An exactly solvable Quantum Field Theory (QFT) model of Lee-type is constructed to study how neutrino flavor eigenstates are created through interactions and how the localization properties of neutrinos follows from the parent particle that decays. The two-particle states formed by the neutrino and the accompanying charged lepton can be calculated exactly as well as their creation probabilities. We can show that the coherent creation of neutrino flavor eigenstates follows from the common negligible contribution of neutrino masses to their creation probabilities. On the other hand, it is shown that it is not possible to associate a well defined "flavor" to mixed states of charged leptons.
We point out a generic correlation between the Friedberg-Lee symmetry of quark mass operators and the vanishing of quark masses. We make phenomenological explorations on two textures of quark mass matrices with the broken Friedberg-Lee symmetry. We present a new pattern of quark mass matrices in agreement with current experimental data. Both analytical and numerical results of our calculations are discussed in detail.
Recently an extension of the standard model (the Lee-Wick standard model) based on ideas of Lee and Wick (LW) was introduced. It does not contain quadratic divergences in the Higgs mass and hence solves the hierarchy puzzle. The LW-standard model contains new heavy LW-resonances at the TeV scale that decay to ordinary particles. In this paper we examine in more detail the flavor structure of the theory. We integrate out the heavy LW-fermions at tree level and find that this induces flavor changing Z boson couplings. However, these flavor changing neutral currents are acceptably small since the…
We consider the Friedberg-Lee symmetry for the quark sector and show that the symmetry closely relates to both quark masses and mixing angles. We also extend our scheme to the fourth generation quark model and find the relation $|V_{tb^{'}}| \simeq |V_{t^{'}b}| \simeq m_b/m_{b^{'}}< λ^2$ with $λ\simeq0.22$ for $m_b=4.2\ \gev$ and $m_{b^{'}}>199\ \gev$.
We investigate the Friedberg-Lee (FL) symmetry and its promotion to include the $μ- τ$ symmetry, and call that the twisted FL symmetry.Based on the twisted FL symmetry, two possible schemes are presented toward the realistic neutrino mass spectrum and the tri-bimaximal mixing.In the first scheme, we suggest the semi-uniform translation of the FL symmetry.The second one is based on the $S_3$ permutation family symmetry.The breaking terms, which are twisted FL symmetric, are introduced.Some viable models in each scheme are also presented.
In this letter, we put forward a special neutrino mass matrix which is invariant under a modified Friedberg-Lee (FL) transformation $ν^{}_e \to ν^{}_e-2θ$ and $ν^{}_{μ, τ} \to ν^{}_{μ, τ}+θ$ with $θ$ being a space-time independent element of the Grassmann algebra. Compared to the original FL symmetry (with the transformation $ν^{}_{e, μ, τ} \to ν^{}_{e, μ, τ}+θ$) which results in the TM2 neutrino mixing, the modified FL symmetry will lead us to the TM1 mixing which has a better agreement with the experimental results. While the original FL symmetry has to be broken in order to produce a realis…
The inverse seesaw mechanism with three pairs of gauge-singlet neutrinos offers a natural interpretation of the tiny masses of three active neutrinos at the TeV scale. We combine this picture with the newly-proposed Friedberg-Lee (FL) symmetry in order to understand the observed pattern of neutrino mixing. We show that the FL symmetry requires only two pairs of the gauge-singlet neutrinos to be massive, implying that one active neutrino must be massless. We propose a phenomenological ansatz with broken FL symmetry and exact μ-τsymmetry in the gauge-singlet neutrino sector and obtain the tri-bi…
I argue that the observed flavor structures of leptons and quarks might imply the existence of certain flavor symmetries. The latter should be a good starting point to build realistic models towards deeper understanding of the fermion mass spectra and flavor mixing patterns. The μ-τpermutation symmetry serves for such an example to interpret the almost maximal atmospheric neutrino mixing angle (θ_23 \sim 45^\circ) and the strongly suppressed CHOOZ neutrino mixing angle (θ_13 < 10^\circ). In this talk I like to highlight a new kind of flavor symmetry, the Friedberg-Lee symmetry, for the effecti…
