General Neutrino Mass Matrix Patterns and Its Underlying Family Symmetries
Asan Damanik, Mirza Satriawan, Pramudita Anggraita, Muslim
备注：
typos corrected, 6 pages, no figure, Proceeding of Asian Physics Symposium 2005, Bandung, Indonesia, 7-8 December 2005. Proceeding of Asian Physics Symposium 2005
Based on current experimental results, such as neutrino oscillations and the neutrinoless double beta decays (i.e. data from Super Kamiokande, KamLAND, SNO, etc.), the neutrino mixing matrix can be adequately determined. Though there are still certain parameters that have possibility limits, but based on the current experimental results it is possible to construct a general form of neutrino mass matrix. Starting from this general form of the neutrino mass matrix we put certain conditions in the context of the seesaw mechanism model to determine the possible pattern of the neutrino mass matrix that has a texture zero. From the obtained neutrino mass matrix pattern, there are three class of patterns, where two of the class are known to be realized in literature by the underlying family symmetries of the $D_{4}$ and $A_{4}$ groups, the dihedral and tetrahedral symmetry groups.
We investigate origins of predictive one-zero neutrino mass textures in a systematic way. Here we search Abelian continuous(discrete) global symmetries, and non-Abelian discrete symmetries, and show how to realize these neutrino masses. Then we propose a concrete model involving a dark matter candidate and an extra gauge boson, and show their phenomenologies.
Discrete non-abelian flavor symmetries give in a natural way tri-bimaximal (TBM) mixing as showed in a prototype model. However neutrino mass matrix pattern may be very different from the tri-bimaximal one if small deviations of TBM will be observed. We give the result of a model independent analysis for TBM neutrino mass pattern.
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.
We review recent work on the interplay between broken family symmetries which give rise to approximate texture zeros in the mass matrices of the quarks and leptons and the presence of certain hierarchy patterns in the spectrum of massive neutrinos.
We use an effective-field-theory approach to construct models with naturally light sterile neutrinos, due to either exact or accidental global symmetries. The most attractive models we find are based on gauge symmetries, either discrete or continuous. We give examples of simple models based on Z_N, U(1)', and SU(2)'.
I review some of the recent progress (up to December 2005) in applying non-Abelian discrete symmetries to the family structure of leptons, with particular emphasis on the tribimaximal mixing ansatz of Harrison, Perkins, and Scott.
The fact that neutrinos have mass allows them to possess many other properties, like a magnetic dipole moment and a finite decay width. Theoretical expectations for these are, however, well beyond current experimental bounds, and the discovery of new exotic neutrino properties would indicate the presence of (more) new physics. Here, I review some of the current bounds on exotic neutrino properties. Neutrino experiments are unique probes of several fundamental space-time symmetries, including invariance under CP and Lorentz transformations. I discuss how precision neutrino experiments are used …
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.
Flavour symmetries are fundamental tools in the search for an explanation to the flavour puzzle: fermion mass hierarchies, the neutrino mass ordering, the differences between the mixing matrices in the quark and lepton sector, can all find an explanation in models where the fermion generations undergo specific geometric relations. An overview on the implementation of continuous symmetries in the flavour sector is presented here, focussing on the lepton sector.
Texture zeroes in neutrino mass matrix $M_ν$ may give us hints about the symmetries involved in neutrino mass generation. We examine the viability of such texture zeroes in a model independent way through a bottom-up approach. Using constraints from the neutrino oscillation data, we develop an analytic framework that can identify these symmetries and quantify deviations from them. We analyze the textures of $M_ν$ as well as those of $M_M$, the mass matrix of heavy Majorana neutrinos in the context of Type-I seesaw. We point out how the viability of textures depends on the absolute neutrino mas…
We constructed a model of neutrino masses using Froggatt-Nielsen mechanism with $U(1) \times Z_3 \times Z_2$ flavor symmetry. The model predicts that $(2/3)m_2/m_3 \sim \sqrt{2}\sinθ_{13}$ at lepton number violating scale $M_1$. It is shown that the small values for $m_2/m_3$ and $\sinθ_{13}$ are consequences of breaking discrete symmetries.
