It has recently been shown that the phenomenologically successful pattern of cobimaximal neutrino mixing ($θ_{13} \neq 0$, $θ_{23} = π/4$, and $δ_{CP} = \pm π/2$) may be achieved in the context of the non-Abelian discrete symmetry $A_4$. In this paper, the same goal is achieved with $S_3 \times Z_2$. The residual lepton $Z_3$ triality in the case of $A_4$ is replaced here by $Z_2 \times Z_2$. The associated phenomenology of the scalar sector is discussed.
If neutrinos are Dirac, the conditions for cobimaximal mixing, i.e. $θ_{23}=π/4$ and $δ_{CP}=\pm π/2$ in the $3 \times 3$ neutrino mixing matrix, are derived. One example with $A_4$ symmetry and radiative Dirac neutrino masses is presented.
It has recently been shown that the phenomenologically successful pattern of cobimaximal neutrino mixing ($θ_{13} \neq 0$, $θ_{23} = π/4$, and $δ_{CP} = \pm π/2$) may be achieved in the context of the non-Abelian discrete symmetry $A_4$, if the neutrino mass matrix is diagonalized by an orthogonal matrix ${\cal O}$. We study how this pattern would deviate if ${\cal O}$ is replaced by an unitary matrix.
We propose a simple framework based on $Δ(27)$ that leads to the successful cobimaximal lepton mixing ansatz, thus providing a predictive explanation for leptonic mixing observables. We explore first the effective neutrino mass operators, then present a specific model realization based on type I seesaw, and also propose a model with radiative 1-loop seesaw which features viable dark matter candidates.
I propose a model of radiative charged-lepton and neutrino masses with $A_4$ symmetry. The soft breaking of $A_4$ to $Z_3$ lepton triality is accomplished by dimension-three terms. The breaking of $Z_3$ by dimension-two terms allow cobimaximal neutrino mixing $(θ_{13} \neq 0, θ_{23} = π/4, δ_{CP} = \pm π/2)$ to be realized with only very small finite calculable deviations from the residual lepton triality. This construction solves a long-standing technical problem inherent in renormalizable $A_4$ models since their inception.
Cobimaximal mixing pattern from a $Δ(27)$ inverse seesaw model
Universidad Técnica Federico Santa María（费德里科·圣玛丽亚技术大学）；Centro Científico-Tecnológico de Valparaíso（瓦尔帕莱索科技中心）；Millennium Institute for Subatomic Physics at the High-Energy Frontier, SAPHIR（高能前沿亚原子物理千年研究所，SAPHIR）；CFTP, Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院物理系，CFTP）；Departamento de Física, Universidad Técnica Federico Santa María（费德里科·圣玛丽亚技术大学物理系）
Within the different patterns of the neutrino mixing matrix, the cobimaximal mixing remains a plausible possibility for understanding the flavor structure of neutrinos as it is consistent with current experimental data. Such a pattern is related to a concrete form of the mass matrix, displaying a $μ-τ$ reflection symmetry, which has motivated many theoretical investigations in recent years. In this paper, we discuss the effects of the Majorana phases over a $μ-τ$ symmetric mass matrix obtained from a cobimaximal mixing matrix. We investigate how these phases could be restricted through deviati…
In the context of $SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)_χ$, where $U(1)_χ$ comes from $SO(10) \to SU(5) \times U(1)_χ$, supplemented by the non-Abelian discrete $Δ(27)$ symmetry for three lepton families, Dirac neutrino masses and their mixing are radiatively generated through dark matter. The gauge $U(1)_χ$ symmetry is broken spontaneously. The discrete $Δ(27)$ symmetry is broken softly and spontaneously. Together, they result in two residual symmetries, a global $U(1)_L$ lepton number and a dark symmetry, which may be $Z_2$, $Z_3$, or $U(1)_D$ depending on what scalar breaks $U(1…
Cobimaximal lepton mixing, i.e. $θ_{23} = 45^\circ$ and $δ= \pm 90^\circ$ in the lepton mixing matrix $V$, arises as a consequence of $S V = V^\ast \mathcal{P}$, where $S$ is the permutation matrix that interchanges the second and third rows of $V$ and $\mathcal{P}$ is a diagonal matrix of phase factors. We prove that any such $V$ may be written in the form $V = U R P$, where $U$ is any predefined unitary matrix satisfying $S U = U^\ast$, $R$ is an orthogonal, i.e. real, matrix, and $P$ is a diagonal matrix satisfying $P^2 = \mathcal{P}$. Using this theorem, we demonstrate the equivalence of t…