We propose a neutrino mass model with $μτ$-flavored CP symmetry, where the effective light neutrino Lagrangian enjoys an additional invariance under a Friedberg-Lee (FL) transformation on the left-handed flavor neutrino fields, that leads to a highly predictive and testable scenario. While both types of the light neutrino mass ordering, i.e., Normal Ordering (NO) as well as the Inverted Ordering (IO) are allowed, the absolute scale of neutrino masses is fixed by the vanishing determinant of light Majorana neutrino mass matrix $M_ν$. We show that for both types of mass ordering, whilst the atmo…
We show that a special type of colliding 7-brane configuration of a codimension-two singularity realizes not only a six-dimensional spectrum with exactly the same quantum numbers as that of the three-generation E7/(SU(5) x U(1)^3) coset family unification model, but also the three sets of nonchiral singlet pairs with precisely the correct U(1) charges needed for explaining the Yukawa hierarchies and large lepton-flavor mixings in a well-known seesaw scenario.
In analogy to the mixing pattern of the pseudoscalar mesons in QCD we discuss the mixing of massive neutrinos. Unlike the quarks flavor mixing angles the leptonic mixing angles are large, nearly maximal. The three massive neutrinos are nearly degenerate.
We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the FL symmetry spontaneously. We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via see-saw mechanism. If the right-handed neutrinos transform non-trivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale see-saw mechanism. Second, we pres…
We discuss the existence of a non-abelian gauge structure associated with flavor mixing. In the specific case of two flavor mixing of Dirac neutrino fields, we show that this reformulation allows to define flavor neutrino states which preserve the Poincaré structure. Phenomenological consequences of our analysis are explored.
Flavor mixing and the quark mass spectrum are intimately related. In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One particular interesting way to describe the flavor mixing emerges, which is particularly suited for models of quark mass matrices based on flavor symmetries. We conclude that the unitarity triangle important for $B$ physics should be close to or identical to a rectangular triangle. $CP$ violation is maximal in this sense.
This dissertation investigates the flavor mixing effects in supersymmetric models on electroweak precision observables, Higgs boson mass predictions, B-physics observables, quark flavor violating Higgs decays, lepton flavor violating charged lepton decays and lepton flavor violating Higgs decays. The flavor mixing effects are studied in model independent way i.e. by putting off-diagonal entries in the sfermion mass matrix by hand as well as in the minimal flavor violating constrained MSSM, where mixing can originate from CKM matrix in the case of squarks and from PMNS matrix in the case of sle…
Recent atmospheric neutrino data at Super-Kamiokande suggest the large flavor mixing of neutrinos. Models for the lepton mass matrix, which give the near-maximal flavor mixing, are discussed in the three family model. Especially, details of the models with the $S_3$ or O(3) flavor symmetry are studied.
The overall characteristics of the solar and atmospheric neutrino oscillation are approximately consistent with a tribimaximal form of the mixing matrix $U$ of the lepton sector. Exact tribimaximal mixing leads to $θ_{13}=0$. However, recent results from Daya Bay and RENO experiments have established a nonzero value for $θ_{13}$. Keeping the leading behavior of $U$ as tribimaximal, we use a generalized Fridberg-Lee neutrino mass model along with a complementary ansatz to incorporate a nonzero $θ_{13}$ along with CP violation. We generalize this model in two stages: In the first stage we assume…
An origin of flavor mixings in quark and lepton sectors is still a mystery, and a structure of the flavor mixings in lepton sector seems completely different from that of quark sector. In this letter, we point out that the flavor mixing angles in quark and lepton sectors could be unified at a high energy scale, when neutrinos are degenerate. It means that a minimal flavor violation at a high energy scale can induce a rich variety of flavor mixings in quark and lepton sectors at a low energy scale through quantum corrections.
