A Model for Neutrino Masses

Quark Masses and Mixings with Hierarchical Friedberg-Lee Symmetry

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 $m_{b^{'}}>199\ \gev$.

A modified Friedberg-Lee symmetry for the TM1 neutrino mixing

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 Friedberg-Lee Symmetry and Minimal Seesaw Model

The Friedberg-Lee (FL) symmetry is generated by a transformation of a fermionic field $q$ to $q + ξz$. This symmetry puts very restrictive constraints on allowed terms in a Lagrangian. Applying this symmetry to $N$ fermionic fields, we find that the number of independent fields is reduced to $N-1$ if the fields have gauge interaction or the transformation is a local one. Using this property, we find that a seesaw model originally with three generations of left- and right-handed neutrinos, with the left-handed neutrinos unaffected but the right-handed neutrinos transformed under the local FL tr…

A Light Sterile Neutrino from Friedberg-Lee Symmetry

Light sterile neutrinos of mass about an eV with mixing $\tilde U_{ls}$ of a few percent to active neutrinos may solve some anomalies shown in experimental data related to neutrino oscillation. How to have light sterile neutrinos is one of the theoretical problems which have attracted a lot of attentions. In this article we show that such an eV scale light sterile neutrino candidate can be obtained in a seesaw model in which the right-handed neutrinos satisfy a softly-broken Friedberg-Lee (FL) symmetry. In this model a right-handed neutrino is guaranteed by the FL symmetry to be light comparin…

Neutrino Mixing: from the Broken μ-τSymmetry to the Broken Friedberg-Lee Symmetry

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…

Generalized Friedberg-Lee model for CP violation in neutrino physics

We propose a phenomenological model of Dirac neutrino mass operator based on the Fridberg-Lee (FL) neutrino mass model to include CP violation. By considering the most general set of complex coefficients, and imposing the condition that the mass eigenvalues are real, we find a neutrino mass matrix which is non-hermitian, symmetric and magic. In particular, we find that the requirement of obtaining real mass eigenvalues by transferring the residual phases to the mass eigenstates self-consistently, dictates the following relationship between the imaginary part of the mass matrix elements $B$ and…

Leptogenesis with Friedberg-Lee Symmetry

We consider the $μ-τ$ symmetric Friedberg-Lee (FL) symmetry for the neutrino sector and show that a specific FL translation leads to the tribimaximal mixing pattern of the Maki-Nakagawa-Sakata (MNS) matrix. We also apply the symmetry to the type-I seesaw framework and address the baryon asymmetry of the universe through the leptogenesis mechanism. We try to establish a relation between the net baryon asymmetry and CP phases included in the MNS matrix.

Friedberg-Lee Symmetry Breaking and Its Prediction for theta_13

We consider an effective Majorana neutrino mass operator with the Friedberg-Lee symmetry; i.e., it is invariant under the transformation ν_α-> ν_α+ z (for α= e, μ, τ) with z being a space-time independent constant element of the Grassmann algebra. We show that this new flavor symmetry can be broken in such a nontrivial way that the lightest neutrino remains massless but an experimentally-favored neutrino mixing pattern is achievable. In particular, we get a novel prediction for the unknown neutrino mixing angle θ_13 in terms of two known angles: \sinθ_13 = \tanθ_12 |(1- \tanθ_23)/ (1+\tanθ_23)…

打破广义弗里德伯格-李模型中的民主极限：对中微子质量和混合的影响

Breaking the Democratic Limit in the Generalized Friedberg-Lee Model: Implications for Neutrino Masses and Mixing

研究广义弗里德伯格-李模型中点D的奇异参数空间，引入最小系统微扰保持TFL对称，打破民主极限，避免特设参数，得到现实的中微子质量层级、非零θ13和固有CP破坏，与全局拟合数据吻合良好。

Neutrino mixing matrix and masses from a generalized Friedberg-Lee model

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…

Tri-Bimaximal Mixing from Twisted Friedberg-Lee Symmetry

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.

