Flavor Symmetry And Flavor Mixing Of Quarks And Leptons

The origin of fermion flavor mixing has always been a very important issue in particle physics.We have studied three schemes to explain quark and lepton mixing patterns from discrete flavor symmetry in combination with generalized CP symmetry.In the first scenario,the flavor and CP symmetry are broken to the residual groups of the structure Z2×CP in the charged lepton(up-type quark)and neutrino(down-type quark)sectors.The resulting lepton(quark)mixing matrices depend on two free parameters?l and ?v(?u and ?d).The second approach is based on the residual symmetry Z2 in the charged lepton(up-type quark)sector and Z2 × CP in the neutrino(down-type quark)sector.All lepton(quark)mixing angles and CP violation phases depend on three real parameters ?l,?l and ?v.The third approach has an abelian subgroup and a single CP transformation as residual symmetries of the charged lepton(up-type quark)and neutrino(down-type quark)sectors respectively.The lepton(quark)mixing would be determined up to a real orthogonal matrix wit three free parameters ?1,2,3.In order to explain the observed result of quark and lepton mixing,we comprehensively study the mixing patterns which can be derived from the flavor group S4,?(6n2)and Dn in combination with CP symmetry.The analysis results are model independent.From S4,we can get viable lepton mixing mode,and only a leading order approximations can be obtained in the quark part.We find ?(294)combined with CP can give a good fit to the experimental data of quark and lepton mixing in all of three approaches.A unified description of the observed structure of the quark and lepton mixing can be achieved if the flavor group Dn and CP are broken to Z2 × CP in all sectors,and the minimal group is D14.Following the second approach,D7 can give the experimentally favored values of CKM and PMNS mixing matrices.To understand the origin of flavor symmetry,we discuss the relation between fla-vor and modular symmetry.In the modular symmetry approach to fermion models,the flavor symmetry emerges as a finite subgroup ?N of the modular symmetry,broken by the vacuum expectation value(VEV)of a modulus field ?.If the VEV of the modulus? takes some special value,a residual subgroup of ?N would be preserved.We derive the fixed points(?)in the fundamental domain.We then generalise these fixed points to all of fixed points in the upper half complex plane.Focussing on ?4?S4,we consider all the resulting triplet modular forms at these fixed points.We then apply the results to lepton mixing,with different residual subgroups in the charged lepton sector and each of the right-handed neutrinos sectors.In the case of two right-handed neutrinos,we find three phenomeno-logically viable cases in which the light neutrino mass matrix only depends on three free parameters,and the lepton mixing takes the trimaximal TM1 pattern for two exam-ples.We then generalize the results to examples with three right-handed neutrinos,also considering the level N=3 case,corresponding to A4 flavor symmetry.We further discuss the application of homogeneous finite modular group ?'N in quark model.We find that the structure of modular forms can naturally generate texture zeros of the fermion mass matrices if we properly assign the representations and weights of the matter fields under the modular group.We perform a comprehensive analysis for the ?'3?T' modular symmetry.we find six possible texture zeros structures of quark mass matrix.We present five benchmark quark models which can produce very good fit to the experimental data.These quark models are further extended to include lepton sector,the resulting models can give a unified description of both quark and lepton masses and flavor mixing simultaneously although they contain less number of free parameters than the observables.In order to solve the mass hiearchy and flavor mixing problems of fermions,we propose a realistic theory of fermion masses and mixings using a five-dimensional warped scenario in combination with flavor symmetry.All fermions propagate in the bulk and the Higgs field is localized on the IR brane.The assumed T' flavor symmetry is broken on the branes by flavon fields,providing a consistent scenario where fermion mass hierarchies arise from adequate choices of the bulk mass parameters,while quark and lepton mixing angles are restricted by the family symmetry.Neutrino mass split-tings,mixing parameters and the Dirac CP phase all arise from the type-I seesaw mech-anism and are tightly correlated,leading to predictions for the neutrino oscillation pa-rameters,as well as neutrioless double beta decay rates.The scheme also provides a good global description of flavor observables in the quark sector.