Recent atmospheric neutrino data at Super-Kamiokande suggest the near-maximal flavor mixing. Models for the lepton mass matrix, which give the near-maximal flavor mixing, are discussed in this report. Mass matrix models are classified according to the mechanism providing the large flavor mixing, and those are reviewed briefly. "Naturalness" of the mass matrix is also discussed in order to select the neutrino mass matrix. Details of the mass matrix with the $S_3$ flavor symmetry are presented.
In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles it is argued that the description of flavor mixing must take this into account. One particular interesting way to describe the flavor mixing, which, however, is not the one used today, emerges, which is best suited for models of quark mass matrices based on flavor symmetries. We conclude that the unitarity triangle important for $B$ physics should be close to or identical to a rectangular triangle. CP violation is maximal in this sense.
The phenomenology of flavor mixing of heavy Majorana neutrinos is studied. The physical degrees of freedom, which propagate like free particles until they decay in the presence of flavor mixing, are identified by diagonalizing the resummed propagator. It is shown that they should be interpreted as quasiparticles which lose Majorana nature.
It is shown that the hierarchical structure of the quark mass terms in the standard model suggests a new description of the flavor mixing. The latter is primarily a heavy quark mixing involving the t and b quarks, followed by a mixing exclusively in the u-channel or the d-channel. The complex phase describing CP violation arises only in the light quark sector. The Cabibbo angle is not a basic parameter, but results as a superposition of both the u-channel and d-channel mixing terms. The new description has a number of significant advantages in comparison with all descriptions previously used. …
We carry out a systematic analysis of flavor mixing and CP violation in the conceptually interesting limit where two quarks or leptons of the same charge are degenerate in mass. We pay some particular attention to the impact of neutrino mass degeneracy and Majorana phase degeneracy on the lepton flavor mixing matrix.
In view of the observed strong hierarchy of the quark and lepton masses and of the flavor mixing angles, it is argued that the description of flavor mixing must take this into account. One particularly interesting way to describe the flavor mixing, which, however, is not the one used today, emerges, which is particularly suited for models of quark mass matrices based on flavor symmetries. We conclude that the unitarity triangle important for B physics should be close to or identical to a rectangular triangle. CP violation is maximal in this sense.
We consider the effects of Planck scale on four flavour neutrino mixings. The gravational interaction at $M_{x}=M_{\rm planck}$, we find that for degenerate neurino mass order, the Planck scale effects changes the mixing angle $θ'_{23}$, $θ'_{12}$ values and $θ'_{13}$, $θ'_{14}$, $θ'_{34}$, $θ'_{24}$ are unchanged above the GUT scale. In this paper, we study neutrino mixing in four flavor above the GUT scale.
The mixing between third and second (or first) generation squarks is very small in supersymmetric models with minimal flavor violation such as gauge-, anomaly- or gaugino-mediation. An opportunity to measure this mixing will arise if the lightest stop is close enough in mass to the lightest neutralino, so that the decays into third generation quarks are kinematically forbidden. We analyze under which circumstances it might become possible to measure at the Large Hadron Collider (LHC) the rate of the flavor changing stop decays.
