W. Grimus, L. Lavoura
We consider trimaximal lepton mixing, defined by |U_{alpha 2}|^2 = 1/3 for all alpha = e, mu, tau. This corresponds to a two-parameter lepton mixing matrix U. We present a model for the lepton sector in which trimaximal mixing is enforced by softly broken discrete symmetries; one version of the model is based on the group Delta(27). A salient feature of our model is that no vacuum alignment is required.
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Modified trimaximal mixing for solar and reactor neutrino mixing angles
针对三极大混合方案无法同时使太阳和反应堆中微子混合角达到最佳拟合值的问题，提出一种最小修正方案，通过引入额外实参数实现两者最佳拟合值的同时预测。
Trimaximal mixing is the mixing hypothesis with maximal symmetry. In trimaximal mixing there remains a still worrying conflict between the large values of $Δm^2$ preferred by the atmospheric fits (possibly supported by the early K2K data) and reactor limits on $ν_e$-mixing. However, the latest solar results do seem to point to energy-independent (ie. `no-scale') solar solutions, like the trimaximal solution.
We present a model which employs the seesaw mechanism with five right-handed neutrinos, leading to trimaximal and CP-conserving lepton mixing. Tri-bimaximal mixing is a natural limiting case of our model which occurs when one particular vacuum expectation value is real and preserves the mu-tau interchange symmetry of the Lagrangian. Our model allows for leptogenesis even in the case of exact tri-bimaximal mixing.
We propose a flavour theory of leptons implementing an $A_4$ family symmetry. Our scheme provides a simple way to derive trimaximal neutrino mixing from first principles, leading to simple and testable predictions for neutrino mixing and CP violation. Dark matter mediates neutrino mass generation, as in the simplest scotogenic model.
We construct a supersymmetric $S_4$ flavor symmetry model with one of the trimaximal neutrino mixing patterns, the so-called TM$_1$, by using the novel way to stabilize flavons, which we proposed recently. The flavons are assumed to have tachyonic supersymmetry breaking mass terms and stabilized by higher-dimensional terms in the potential. We can obtain the desired alignment structure of the flavon vacuum expectation values to realize neutrino masses and mixings consistent with the current observations. This mechanism naturally avoids the appearance of dangerous cosmological domain walls.
In this paper we study a parametrized description of neutrino mixing from a phenomenological point of view. We concentrate on the parametrization in terms of higher order corrections to the leading order mixing matrix. A method to describe subleading contributions and its applications to tri-bimaximal mixing are discussed. We show that mixing matrices similar to tri-bimaximal-Cabibbo mixing can be obtained by straightforward choices of parameters. To achieve better agreement with the experimental data without increasing the number of free parameters, we impose a simple phenomenological relatio…
We construct two flavor models based on $S_4$ family symmetry and generalised CP symmetry. In both models, the $S_4$ family symmetry is broken down to the $Z^{SU}_2$ subgroup in the neutrino sector, as a consequence, the trimaximal $\text{TM}_1$ lepton mixing is produced. Depending on the free parameters in the flavon potential, the Dirac CP is predicted to be either conserved or maximally broken, and the Majorana CP phases are trivial. The two models differ in the neutrino sector. The flavon fields are involved in the Dirac mass terms at leading order in the first model, and the neutrino mass…
We discuss a minimal flavour model with twin modular symmetries, leading to trimaximal TM$_1$ lepton mixing in which the first column of the tri-bimaximal lepton mixing matrix is preserved. The model involves two modular $S_4$ groups, one acting in the neutrino sector, associated with a modulus field value $τ_{SU}$ with residual $Z^{SU}_2$ symmetry, and one acting in the charged lepton sector, associated with a modulus field value $τ_{T}$ with residual $Z^{T}_3$ symmetry. Apart from the predictions of TM$_1$ mixing, the model leads to a new neutrino mass sum rule which implies lower bounds on …
Recent T2K results indicate a sizeable reactor angle theta_13 which would rule out exact tri-bimaximal lepton mixing. We study the vacuum alignment of the Altarelli-Feruglio A4 family symmetry model including additional flavons in the 1' and 1" representations and show that it leads to trimaximal mixing in which the second column of the lepton mixing matrix consists of the column vector (1,1,1)^T/sqrt{3}, with a potentially large reactor angle. In order to limit the reactor angle and control the higher order corrections, we propose a renormalisable S4 model in which the 1' and 1" flavons of A4…
We analyze in detail the predictions of "trimaximal" neutrino mixing, which is defined by a mixing matrix with identical second column elements. This column is therefore identical to the second column in the case of tri-bimaximal mixing. We also generalize trimaximal mixing by assuming that the other rows and columns of the mixing matrix individually have the same forms as for tri-bimaximal mixing. The phenomenology of these new mixing scenarios is studied. We emphasize how trimaximal mixings can be distinguished experimentally from broken tri-bimaximal mixing.
