The three electroweak doublet neutrinos $ν_{e,μ,τ}$ of the Standard Model may acquire small seesaw masses, using either three Majorana fermion singlets $N$ or three Majorana fermion triplets $(Σ^+,Σ^0,Σ^-)$. It is well-known that the former accommodates the U(1) gauge symmetry $B-L$. It has also been shown some years ago that the latter supports a new $U(1)_X$ gauge symmetry. Here we study two variations of this $U(1)_X$, one for two $N$ and one $Σ$, the other for one $N$ and two $Σ$. Phenomenological consequences are discussed.
A variation of the original 2006 radiative seesaw model of neutrino mass through dark matter is shown to realize the notion of inverse seesaw naturally. The dark-matter candidate here is the lightest of three real singlet scalars which may also carry flavor.
We study the possibility of connecting leptonic Dirac CP phase $δ$, lightest neutrino mass and baryon asymmetry of the Universe within the framework of a model where both type I and type II seesaw mechanisms contribute to neutrino mass. Type I seesaw gives rise to Tri-Bimaximal (TBM) type neutrino mixing whereas type II seesaw acts as a correction in order to generate non-zero $θ_{13}$. We derive the most general form of type II seesaw mass matrix which can not only give rise to correct neutrino mixing angles but also can generate non-trivial value of $δ$. Considering both the cases where type…
The radiative seesaw mechanism proposed recently is minimally extended to include supersymmetry in a specific model. Relevant related issues such as leptogenesis and dark matter are discussed.
We discuss the linkage between dark matter mass in the one-loop radiative seesaw model and the effective neutrino mass for the neutrino less double beta decay. This linkage, which has been already numerically suggested, is confirmed to be a reasonable relationship by deriving analytical expressions for two zero flavor neutrino mass texture.
We discuss neutrino mass and mixing in the framework of the classic seesaw mechanism, involving right-handed neutrinos with large Majorana masses, which provides an appealing way to understand the smallness of neutrino masses. However, with many input parameters, the seesaw mechanism is in general not predictive. We focus on natural implementations of the seesaw mechanism, in which large cancellations do not occur, where one of the right handed neutrinos is dominantly responsible for the atmospheric neutrino mass, while a second right-handed neutrino accounts for the solar neutrino mass, leadi…
We propose two different seesaw models namely, type I and inverse seesaw to realise light Dirac neutrinos within the framework of $A_4$ discrete flavour symmetry. The additional fields and their transformations under the flavour symmetries are chosen in such a way that naturally predicts the hierarchies of different elements of the seesaw mass matrices in these two types of seesaw mechanisms. For generic choices of flavon alignments, both the models predict normal hierarchical light neutrino masses with the atmospheric mixing angle in the lower octant. Apart from predicting interesting correla…
If it can be ascertained experimentally that the 3X3 Majorana neutrino mass matrix M_nu has vanishing determinants for one or more of its 2X2 submatrices, it may be interpreted as supporting evidence for the theoretically well-known canonical seesaw mechanism. I show how these two things are connected and offer a realistic M_nu with two zero subdeterminants as an example.
RGEs for coefficients of dim-5 operators giving rise to neutrino masses in the seesaw mechanism are written down in the SM, 2HDM and MSSM, and solved numerically. RG evolution of these coefficients modifies tree-level seesaw predictions for neutrino masses and mixing angles in SO(10)-type GUT models as strongly as quark Yukawa coupling evolution.
The inverse seesaw mechanism of neutrino mass, i.e. m_nu = (m_D^2/m_N^2)epsilon_L where epsilon_L is small, is discussed in the context of the U(1)_Sigma model. This is a gauge extension of the Standard Model of particle interactions with lepton triplets (Sigma^+,Sigma^),Sigma^-) as (Type III) seesaw anchors for obtaining small Majorana neutrino masses.
In the standard seesaw model, finite corrections to the neutrino mass matrix arise from one-loop self-energy diagrams mediated by heavy neutrinos. We discuss the impact that these corrections may have on the different entries of the tree-level effective neutrino mass matrix, paying special attention to their dependence with the seesaw model parameters. We also briefly comment on the implications these corrections might have on low-energy neutrino observables.