Recently, we have a confidence that neutrino has a tiny mass and mixing does exist among neutrino flovors as one can see from experimental data that reported by many collaborations. Based on experimental data that flavor mixing does exist in neutrino sector which imply that all three mixing angles are nonzero, we derive the neutrino mass matrix from a cobimaximal neutrino mixing matrix. We also evaluate the prediction of neutrino mass matrix with texture zero from a cobimaximal neutrino mixing matrix on neutrino masses and effective Majorana mass. By using the advantages of experimental data, …
In the context of the non-Abelian discrete symmetry $A_4$, the neutrino mass matrix has been studied extensively. A brief update is presented to focus on the conceptual shift from tribimaximal mixing ($θ_{13} = 0$, $θ_{23} = π/4$, $\tan^2 θ_{12} = 1/2$) to $\underline{\rm cobimaximal}$ mixing ($θ_{13} \neq 0$, $θ_{23} = π/4$, $δ_{CP} = \pm π/2$) which agrees well with present data. Three specific realistic examples are proposed, two with three and the third with just two parameters.
Choosing how gauge $U(1)_χ$ breaks in the context of $SO(10) \to SU(5) \times U(1)_χ$, $Z_4$ lepton number may be obtained which maintains neutrinos as Dirac fermions. Choosing $Δ(27)$ as the family symmetry of leptons, tree-level Dirac neutrino masses may be forbidden. Choosing a specific set of self-interacting dark-matter particles, Dirac neutrino masses and mixing may then be generated in two loops. This framework allows the realization of cobimaximal neutrino mixing, i.e. $θ_{13} \neq 0$, $θ_{23} = π/4$, $δ_{CP} = \pm π/2$, as well as the desirable feature that the light scalar mediator o…
We propose a 3+1 Higgs Doublet Model based on the $Δ(27)$ family symmetry supplemented by several auxiliary cyclic symmetries leading to viable Yukawa textures for the Standard Model fermions, consistent with the observed pattern of fermion masses and mixings. The charged fermion mass hierarchy and the quark mixing pattern is generated by the spontaneous breaking of the discrete symmetries due to flavons that act as Froggatt-Nielsen fields. The tiny neutrino masses arise from a radiative seesaw mechanism at one loop level, thanks to a preserved $Z_2^{\left( 1\right)}$ discrete symmetry, which …
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.
In analogy to the mixing pattern of the pseudoscalar mesons in QCD we discuss the mixing of massive neutrinos. Unlike the quarks flavor mixing angles the leptonic mixing angles are large, nearly maximal. The three massive neutrinos are nearly degenerate.
We 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.
In a model with four neutrino mass eigenstates grouping in two narrow doublets the condition of maximal mixing of the doublet neutrino components leads to a simple four-neutrino mixing matrix which is related to two connected effective two-neutrino mixing patterns. As a result, large values of the neutrino oscillation amplitudes for both the solar and atmospheric neutrino anomalies appear quite naturally if the LSND data are accepted.
This brief report is an extension of a prediction of neutrino oscillation with a sterile neutrino using parameters of the sterile neutrino mass and mixing angle recently extracted from experiment.
We explore the possibility of generating a non-zero $U_{e3}$ element of the neutrino mixing matrix from tribimaximal neutrino mixing by adding a light sterile neutrino to the active neutrinos. Small active-sterile mixing can provide the necessary deviation from tribimaximal mixing to generate a non-zero $θ_{13}$ and atmospheric mixing $θ_{23}$ different from maximal. Assuming no CP-violation, we study the phenomenological impact of sterile neutrinos in the context of current neutrino oscillation data. The tribimaximal pattern is broken in such a manner that the second column of tribimaximal mi…
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 the consequences of neutrino mixing in the early universe. For both active-sterile mixing or mixing between three active neutrinos only, the consequences of oscillations depend crucially upon the size of the universe's lepton number (relic neutrino asymmetry.)