Recent T2K, MINOS and Double CHOOZ results, together with global fits of mixing parameters, indicate a sizeable reactor angle theta13 ~ 8 deg which, if confirmed, would rule out tri-bimaximal (TB) lepton mixing. Recently two of us studied the vacuum alignment of the Altarelli-Feruglio A4 family symmetry model including additional flavons in the 1' and 1" representations, leading to so-called "trimaximal" neutrino mixing and allowing a potentially large reactor angle. Here we show how such a model may arise from a Supersymmetric (SUSY) Grand Unified Theory (GUT) based on SU(5), leading to sum r…
In this paper, we make an attempt to combine the neutrino trimaximal (TM1 and TM2) mixings and $μ$-$τ$ reflection symmetry in the type-I seesaw model. Such a scenario is highly restrictive and predictive: in addition to three right-handed neutrino masses, there are only five real parameters; all the lepton flavor mixing parameters except for $θ^{}_{13}$ will be predicted. The relations between the model parameters and the measurable neutrino parameters will be derived. The implications of this scenario for leptogenesis will be explored in detail. A further reduction of this scenario to the mor…
Revisiting Trimaximal TM2 mixing in two $A_4$ modular symmetries
本研究构建含两种模$A_4$对称的最小轻子味模型，通过限制模场稳定子、扫描可行稳定子预测出唯一三极大TM2混合，并将最轻中微子质量等相关参数的预测分为三类。
The measurement of the reactor angle by the Daya Bay and RENO experiments in 2012 has ruled out the tri-bimaximal paradigm. Adopting an S4 family symmetry, we propose direct models of the trimaximal type TM1 in which the tri-bimaximal Klein symmetry of the neutrino sector is broken to a residual Z2 symmetry. In such a scenario, the solar mixing angle is decreased compared to its tri-bimaximal value by about one degree, thus bringing it in excellent agreement with experimental observation. The atmospheric mixing angle, on the other hand, depends on the CP violating Dirac phase delta. Imposing C…
In this paper, we consider the imbedding of the popular and well-motivated trimaximal mixing and $μ$-$τ$ reflection symmetry (which can help us shape the forms of the neutrino mass matrix) in the minimal seesaw model (which contains much fewer parameters than the general seesaw model) with two TeV-scale right-handed neutrinos (for realizing a low-scale seesaw) of nearly degenerate masses (for realizing a resonant leptogenesis). However, either for the trimaximal mixing scenario (which is realized through the Form Dominance approach here) or for the $μ$-$τ$ reflection symmetry scenario, leptoge…
When the neutrino mass eigenstate $ν_2$ is trimaximally mixed, the mixing matrix is called trimaximal. The middle column of trimaximal mixing matrix is identical to tri-bimaximal mixing and the other two columns are subject to unitarity constraints. This corresponds to a mixing matrix with four independent parameters in the most general case. Apart from the two Majorana phases, the mixing matrix has only one free parameter in the CP conserving limit. Trimaximality results into interesting interplay between mixing angles and CP violation. A notion of maximal CP violation naturally emerges here:…