Phenomenological implications of the Friedberg-Lee transformation in a neutrino mass model with $μτ$-flavored CP symmetry

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…

Extended Friedberg Lee hidden symmetries, quark masses and CP-violation with four generations

Motivated in part by the several observed anomalies involving CP asymmetries of B and B_s decays, we consider the Standard Model with a 4th sequential family (SM4) which seems to offer a rather simple resolution. We initially assume T-invariance by taking the up and down-quark 4x4 mass matrix to be real. Following Friedberg and Lee (FL), we then impose a "hidden" symmetry on the unobserved ("hidden") up and down-quark SU(2) states. The hidden symmetry for four generations ensures the existence of two zero-mass eigenstates, which we take to be the (u,c) and (d,s) states in the up and down-quark…

多场振子/Ⅰ球在弗里德伯格-李-斯里林模型中

Multi-field oscillons/I-balls in the Friedberg-Lee-Sirlin model

研究多场振子/Ⅰ球解的条件及特性，揭示其作为双场束缚态的性质，扩展单场振子的理论框架。

Oscillating Neutrinos and Majorana Neutrino Masses

The texture zero mass matrices for the leptons and the seesaw mechanism are used to derive relations between the matrix elements of the lepton mixing matrix and the ratios of the neutrino masses.

Neutrino masses and mixings in a predictive theory of fermion masses

A framework for predicting charged fermion masses in supersymmetric grand unified theories is extended to make predictions in the neutrino sector. Eight new predictions are made, and their relevance to neutrino oscillation experiments and the solar neutrino problem are discussed.

What are the neutrino masses. Mixing

The possible mechanisms of generation of the neutrino of small masses and sterile neutrino are considered. In the supposition of stability of tracks of a left-right symmetry concerning masses of constituent quarks, the angles of mixing of quarks are evaluated. With usage of experimental data on neutrino oscillation parameters the neutrino masses on order of magnitude are computed.

Neutrino Masses in a Neutrinosphere

The energies of neutrinos in a neutrinosphere, the dense matter created after the gravitational collapse of a massive star, are estimated. Cubic equations for energy eigenvalues of neutrinos are used, with the effective masses found by taking the neutrinos at rest in neutrinosphere matter. Large differences in the effective mass of some neutrino species in a neutrinosphere compared to vacuum are found.

Neutrino masses: hierarchy without hierarchy

A large hierarchy of the Dirac masses can result in a small hierarchy for the low energy masses of the active neutrinos. This can happen even if the Majorana masses of right-handed neutrinos are all equal. A realistic description of the observed neutrino masses and mixing can be obtained starting from a large hierarchy in the Dirac masses. A large mixing for solar neutrinos results from the neutrino sector. The small value of the MNS matrix element U_e3 is a natural consequence of the scheme. The masses of the two lighter neutrinos are related to the solar neutrino mixing angle: mu_1/mu_2 = ta…

Neutrino masses and mixing from neutrino oscillation experiments

We discuss which information on neutrino masses and mixing can be obtained from the results of all neutrino oscillation experiments in the cases of three and four massive neutrinos. We show that in the three-neutrino case the neutrino oscillation data are not compatible with a hierarchy of couplings. In the case of four neutrinos, a hierarchy of masses is disfavored by the data and only two schemes with two pairs of neutrinos with close masses separated by a gap of the order of 1 eV can accommodate the results of all experiments.