In the framework of the three-neutrino mixing the neutrino oscillations in the atmospheric and solar ranges of neutrino mass-squared differences are considered in the leading approximation. Neutrinoless double $β$- decay is also discussed.
We derive the constraints imposed on neutrino masses and mixing angles by performing a combined analysis of the data from the Los Alamos and the other terrestrial neutrino oscillation experiments with the assumption of the flavor-mixing solutions to the solar neutrino problem. In a three-flavor mixing scheme which ignores the possibility of sterile neutrinos, we obtain severe constraints on the pattern of masses and flavor mixing of neutrinos. For example, we show that in the standard Kobayashi-Maskawa type mixing matrix $s_{13}^2 \lsim 10^{-2}$ independent of the choice of the solar neutrino …
The compelling experimental evidences for oscillations of solar, atmospheric and reactor neutrinos imply the existence of 3-neutrino mixing in vacuum. We review the phenomenology of 3-neutrino mixing, and the current data on the 3-neutrino mixing parameters. The opened questions and the main goals of future research in the field of neutrino mixing and oscillations are outlined. A phenomenological approach for understanding the pattern of neutrino mixing as an interplay between the mixing, arising from the charged lepton sector, and bimaximal mixing, arising from a neutrino Majorana mass matrix…
Neutrino mixing and basics of neutrino oscillations are considered. Recent evidences in favour of neutrino oscillations, obtained in the solar and atmospheric neutrino experiments, are discussed. Neutrino oscillations in the solar and atmospheric ranges of $Δm^{2}$ are considered in the framework of the minimal scheme with the mixing of three massive neutrinos.
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.
The 2-neutrino exchange potential (2NEP) is a Standard Model (SM) weak potential due to the exchange of virtual neutrino-antineutrino pairs. Consequently, many aspects of neutrino physics, such as the number of flavors, their masses, fermionic nature (Dirac or Majorana), low-energy neutrino physics and CP-violation, can be examined via the 2NEP. We present a new approach for calculating the 2NEP taking into account the phenomenon of neutrino mixing and CP-violation which arises from the structure of the SM weak interaction Lagrangian. Lastly, we explore implications of our result in various ph…
We discuss what information about the neutrino mass spectrum and the elements of the neutrino mixing matrix can be inferred from the results of neutrino oscillation experiments. The cases of three and four massive neutrinos are considered. It is shown that the general characteristics of the neutrino mixing matrix are quite different from those of the quark mixing matrix.
Exotic explanations are considered for atmospheric neutrino observations. Our analysis includes matter effects and the mixing of all three neutrinos under the simplifying assumption of only one relevant mixing scale. Constraints from accelerator, reactor and solar neutrinos are included. We find that the proposed mixing mechanisms based on violations of Lorentz invariance or on violations of the equivalence principle cannot explain the recent observations of atmospheric neutrino mixing. However the data still allow a wide range of energy dependences for the vacuum mixing scale, and also allow …
We study neutrino masses and mixings based on the simplest SO(10) mass relations and the seesaw mechanism. We find that the requirement of large neutrino mixings determines the relative magnitude of the heavy Majorana neutrino masses in terms of the known quark mass hierarchy. This leads to specific predictions for the structure of the neutrino mixing matrix, the light neutrino masses, CP violation in neutrino oscillations, neutrinoless double b-decay and the baryon asymmetry.
A short review of the status of neutrino mixing and neutrino oscillations is given. The basics of neutrino mixing and oscillations is discussed. The latest evidences of neutrino oscillations obtained in the Super-Kamiokande and the SNO solar neutrino experiments and in the Super-Kamiokande atmospheric neutrino experiment are considered. The results of solar and atmospheric neutrino experiments are discussed from the point of view of the three-neutrino mixing.
In the wake of the SuperKamiokande announcement of atmospheric neutrino oscillations which favor the large mixing of $ν_μ$ with $ν_τ$, there is considerable theoretical activity towards a possible understanding of the solar neutrino deficit also in terms of the mixing of $ν_e$ with the other two neutrinos. A specific dynamical model is presented here for the first time which naturally chooses the large (small) mixing solution to atmospheric (solar) neutrino oscillations.