In the seesaw framework, in the basis of $M^{}_{\rm R}$ being diagonal, we explore the simplified textures of $M^{}_{\rm D}$ that can naturally yield the trimaximal neutrino mixings and their consequences for the neutrino parameters and leptogenesis. We first formulate the generic textures of $M^{}_{\rm D}$ that can naturally yield the trimaximal mixings and then examine if their parameters can be further reduced. Our analysis is restricted to the simple but instructive scenario that there is only one phase parameter $ϕ$ responsible for both the CP violating effects at low energies and leptoge…
We analyze neutrino mass matrices having one texture zero, assuming that the neutrino mixing matrix has either its first (TM$_1$) or second (TM$_2$) column identical to that of the tribimaximal mixing matrix. We found that all the six possible one texture zero neutrino mass matrices are compatible with the present neutrino oscillation data when combined with TM$_1$ or TM$_2$ mixing. These textures have interesting predictions for the presently unknown parameters such as the effective Majorana neutrino mass, the Dirac CP violating phase and the neutrino mass scale. We also present a way to theo…
We study neutrino mass matrices with one texture equality and the neutrino mixing matrix having either its first (TM$_1$) or second (TM$_2$) column identical to that of the tribimaximal mixing matrix. We found that out of total fifteen possible neutrino mass matrices with one texture equality, only seven textures are compatible with $TM_1$ mixing and six textures are compatible with $TM_2$ mixing in the light of the current neutrino oscillation data. These textures have interesting implications for the presently unknown parameters such as the neutrino mass scale, effective Majorana neutrino ma…
One vanishing minor in neutrino mass matrix using trimaximal mixing
本文基于trimaximal混合矩阵研究中微子质量矩阵中一个零子式的六种模式，验证其现象学可行性，预测有效中微子质量等参数，并提出在seesaw模型中实现该模式的味模型。
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 …
In this paper, we impose a magic symmetry on the neutrino mass matrix $m_ν$ with universal four-zero texture and diagonal reflection symmetries. Due to the magic symmetry, the MNS matrix has trimaximal mixing inevitably. Since the lepton sector has only six free parameters, physical observables of leptons are all determined from the charged leptons masses $m_{ei}$, the neutrino mass differences $Δm_{i1}^{2}$, and the mixing angle $θ_{23}$. This scheme predicts $\sin θ_{13} = 0.149$, that is almost equal to the latest best fit, as a function of the lepton masses $m_{e, μ}$ and the mass differen…
Phenomenological study of two minor zeros in neutrino mass matrix using trimaximal mixing
本文利用三极大混合矩阵系统分析中微子质量矩阵中两个次零点的十五种可能情形，发现仅Class A1和A2与现有振荡数据相容，并给出质量与CP相位预言及基于Z8对称群的seesaw味模型实现。