We consider a class of models of neutrino mixing with $S_4$ flavour symmetry and generalised CP symmetry, broken to $Z_2$ and $Z_2 \times {\rm CP}$ residual symmetries in the charged lepton and neutrino sectors, respectively. In this scheme, and up to discrete ambiguities, the neutrino mixing matrix is determined by two angles and one phase. We classify the phenomenologically viable mixing patterns, deriving predictions for the Dirac and Majorana CPV phases and for the effective Majorana mass in neutrinoless double beta decay.
Flavour symmetries are fundamental tools in the search for an explanation to the flavour puzzle: fermion mass hierarchies, the neutrino mass ordering, the differences between the mixing matrices in the quark and lepton sector, can all find an explanation in models where the fermion generations undergo specific geometric relations. An overview on the implementation of continuous symmetries in the flavour sector is presented here, focussing on the lepton sector.
The current status of our knowledge of the 3-neutrino mixing parameters and of the CP violation in the lepton sector is summarised. The discrete symmetry approach to understanding the observed pattern of neutrino mixing and the related predictions for neutrino mixing angles and leptonic Dirac CP violation are reviewed.
The recent discovery by SuperKamiokande of evidence for neutrino masses requires the addition of at least seven new parameters to the Standard Model. We discuss the general theoretical schemes which require their inclusion, and point out how quark-lepton symmetries, either in the framework of Grand Unification, or of string theories, can be used to determine them
We investigate a model with an extra $Z_{2}$ gauge symmetry in the Standard Model. We assume that only the scalars and the leptons carry non-zero charge. The symmetry gives a structure to the mass matrix for the neutrinos. With two extra Higgs singlets and two extra singlet right-handed neutrinos we can build a model that fits the requirements of the MSW-solution of the Solar neutrino problem. With a third singlet right-handed neutrino it is also possible to have a 10 eV neutrino, a dark matter candidate.
Tri-bimaximal mixing is a specific lepton mixing ansatz, which has been shown to account very successfully for the established neutrino oscillation data. Working in a particular basis (the `circulant basis'), we identify three independent symmetries of tri-bimaximal mixing, which we exploit to set the tri-bimaximal hypothesis in context, alongside some simple, phenomenologically interesting CP-conserving and CP-violating generalisations.
We have studied the most general neutrino mass matrices in models with SU(2) and SU(3) horizontal symmetries. Without going into the details of the models it is possible to write down the effective operators, which predict the structure of the Majorana neutrino mass matrices. Unlike other extensions of the standard model, the structure is now independent of the effective Yukawa couplings and depends entirely on the Higgs which gives mass to the other fermions. In the case of SU(3) symmetries the lowest dimensional operators are forbidden requiring a low mass scale for lepton number violation.
Recent neutrino experiments have made very significant progresses and our knowledge of neutrino masses and mixing has considerably improved. In a model independent Monte Carlo approach, we have examined a very large class of textures, in the context of non abelian horizontal symmetries; we have found that neutrino data select only those charged lepton matrices with left-right asymmetric texture. The large atmospheric mixing angle needs m_{23} ~= m_{33}. This result,if combined with similar recent findings for the quark sector in the B oscillations, can be interpreted as a hint for SU(5) unific…
In this talk we discuss the implications of the Minimal Supersymmetric Standard Model augmented by a single U(1) anomalous family symmetry for neutrino masses and mixing angles. The left-handed neutrino states are provided with Majorana masses through a dimension-five operator in the absence of right handed neutrino components. Assuming symmetric lepton mass matrices, the model predicts inverse hierarchical neutrino mass spectrum, theta_13=0 and large mixing while at the same time it provides acceptable mass matrices for the charged fermions.