Assuming the solar and atmospheric neutrino deficits to be due to neutrino oscillations, it is shown that the 3X3 mass matrix spanning the e, mu, and tau neutrinos may have already revealed a seesaw mass pattern. Also, this matrix is the natural reduction of a simple 5X5 seesaw mass matrix with one large scale, the 4X4 reduction of which predicts that a fourth neutrino would mix with the e and mu neutrinos in such a way that oscillations between them may occur just within the detection capability of the LSND (Liquid Scintillator Neutrino Detector) experiment.
So far we have not been able to establish that, as theoretically expected, neutrinos are their own anti-particles. Here we propose a dynamical way to account for the Dirac nature of neutrinos and the smallness of their mass in terms of a new variant of the seesaw paradigm in which the energy scale of neutrino mass generation could be accessible to the current LHC experiments.
In the canonical up-quark seesaw, the ratios of light neutrino masses are more easily predicted than the masses themselves. Under explicitly enumerated neccesary but minimal assumptions, these ratios are obtained, including radiative corrections. The predictions remain uncertain only by the top quark mass and triviality mass limit, and the power law of the seesaw. The tau neutrino is specially affected by the non-linear effect of the heavy top quark mass. The derived ratios have application to solar, atmospheric, and cosmological neutrinos and laboratory neutrino oscillation searches. The sees…
We reformulate the canonical seesaw mechanism in the case that the electroweak gauge symmetry is unbroken, and show that it can "formally" work and allow us to derive an exact seesaw formula for the light and heavy Majorana neutrinos. We elucidate the reason why there is a mismatch between the mass eigenstates of heavy Majorana neutrinos associated with thermal leptogenesis and those associated with the seesaw framework, and establish the exact and explicit relations between the "original" and "derivational" seesaw parameters by using an Euler-like parametrization of the $6\times 6$ active-ste…
The seesaw mechanism can play a key role in the generation of the leptonic mixing in unified models. We consider an unified model with a family symmetry and extended seesaw, and obtain viable fermion masses and mixing (leptonic mixing is close to tri-bi-maximal).
In the framework of type II seesaw mechanism we discuss the number of sterile right-handed Majorana neutrinos being the warm dark matter (WDM). When the type II seesaw mass term $M_ν^{II}$ is far less than the type I seesaw mass term $M_ν^{I}$, only one of three sterile neutrinos may be the WDM particle. On the contrary, the WDM particles may contain all sterile neutrinos. If $M_ν^{II} \sim M_ν^{I}$, the allowed number is not more than $N - 1$ for $N$ sterile neutrinos. It is worthwhile to stress that three different types of neutrino mass spectrum are permitted when $M_ν^{II} \gg M_ν^{I}$ and…
If the canonical seesaw mechanism alone is responsible for neutrino mass, i.e. m_nu = -m_D^2/m_N, it can neither be proved nor disproved at the TeV energy scale. A new verifiable mechanism of neutrino mass is proposed, using the "inverse" seesaw, with new physics at the TeV scale, such that m_nu = m_D^2 epsilon_L/m_N^2, where epsilon_L is a two-loop effect. Dark-matter candidates also appear naturally.
We consider the threshold effect on the renormalization group (RG) evolution of the neutrino masses and mixing angles in TeV scale seesaw models. We obtain the analytic expressions using the factorization method in presence of threshold effects. We also perform numerical study of RG effects in two specific low scale seesaw models following the bottom-up approach and ascertain the role of seesaw thresholds in altering the values of masses and mixing angles during RG evolution.
We propose a Standard Model extension with underlying A4 flavour symmetry where small Dirac neutrino masses arise from a Type-II seesaw mechanism. The model predicts the "golden" flavour-dependent bottom-tau mass relation, requires an inverted neutrino mass ordering and non-maximal atmospheric mixing angle. Using the latest neutrino oscillation global fit we derive restrictions on the oscillation parameters, such as a correlation between Dirac CP phase and the lightest neutrino mass.