Flavor Mixing, Quark Masses, Neutrino Masses and Neutrino Oscillations

We discuss first the flavor mixing of the quarks, using the texture zero mass matrices. Then we study a similar model for the mass matrices of the leptons. We are able to relate the mass eigenvalues of the charged leptons and of the neutrinos to the mixing angles and can predict the masses of the neutrinos. We find a normal hierarchy - the masses are 0.004 eV, 0.01 eV and 0.05 eV. The atmospheric mixing angle is given by the mass ratios of the charged leptons and the neutrinos. we find about 40 degrees, consistent with the experiments. The mixing element, connecting the first neutrino wit the …

See-Sawless Neutrino Masses

An alternative to the famous see-saw mechanism is proposed to explain the smallness of the neutrino masses (if present). This model involves a fourth family which mixes very little with the other three. It contains one heavy neutrino (mN > mZ /2) and three very light neutrinos whose masses are radiatively induced. In contrast with the see-saw mechanism, all neutrino masses are Dirac masses. In one particular scenario, the three light neutrinos are almost degenerate in mass and are found to be consistent with fits to the Solar and Atmospheric neutrino deficits. They might even account for the H…

Absolute neutrino masses

We discuss the possibility of using experiments timing the propagation of neutrino beams over large distances to help determine the absolute masses of the three neutrinos.

Phenomenology of Absolute Neutrino Masses

The phenomenology of absolute neutrino masses is reviewed, focusing on tritium beta decay, cosmological measurements and neutrinoless double-beta decay.

Neutrino Masses and Grand Unification

We discuss some models of neutrino masses and mixings in the context of fermion masses in Grand Unified Theories.

Neutrino physics beyond neutrino masses

We briefly summarise the current status of neutrino masses and mixing, paying special attention to the prospects for observing new leptonic interactions.

Neutrino masses and mixings

We propose a novel theoretical understanding of neutrino masses and mixings, which is attributed to the intrinsic vector-like feature of the regularized Standard Model at short distances. We try to explain the smallness of Dirac neutrino masses and the decoupling of the right-handed neutrino as a free particle. Neutrino masses and mixing angles are completely related to each other in the Schwinger-Dyson equations for their self-energy functions. The solutions to these equations and a possible pattern of masses and mixings are discussed.

Status of Neutrino Masses and Mixing

The experimental evidences in favor of oscillations of solar (and KamLAND) and atmospheric (and K2K) neutrinos are briefly reviewed and accommodated in the framework of three-neutrino mixing. The implications for the values of neutrino masses are discussed and the bounds on the absolute scale of neutrino masses from Tritium beta-decay and cosmological data are reviewed. Finally, we discuss the implications of three-neutrino mixing for neutrinoless double-beta decay.

Neutrino Masses and Mixing - Theory

In this talk I review what we know and don't know about neutrinos, neutrino masses and lepton mixing. I also discuss the importance of the discovery that neutrinos have nonzero masses, and illustrate how little is currently known about the physics behind them.

Supersymmetry and Neutrino Masses

Neutrino masses are zero in the minimal supersymmetric standard model. I discuss how they may become nonzero with new interactions which may or may not violate R-parity conservation.

Model for Small neutrino masses at the TeV Scale

We propose a model for neutrino mass generation in wich no physics beyond a TeV is required. We extend the standard model by adding two charged singlet fields with lepton number two. Dirac neutrino masses $m_{ν_D} \leq MeV$ are generated at the one loop level. Small left handed majorana neutrino masses can be generated via the seesaw mechanism with right handed neutrino masses $M_R$ are of order TeV scale.

Neutrino Masses in Astrophysics and Cosmology

Cosmology yields the most restrictive limits on neutrino masses and conversely, massive neutrinos would contribute to the cosmic dark-matter density and would play an important role for the formation of structure in the universe. Neutrino oscillations may well solve the solar neutrino problem and can have a significant impact on supernova physics. The neutrino signal from a future galactic supernova could provide evidence for cosmologically interesting neutrino masses or set interesting limits.

Neutrino Masses and Mixing Matrix from SU(1,1) Horizontal Symmetry

A new mechanism is proposed to explain neutrino masses and their mixing via SU(1,1) horizontal symmetry breaking. Based on this mechanism smallness of neutrino masses is naturally realized and inverted hierarchical spectrum with large mixing is given.