Here we propose an $A_4$ flavour symmetry model which implies a lower bound on the neutrinoless double beta decay rate, corresponding to an effective mass parameter $M_{ee} \gsim 0.03$ eV, and a direct correlation between the expected magnitude of CP violation in neutrino oscillations and the value of $\sin^2θ_{13}$, as well as a nearly maximal CP phase $δ$.
The problem of neutrino masses and mixing angles is analysed in a class of supersymmetric grand unified models, with SO(10) gauge symmetry and global U(2) flavour symmetry. Adopting the seesaw mechanism for the generation of the neutrino masses, one obtains a mass matrix for the left-handed neutrinos which is directly related to the parameters of the charged sector, while the unknown parameters of the right-handed Majorana mass matrix are inglobed in a single factor.
We construct and present a model for leptonic mixing based on higher-dimensional operators, using the Froggatt-Nielsen mechanism, and Abelian horizontal symmetries (flavor symmetries) of continuous and discrete type. Our model naturally yields bilarge leptonic mixing, coming from both the charged leptons and the neutrinos, and an inverted neutrino mass hierarchy spectrum. The obtained values of the parameters, i.e., the leptonic mixing parameters and the neutrino mass squared differences, are all consistent with the atmospheric neutrino data and the Mikheyev-Smirnov-Wolfenstein large mixing an…
The experimental data on atmospheric and solar neutrinos suggest that there is near-maximal mixing between ν_μand ν_τbut that their masses are hierarchically separated. In models of Abelian horizontal symmetries, mixing of O(1) generically implies that the corresponding masses are of the same order of magnitude. We describe two new mechanisms by which a large hierarchy between strongly mixed neutrinos can be achieved in this framework. First, a discrete Abelian symmetry can give the desired result in three ways: mass enhancement, mixing enhancement and mass suppression. Second, holomorphic zer…
The experimental data on atmospheric and solar neutrinos are used to test the framework of non-anomalous Abelian horizontal gauge symmetries with only three light active neutrinos. We assume that the hierarchy in mass-squared splittings is not accidental and that the small breaking parameters are not considerably larger than 0.2. We find that the small angle MSW solution of the solar neutrino problem can only be accommodated if the $ν_μ-ν_τ$ mass hierarchy depends on the charges of at least three sterile neutrinos. The large angle MSW solution can be accommodated in simpler models if $ν_e$ and…
The neutrino oscillation data are well explained by the tri-bimaximal pattern. Recently it has been shown that also the bimaximal pattern could be a very good starting point in order to describe the lepton mixing. In this paper I review both the flavour structures and then I present an explicit example.
The existence of maximal and minimal mixing angles in the neutrino mixing matrix motivates the search for extensions to the Standard Model that may explain these angles. A previous study (C.I.Low and R.R.Volkas, Phys.Rev.D68,033007(2003)), began a systematic search to find the minimal extension to the Standard Model that explains these mixing angles. It was found that in the minimal extensions to the Standard Model which allow neutrino oscillations, discrete unbroken lepton family symmetries only generate neutrino mixing matrices that are ruled out by experiment. This paper continues the searc…
We demonstrate that Abelian family symmetries allow one to enforce texture zeros in arbitrary entries of the fermion mass matrices. Placing zeros in any number of elements of all occurring mass matrices can be done with two alternative methods; one of them utilizes the group Z_n with n sufficiently high. Concentrating on the lepton sector and on neutrino masses, we discuss the methods in the case of seesaw models and scalar triplet models. As an illustration, we present an example for each type of model.
In view of the fact that the data on neutrino mixing are still compatible with a situation where Bimaximal mixing is valid in first approximation and it is then corrected by terms of order of the Cabibbo angle, we present examples where these properties are naturally realized. The models are supersymmetric in 4-dimensions and based on the discrete non-Abelian flavour symmetry S4.