We suggest a hybrid seesaw model where relatively ``light''right-handed neutrinos give no contribution to the neutrino mass matrix due to a special symmetry. This allows their Yukawa couplings to the standard model particles to be relatively strong, so that the standard model Higgs boson can decay dominantly to a left and a right-handed neutrino, leaving another stable right-handed neutrino as cold dark matter. In our model neutrino masses arise via the type-II seesaw mechanism, the Higgs triplet scalars being also responsible for the generation of the matter-antimatter asymmetry via the lepto…
Renewed interest in GeV-scale sterile neutrinos capable of explaining active neutrino oscillations via see-saw type I mechanism has been expressed in several proposals of direct searches. Given this activity we estimate the minimal values of sterile-active mixing angles provided one, two, or three sterile neutrinos are lighter than D-meson.
We study parameters of an extended standard model. The neutrino sector is enlarged by one or two right-handed singlet fields and the Higgs sector contains one additional doublet. One-loop radiative corrections generate the mass for the light neutrino fields. The numerical analysis is performed varying the masses of heavy neutrinos and of the additional neutral Higgses. The parameters of the neutrino sector, allowing for the seesaw type-I mechanism, are restricted by experimental neutrino oscillation data. Both normal and inverted hierarchies of the light neutrino masses are discussed.
In the minimal seesaw model, we derive required constraints on Dirac neutrino masses inducing maximal CP violation in neutrino oscillations. If the maximal atmospheric neutrino mixing is further assumed, Dirac neutrino masses are uniquely determined to respect $μ$-$τ$ flavored CP symmetry for neutrinos.
If neutrino masses are obtained via the canonical seesaw mechanism, based on an underlying 2X2 mass matrix, unitarity violation of the neutrino mixing matrix is unavoidable, but its effect is extremely small. On the other hand, in the inverse (and linear) seesaw mechanisms, based on an underlying 3X3 mass matrix, it can be significant and possibly observable. This 3X3 matrix is examined in more detail, and a NEW variation (the lopsided seesaw) is proposed which has features of both mechanisms. A concrete example based on U(1)_N is discussed.
We perform a detailed analysis of the one-loop corrections to the light neutrino mass matrix within low scale type I seesaw extensions of the Standard Model and their implications in experimental searches for neutrinoless double beta decay. We show that a sizable contribution to the effective Majorana neutrino mass from the exchange of heavy Majorana neutrinos is always possible, provided one requires a fine-tuned cancellation between the tree-level and one-loop contribution to the light neutrino masses. We quantify the level of fine-tuning as a function of the seesaw parameters and introduce …
We study the RH neutrino properties from the low energy neutrino data in the seesaw mechanism. Reonance behavior is found for the right-handed (RH) mixing angle as a function of light neutrino mass ratios in two favored region of the solar neutrino problem and, at the resonance point, the two corresponding RH Majorana neutrino masses are degenerate. This phenomenon is similar with that in the matter-enhanced conversion of neutrinos. The physical significance it infers for the electron neutrino mass and other neutrino parameters is discussed.
The seesaw model of heavy and light Majorana neutrinos and its low-energy effective theory are studied, when the number of heavy neutrinos is equal to or less than the number of light lepton generations. We establish a general relationship between the high-energy parameters and the low-energy observables involving only the light fields. It is shown how low-energy measurements of the properties of light neutrinos suffice a priori to determine all couplings of the unobserved heavy neutrinos. CP violation is present in low-energy processes if seesaw-model leptogenesis creates the matter-antimatte…
We study the possibility of generating deviations from tri-bimaximal (TBM) neutrino mixing to explain the non-zero reactor mixing angle within the framework of both type I and type II seesaw mechanisms. The type I seesaw term gives rise to the $μ-τ$ symmetric TBM pattern of neutrino mass matrix as predicted by generic flavor symmetry models like $A_4$ whereas the type II seesaw term gives rise to the required deviations from TBM pattern to explain the non-zero $θ_{13}$. Considering extremal values of Majorana CP phases such that the neutrino mass eigenvalues have the structure $(m_1, -m_2, m_3…
In minimal trinification models light neutrino masses can be generated via a radiative see-saw mechanism, where the masses of the right-handed neutrinos originate from loops involving Higgs and fermion fields at the unification scale. This mechanism is absent in models aiming at solving or ameliorating the hierarchy problem, such as low-energy supersymmetry, since the large seesaw-scale disappears. In this case, neutrino masses need to be generated via a TeV-scale mechanism. In this paper, we investigate an inverse seesaw mechanism and discuss some phenomenological consequences.
