S<Subscript>3</Subscript> symmetry and neutrino masses and mixings

Based on the universal seesaw mass matrix model with the three scalars φ_i, and by assuming S₃ flavor symmetry for the Yukawa interactions, the lepton masses and mixings are investigated systematically. In order to understand the observed neutrino mixing, the charged leptons (e,μ,τ) are regarded as the three objects (e₁,e₂,e₃) of S₃, while the neutrino mass eigenstates are regarded as the irreducible representation (ν_η,ν_σ,ν_π) of S₃, where (ν_π,ν_η) and ν_σ are a doublet and a singlet, respectively, which are composed of the three objects (ν₁,ν₂,ν₃) of S₃.     

Direct calculation of transition intensities in LiYF<Subscript>4</Subscript>: Nd<Superscript>3+</Superscript>

Duan’s simple model is extended to analyze the mixing of the 4f ^{N − 1}5d configuration with the 4f ^N states. The explicit static coupling and traditional dynamic coupling are considered, and the parameters are fitted according to the absorption spectrum in LiYF₄: Nd³⁺. The parameter values obtained are as follows: T ₃₂ = −28i × 10⁻⁷, T ₅₂ = −1151i × 10⁻⁷, A ₃₂² = 192i × 10⁻¹² cm, A ₅₂⁴ = i × 10⁻¹² cm, A ₇₂⁶ = 54i × 10⁻¹² cm, and A ₇₆⁶ = −680i × 10⁻¹² cm. Compared to the experimental measurements, the present model yields better results than those obtained from the Judd-Ofelt theory. The text was submitted by the authors in English.     

具有整体代对称性的左右对称模型中的中微子质量

本文基于具有整体U(1)代对称性的SU(2)_L×SU(2)_R×U(1)模型推导了轻子的味混合矩阵,对中微子的质量问题进行了研究.在本文的模型中,产生轻子Dirac质量的汤川耦合拉格朗日密度具有整体U(1)代对称性,所以,模型中的带电轻子质量矩阵和中微子Dirac质量矩阵是Fritzsch形式的.但是,中微子除了具有Dirac质量,一般还具有Majorana质量,在这种一般情况下, 关键词： 中微子质量 轻子味混合矩阵 左右对称模型 代对称性     

The neutrino mass matrix and (selected) variants of <Emphasis Type="Italic">A</Emphasis><Subscript>4</Subscript>

Recent neutrino oscillation experiments have measured leptonic mixing angles with considerable precision. Many theoretical attempts to understand the peculiar mixing structure, observed in these measurements, are based on non-Abelian flavour symmetries. This talk concentrates exclusively on models based on the non-Abelian symmetry A ₄. A ₄ is particularly well suited to describe three family mixing, and allows to explain the near tri-bimaximal mixing observed. Special emphasis is put here on the discussion of the neutrinoless double beta decay observable 〈:m _ν 〉. Different models based on A ₄ with very similar predictions for neutrino angles can yield vastly different expectations for 〈m _ν 〉. Neutrinoless double beta decay can thus serve, in principle, as a discriminator between different neutrino mass models.      

Renormalization group running of lepton mixing parameters in see-saw models with <Emphasis Type="Italic">S</Emphasis><Subscript>4</Subscript> flavor symmetry

We study the renormalization group running of the tri-bimaximal mixing predicted by the two typical S ₄ flavor models at leading order. Although the textures of the mass matrices are completely different, the evolution of neutrino mass and mixing parameters is found to display approximately the same pattern. For both normal hierarchy and inverted hierarchy spectrum, the quantum corrections to both atmospheric and reactor neutrino mixing angles are so small that they can be neglected. The evolution of the solar mixing angle θ ₁₂ depends on tanb\tan\beta and neutrino mass spectrum, the deviation from its tri-bimaximal value could be large. Taking into account the renormalization group running effect, the neutrino spectrum is constrained by experimental data on θ ₁₂ in addition to the self-consistency conditions of the models, and the inverted hierarchy spectrum is disfavored for large tanb\tan\beta. The evolution of light-neutrino masses is approximately described by a common scaling factor.     

