Researches On Neutrino Mass And Mixing With Flavor Symmetry

Neutrino oscillation experiments have confirmed that neutrinos have tiny masses and mixings between flavor states with solid evidences, which implies neutrinos would convert into other flavors in propagation.Due to the unaccountability of neutrino masses and mixings in standard model, one has to add new chiral fields or scalars in extended standard model for obtaining non-zero masses. For mixing patterns one often introduces non-Abelian discrete symmetries which can give rise to a neutrino mass matrix with certain symmetries, in its diagonalization we can obtain some mixing patterns that is simple and compatible with experiments. The main topic of this dissertation focuses on the neutrino masses and mixing models with finite non-Abelian discrete symmetry group as flavor symmetry group, which can give rise to TriBiMaximal mixing pattern at leading order, and obtain a sizable reactor mixing angle θ₁₃ with the corrections from charged lepton. Besides we explore the scenarios that can obtain a nonvanishing θ₁₃, and constrain the neutrino Yukawa elements for obtaining the textures as simple as possible which can be realized in specific discrete flavor model. The thesis is organized with the following chapters:Chap.1, Introduction. We first introduce the theories and experiments in the de-velopment of neutrino and weak interaction, and describe the endless contradictions about neutrino. We also outline the fundamental knowledge of neutrinos masses and mixings until nowadays, and present the mass puzzle as well as the flavor puzzle.Chap.2, Neutrino mixing and oscillation. As the fundamental knowledges in neutrino researches, we present the theories of neutrino masses and mixing in detail, and introduce the oscillation behaviour systematically.Firstly we overview the stan-dard model of electroweak unification, including the Lagrangian, the Higgs mechanism which endows the masses of matter and gauge particles and introduce the concept of mixings; then we extend the standard model for obtaining different kinds of the masses and the seesaw mechanism which can explain the smallness of masses. Secondly the parametrization of mixing matrix are briefly discussed, at last we give the standard oscil-lation probabilities in vacuum and matter, and the main types of oscillation experiments as well.Chap.3. Neutrino mixing pattern and discrete flavor symmetry. We overview the main problems in flavor puzzle, then introduce some simple constant mixing patterns which are all bilarge form without θ₁₃。 As an elucidation we show how to construct a flavor model with A4 as flavor group. At leading order we obtain the tribimaximal mixing, and obtain non-zero θ₁₃ at subleading corrections despite of its value is not experimental favored.Chap.4, GUT flavor symmetry model. We combine the flavor group S4 with GUT SU（5） gauge group in order to obtain a desired mass texture and mixing. The specific GUT relation between masses and mixing angle are fulfilled, which arises from the specific Yukawa textures of down-type quark and charged leptons with the constrained CG ratio. The tribimaximal mixing is obtained in neutrino sector at LO. and the adjoint H24 leads to the desired novel CG factors which give rise to a new mass relation between electron and down quark:mc=8md/27, meanwhile the Georgi-Jarlskog relation and bottom-tau unification are retained as well. We also get the quark CKM mixing matrix correctly, and the CKM-like mixing of charged leptons with a mixing angle θ12c size of the Cabibbo angle θC.The final lepton PMNS mixing matrix can give rise to the empirical relation θ₁₃PMNA（?）θC/（?） which is agreement with experiments.Chap.5, Nonvanishing θ₁₃ and Yukawa texture. We explore the possibility to gen-erate a nonvanishing θ₁₃ in neutrino sector, and give two minimal scenarios in flavor basis, which has four texture zeros in pre-diagonal neutrino effective coupling matrix. We classify the constraint conditions on corresponding Yukawa matrix. By solving the constraints and taking specific choice of some parameters, we may obtain a simple Yukawa matrix which can be realized in non-Abelian discrete flavor model. A nonva-nishing θ₁₃ can be achieved by the diagonalization of neutrino mass matrix.Chap.6, Conclusion and Outlook. We give the conclusion of neutrino mass and mixing in flavor problems, and attempt to describe the future development and problems as well as solutions of neutrino.