Following the recent T2K indication of a sizeable reactor angle, we present a class of models which fix θ_{13} while preserving trimaximal solar mixing. The models are based on a new type of constrained sequential dominance involving new vacuum alignments, along the (1,2,0)^T or (1,0,2)^T directions in flavour space. We show that such alignments are easily achieved using orthogonality, and may replace the role of the subdominant flavon alignment (1,1,1)^T in constrained sequential dominance. In such models, with a normal hierarchical spectrum, the reactor angle is related to a ratio of neutrin…
Trimaximal mixing with one texture zero from type II seesaw and $Δ(54)$ family symmetry
本文提出基于Δ(54)味对称性和II型跷跷板机制的中微子模型，其质量矩阵含一个纹理零并满足魔幻对称性，预言正质量等级、大气角下八分圆及CP必然破坏，并给出可被未来实验检验的有效马约拉纳质量范围。
Leptogenesis consequences of trimaximal mixing and $μ$-$τ$ reflection symmetry in the most minimal seesaw model
该研究在含赝狄拉克右手中微子对的最极简跷跷板模型中，探究TM1中微子混合与μ-τ反射对称性的实现及轻子生成效应，提出两种右手中微子质量分裂方案，并分析味依赖转换效率与对称性破缺对轻子生成的作用。
Neutrino mixing model for best-fit values of $θ_{12}$ and $θ_{13}$
本文针对三极大混合模型无法同时复现θ₁₂和θ₁₃最佳拟合值的问题，提出一种新型中微子混合模型，可同时再现这两个混合角的最佳拟合值。
Trimaximal Mixing and Extended Magic Symmetry in a Model of Neutrino Mass Matrix
本文提出扩展magic对称性的中微子质量矩阵现象学ansatz，减少自由参数并提高可预测性，发现TM2混合下各参数强相关，结合宇宙学界限排除倒序等级，并在Type-I+II seesaw框架下用Δ(54)对称性实现该构建。
The $π/12$ model: trimaximal first-column lepton mixing with charged-lepton $μ$--$τ$ breaking
该论文提出π/12模型，描述带带电轻子μ-τ破缺的轻子混合，通过TM₁中微子部分与带电轻子2-3旋转构造，预测CP相位、ε₂等，可由Hyper-Kamiokande检验，质量预测符合DESI限制。
The $μ$-$τ$ reflection symmetry $(ν_{e},\thinspaceν_μ,\thinspaceν_τ)\rightarrow(\overlineν_{e},\thinspace\overlineν_τ,\thinspace\overlineν_μ)$ and the TM1 mixing (a PMNS matrix with the first column fixed to the TBM form) are both well compatible with experiments. If both approaches are simultaneously assumed, all lepton mixing parameters except for $θ_{13}$ are predicted. In particular, one expects maximal CP violation ($|δ|=90^{\circ}$), maximal atmospheric mixing ($θ_{23}=45^{\circ}$), a slightly less-than-TBM solar mixing angle ($θ_{12}\approx34^{\circ}$), as well as values of $0$ or $π$ f…
On Lepton Flavor Violation and Dark Matter in Scotogenic model with Trimaximal Mixing
本文研究了采用TM$_2$混合的Scotogenic模型，分析了暗物质遗迹密度与轻子味破坏，发现最轻 sterile neutrino 质量分裂最高约15%，并引入扩展魔对称性完全确定Yukawa耦合矩阵，排除了倒立层级场景。
Trimaximal Mixing Patterns Meet the First JUNO Result
研究JUNO结果对三重最大混合模式TM1和TM2的影响，发现TM1在1σ范围内，TM2在3σ外，通过RG修正使两者与JUNO数据一致，但Majorana情况受限，TM2被排除。
Encouraged by the latest SNO results, we consider the lepton mixing matrix in the approximation that the nu_2 mass eigenstate is trimaximally (democratically) mixed. This suggests a new parameterization of the remaining mixing degrees of freedom, which eschews mixing angles, dealing instead, directly with the complex parameter U_e3 of the mixing matrix. Unitarity triangles then take a particularly simple form, which we hope will faciltate comparison with experiment.
