetries, will emphasis on A4 discrete group,
SUSY A4 models, bimaximal and tri-bimaximal mixing. Also, we focused
attention on the Altarelli- Ferruccio SUSY model as the basic preliminary
ingredient for the proposed model.
Chapter 4- :
In this chapter, we proposed an extension for Altarelli model to explain the
small mixing in the quark sector and the large hierarchy in the masses of the
quarks by assuming different representation for the quarks without spoiling
the results of Altarelli model. We required the Lagrangian to be invariant
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under the proposed symmetry SU(2)L x U(l)y X A4 x Z3 X U(l)R X U(l)e·
We determined the superpotential Wq which is invariant under the proposed
symmetry. from this superpotential, we calculated the mass matrices M; and
Md. We diagonalized these matrices to find the proper mass ratios and mixing
angles in the quark sector. The obtained results are found to agree with the
corresponding experimental observations. We arrived to the mathematical
justification for the well-known experimental relation between the ratios of
the quark masses and their mixing elements.