We revisit the flavor composition of high-energy astrophysical neutrinos observed at neutrino telescopes. Assuming unitary time evolution of the neutrino flavor states, the flavor composition observable at Earth is related to the initial composition at their sources via oscillation-averaged flavor transitions. In a previous study we derived general bounds on the flavor composition of TeV-PeV astrophysical neutrinos assuming three-flavor unitary mixing. We extend these bounds to the case of active-sterile neutrino mixing. Our bounds are analytical, derived based only on the unitarity of the mix…
There are experimental indications of large flavor mixing between $ν_{μ}$ and $ν_τ$. In the unification models, in which the massless sector includes extra particles beyond the standard model, there possibly appear the mixings between quarks (leptons) and the extra particles. When large mixings occur, lepton flavor mixings can be quite different from quark flavor mixings. By taking the string inspired $SU(6) \times SU(2)_R$ model with global flavor symmetries, we obtain the neutrino flavor mixing $\sin θ_{23} \simeq λ= \sin θ_C$ around the unification scale. It can be expected that due to larg…
New physics at high energy scale often contributes to K-\bar K and D-\bar D mixings in an approximately SU(2)_L invariant way. In such a case, the combination of measurements in these two systems is particularly powerful. The resulting constraints can be expressed in terms of misalignments and flavor splittings.
The fact that quarks of the same electric charge possess a mass hierarchy is a big puzzle in particle physics, and it must be highly correlated with the hierarchy of quark flavor mixing. This review article is intended to provide a brief description of some important issues regarding quark masses, flavor mixing and CP violation. A comparison between the salient features of quark and lepton flavor mixing structures is also made.
Parity nonconservation led Lee and Yang (1956) to the hypothesis of additional fermions with properties that mirror those of usual particles. It is shown here that the well-known observed qualitative structure of the quark mixing matrix (CKM matrix) is precisely reproduced when usual quark mass hierarchies result from mass hierarchies of heavy mirror generations. The last ones are of the Lee--Yang type only. The usual quark spectrum is formed likewise the see--saw spectrum of the neutrino physics. The lightest mirror quark is closely related with the t quark and might be available even in a re…
The three-flavor mixing matrix can be parameterized by the rephasing invariants Gamma_{ijk} = V_{1i} V_{2j} V_{3k}. This formulation brings out the inherent symmetry of the problem and has some appealing features. Examples illustrating the parametrization and applications to quark mixing are presented.
The renormalization of theories with flavor mixing is discussed, and it is shown that the physical unstable particles should be interpreted as quasiparticles which cannot be regarded as external states. Several popular beliefs on renormalization are disproved accordingly, and the limitations of physical renormalization schemes are discussed. In addition, the properties of unstable particles with flavor mixing such as decay widths are studied from scattering mediated by them.
Neutrino flavor mixing is discussed in terms of two-component coupled left-handed flavor fields. This is to take into account the fact that the weak interaction couples only to left-handed fields. The flavor fields are written through a rotation matrix, as a linear combination of left-handed free fields. In order to obtain properly normalized wave functions directly from those free fields, states of mixed helicity have to be considered. Neutrino flavor oscillation amplitudes are also derived.
We discuss potential to measure squark flavor mixings based on future data at super B factory and LHC. In particular we focus on the imaginary part of the mixings by investigating the CP violating observables. As a result, we find they are determined with the uncertainty about 10 % at best.
We compare the effectiveness of various tests of three-flavor mixing in future long-baseline neutrino oscillation experiments. We analyze a representative case of mixing in a simplified three-flavor scheme, whose relevant parameters are one neutrino mass-square difference, $m^2$, and two mixing angles, $ψ$ and $ϕ$. We show that an unambiguous determination of $ψ$ and $ϕ$ requires flavor-appearance tests in accelerator experiments, as well as supplementary information from reactor experiments.
The recent 71Ga solar neutrino observation is combined with the 37Cl and Kamiokande-II observations in an analysis for neutrino masses and mixings. The allowed parameter region is found for matter enhanced mixings among all three neutrino flavors. Distortions of the solar neutrino spectrum unique to three flavors are possible and may be observed in continuing and next generation experiments.