If a family symmetry exists so that all three neutrinos have equal Majorana masses (via the seesaw mechanism), then the breaking of this symmetry from charged-lepton masses (via two-loop double $W$ exchange) implies $Δm$ less than about $10^{-9}m_0$. With the common mass $m_0 \sim$ eV for hot dark matter, $Δm^2 \sim 10^{-10}$ eV$^2$ is natural for vacuum solar neutrino oscillations.
Neutrino flavor mixing is explained within the recently proposed low-scale minimal linear seesaw model of neutrino mass generation, a variant of the standard linear seesaw led by a Dirac pair of extra sterile neutrinos which is odd under a discrete $Z_2$ symmetry and has a mass at or below the GeV scale. The tri-bimaximal mixing and its deviations are derived straightforwardly on the basis of the symmetry between $μ$ and $τ$ flavors, without introducing non-abelian discrete flavor symmetries in the first place.
In the standard seesaw model, finite corrections to the neutrino mass matrix arise from one-loop self-energy diagrams mediated by a heavy neutrino. We discuss the impact that these corrections may have on the different low-energy neutrino observables paying special attention to their dependence with the seesaw model parameters. It is shown that sizable deviations from the tri-bimaximal mixing pattern can be obtained when these corrections are taken into account.
The seesaw mechanism for three neutrinos is discussed, clarifying the situation where the seesaw texture results in three approximately zero mass eigenvalues. The true underlying mechanism is shown to be just the $inverse$ (or $linear$) seesaw, which explains why there could be large mixing. However, these zeroes cannot occur naturally, unless there is a conserved symmetry, i.e. lepton number $L$, either global or gauged, which is softly or spontaneously broken at the TeV scale. We discuss in particular the case where the three heavy singlet neutrinos have $L=3,-2,-1$.
We consider different extensions of the standard model which can give rise to the small active neutrino masses through seesaw mechanisms, and their mixing. These tiny neutrino masses are generated at some high energy scale by the heavy seesaw fields which then get sequentially decoupled to give an effective dimension-5 operator. The renormalization group evolution of the masses and the mixing parameters of the three active neutrinos in the high energy as well as the low energy effective theory is reviewed in this article.
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.
A simplified but very instructive analysis of the seesaw mechanism is here performed. Assuming a nearly diagonal Dirac neutrino mass matrix, we study the forms of the Majorana mass matrix of right-handed neutrinos, which reproduce the effective mass matrix of left-handed neutrinos. As a further step, the important effect of a non diagonal Dirac neutrino mass matrix is explored. The corresponding implications for the baryogenesis via leptogenesis and for the neutrinoless double beta decay are reviewed. We propose two distinct models where the baryon asymmetry is enhanced.
In the framework of type II seesaw mechanism we propose two simple but instructive ansatze for neutrino mixing and leptogenesis. In each ansatz, the effective Majorana neutrino mass matrix is composed of two parts -- the part with Z_2 symmetry arises from the ordinary type I seesaw mechanism and the part with S_3 symmetry arises from an additional Higgs triplet vacuum expectation value. The two ansatze can simultaneously account for the current neutrino oscillation data and the cosmological baryon number asymmetry via leptogenesis.
A four-neutrino spectrum with a sterile neutrino without significant involvement in the atmospheric and solar neutrino oscillation experiments has been recently advocated as the correct picture to explain all existing experimental data. We propose a supersymmetric model in which this picture can be naturally implemented. In this model, the mass for the mainly active neutrino eigenstates is induced by the seesaw mechanism with a large intermediate scale $M_R$, whereas the mass for the mainly sterile neutrino state is closely related to supersymmetry breaking.
In the two zero flavor neutrino mass matrix scheme with nonvanishing Majorana effective mass $M_{ee}$ for the neutrino less double beta decay, four textures are compatible with observed data. We obtain the complete list of the possible textures of four zero Dirac neutrino mass matrix $m_D$ in the seesaw mechanism providing these four flavor neutrino textures. Explicit analytical analysis of $m_D$ turns out to provide the relation of $m_D \propto \sqrt{M_{ee}}$.