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 study the role of a very general type of flavor symmetry in controlling the strength of R-parity violation in supersymmetric models. We assume that only leptons are charged under a global symmetry whose breaking induces lepton number (and, hence, R-parity) violation. The charge assignments of leptons under this symmetry are such that the total number of independent lepton number violating couplings is reduced from 39 to 6. The most severe constraints on these flavor-correlated couplings arise from neutrino masses and mixing as well as from the non-observation of K_L -> eμ. We find that such…
Expressions for neutrino oscillations contain a high degree of symmetry, but typical forms for the oscillation probabilities mask these symmetries of the oscillation parameters. We elucidate the $2^7$ parameter symmetries of the vacuum parameters and draw connections to the choice of definitions of the parameters as well as interesting degeneracies. We also show that in the presence of matter an \emph{additional} set of $2^7$ parameter symmetries exist of the matter parameters. Due to the complexity of the exact expressions for neutrino oscillations in matter, numerous approximations have been…
Motivated by effective low energy models of string origin, we discuss the neutrino masses and mixing within the context of the Minimal Supersymmetric Standard Model supplemented by a U(1) anomalous family symmetry and additional Higgs singlet fields charged under this extra U(1). In particular, we interpret the solar and atmospheric neutrino data assuming that there are only three left-handed neutrinos which acquire Majorana masses via a lepton number violating dimension-five operator. We derive the general form of the charged lepton and neutrino mass matrices when two different pairs of singl…
The hypothesis of an additional abelian symmetry acting in a different way on the three families of leptons leads to interesting predictions in the neutrino sector. Contrary to what happens in most seesaw models, the structures of the Dirac and the Majorana matrices are determined without any ansatz, and the neutrino masses and mixing angles are fixed once the lepton charges under the family symmetry have been chosen. Two explicit models using this idea are presented.
Neutrinoless double beta decay ($β\beta0ν$) is among the only realistic probes of Majorana neutrinos. In the standard scenario, dominated by light neutrino exchange, the process amplitude is proportional to $m_{ee}$, the $e-e$ element of the Majorana mass matrix. Naively, current data allows for vanishing $m_{ee}$, but this should be protected by an appropriate flavor symmetry. All such symmetries lead to mass matrices inconsistent with oscillation phenomenology. I perform a spurion analysis to break all possible Abelian symmetries that guarantee vanishing $β\beta0ν$ rates and search for minim…
We construct phenomenologically viable models of lepton masses and mixing based on modular $A_4$ invariance broken to residual symmetries $\mathbb{Z}^{T}_3$ or $\mathbb{Z}^{ST}_3$ and $\mathbb{Z}^S_2$ respectively in the charged lepton and neutrino sectors. In these models the neutrino mixing matrix is of trimaximal mixing form. In addition to successfully describing the charged lepton masses, neutrino mass-squared differences and the atmospheric and reactor neutrino mixing angles $θ_{23}$ and $θ_{13}$, these models predict the values of the lightest neutrino mass (i.e., the absolute neutrino …
We study the approximate flavour symmetries imposed on the lepton sector assuming see-saw mechanism as the neutrino mass structure. We apply the symmetry to various neutrino phenomenologies and obtain constraints on neutrino masses and mixings.
Given the particle content of the standard model without and with a right-handed neutrino, the requirement that all anomalies cancel singles out a set of possible global symmetries which can be gauged. I review this topic and propose a new gauge symmetry B - 3L_tau in the context of the minimal standard model consisting of the usual three families of quarks and leptons plus just one nu_R. The many interesting phenomenological consequences of this hypothesis are briefly discussed.