This study indicates that in E6 grand unified theories (GUTs), once a hierarchical structure of up-quark-type Yukawa couplings is given as a basic structure of flavor, larger lepton mixings than the quark mixings and milder down-quark-type (and charged-lepton-type) mass hierarchies than up-quark-type mass hierarchy can generically be obtained under a few natural assumptions. The basic flavor structure is compatible with non-Abelian horizontal symmetry, which can solve the SUSY flavor problem. It is shown that in solving the SUSY flavor problem, the E6 structure, which realizes bi-large neutrin…
A new framework for handling flavor symmetry breaking in the neutrino sector is discussed where the source of symmetry breaking is traced to the global property of right-handed neutrinos in extra-dimensional space. Light neutrino phenomenology has rich and robust predictions such as the tri/bi-maximal form of generation mixing, controlled mass spectrum, and no need of flavor mixing couplings in the theory.
In this paper, we suggest a simple model which induces realistic flavor structure from mixing of flavored Higgs doublets. The idea is based on the decoupling limit. In a model with many Higgs doublets, the mass eigenstates of scalars are linear combinations of Higgs doublets. If the mass matrix of Higgs fields has only one massless mode, and if the linear combination has flavor dependence, the induced Yukawa coupling will have nontrivial flavor structure. We suggest a mass matrix of flavored Higgs fields in a $U(2)_{L} \times U(2)_{R}$ toy model. An advantage of this model is that all of the e…
We explore the phenomenological implications on charged lepton flavor violating (LFV) processes from slepton flavor mixing within the Minimal Supersymmetric Standard Model. We work under the model-independent hypothesis of general flavor mixing in the slepton sector, being parametrized by a complete set of dimensionless delta^AB_ij (A,B = L,R; i,j = 1, 2, 3) parameters. The present upper bounds on the most relevant LFV processes, together with the requirement of compatibility in the choice of the MSSM parameters with the recent LHC and (g-2) data, lead to updated constraints on all slepton fla…
We address two fundamental aspects of flavor physics: the mass hierarchy and the large lepton mixing angles. On one side, left-right flavor symmetry realizes the democratic mass matrix patterns and explains why one family is much heavier than the others. On the other side, discrete flavor symmetry such as A4 leads to the observed tribimaximal mixing for the leptons. We show that, by explicitly breaking the left-right flavor symmetry into the diagonal A4, it is possible to explain both the observed charged fermion mass hierarchies and quark and lepton mixing angles. In particular we predict a h…
We review the application of non abelian discrete groups to the theory of neutrino masses and mixing, which is strongly suggested by the agreement of the Tri-Bimaximal mixing pattern with experiment. After summarizing the motivation and the formalism, we discuss specific models, based on A4, S4 and other finite groups, and their phenomenological implications, including lepton flavor violating processes, leptogenesis and the extension to quarks. In alternative to Tri-Bimaximal mixing the application of discrete flavor symmetries to quark-lepton complementarity and Bimaximal Mixing is also consi…
We clarify the domain needed for the mixing angles in three flavor neutrino oscillations. By comparing the ranges of the transition probabilities as functions of the domains of the mixing angles, we show that it is necessary and sufficient to let all mixing angles be in $[ 0, π/2 ]$. This holds irrespectively of any assumptions on the neutrino mass squared differences.
We derive the constraints imposed on neutrino masses and mixing angles by performing a combined analysis of the data from the Los Alamos and the other terrestrial neutrino oscillation experiments with the assumption of the flavor-mixing solutions to the solar neutrino problem. In a three-flavor mixing scheme which ignores the possibility of sterile neutrinos, we obtain severe constraints on the pattern of masses and flavor mixing of neutrinos. For example, we show that in the standard Kobayashi-Maskawa type mixing matrix $s_{13}^2 \lsim 10^{-2}$ independent of the choice of the solar neutrino …
Large mixing parameters of neutrino mass eigenstates in the neutrino flavor eigenstates are determined, and interpreted as closely related to the neutrino and charged lepton mass-ratio patterns. The three known seemingly different charged lepton and quasi-degenerate neutrino deviation-from-extreme hierarchies are shown to be three particular manifestations of one unifying quadratic hierarchy-rule in lepton flavor physics.
