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 generated by the postulated remnant CP transformations arises from a finite flavor symmetry group, the phenomenologically viable lepton flavor mixing would be the trimaximal pattern, both Dirac CP phase $δ_{CP}$ and Majorana phase $α_{31}$ are either $0$ or $π$ while another Majorana phase $α_{21}$ is a rational multiple of $π$. These general results are confirmed to be true in the case that the finite flavor symmetry group is $Δ(6n^2)$.
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…
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.
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.
A new mechanism is proposed to explain neutrino masses and their mixing via SU(1,1) horizontal symmetry breaking. Based on this mechanism smallness of neutrino masses is naturally realized and inverted hierarchical spectrum with large mixing is given.
We study a possibility to explain neutrino masses and mixings based on supersymmetry. If we introduce a flavor diagonal but generation dependent extra U(1) gauge interaction at a TeV region, we can obtain masses and mixings of neutrinos required for the explanation of both solar and atmospheric neutrinos. In this model, differently from the usual bilinear R-parity violating scenario, the neutrino mass degeneracy can be resolved at a tree level by the neutrino-gaugino mixing caused by an R-parity violation. The model is straightforwardly extended to include the quark sector by introducing an an…
The possible mechanisms of generation of the neutrino of small masses and sterile neutrino are considered. In the supposition of stability of tracks of a left-right symmetry concerning masses of constituent quarks, the angles of mixing of quarks are evaluated. With usage of experimental data on neutrino oscillation parameters the neutrino masses on order of magnitude are computed.
Detection of 5 events by the Liquid Scintillation Detector (LSD) on February, 23, 1987 was recently interpreted as a detection of the electron neutrino flux from the first stage of the two-stage Supernova collapse. We show that, if neutrino mass hierarchy is normal, such interpretation excludes values of neutrino mixing angle θ_{13} larger than 3\cdot 10^{-2}, independently of the particular Supernova collapse model. Also constraints on the original fluxes of neutrinos and antineutrinos of different flavours are obtained.
We show that the bimaximal neutrino mixing pattern suggested by the solar and atmospheric neutrino data can be derived from the maximal, symmetric, four neutrino mixing in the limit that one of the neutrinos is made heavy. Imposing the constraints of no neutrinoless double beta decay and a 20% hot dark matter component of the universe leads to a three neutrino mass matrix recently suggested by Georgi and Glashow. Our result can be useful in constructing theoretical models for the bimaximal pattern. We illustrate this by a simple example.
The recent 71Ga solar neutrino observation is combined with the 37Cl and Kamiokande-II observations in an analysis for neutrino masses and mixings. The allowed parameter region is found for matter enhanced mixings among all three neutrino flavors. Distortions of the solar neutrino spectrum unique to three flavors are possible and may be observed in continuing and next generation experiments.
Assuming the existence of one light sterile neutrino, we investigate the neutrino flavor mixing matrix in matter. Sum rules between the mixing parameters in vacuum and their counterparts in matter are derived. By using these new sum rules, we obtain the simple but exact expressions of the effective flavor mixing matrix in matter in terms of neutrino masses and the mixing parameters in vacuum. The rephasing invariants, sides of unitarity quadrangles and oscillation probabilities in matter are also achieved. Our model-independent results will be very helpful for analyzing flavor mixing and CP vi…
The concepts of effective and dynamical neutrino mixing matrices are introduced in order to describe the behavior of neutrinos in matter. The former relates weak eigenstates to mass eigenstates, whereas the latter relates weak eigenstates to energy eigenstates in matter. It is shown that the dynamical mixing angles enable us to express the neutrino survival probability in the Sun without any resort to the Landau-Zener transition probability for the non-adiabatic process. Also discussed are effective CP violating phases that appear in the effective and dynamical mixing matrices in matter. Both …
The measurement of the charged-current 8B solar neutrino reaction on deuterium at the Sudbury Neutrino Observatory confirms the neutrino oscillation hypothesis for the solar neutrino problem, and the result favours the solution with large neutrino mixing angles. We demonstrate that the current neutrino oscillation data (including atmospheric and reactor neutrinos) are sufficient to construct the lepton flavour mixing matrix with a reasonable accuracy. We also infer the maximum size of CP violation effects consistent with the current neutrino oscillation experiments.
We examine how a parametrization of neutrino mixing matrix reflecting quark-lepton complementarity can be probed by considering phase-averaged oscillation probabilities, flavor composition of neutrino fluxes coming from atmospheric and astrophysical neutrinos and lepton flavor violating radiative decays. We discuss about some distinct features of the parametrization by comparing with the triminimal parametrization of perturbations to tri-bimaximal neutrino mixing matrix.
We have studied structures of the neutrino flavor mixing matrix focusing on the neutrino oscillations at CHORUS and NOMAD as well as the one at LSND(or KARMEN). We have assumed two typical neutrino mass hierarchies $m_3\simeq m_2\gg m_1$ and $m_3\gg m_2\gg m_1({\rm or}\simeq m_1)$. Taking into account the see-saw mechanism of neutrino masses, the reasonable neutrino flavor mixing patterns have been discussed. The observation of the neutrino oscillation at CHORUS and NOMAD presents us the important constraint for the structure of the neutrino flavor mixing matrix. The atomospheric neutrino anom…
Evidences in favor of neutrino oscillations, obtained in the solar and atmospheric neutrino experiments, are discussed. Neutrino oscillations in the solar and atmospheric ranges of the neutrino mass-squared differences are considered in the framework of the minimal scheme with the mixing of three massive neutrinos.
We propose a scenario that the mass splitting between the first generation of the heavy Majorana neutrino and the other two generations of degenerate heavy neutrinos in the seesaw framework is responsible for the deviation of the solar mixing angle from the maximal mixing, while keeping the maximal mixing between the tau and muon neutrinos as it is. On top of the scenario, we show that the tiny breaking of the degeneracy of the two heavy Majorana neutrinos leads to the non-zero small mixing angle $U_{e3}$ in the PMNS matrix and the little deviation of the atmospheric neutrino mixing angle from…
We briefly review the recent activity on neutrino masses and mixings which was prompted by the confirmation of neutrino oscillations by the Superkamiokande experiment.