Neutrino Masses and Oscillations

New effects related to refraction of neutrinos in different media are reviewed and implication of the effects to neutrino mass and mixing are discussed. Patterns of neutrino masses and mixing implied by existing hints/bounds are described. Recent results on neutrino mass generation are presented. They include neutrino masses in SO(10) GUT's and models with anomalous $U(1)$, generation of neutrino mass via neutrino-neutralino mixing, models of sterile neutrino.

Flavor Symmetries, Neutrino Masses and Neutrino Mixing

We discuss the neutrino mixing, using the texture 0 mass matrices, which work very well for the quarks. The solar mixing angle is directly linked to the mass ratio of the first two neutrinos. The neutrino masses are hierarchical, but the mass ratios turn out to be much smaller than for quarks. The atmospheric mixing angle is 38$^{\circ}$. The CP violation for leptons should be much smaller than for quarks.

Neutrino masses beyond the minimal seesaw

The simplest possibility to generate small Majorana neutrino masses is the seesaw mechanism. However, the smallness of the observed neutrino masses can also be understood, if neutrino masses are generated by higher-dimensional operators and/or at higher loop level. In this talk recent work on systematic classifications of higher-dimensional and radiative neutrino mass models is summarized. Two particular classes of special genuine loop diagrams, i.e. diagrams which can lead to genuine neutrino mass models only under some specific, well-defined conditions, are also discussed.

Absolute neutrino masses: physics beyond SM, double beta decay and cosmic rays

Absolute neutrino masses provide a key to physics beyond the standard model. We discuss the impact of absolute neutrinos masses on physics beyond the standard model, the experimental possibilities to determine absolute neutrinos masses, and the intriguing connection with the Z-burst model for extreme-energy cosmic rays.

The masses of the neutrinos

If the cosmological limits on the sum of the neutrino masses are taken seriously we have first measurements of the masses of the neutrinos. Using the Planck experiment's limit $\sum_{i=1}^3{m_i} < 230 ~meV$ and some simple assumptions on measurement uncertainties the mass of the heaviest neutrino is $63\pm11 ~meV$ and the lightest $40\pm18 ~meV$ for either hierarchy.

Neutrino Masses in R Parity Violating Supersymmetry

We discuss a model for neutrino masses and mixings based on R parity violating Yukawa couplings. The model requires no right-handed neutrinos. It accommodates the SuperKamiokande data on atmospheric neutrinos and successfully relates this data to the mass difference for solar neutrinos in the small-angle MSW solution. We obtain an unexpected testable pattern for the three neutrino flavors.

Flavor Mixing, Neutrino Masses and Neutrino Oscillations

We study a model for the mass matrices of the leptons. We are ablte to relate the mass eigenvalues of the charged leptons and of the neutrinos to the mxiing angles and can predict the masses of the neutrinos. We find a normal hierarchy -the masses are 0.004 eV, 0.01 eV and 0.05 eV. The atmospheric mixing angle is given by the mass ratios of the charged leptons and of the neutrinos. We find 38 degrees, consistent with the experiments. The mixing element, connecting the first neutrino with the electron, is found to be 0.05.

Neutrino Masses and Mixings: a Theoretical Perspective

We briefly review the recent activity on neutrino masses and mixings which was prompted by the confirmation of neutrino oscillations by the Superkamiokande experiment.

Models for Neutrino Masses and Mixings

We review recent developments towards models for neutrino masses and mixings.

Lepton Number And Neutrino Masses

I briefly review the arguments which in the 1970's convinced many theoretical physicists to anticipate lepton number violation, and to guess a range of neutrino masses.

Relating Neutrino Masses by dilepton modes of Doubly Charged Scalars

We study a model with Majorana neutrino masses generated through doubly charged scalars at two-loop level. We give explicit relationships between the neutrino masses and the same sign dilepton decays of the doubly charged scalars. In particular, we demonstrate that at the tribimaximal limit of the neutrino mixings, the absolute neutrino masses and Majorana phases can be extracted through the measurements of the dilepton modes at colliders.