From seesaw over-suppression to trimaximal mixing: why $A_4$ is the minimal resolution of the $Z_3$ neutrino failure
本文研究了I型锯齿机制能否拯救 $Z_3$ Froggatt--Nielsen 框架，发现无法实现。通过右 handed Majorana 质量的 $Z_3$ 电荷结构，导致轻中微子质量被过度抑制，同时 $A_4$ 对称性提供了解决方案。
We perform a systematical and analytical study of lepton mixing which can be derived from the subgroups of $SU(3)$ under the assumption that neutrinos are Dirac particles. We find that type D groups can predict lepton mixing patterns compatible with the experimental data at $3σ$ level. The lepton mixing matrix turns out to be of the trimaximal form, and the Dirac CP violating phase is trivial. Moreover, we extend the flavor symmetry to the quark sector. The Cabibbo mixing between the first two generations of quarks can be generated by type D groups. Since all the finite subgroups of $U(3)$ whi…
Recent stringent experiment data of neutrino oscillations induces partial symmetries such as $Z_{2}$, $Z_{2}\times CP$ to derive lepton mixing patterns. New partial symmetries expressed with elements of group algebras are studied. A specific lepton mixing pattern could correspond to a set of equivalent elements of a group algebra. The transformation which interchanges the elements could express a residual $CP$ symmetry. Lepton mixing matrices from $S_{3}$ group algebras are of the trimaximal form with the $μ-τ$ reflection symmetry. Accordingly, elements of $S_{3}$ group algebras are equivalent…
Although the measurement of the reactor angle has killed tribimaximal lepton mixing, its descendants survive with charged lepton corrections, or in less constrained forms such as trimaximal mixing and/or mu-tau symmetry, each with characteristic predictions. Such patterns may be enforced by a remnant of some non-Abelian discrete family symmetry, possibly together with a generalised CP symmetry, which could originate from continuous gauge symmetry and/or superstring theory in compactified extra dimensions, as a finite subgroup of the modular symmetry.
We obtain predictions of lepton mixing parameters for direct models based on Delta(6n^2) family symmetry groups for arbitrarily large n in which the full Klein symmetry is identified as a subgroup of the family symmetry. After reviewing and developing the group theory associated with Delta(6n^2), we find many new candidates for large n able to yield reactor angle predictions within 3 sigma of recent global fits. We show that such Delta(6n^2) models with Majorana neutrinos predict trimaximal mixing with reactor angle theta_{13} fixed up to a discrete choice, an oscillation phase of either zero …
We postulate that the neutrino mass matrix in the lepton flavour basis is an S3 group matrix in the natural representation of S3. This immediately requires one neutrino to be trimaximally mixed, as suggested by the solar neutrino data. We go on to postulate that the charged-lepton mass matrix in the neutrino mass-basis is an S3 class matrix in the natural representation of the S3 class-algebra, leading to exact tri-bimaximal mixing, which is compatible with data overall. The tri-bimaximal mixing matrix is seen to be closely related to the S3 character table, and is properly the S2 C S3 table o…
The neutrino mass matrix has remnant CP symmetry expressed in terms of the lepton mixing matrix, and vice versa the remnant CP transformations allow us to reconstruct the mixing matrix. We study the scenario that all the four remnant CP transformations are preserved by the neutrino mass matrix. The most general parameterization of remnant CP transformations is presented. The lepton mixing matrix is completely fixed by the remnant CP, and its explicit form is derived. The necessary and sufficient condition for conserved Dirac CP violating phase is found. If the Klein four flavor symmetry genera…
Generalised CP transformations are the only known framework which allows to predict Majorana phases in a flavour model purely from symmetry. For the first time generalised CP transformations are investigated for an infinite series of finite groups, $Δ(6n^2)=(Z_n\times Z_n)\rtimes S_3$. In direct models the mixing angles and Dirac CP phase are solely predicted from symmetry. $Δ(6n^2)$ flavour symmetry provides many examples of viable predictions for mixing angles. For all groups the mixing matrix has a trimaximal middle column and the Dirac CP phase is 0 or $π$. The Majorana phases are predicte…
We parametrize lepton mixing matrix, known as PMNS matrix, in terms of three parameters which account deviations of three mixing angles from their bi-maximal or tri-bimaximal values. On the basis of this parametrization we can determine corresponding charged lepton mixing matrix in terms of those three parameters which can deviate bi-maximal or tri-bimaximal mixing. We find that the charged lepton mixing matrices which can deviate bi-maximal mixing matrix and tri-bimaximal mixing matrix exhibit similar structures. Numerical analysis shows that these charged lepton mixing matrices are close to …
We discuss the neutrino oscillations, using texture zero mass matrices for the leptons, including radiative correction. The neutrino mixing angle theta_13 is calculated and agrees with the result of the new Daya Bay experiment.
