Mass matrices of quarks and neutrinos

Shao-Hsuan Chiu, Purdue University

Abstract

The correlation between masses and mixings for quarks and neutrinos constructs the main theme of this thesis. To search for physically allowed textures of the quark mass matrices, a complete and systematic analysis of hermitian, hierarchical quark mass matrices with four texture zeros is provided. Using triangular mass matrices, each pattern of texture zeros is readily shown to lead to a definite relation between the CKM mixing parameters and the quark masses. Nineteen pairs of up and down mass matrices are found to be consistent with present data, while one other is marginally acceptable. In particular, no parallel structure between the up and down mass matrices is found to be favored by current data. For the neutrinos, due to recent atmospheric neutrino experiments which imply nearly maximal mixing in the neutrino sector, an important theoretical problem is how the seesaw model for neutrinos can generate large mixing angles. To this end, the mathematical structure of the seesaw model is studied. For two flavors, the seesaw matrix can be identified as a two dimensional representation of the Lorentz group. This analogy facilitates the computation of physical neutrino parameters, while giving an intuitive understanding to the results of the seesaw model. It is found that the induced mixing angle exhibits resonance behavior. For maximal mixing, a precise relation among the right-handed mixing angle, the Majorana mass ratio, and the phase is derived.

Degree

Ph.D.

Advisors

Kuo, Purdue University.

Subject Area

Particle physics

COinS