Hierarchical matrices in the see-saw mechanism,large neutrino mixing and leptogenesis

We consider the see-saw mechanism for hierarchical Dirac and Majorana neutrino mass matrices m _D and M _R, including the CP violating phases. Simple arguments about the structure of the neutrino mass matrix and the requirement of successful leptogenesis lead to the situation that one of the right-handed Majorana neutrinos is much heavier than the other two, which in turn display a rather mild hierarchy. It is investigated how for the neutrino mixing one small and two large mixing angles are generated. The mixing matrix element |U _e3|² is larger than 10^-3 and a characteristic ratio between the branching ratios of lepton flavor violating charged lepton decays is found. Successful leptogenesis implies sizable CP violation in oscillation experiments. As in the original minimal see-saw model, the signs of the baryon asymmetry of the universe and of the CP asymmetry in neutrino oscillations are equal and there is no connection between the leptogenesis phase and the effective mass as measurable in neutrinoless double beta decay.Received: 28 May 2003, Revised: 13 September 2003, Published online: 26 November 2003     

Quark–lepton complementarity with lepton and quark mixing data predict θ<Subscript>13</Subscript><Superscript>PMNS</Superscript>=(9<Superscript>+1</Superscript><Subscript>-2</Subscript>)°

The complementarity between the quark and lepton mixing matrices is shown to provide a robust prediction for the neutrino mixing angle θ₁₃ ^PMNS. We obtain this prediction by first showing that the matrix V_M, product of the CKM and PMNS mixing matrices, may have a zero (1,3) entry, which is favored by the experimental data. Hence models with bimaximal or tribimaximal forms of the correlation matrix V_M are quite possible. Any theoretical model with a vanishing (1,3) entry of V_M, which is in agreement with the quark data, and the solar and the atmospheric mixing angle leads to θ₁₃ ^PMNS=(9⁺¹ _-2)^°. This value is consistent with the present 90% CL experimental upper limit. PACS 14.60.Pq; 14.60.Lm; 96.40.Tv     

Top squark and neutralino decays in a <Emphasis Type="Italic">R</Emphasis>-parity violating model constrained by neutrino oscillation data

In a R-parity violating (RPV) model of neutrino mass with three bilinear couplings μ _i and three trilinear couplings λ′ _i33, where i is the lepton index, we find six generic scenarios each with a distinctive pattern of the trilinear couplings consistent with the neutrino oscillation data. These patterns may be reflected in direct RPV decays of the lighter top squark or in the RPV decays of the lightest superparticle, assumed to be the lightest neutralino. Typical signal sizes at the Tevatron RUN II and the LHC have been estimated and the results turn out to be encouraging.      

A4-based tri-bimaximal mixing within inverse and linear seesaw schemes

We consider tri-bimaximal lepton mixing within low-scale seesaw schemes where light neutrino masses arise from TeV scale physics, potentially accessible at the Large Hadron Collider (LHC). Two examples are considered, based on the A₄$A_4$ flavor symmetry realized within the inverse or the linear seesaw mechanisms. Both are highly predictive so that in both the light neutrino sector effectively depends only on three mass parameters and one Majorana phase, with no CP violation in neutrino oscillations. We find that the linear seesaw leads to a lower bound for neutrinoless double beta decay while the inverse seesaw does not. The models also lead to potentially sizeable decay rates for lepton flavor violating processes, tightly related by the assumed flavor symmetry.     

The τ→μν<Subscript>i</Subscript>̄ν<Subscript>i</Subscript> decay in the Randall–Sundrum background with localized U(1)<Subscript>Y</Subscript> gauge boson

We study the effects of localization of the U(1)_Y gauge boson around the visible brane and the contributions of the Kaluza–Klein modes of Z bosons on the branching ratio of the lepton flavor violating τ→μν_īν_i decay. We observe that the branching ratio is sensitive to the amount of localization of the Z boson in the bulk of the Randall–Sundrum background.     

Probing neutrino masses and tri-bimaximality with lepton flavor violation searches

We examine relation between neutrino oscillation parameters and prediction of lepton flavor violation, in light of deviations from tri-bimaximal mixing. Our study shows that upcoming experimental searches for lepton flavor violation process can provide useful implications for neutrino mass spectrum and mixing angles. With simple structure of heavy right-handed neutrino and supersymmetry breaking sectors, the discovery of τ→μγ$\tau \to \mu \gamma$ decay determines neutrino mass hierarchy if large (order 0.1) reactor angle is established.     

