Origin Of Neutrino Masses And Flavor Mixing

The origin of neutrino masses and flavor mixing is always a hot topic in particle physics.With the steady advance of neutrino experiments,the three mixing angles of the lepton sector are accurately measured,the CP phases are also expected to be measured in future neutrino oscillation experiments,which will provide good conditions for further exploration of neutrino flavor physics and neutrino masses.To obtain the model-independent predictions of discrete flavor symmetry for lepton and quark mixing patterns,we perform a systematical and analytical study of lepton mixing which can be derived from the subgroups of SU(3)under the assumption that neutrinos are Dirac particles.We find that type D groups can predict lepton mixing patterns compatible with the experimental data at 3? level.The lepton mixing matrix turns out to be of the trimaximal form,and the Dirac CP violating phase is trivial.Moreover,we extend the flavor symmetry to the quark sector.The Cabibbo mixing between the first two generations of quarks can be generated by type D groups.Moreover,we perform an exhaustive scan over all finite discrete groups up to order 2000 with the help of the computer algebra system GAP.We find that only 90(10)groups for Dirac(Majorana)neutrinos can generate the lepton mixing angles in the experimentally preferred ranges.The lepton mixing matrix is still the trimaximal pattern and the Dirac CP phase remains trivial.The smallest groups that lead to viable mixing angles are[162,10],[162,12]and[162,14].For quark flavor mixing,the correct order of magnitude of the Cabibbo-Kobayashi-Maskawa matrix elements can not be generated.Only the Cabibbo mixing is allowed.The observed Cabibbo mixing angle can easily be accommodated if the first two left-handed quark fields are assigned to a doublet.The groups that can give rise to both phenomenologically viable lepton mixing angles and acceptable Cabibbo angles are discussed.Including the generalized CP symmetry,we have performed a comprehensive scan of leptonic mixing patterns which can be obtained from finite discrete groups with order less than 2000.Both the semidirect approach and its variant are considered.The lepton mixing matrices which can admit a good agreement with experimental data can be or-ganized into eight different categories.These viable mixing patterns can be completely obtained from the discrete flavor groups ?(6n2),D9n,3n(1),A5 and ?(168)combined with CP symmetry.We perform a detailed analytical and numerical analysis for each possi-ble mixing patterns.The resulting predictions for lepton mixing parameter,neutrinoless double decay and flavored leptogenesis are studied.As an example of analytical study of the flavor symmetry with generalized CP,we have performed a comprehensive anal-ysis of the type D group Dgn,3n(1)as flavor symmetry and the generalized CP symmetry.All possible residual symmetries and their consequences for the prediction of the mix-ing parameters are studied.It is remarkable that the first two smallest Dgn,3n(1)groups with n = 1,2 can fits the experimental data very well.In order to naturally generate the Dirac neutrino masses,We perform a systematic study of both dimension five and dimension six effective operators of neutrino masses.We identify all possible realizations of these two operators at tree level and one-loop level.The corresponding predictions for the particle content and neutrino mass ma-trix are presented.The lower order contributions to neutrino masses can be forbidden by introducing soft breaking abelian symmetry or finite non-abelian symmetry.The electrically neutral particle mediating the loop diagram could be dark matter candidate.The possible dark matter candidates and the corresponding constraints on the parameter? are analyzed for each model.The results of our systematic classification provide a series of new models of neutrino masses,providing a more comprehensive reference for people to understand and explore the Dirac neutrino masses.