Neutrino mass matrix via a seesaw mechanism is constructed by assuming that the underlying symmetry of both heavy Majorana and Dirac mass matrices is the discrete subgroup $Δ(27)$ symmetry of SU(3). Using the experimental data of neutrino oscillation, the neutrino mass matrix exhibits maximal $ν_μ-ν_τ$ mixing and has a specific prediction on the effective neutrino mass in neutrinoless double beta decay which can be tested in future experiment.
Lepton flavor violating Higgs boson decays are studied within the context of seesaw models with Majorana massive neutrinos. Two models are considered: The SM-seesaw, with the Standard Model Particle content plus three right handed neutrinos, and the MSSM-seesaw, with the Minimal Supersymmetric Standard Model particle content plus three right handed neutrinos and their supersymmetric partners. The widths for these decays are derived from a full one-loop diagrammatic computation in both models, and they are analyzed numerically in terms of the seesaw parameters, namely, the Dirac and Majorana ma…
We study neutrinoless double beta decay in left-right symmetric extension of the standard model with type I and type II seesaw origin of neutrino masses. Due to the enhanced gauge symmetry as well as extended scalar sector, there are several new physics sources of neutrinoless double beta decay in this model. Ignoring the left-right gauge boson mixing and heavy-light neutrino mixing, we first compute the contributions to neutrinoless double beta decay for type I and type II dominant seesaw separately and compare with the standard light neutrino contributions. We then repeat the exercise by con…
We evaluate the predictive power of the neutrino mass matrices arising from seesaw mechanism subjected to texture zero and satisfying a cyclic permutation invariant. We found that only two from eight possible patterns of the neutrino mass matrices are invariant under a cyclic permutation. The two resulted neutrino mass matrices which are invariant under a cyclic permutation can be used qualitatively to explain the neutrino mixing phenomena for solar neutrino and to derive the mixing angle that agress with the experimental data.
We generalize the democratic neutrino mixing Ansatz by incorporating the type-II seesaw mechanism with S(3) flavor symmetry. We find that bilarge neutrino mixing can naturally appear if the flavor democracy contribution is strongly suppressed due to significant cancellation between the conventional seesaw and triplet mass terms. Explicit S(3) symmetry breaking yields successful neutrino phenomenology and various testable correlations between the neutrino mass and mixing parameters. Among the results are a normal neutrino mass ordering, $0.005 \le |U_{e3}| \le 0.057$, $1 - \sin^2 2θ_{23} \ge 0.…
Models of type I seesaw can be implemented at the electroweak scale in a natural way provided that the heavy neutrino singlets are quasi-Dirac particles. In such case, their contribution to light neutrino masses has the suppression of a small lepton number violating parameter, so that light neutrino masses can arise naturally even if the seesaw scale is low and the heavy neutrino mixing is large. We implement the same mechanism with fermionic triplets in type III seesaw, deriving the interactions of the new quasi-Dirac neutrinos and heavy charged leptons with the SM fermions. We then study the…
The observation of neutrino oscillations requires new physics beyond the standard model (SM). A SM-like gauge theory with p lepton families can be extended by introducing q heavy right-handed Majorana neutrinos but preserving its SU(2)_L x U(1)_Y gauge symmetry. The overall neutrino mass matrix M turns out to be a symmetric (p+q) x (p+q) matrix. Given p>q, the rank of M is in general equal to 2q, corresponding to 2q non-zero mass eigenvalues. The existence of (p-q) massless left-handed Majorana neutrinos is an exact consequence of the model, independent of the usual approximation made in deriv…
Motivated by the recent observations on sterile neutrinos, we present a minimal extension of the canonical type-I seesaw by adding one extra singlet fermion. After the decoupling of right-handed neutrinos, an eV-scale mass eigenstate is obtained without the need of artificially inserting tiny mass scales or Yukawa couplings for sterile neutrinos. In particular, the active-sterile mixing is predicted to be of the order of 0.1. Moreover, we show a concrete flavor A_4 model, in which the required structures of the minimal extended seesaw are realized. We also comment on the feasibility of accommo…
We give a general analysis of neutrino mixing in the seesaw mechanism with three flavors. Assuming that the Dirac and u-quark mass matrices are similar, we establish simple relations between the neutrino parameters and individual Majorana masses. They are shown to depend rather strongly on the physical neutrino mixing angles. We calculate explicitly the implied Majorana mass hierarchies for parameter sets corresponding to different solutions to the solar neutrino problem.