A recent parameterisation scheme developed for the quark mixing matrix is shown to be easily applicable to the lepton mixing matrix as well.
We present a model for leptonic mixing and the lepton masses based on flavor symmetries and higher-dimensional mass operators. The model predicts bilarge leptonic mixing (i.e., the mixing angles theta_{12} and theta_{23} are large and the mixing angle theta_{13} is small) and an inverted hierarchical neutrino mass spectrum. Furthermore, it approximately yields the experimental hierarchical mass spectrum of the charged leptons. The obtained values for the leptonic mixing parameters and the neutrino mass squared differences are all in agreement with atmospheric neutrino data, the Mikheyev--Smirn…
We revisit the possibility of relating lepton mixing angles with lepton mass hierarchies in a model-independent way. Guided by the existence of such relations in the quark sector, we first consider all the mixing angles, both in charged lepton and neutrino sectors to be related to the respective mass ratios. This allows us to calculate the leptonic mixing angles observed in neutrino oscillations as functions of the lightest neutrino mass. We show that for both normal and inverted hierarchical neutrino masses, this scenario does not give rise to correct leptonic mixing angles. We then show that…
Recent results from the Daya Bay and RENO reactor experiments have measured the smallest lepton mixing angle and found it to have a value of theta_13 approximately 9 degrees. This result presents a new challenge for the existing paradigms of discrete flavour symmetries which attempt to describe all quark and lepton masses and mixing angles. Here we propose a Supersymmetric Grand Unified Theory of Flavour based on Delta(96) x SU(5), together with a U(1) x Z3 symmetry, including a full discussion of Delta(96) in a convenient basis. The Grand Delta(96) x SU(5) Flavour Model relates the quark mixi…
We discuss the special class of models where nearly maximal neutrino mixing is produced through the see-saw mechanism, starting from only nearly diagonal matrices for charged leptons, Dirac neutrinos and Majorana right-handed neutrinos.
We reanalyze the mass matrix model of quarks and leptons that gives a unified description of quark and lepton mass matrices with the same texture form. By investigating possible types of assignment for the texture components of the lepton mass matrix, we find that a different assignment for neutrinos than for charged leptons can also lead to consistent values of the MNSP lepton mixing matrix. We also find that the predicted value for the lepton mixing matrix element $U_{13}$ of the model depends on the assignment. A proper assignment will be discriminated by future experimental data for $U_{13…
A model independent analysis of the leptonic Dirac CP-violating phase (δ) is presented. The analysis uses the experimentally determined values of the mixing angles in the lepton mixing matrix in order to explore the allowed values for δ and possible general forms for the charged lepton mixing matrix. This is done under two general assumptions: 1) that the mixing matrix in the neutrino sector is the so-called tribimaximal matrix and hence the non zero value for θ13 arises due to the mixing matrix in the charged lepton sector and 2) the charged lepton mixing matrix is parametrized in terms of th…
Based on a supersymmetric Yukawaon model with O(3) family symmetry, possible forms of quark and lepton mixing matrices are systematically investigated under a condition that the up-quark mass matrix form leads to the observed nearly tribimaximal mixing in the lepton sector. Although the previous model could not provide a good fitting of the observed quark mixing, the present model can give a reasonably good fitting not for lepton mixing but also the quark mixing by using a different origin of the $CP$ violation from one in the previous model.
Quark-lepton unification suggests Cabibbo-sized effects in lepton mixings, which we call Cabibbo haze. We give simple examples and explore possible Wolfenstein-like parametrizations of the MNSP matrix which incorporate leptonic Cabibbo shifts. We find that the size of the CHOOZ angle is not always correlated with the observability of CP violation.