Majorana Neutrino Masses and Neutrino Oscillations

We examine some patterns of Majorana neutrino mass matrix which is compatible with the phenomenological lepton flavor mixing matrix and non-observation of neutrinoless double beta decay. Imposing $(M_ν)_{ee}=0$ for the Majorana neutrino mass matrix in the leading order, we obtain a relationship between the solar mixing angle and the neutrino masses $m_1$ and $m_2$. Additional possible texture zeros are assigned to the mass matrix so as for the nonvanishing $θ_{13}$ to be predictable in terms of neutrino masses. We also show how three neutrino masses can be predicted from the solar mixing angle…

On neutrino masses and leptonic mixing

Using recent data on neutrino oscillations, we argue that a hierarchical solution for neutrino masses in a three-family context is possible, and that the masses of the tau and mu neutrinos are very nearly determined within that possibility. We also examine the predictions of a model that determines neutrino and charged lepton mass matrices as well as its consistency with data.

Neutrino Masses in the Supersymmetric Standard Model with Right-Handed Neutrinos and Spontaneous R-Parity Violation

We propose an extension of the supersymmetric standard model with right-handed neutrinos and a singlet Higgs field, and study the neutrino masses in this model. The Majorana masses for the right-handed neutrinos are generated around the supersymmetry breaking scale through the vacuum expectation value of the singlet Higgs field. This model may induce spontaneous R-parity violation via the vacuum expectation value of the right-handed sneutrino. In the case, the effective theory is similar to a bilinear R-parity violating model. There are two sources for the neutrino masses: one is this bilinear…

Neutrino Physics - Models for Neutrino Masses and Lepton Mixing

In these lecture notes we present mechanisms for the generation of Majorana neutrino masses and lepton mixing. We consider simple extensions of the Standard Model. Apart from a section about radiative mass generation, we put special emphasis on the seesaw mechanism and mu-tau interchange symmetry.

Atmospheric and Solar Neutrino Masses and Abelian Flavor Symmetry

Recent atmospheric and solar neutrino experiments suggest that neutrinos have small but nonzero masses. They further suggest that mass eigenvalues have certain degree of hierarchical structures, and also some mixing angles are near-maximal while the others are small. We first survey possible explanations for the smallness of neutrino masses. We then discuss some models in which the hierarchical pattern of neutrino masses and mixing angles arises as a consequence of U(1) flavor symmetries which would explain also the hierarchical quark and charged lepton masses.

Neutrino masses and mixing

The status of the problem of neutrino masses and mixing is shortly reviewed. Different schemes of mixing of (Dirac or Majorana) massive neutrinos are considered. The theory of neutrino oscillations in vacuum and in matter is presented. Existing indications in favor of neutrino mixing are shortly discussed.

Status of Neutrino Masses and Mixing and Future Perspectives

Status of the problem of neutrino masses, mixing and oscillations is discussed. Future perspectives are briefly considered.

Neutrino Masses and Leptogenesis

I discuss the connection between neutrino masses and leptogenesis. I use three prime examples: (1) canonical seesaw, (2) triplet Higgs, and (3) $R$ parity violation.

ICTP Lectures on Theoretical Aspects of Neutrino Masses and Mixings

Recent neutrino oscillation experiments are yielding valuable information on the nature of neutrino masses and mixings even though we are far from a complete understanding of the new physics implied by them. In these lectures, I summarize the current theoretical status of neutrino mass physics.

Neutrino Masses from the Point of View of Economy and Simplicity

In the framework of such basic principles as local gauge invariance, unification of the weak and electromagnetic interactions and spontaneous symmetry breaking in the Standard Model the most economical and simplest possibilities are realized. We discuss the problem of neutrino masses from the point of view of economy and simplicity. It is unlikely that neutrino masses are of the same SM origin as masses of leptons and quarks. The Weinberg effective Lagrangian is the simplest and the most economical, beyond the Standard Model mechanism of the generation of small Majorana neutrino masses. The re…