A five-dimensional seesaw framework is analyzed with the lepton-number-violating propagator of bulk right-handed neutrinos. That can bypass summing up the effects of heavy Majorana particles whose masses and wavefunctions are not exactly known. The propagator method makes it easier to evaluate the seesaw-induced neutrino mass for various boundary conditions of bulk neutrinos and in a general background geometry, including the warped extra dimension. It is also found that the higher-dimensional seesaw gives a natural framework for the inverse seesaw suppression of low-energy neutrino masses.
A minimal extension of the Standard Model is proposed, where the observed left-handed neutrinos obtain naturally small Majorana masses from a one-loop radiative seesaw mechanism. This model has two candidates (one bosonic and one fermionic) for the dark matter of the Universe. It has a very simple structure and should be verifiable in forthcoming experiments at the Large Hadron Collider.
The seesaw mechanism provides a simple explanation for the lightness of the known neutrinos. Under the standard assumption of a weak scale Dirac mass and a heavy sterile Majorana scale the neutrino mass is naturally suppressed below the weak scale. However, Nature may employ Dirac and Majorana scales that are much less than typically assumed, possibly even far below the weak scale. In this case the seesaw mechanism alone would not completely explain the lightness of the neutrinos. In this work we consider a warped framework that realizes this possibility by combining naturally suppressed Dirac…
We investigate an alternative seesaw mechanism for neutrino mass generation. Neutrino mass is generated at loop level but the basic concept of usual seesaw mechanism is kept. One simple model is constructed to show how this mechanism is realized. The applications of this seesaw mechanism at weak scale to cosmology and neutrino physics are discussed.
Many studies have been made on extensions of the standard model with $B-L$ gauge symmetry. The addition of three singlet (right-handed) neutrinos renders it anomaly-free. It has always been assumed that the spontaneous breaking of $B-L$ is accomplished by a singlet scalar field carrying two units of $B-L$ charge. This results in a very natural implementation of the Majorana seesaw mechanism for neutrinos. However, there exists in fact another simple anomaly-free solution which allows Dirac or inverse seesaw neutrino masses. We show for the first time these new possibilities and discuss an appl…
We study a minimal one-loop radiative mechanism for generating small Majorana neutrino masses in inverse seesaw extensions of the Standard Model with two singlet fermions per family. The new feature of this radiative mechanism is that the one-loop induced left-handed neutrino mass matrix is directly proportional to the Majorana mass matrix of the right-handed neutrinos. This is a very economical scenario without necessitating the existence of non-standard scalar or gauge fields.
There are no upper limits on the possible number of massive, singlet (right--handed) neutrinos that may participate in the seesaw mechanism, and some string constructions motivate seesaw models with up to O(100) right--handed neutrinos. In this case, the seesaw mass scale can be significantly higher than that in the traditional scheme with just 3 right--handed neutrinos. We consider the possible phenomenological implications of such models, in particular, for lepton-flavour violation and electric dipole moments. Since the neutrino masses depend on the Majorana mass scale linearly, while supers…
We discuss the minimal seesaw model for the Dirac CP violating phase of the lepton mixing matrix. We introduce two right-handed Majorana neutrinos and obtain several textures of the tri-maximal lepton mixing matrices. Moreover, we discuss the observed baryon asymmetry of the universe through the leptogenesis mechanism. As the result, we obtain the specific model which predicts the negative sign of maximal Dirac CP violating phase and normal hierarchy of neutrino masses.
We discuss the scenario with gauge singlet fermions (right-handed neutrinos) accessible at the energy of the Large Hadron Collider. The singlet fermions generate tiny neutrino masses via the seesaw mechanism and also have sizable couplings to the standard-model particles. We demonstrate that these two facts, which are naively not satisfied simultaneously, are reconciled in the five-dimensional framework in various fashions, which make the seesaw mechanism observable. The collider signal of tri-lepton final states with transverse missing energy is investigated for two explicit examples of the o…
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…