We perform a detailed study of lepton mixing patterns arising from a scenario with three Majorana neutrinos in which a discrete flavor group Gf=Delta (3 n^2) or Gf=Delta(6 n^2) and a CP symmetry are broken to residual symmetries Ge=Z3 and Gnu=Z2 x CP in the charged lepton and neutrino sectors, respectively. While we consider all possible Z3 and Z2 generating elements, we focus on a certain set of CP transformations. The resulting lepton mixing depends on group theoretical indices and one continuous parameter. In order to study the mixing patterns comprehensively for all admitted Ge and Gnu, it…
I review some of the recent progress (up to September 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.
We consider a parametrization of the lepton mixing matrix in which the deviations from maximal atmospheric mixing and vanishing reactor mixing are obtained in terms of small corrections from the charged lepton sector. Relatively large deviations for the reactor mixing angle from zero as indicated by T2K experiment can be obtained in this parametrization. We are able to further reduce the number of complex phases, thus, simplifying the analysis. In addition, we have obtained the sides of unitarity triangles and the vacuum oscillation probabilities in this parametrization. The Jarlskog rephasing…
The strategy of constraining the lepton flavor mixing from remnant CP symmetry is investigated in a rather general way. The neutrino mass matrix generally admits four remnant CP transformations which can be derived from the measured lepton mixing matrix in the charged lepton diagonal basis. Conversely, the lepton mixing matrix can be reconstructed from the postulated remnant CP transformations. All mixing angles and CP violating phases can be completely determined by the full set of remnant CP transformations or three of them. When one or two remnant CP transformations are preserved, the resul…
In drawing on an analogy with the flavor mixing observed in the quark sector we discuss a pattern of large flavor mixing angles in the lepton sector. Simple arguments based on a democratic symmetry and its violation in the lepton sector allow us to determine the flavor mixing matrix of leptons. The mixing angle relevant for solar neutrino oscillations is maximal (close to $45^{\circ}$), while the angle relevant for atmospheric neutrino oscillations is given by $\sin^2 2 θ= 8/9$. The emerging pattern is consistent with the results of the solar and atmospheric neutrino experiments.
The impact of possible sources of lepton-flavor mixing on $K \to πν\barν$ decays is analysed. At the one-loop level lepton-flavor mixing originated from non-diagonal lepton mass matrices cannot generate a CP-conserving $K_L \to π^0ν\barν$ amplitude. The rates of these modes are sensitive to leptonic flavor violation when there are at least two different leptonic mixing matrices. New interactions that violate both quark and lepton universalities could enhance the CP-conserving component of $Γ(K_L \to π^0ν\barν)$ and have a substantial impact. Explicit examples of these effects in the context of…
We produce five flavour models for the lepton sector. All five models fit perfectly well---at the one-sigma level---the existing data on the neutrino mass-squared differences and on the lepton mixing angles. The models are based on the type-I seesaw mechanism, on a Z_2 symmetry for each lepton flavour, and either on a (spontaneously broken) symmetry under the interchange of two lepton flavours or on a (spontaneously broken) CP symmetry incorporating that interchange---or on both symmetries simultaneously. Each model makes definite predictions both for the scale of the neutrino masses and for t…
We investigate a general structure of lepton mixing matrix resulting from the SU$_F$(3) gauge family model with an appropriate vacuum structure of SU$_F$(3) symmetry breaking. It is shown that the lepton mixing matrix can be parametrized by using the Wolfenstein parametrization method to characterize its deviation from the tri-bimaximal mixing. A general analysis for the allowed leptonic CP-violating phase $δ_e$ and the leptonic Wolfenstein parameters $λ_e$, $A_e$, $ρ_e$ is carried out based on the observed lepton mixing angles. We demonstrate how the leptonic CP violation correlates to the le…
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