Mixing angles of quarks and leptons in quantum field theory

Arguments coming from Quantum Field Theory are supplemented with a 1-loop perturbative calculation to settle the non-unitarity of mixing matrices linking renormalized mass eigenstates to bare flavor states for non-degenerate coupled fermions. We simultaneously diagonalize the kinetic and mass terms and counterterms in the renormalized Lagrangian. SU(2) _L gauge invariance constrains the mixing matrix in charged currents of renormalized mass states, for example the Cabibbo matrix, to stay unitary. Leaving aside CP violation, we observe that the mixing angles exhibit, within experimental uncertainty, a very simple breaking pattern of SU(2) _f horizontal symmetry linked to the algebra of weak neutral currents, the origin of which presumably lies beyond the Standard Model. It concerns on the one hand the three quark mixing angles; on the other hand a neutrino-like pattern in which θ ₂₃ is maximal and tan (2θ ₁₂)=2. The Cabibbo angle fulfills the condition tan (2θ _c )=1/2 and θ ₁₂ for neutrinos satisfies accordingly the “quark–lepton complementarity condition” θ _c +θ ₁₂=π/4. θ ₁₃=±5.7⋅10⁻³ are the only values obtained for the third neutrino mixing angle that lie within present experimental bounds. Flavor symmetries, their breaking by a non-degenerate mass spectrum, and their entanglement with the gauge symmetry, are scrutinized; the special role of flavor rotations as a very mildly broken symmetry of the Standard Model is outlined.     

Fermion Mass and Mixing in a Simple Extension of the Standard Model Based on T7 Flavor Symmetry

We build a simple Standard Model extension based on T₇ flavor symmetry which accommodates lepton mass, mixing with non-zero θ₁₃, and CP violation phase. The lepton mixing matrix is obtained from three triplets and one singlet under T₇ symmetry, and the charged-lepton mass is derived through the spontaneous symmetry breaking by just one T₇ triplet (φ), while neutrinos get small masses from one SU(2) _L doublet and two SU(2)_L singlets in which one is in 1 and the two others are in 3 and 3* under T₇, respectively. There exist viable parameters of the model that predict the effective Majorana neutrino mass with values m_β ≃ 10⁻² eV and 4.95 × 10⁻² eV as well as a lightest neutrino mass m_light ≃ 4.97 × 10⁻³ eV and 1.61 × 10⁻³ eV for the normal and inverted neutrino mass hierarchies, respectively. The model also gives a remarkable prediction of Dirac CP violation δ_CP ≃ 303.3° in the normal hierarchy and δ_CP ≃ 56.69° in the inverted hierarchy which is still missing in the neutrino mixing matrix. The quark mixing angles of the model are closed to the experimental data, whereas the obtained values for the quark masses are consistent with with the experimental data at the tree level.

     

Final-state polarization in <Emphasis Type="Italic">B</Emphasis><Stack><Subscript><Emphasis Type="Italic">s</Emphasis></Subscript><Superscript>0</Superscript></Stack> decays

Certain B _s ⁰→V ₁ V ₂ decays (V _i is a vector meson) can be related by flavor SU(3) symmetry to corresponding B _d ⁰→V ₃ V ₄ decays. In this paper, we show that the final-state polarization can be predicted in the B _s ⁰ decay, assuming polarization measurements of the B _d ⁰ decay. This can be done within the scenario of penguin annihilation (PA), which has been suggested as an explanation of the unexpectedly large transverse polarization in B→φ K ^*. PA is used to estimate the breaking of flavor SU(3) symmetry in pairs of decays. Two of these for which PA makes a reasonably precise prediction of the size of SU(3) breaking are (B _s ⁰→φ φ,B _d ⁰→φ K ^0*) and ( ). The polarization measurement in the B _d ⁰ decay can be used to predict the transverse polarization in the B _s ⁰ decay and will allow for testing of PA as well as the other assumptions in the analysis.     

Majorana neutrino masses in the three-flavor Pauli model

A special Majorana model for three neutrino flavors is developed on the basis of the Pauli transformation group. In this model, the neutrinos possess a partially conserved generalized lepton (Pauli) charge that makes it possible to discriminate between neutrinos of different type. It is shown that, within the model in question, a transition from the basic “mass” representation, where the average value of this charge is zero, to the representation associated with physical neutrinos characterized by specific Pauli “flavor” charges establishes a relation between the neutrino mixing angles θ _{mix, 12}, θ _{mix, 23}, and θ _{mix, 13} and an additional relation between the Majorana neutrino masses. The Lagrangian mass part, which includes a term invariant under Pauli transformations and a representation-dependent term, concurrently assumes a “quasi-Dirac” form. With allowance for these relations, the existing set of experimental data on the features of neutrino oscillations makes it possible to obtain quantitative estimates for the absolute values of the neutrino masses and the 2β-decay mass parameter m _ββ and a number of additional constraints on the neutrino mixing angles.     

