Triangular textures for quark and lepton mass matrices

Sadek Wagdy Mansour, Purdue University

Abstract

The purpose of this dissertation is to present a comprehensive analysis of the quark and lepton mass matrices that are allowable by present data. It is found that the hierarchical nature of quark masses and their small mixing angles lead to a simple upper triangular form for both the up and down type quark mass matrices. This form has the advantage of eliminating all the unphysical content of the mass matrices. The unphysical parameters usually appear in the study of mass matrices due to the freedom in rotating the right-handed quark fields. Moreover, tine matrix elements of the triangular form are all written in terms of simple ratios of quark masses and mixing parameters. It is shown that every physical viable pair of the up and down type quark mass matrices can always be reduced to one of ten triangular patterns which are listed explicitly. The predictions for the CP violating parameters are calculated for each pattern. Using this parametrization, an analysis of hermitian matrices with five texture zeros is performed. Also, a systematic way of deriving the analytic predictions for the relations between quark masses and mixing parameters is presented. This enables us to derive new analytic predictions for some new textures. It is found, for example, that only one viable hermitian pair with five texture zeros is in good agreement with present experimental data. The application of triangular forms to the neutrino sector allows for an analysis of the Majorana sector for neutrinos. In the see-saw scenario, neutrinos exhibit two types of mass terms, Dirac and Majorana, each described by a 3 x 3 matrix. They combine to form an effective mass matrix which describes the observable neutrino properties and can be compared with data coming from the different experiments studying the phenomenon of neutrino oscillations. In GUT SO(10) theories, the Dirac mass matrix mD is analogous to the up-quark mass matrix and therefore the assumption for small mixings and large mass hierarchies can be utilized. The result of this study is that in order to obtain the observed large mixings in the neutrino sector one needs a large hierarchy in the Majorana sector.

Degree

Ph.D.

Advisors

Kuo, Purdue University.

Subject Area

Particle physics

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