We present an analysis of neutrino oscillations which are consistent with current solar, atmospheric and terrestrial experiments in a framework with three neutrino mixing. The solutions satisfying these experiments have the large mixing (not maximal mixing) between electron neutrino- muon neutrino or muon neutrino-tau neutrino in m3 to be about several eV, where m3 is the heaviest neutrino mass. From these results, we conjecture a form for the mass matrices of charged lepton and neutrino which are described by the universal Yukawa coupling with small violations.
We show that the neutrino mixing pattern with the large mixing required for the atmospheric neutrino problem and the small mixing angle MSW solution for the solar neutrino problem can be naturally generated through radiative magnification, even though all the mixing angles at the seesaw scale may be small. This can account for the neutrino anomalies as well as the CHOOZ constraints in the context of quark-lepton unified theories, where the quark and lepton mixing angles are expected to be similar in magnitude at the high scale. We also indicate the 4$ν$ mixing scenarios for which this mechanis…
In the first part of these lectures the neutrino mixing hypothesis will be considered in detail. We will discuss the possible schemes of neutrino mixing and present the data of the recent experiments searching for effects due to nonvanishing neutrino masses and mixing angles.In the second part of these lectures the physics of solar neutrinos will be considered.We will discuss the MSW resonance solution of the equation of evolution of a neutrino in matter and present data of solar neutrino experiments.
Three schemes of neutrino mixings (oscillations) together with their mixing matrices (analogous to Kabibbo-Kobayashi-Maskawa matrices) are considered. In these schemes neutrino transitions are virtual if neutrino masses are different. Two of them belong to the so called mass mixing schemes (mixing parameters are expressed by elements of mass matrices) and the third scheme belongs to the charge mixing scheme (mixing parameters are expressed through charges). In the first scheme system of 6 equations for determination of the all elements of the mass matrix (neutrino masses and transition widths)…
We propose new mixing schemes for (3+1) neutrinos which describe mixing among active-active and active-sterile neutrinos. The mixing matrix in these mixing schemes can be factored into a zeroth order flavor symmetric part and another part representing small perturbations needed for generating non-zero $U_{e3}$, nonmaximal $θ_{23}$, CP violation and active-sterile mixing. We find interesting correlations amongst various neutrino mixing angles and, also, calculate the parameter space for various parameters.
We study leptonic CKM mixing matrices when the neutrino Yukawa matrices are antisymmetric which gives rise to mass patterns suitable to explain solar, atmospheric and LSND neutrino oscillation experiments. Taking diagonal leptonic matrices which can give rise to hierarchical lepton masses, we compute the leptonic CKM matrix.
In the Standard theory of neutrino oscillations is used scheme of mass mixings, i.e., oscillation parameters are expressed via terms of mass matrix. In this work neutrino oscillations generated by charge (the weak interaction couple constants) mixings are considered. Expressions for angle mixings and lengths of oscillations are obtained. The expressions of the probability for three neutrino oscillations are given. Neutrino oscillations in this scheme (mechanism) are virtual if neutrino masses are not equal and real if neutrino masses are equal.
We review some fundamental aspects of the theory of neutrino masses and mixing. The results of neutrino oscillation experiments are interpreted as evidence of three-neutrino mixing. Implications for the mixing parameters and the neutrino masses are discussed, with emphasis on the connection with the measurements of the absolute values of neutrino masses in beta decay and neutrinoless double-beta decay experiments and cosmological observations.
The neutrino oscillation experiments increasingly point towards a mixing pattern that can be parametrised with two near maximal and one small mixing angle. We investigate whether such a mixing pattern can be generated as a fixed point of renormalisation group evolution.
The evidences in favor of solar and atmospheric neutrino oscillations are briefly reviewed and shown to be gracefully accommodated in the framework of three-neutrino mixing with bilarge mixing.