Motivated by the Super-Kamiokande data, we revisit models with U(1) symmetries and discuss the origin of neutrino masses and mixings in such theories. We show that, in models with just three light neutrinos and a hierarchy of neutrino masses, large (2-3) mixing fixes the lepton doublet U(1) charges and is thus related to the structure of the charged lepton mass matrix. We discuss the fermion mass structure that follows from the Abelian family symmetry with an extended gauge group. Requiring that the quark and lepton masses be ordered by the family symmetry, we identify the most promising schem…
We propose a radiative seesaw model at one-loop level, introducing fields with large multiplet of $SU(2)_L$. Thanks to large representations, any additional symmetries are not needed. In this framework, we formulate lepton and new fermion sector such as mass matrices, LFVs, and muon $g-2$. Furthermore, we show our cut-off scale via RGEs of $SU(2)_L$, and numerical analysis at a benchmark point included in dark matter candidate. Finally, we brief discuss possibility to detect at colliders.
In this paper we discuss a new way to derive neutrino mixing patterns, which originates from the idea proposed in a recent article by Hernandez and Smirnov. Its applications to various cases are discussed. We first present the complete set of possible mixing patterns for the minimal case where unbroken residual symmetries of the Majorana neutrino and left-handed charged-lepton mass matrices obey some general assumptions that are also satisfied by many models based on discrete symmetries. We find that they are either well-known mixing patterns or phenomenologically disfavored ones. It shows cle…
The flavour neutrino puzzle is often addressed by considering neutrino mass matrices $m$ with a certain number of vanishing entries ($m_{ij}=0$ for some values of the indices), since a reduction in the number of free parameters increases the predictive power. Symmetries that can enforce textures zero can also enforce a more general type of conditions $f(m_{ij})=0$ with $f$ some function of the matrix elements $m_{ij}$. In this case $m$ can have all entries non-vanishing with no reduction in its predictive power. We classify all generation-dependent $U(1)$ symmetries which, in the presence of t…
We consider a class of models of neutrino mixing with $S_4$ lepton flavour symmetry combined with a generalised CP symmetry, which are broken to residual $Z_2$ and $Z_2 \times H^ν_{\rm CP}$ symmetries in the charged lepton and neutrino sectors, respectively, $H^ν_{\rm CP}$ being a remnant CP symmetry of the neutrino Majorana mass term. In this set-up the neutrino mixing angles and CP violation (CPV) phases of the neutrino mixing matrix depend on three real parameters - two angles and a phase. We classify all phenomenologically viable mixing patterns and derive predictions for the Dirac and Maj…
Approximate flavor symmetries in the quark sector have been used as a handle on physics beyond the Standard Model. Due to the great interest in neutrino masses and mixings and the wealth of existing and proposed neutrino experiments it is important to extend this analysis to the leptonic sector. We show that in the see-saw mechanism, the neutrino masses and mixing angles do not depend on the details of the right-handed neutrino flavor symmetry breaking, and are related by a simple formula. We propose several ansätze which relate different flavor symmetry breaking parameters and find that the M…
A very simple extension of the standard model to include an Abelian family symmetry is able to describe the hierarchy of quark and lepton masses and their mixing angles together with the unification of gauge couplings. We consider the implications of this model for neutrino masses and mixing angles and show that they are determined up to a discrete ambiguity corresponding to the representation content of the Higgs sector responsible for the Majorana mass matrix.