We present an overview of recent progress in the phenomenological study of neutrino masses, lepton flavor mixing and CP violation. We concentrate on the model-independent properties of massive neutrinos, both in vacuum and in matter. Current experimental constraints on the neutrino mass spectrum and the lepton flavor mixing parameters are summarized. The Dirac- and Majorana-like phases of CP violation, which are associated respectively with the long-baseline neutrino oscillations and the neutrinoless double beta decay, are discussed in detail. The seesaw mechanism, the leptogenesis scenario an…
In the minimal supersymmetric standard model, we have studied the evolution of the neutrino flavor mixing by using the renormalization group equation(RGE) with the Georgi-Jarlskog texture for the Yukawa coupling matrices.For the large Yukawa coupling of the charged lepton, i.e.,$\tan\b \gg 1$, the neutrino flavor mixing increases significantly with running down to the electroweak scale by the RGE. If one wishes to get the large neutrino flavor mixing $\sin þ_{23}$ at the electroweak scale, which is suggested by the muon neutrino deficit in the atomospheric neutrino flux, the initial condition …
We consider the problem of time-to-space conversion in quantum field theory of flavor mixing using a generalization of the wave-packet method in quantum mechanics. We work entirely within the canonical formalism of creation and annihilation operators that allows us, unlike the usual wave-packet formulation, to include the nontrivial effect due to flavor condensation in the vacuum.
My talk is concentrating on the quantum effects on neutrino mass and lepton flavor mixing matrices in the framework of the minimal supersymmetric standard model with the effective dimension-five operator which gives the Majorana masses of neutrinos.
We explore the phenomenological implications on non-minimal flavor violating (NMFV) processes from squark flavor mixing within the Minimal Supersymmetric Standard Model. We work under the model-independent hypothesis of general flavor mixing in the squark sector, being parametrized by a complete set of dimensionless delta^AB_ij (A,B = L, R; i,j = u, c, t or d, s, b) parameters. The present upper bounds on the most relevant NMFV processes, together with the requirement of compatibility in the choice of the MSSM parameters with the recent LHC and g-2 data, lead to updated constraints on all squa…
To search for possible textures of lepton mass matrices, we systematically examine flavor mixing structures which can lead to large lepton mixing angles. We find out 37 mixing patterns are consistent with experimental data, taking into account phase factors in the mixing matrices. Only six of the patterns can explain the observed data without any tuning of parameters, while the others need particular choices for the phase values. It is found that these six mixing patterns are those predicted by the models which have been proposed to account for fermion mass hierarchies. On the other hand, the …
In this paper we study dynamical chiral symmetry breaking of a generic quantum field theoretical model with global chiral flavor symmetry. By purely algebraic means we analyze the vacuum structure for different symmetry breaking schemes and show explicitly how the ensuing non-trivial flavor vacuum condensate characterizes the phenomenon of field mixing. In addition, with the help of Ward-Takahashi identities we demonstrate the emergence of a correct number of Nambu-Goldstone modes in the physical spectrum.
The $μν$SSM, one of supersymmetric extensions of the Standard Model, introduces three right-handed neutrino superfields to solve the $μ$ problem and violates lepton number. Within framwork of the $μν$SSM, we investigate the lepton flavor violating (LFV) processes $Z\rightarrow l_i^\pm l_j^\mp$ with slepton flavor mixing. Simultaneously, we consider the LFV processes $l_j^-\rightarrow l_i^-γ$, $l_j^- \rightarrow l_i^- l_i^- l_i^+$ and muon conversion to electron in nuclei.
We address the problem of rationalizing the pattern of fermion masses and mixings by adding a nonabelian flavor symmetry in a grand unified framework. With this purpose, we include an A4 flavor symmetry into a unified renormalizable SUSY GUT SU(5) model. With the help of the "Type II Seesaw" mechanism we are able to obtain the pattern of observed neutrino mixings in a natural way, through the so called tribimaximal matrix.
