The Applications Of Discrete Flavor And Generalized CP In Lepton And Quark Mixing And Model Building

The origin of flavor mixing is one of the most fascinating unsolved problems in particle physics.The precise measurement of neutrino oscillation provides us new win-dow to solve the flavor puzzles.The most popular approach to understand the observed lepton mixing pattern is based on the assumption that a flavor symmetry group?usually finite and nonabelian?is broken down to different subgroups in the charged lepton and neutrino sectors and the mismatch between the two subgroups allows one to predict the lepton mixing matrix up to permutations of rows and columns.We study a second CP symmetry compatible with the A4 flavor group,which in-terchanges the representations 1' and 1".We analyze the lepton mixing patterns arising from the A4 and CP symmetry broken to residual subgroups Z3 and Z2 × CP in the charged lepton and neutrino sectors respectively.TM2 mixing matrix is found,and it predicts maximal atmospheric mixing angle as well as maximal Dirac CP phase,trivial Majorana phases and the correlation sin² ?12 cos2 ?13 = 1/3.We construct a concrete model based on the A4 and the second CP symmetry,the above interesting mixing pat-tern is achieved,the observed charged lepton mass hierarchy is reproduced,and the reactor mixing angle ?13 is of the correct order.From the model independent analysis,TM1,BM2 and BM3'?BM2'?mixing ma-trices can be obtained based on S4 family symmetry and generalised CP symmetry.All the three mixing matrices depend on only one free parameter ? which can take the values from 0 to ?.In all those three mixing patterns,the Dirac CP is conserved or maximally broken while both of the two Majorana CP phases are trivial.We construct two flavor models based on S4 family symmetry and generalised CP symmetry to realize TM1 and BM3'?BM2'?mixing patterns.In the TM1 model,the leading order?LO?lepton mixing is of the tri-bimaximal?TB?form which is broken down to TM1 by the next to leading order?NLO?contributions.In other model,the lepton flavor mixing is the BM pattern at LO and the neutrino mass matrix contains three real parameters such that the absolute neutrino masses are fixed.NLO correction terms of the model break BM mixing pattern to BM3'?BM2'?,The correct mass hierarchy among the charged leptons is achieved.The vacuum alignment and higher order corrections are discussed.We study lepton mixing patterns which can be derived from the A5 family symme-try and generalized CP.We find five phenomenologically interesting mixing patterns for which one column of the PMNS matrix is????the first col-umn of the golden ratio mixing?,????the second column of thegolden ratio mixing?,?1,1,1?T?3 or??5+1,-2,?5-1?T/4.The three lepton mixing angles are determined in terms of a single real parameter ?,and agreement with experimental data can be achieved for certain values of 9.The Dirac CP violating phase is predicted to be trivial or maximal while Majorana phases are trivial.We construct a supersymmetric model based on A5 family symmetry and generalized CP.The lepton mixing is exactly the golden ratio pattern at leading order,and the mixing patterns of case??.3?and case??.4?are reproduced after higher order corrections are considered.We have performed a comprehensive analysis of the type D group D_9n,3n¹as flavor symmetry and the generalized CP symmetry.All possible residual symmetries and their consequences for the prediction of the mixing parameters are studied.We find that only one type of mixing pattern is able to accommodate the measured values of the mixing angles in both "direct" and "variant of semidirect" approaches,and four types of mixing patterns are phenomenologically viable in the "semidirect" approach.The admissible values of the mixing angles as well as CP violating phases are studied in detail for each case.It is remarkable that the first two smallest D9n13n?1?groups with n = 1,2 can fits the experimental data very well.The phenomenological predictions for neutrinoless double beta decay are discussed.We perform a detailed analysis of the group ??6n²?as flavor symmetry and the generalized CP symmetry H_CP in the lepton and quark sector.We discuss all possi-ble independent mixing patterns with the different remnant symmetry Z2 × CP in the charged lepton,neutrino,up quark and down quark sectors.In general only one element of PMNS and CKM matrices is fixed.And the six lepton mixing parameters and four quark mixing parameters depend on two free parameters ?l and ?v?or ?u and ?d for quark sector?which can take the values from 0 to ?.Four types phenomenologically viable lepton mixing patterns and one type phenomenologically viable quark mixing pattern are obtained.The consequences for the prediction of the lepton mixing parameters and the neutrinoless double decay are studied.In quark sector,the admissible values of the mixing angles as well as CP violating phases are studied in detail.We find that the minimum phenomenologically viable n is 69.But the results of n = 7 can be a good leading order approximate.