We consider the explanation of both data of the atmospheric neutrino and the solar neutrino by the neutrino mass matrix derived from the mixing of neutrinos and gauginos in the extended MSSM with an extra U(1) gauge symmetry. This scenario directly relates the neutrino mass to supersymmetry. The structure of the mass hierarchy and the mixing is determined only by the extra U(1)-charge of neutrinos. Although the model is rather simple, it may be able to realize both the small and large mixing angle solutions for the solar neutrino problem. In particular, the large mixing angle MSW solution for …
In the Standard Model (and MSSM), renormalization effects on neutrino mixing are generally very small and the attractive fixed points are at vanishing neutrino mixing. However for multi-higgs extensions of the Standard Model, renormalization effects on neutrino mixing can be large and nontrivial fixed points are possible. Here we examine a simple two-higgs model. For two flavors, maximal mixing is an attractive infrared fixed point. For three flavors, the neutrino mass matrix evolves towards large off-diagonal elements at low energies. The experimentally suggested bimaximal neutrino mixing pat…
The predictions for the effective Majorana mass |<m>| in neutrinoless double-beta decay in the case of 3-neutrino mixing and massive Majorana neutrinos are reviewed. The physics potential of the experiments, searching for neutrinoless double-beta decay and having sensitivity to $|<m>| \gtap 0.01$ eV, for providing information on the type of the neutrino mass spectrum, on the absolute scale of neutrino masses and on the Majorana CP-violation phases in the PMNS neutrino mixing matrix is also discussed.
Non-unitary neutrino mixing in the light neutrino sector is a direct consequence of type-I seesaw neutrino mass models. In these models, light neutrino mixing is described by a sub-matrix of the full lepton mixing matrix and, then, it is not unitary in general. In consequence, neutrino oscillations are characterized by additional parameters, including new sources of CP violation. Here we perform a combined analysis of short and long-baseline neutrino oscillation data in this extended mixing scenario. We did not find a significant deviation from unitary mixing, and the complementary data sets h…
Explicit analytical expression is derived for mixing matrix of three neutrinos in matter using a set of direct vacuum physical parameters. Results are presented in simple, symmetrical form. The physical contents are more clear than using of traditional mixing angles. There is no problem about mixing orders.
We show how neutrino mixing leads to a softening of the UV behavior of neutrino loops, and can give rise to anomaly-like, but manifestly UV finite amplitudes. This mechanism may be of special significance for the coupling of dark matter-like particles to the Standard Model, as we illustrate with a one-loop example involving the coupling to $W$-bosons.
Three schemes of neutrino mixings (oscillations) are proposed. The problems of origin of angle mixings, with the law of energy-momentum conservation and disintegration of neutrino as wave pocket are solved. These two schemes belong to mass mixings schemes, where mixing angles and oscillation lengths are expressed via elements of mass matrix. The third scheme belongs to the charge mixings scheme, where mixing parameters are expressed via neutrino weak charges, as it takes place in the vector dominance model. Using experiments we must decide which of these schemes is realized indeed. Analysis of…
Restrictions on the neutrino masses and lepton mixing are reviewed. Solar, atmospheric and relic neutrinos give the indications of existence of nonzero neutrino masses and mixing. The data pick up two regions of mixing angles which are or appreciably larger or appreciably smaller than the Cabibbo angle. Some theoretical schemes with {\it large} or {\it small} lepton mixing are discussed.
We consider neutrino mixing and oscillations in quantum field theory and compute the neutrino lepton charge in decay processes where neutrinos are generated. We also discuss the proper definition of flavor charge and states and clarify the issues of the possibility of different mass parameters in field mixing.
The nonzero and relatively large $θ_{13}$ have been reported by Daya Bay, T2K, MINOS, and Double Chooz Collaborations. In order to accommodate the nonzero $θ_{13}$, we modified the tribimaximal (TB), bimaxima (BM), and democratic (DC) neutrino mixing matrices. From three modified neutrino mixing matrices, two of them (the modified BM and DC mixing matrices) can give nonzero $θ_{13}$ which is compatible with the result of the Daya Bay and T2K experiments. The modified TB neutrino mixing matrix predicts the value of $θ_{13}$ greater than the upper bound value of the latest experimental results. …
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.
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 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.