Searching for new physics in future neutrino factory experiments

An extension of the new standard model, by introducing a mixing of the low mass “active” neutrinos with heavy ones, or by any model with lepton flavor violation, is considered. This leads to non-orthogonal neutrino production and detection states and to modifications of neutrino oscillations in both vacuum and matter. The possibility of the discovery of such effects in current and future neutrino oscillation experiments is discussed. First order approximation formulas for the flavor transition probabilities in constant density matter, for all experimentally available channels, are given. Numerical calculations of flavor transition probabilities for two sets of new physics parameters describing a single “effective” heavy neutrino state, both satisfying present experimental constraints, have been performed. Two energy ranges and several baselines, assuming both the current (±2σ) and the expected future errors (±3%) of the neutrino oscillation parameters are considered, keeping their present central values. It appears that the biggest potential of the discovery of the possible presence of any new physics is pronounced in oscillation channels in which ν_e and ν_ē are not involved at all, especially for two baselines, L=3000 km and L=7500 km, which for other reasons are also called “magic” for future Neutrino Factory experiments. PACS 13.15.+g; 14.60.Pq; 14.60.St     

Analytic Calculation of Neutrino Mass Eigenvalues

Implication of the neutrino oscillation search for the neutrino mass square difference and mixing are discussed. We have considered the effective Majorana mass m _ee , related for ββ _0ν decay. We find limits for neutrino mass eigen value m _i in the different neutrino mass spectrum,which explain the different neutrino data.     

Electrical properties,equivalent circuit,and dielectric relaxation studies on [(C<Subscript>3</Subscript>H<Subscript>7</Subscript>)<Subscript>4</Subscript>N]<Subscript>2</Subscript>Cd<Subscript>2</Subscript>Cl<Subscript>6</Subscript> polycrystalline

The Ac electrical conductivity and the dielectric relaxation properties of the [(C₃H₇)₄N]₂Cd₂Cl₆ polycrystalline sample have been investigated by means of impedance spectroscopy measurements over a wide range of frequencies and temperatures, 209 Hz–5 MHz and 361–418 K, respectively. The purpose is to make a difference between the electrical and dielectric properties of the polycrystalline sample and single crystal. Besides, a detailed analysis of the impedance spectrum suggests that the electrical properties of the material are strongly temperature-dependent. Plots of (Z" versus Z') are well fitted to an equivalent circuit model consisting of a series combination of grains and grains boundary elements. Moreover, the temperature dependence of the electrical conductivity in the different phases follows the Arrhenius law and the frequency dependence of σ (ω) follows the Jonscher’s universal dynamic law. Furthermore, the modulus plots can be characterized by full width at half height or in terms of a nonexperiential decay function φ(t) = exp(t/t)^β. Finally, the imaginary part of the permittivity constant is analyzed with the Cole–Cole formalism.     

Mesonic decays of τ− lepton: Effects of neutrino mass and mass mixing

Experimentally established mesonic decays ofτ ⁻ lepton have been reexamined with the inclusion of the effects of finite neutrino mass and the associated mass mixing in the form of Kobayashi-Maskawa mixing matrix. A comparison with the experimentally predicted decay probabilities provides limits for thev _τ mass which are finite in all decays except for the lower limit in mass mixing case of the decayτ ⁻→K*⁻ (892)+v _τ for which MeV. The large error in this value is because of (i) large errors in the experimental values of life time and branching ratio for this decay and (ii) thekm mixing used in the calculations. The ratio of parity-violating to parity-conserving terms in the differential decay probabilities of various decays differs slightly from their values corresponding to those with varishingv _τ mass.     

Elementary muon, pion, and kaon particles as resonators for neutrino quanta. Calculations of mass ratios for e, μ, π0, π±, K 0, K ±, and ν e

Masses of a number of elementary particles are calculated on the basis of the model suggested in [1] with the use of one parameter. In this model, an electron is considered as an electric cloud enclosed inside an elastic lepton shell, electron neutrino ν _е is considered as an elastic lepton shell contracted to a minimal size, and muon, pion and kaon are considered as resonators for quanta of virtual neutrinos excited inside the elastic lepton shell. The number and type of these quanta are determined from the decay scheme for μ, π, and K: 2 for the muon (ν _е and ), 3 for the pion (ν _е , ν _μ, and ), and at least 21 for the kaon. The model allows mass ratios approximating the experimental data for these particles to be obtained for the first time, with the ratio of μ and е masses equal to (6πℏс/е ²)^2/3 ≅ 188, the ratio of π ⁰ and μ masses equal to (3/2)^2/3, and the ratio of K ⁰ and π ⁰ equal masses to 7^2/3. The calculated e, μ , π ⁰, and K ⁰ masses are in the 0.547:105.707:134.963:493.87 (MeV) ratios (normalized by the neutral pion mass). This is in good agreement with the available experimental data. The mass ν _е (≅ 0.02 eV) is also estimated in this model, and the variety of K-meson decay schemes is naturally explained as a result of the variety of excited intrinsic neutrino field structures with the same energy. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 23–29, January, 2009.