In this letter we consider that assuming: a) that the only left-handed neutral fermions are the active neutrinos, b) that $B-L$ is a gauge symmetry, and c) that the $L$ assignment is restricted to the integer numbers, the anomaly cancellation imply that at least three right-handed neutrinos must be added to the minimal representation content of the electroweak standard model. However, two types of models arise: i) the usual one where each of the three identical right-handed neutrinos has total lepton number L=1; ii) and the other one in which two of them carry L=4 while the third one carries $…
We present a low-scale type-I seesaw scenario with discrete flavor and CP symmetries. This scenario not only explains the measured values of the lepton mixing angles, but also makes predictions for leptonic CP violation, and connects the low-energy CP phases relevant for neutrino oscillation and neutrinoless double beta decay experiments with the high-energy CP phases relevant for leptogenesis. We show that the three right-handed Majorana neutrinos in this scenario have (almost) degenerate masses and their decays can explain the observed baryon asymmetry of the Universe via resonant leptogenes…
Augmenting the Standard Model by three right-handed neutrinos allows for an anomaly-free gauge group extension G_max = U(1)_(B-L) x U(1)_(L_e-L_mu) x U(1)_(L_mu-L_tau). While simple U(1) subgroups of G_max have already been discussed in the context of approximate flavor symmetries, we show how two-zero textures in the right-handed neutrino Majorana mass matrix can be enforced by the flavor symmetry, which is spontaneously broken very economically by singlet scalars. These zeros lead to two vanishing minors in the low-energy neutrino mass matrix after the seesaw mechanism. This study may provid…
We consider the $A_4$, $S_4$ and $A_5$ discrete lepton flavour symmetries in the case of 3-neutrino mixing, broken down to non-trivial residual symmetries in the charged lepton and neutrino sectors in such a way that at least one of them is a $Z_2$. Such symmetry breaking patterns lead to predictions for some of the three neutrino mixing angles and/or the leptonic Dirac CP violation phase $δ$ of the neutrino mixing matrix. We assess the viability of these predictions by performing a statistical analysis which uses as an input the latest global data on the neutrino mixing parameters. We find 14…
Motivated by the possibility that new (gauge) symmetries which are broken at the grand- (string-) unification scale give rise to texture zeros in the fermion mass matrices which are at the origin of the hierarchy of masses and mixings we explore the effect of such zeros on the neutrino spectrum of SUSY-GUT models. We find that the quadratic-seesaw spectrum on which most expectations are focused is neither the only nor the most interesting possibility. Cases of strong $ν_μ - ν_τ$ or $ν_e - ν_τ$ mixing are present for a specific texture structure of the Yukawa matrices and experimental evidence …
Recent progress is reviewed regarding the application of the non-Abelian symmetries S_3, D_4, and A_4 to the understanding of family structure in leptons and quarks.
Status of the discrete symmetry approach to explanation of the lepton masses and mixing is summarized in view of recent experimental results, in particular, establishing relatively large 1-3 mixing. The lepton mixing can originate from breaking of discrete flavor symmetry $G_f$ to different residual symmetries $G_{\ell}$ and $G_ν$ in the charged lepton and neutrino sectors. In this framework the {\it symmetry group condition} has been derived which allows to get relations between the lepton mixing elements immediately without explicit model building. The condition has been applied to different…
Lepton mixing can originate from the breaking of a flavor symmetry in different ways in the neutrino and the charged lepton sector. We propose an extension of this framework which allows to connect the mixing parameters with masses, and more precisely, with certain types of degeneracy of the neutrino mass spectrum. We obtain relations between the mixing parameters for the cases of partial degeneracy, m1 = m2, and complete degeneracy, m1 = m2 = m3. These relations determine also the Majorana phases. It is shown that relatively small corrections to these lowest order results can produce the requ…
We propose a one-loop radiative Majorana-type neutrino-mass matrix without any kind of additional symmetries by introducing two leptoquark-like bosons only. In this scenario, we show that the anomaly appearing in the process $b\to s\ell\bar\ell$ can be explained without any conflicts against various constraints such as lepton-flavor violations, flavor-changing neutral currents, oblique parameters $ΔS,\ ΔT$, and the Drell-Yan process. We make the predictions for the flavor-violating lepton-pair production ($eμ$, $eτ$, and $μτ$) at the LHC, as well as the cross sections for pair production of th…
We re-examine the constraints on continuous family symmetries coming from flavour changing neutral current limits on the D-term contributions to squark and slepton masses. We show that, for a restricted choice of the familon sector, continuous family symmetries are consistent with even the most conservative limits both for the case of gauge mediated supersymmetry breaking and the case of gravity mediated supersymmetry breaking.
