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.      

Dielectric relaxation and ionic conductivity studies of Ag<Subscript>2</Subscript>ZnP<Subscript>2</Subscript>O<Subscript>7</Subscript>

The complex impedance of the Ag₂ZnP₂O₇ compound has been investigated in the temperature range 419–557 K and in the frequency range 200 Hz–5 MHz. The Z′ and Z′ versus frequency plots are well fitted to an equivalent circuit model. Dielectric data were analyzed using complex electrical modulus M* for the sample at various temperatures. The modulus plot can be characterized by full width at half-height or in terms of a non-exponential decay function f( \textt ) = exp( - \textt/t )^b \phi \left( {\text{t}} \right) = \exp {\left( { - {\text{t}}/\tau } \right)^\beta } . The frequency dependence of the conductivity is interpreted in terms of Jonscher’s law: s( w) = s_\textdc + \textAwⁿ \sigma \left( \omega \right) = {\sigma_{\text{dc}}} + {\text{A}}{\omega^n} . The conductivity σ _dc follows the Arrhenius relation. The near value of activation energies obtained from the analysis of M″, conductivity data, and equivalent circuit confirms that the transport is through ion hopping mechanism dominated by the motion of the Ag⁺ ions in the structure of the investigated material.     

Deviation from tri-bimaximal mixings through flavour twisters in inverted and normal hierarchical neutrino mass models

We explore a novel possibility for lowering the solar mixing angle (θ ₁₂) from tri-bimaximal mixings, without sacrificing the predictions of maximal atmospheric mixing angle (θ ₂₃ = 45°) and zero reactor angle (θ ₁₃ = 0°) in the inverted and normal hierarchical neutrino mass models having 2–3 symmetry. This can be done through the identification of a flavour twister term in the texture of neutrino mass matrix and the variation of such term leads to lowering of solar mixing angle. For the observed ranges of Δm ₂₁² and Δm ₂₃², we calculate the predictions on tan² θ ₁₂ = 0.5, 0.45, 0.35 for different input values of the parameters in the neutrino mass matrix. We also observe a possible transition from inverted hierarchical model having even CP parity (Type-IHA) to inverted hierarchical model having odd CP parity (Type-IHB) in the first two mass eigenvalues, when there is a change in input values of parameters in the same mass matrix. The present work differs from the conventional approaches for the deviations from tri-bimaximal mixing, where the 2–3 symmetry is broken, leading to θ ₂₃ ≠ 45° and θ ₁₃ ≠ 0°.      

Neutrino Mixing Matrix and Leptogenesis from Quantum Gravity

We consider non renormalization 1/M _x interaction term as a perturbation of the neutrino mass matrix. We find that for the degenerate neutrino mass spectrum. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. We also assume, above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is bimaximal. The perturbation generates a non zero value of θ ₁₃, which is within reach of the high performance neutrino factory. In this paper, we find that the non zero value of θ ₁₃ due to Planck scale effects indicates the possibility of CP violation.     

Dielectric spectroscopy study of the new compound [C<Subscript>12</Subscript>H<Subscript>17</Subscript>N<Subscript>2</Subscript>]<Subscript>2</Subscript>CdCl<Subscript>4</Subscript>

The temperature dependence of the electrical conductivity of the compound 2,4,4-trimethyl-4,5-dihydro-3H-benzo[b] [1,4] diazepin-1-ium tetrachlorocadmiate in the different phases follows the Arrhenius law. The imaginary part of the permittivity constant is analyzed with the Cole–Cole formalism. In the temperature range 348–394 K, the activation energy of conductivity obtained from complex permittivity in regions I and II are, respectively, 1.03 and 0.33 eV, and E _m (in regions I and II are, respectively, 0.97 and 0.36 eV) obtained from the modulus spectra is close, suggesting that the ion transport is probably due to a hopping mechanism. The Kohlrausch–Williams–Watts function, j(t) = exp( - ( \fractt_\textKWW )^b ) \varphi (t) = \exp \left( { - {{\left( {\frac{t}{{{\tau_{\text{KWW}}}}}} \right)}^\beta }} \right) , and the coupling model are utilized for analyzing electric modulus at various temperatures. The decreasing of β at 373 K is due to approaching the temperatures of change in the conduction mechanism of the sample.     

A<Subscript>4</Subscript> symmetry and lepton masses and mixing

Stimulated by Ma’s idea, which explains the tribimaximal neutrino mixing by assuming an A₄ flavor symmetry, a lepton mass matrix model is investigated. A Frogatt–Nielsen-type model is assumed, and the flavor structures of the masses and mixing are caused by the VEVs of SU(2)_L singlet scalars φ_i ^u and φ_i ^d (i=1,2,3), which are assigned to 3 and (1 ,1 ’,1 ”) of A₄, respectively. Possible charged lepton and neutrino mass spectra and mixing are investigated.     

Level structures in the <Stack><Subscript>49</Subscript><Superscript>107</Superscript></Stack>In nucleus and their microscopic description

Excited states of the ₄₉¹⁰⁷In nucleus were populated through the ⁷⁸Se ( ³²S , p2n) fusion-evaporation reaction at beam energy, E _lab = 125 MeV. The de-excitations were studied using in-beam g \gamma -ray spectroscopic techniques involving the Compton-suppressed clover detector array. The level scheme of ¹⁰⁷In consisting of about seven bands is established up to spin ∼ 45/2ℏ with the addition of 25 new transitions. Spins and parities of various levels have been assigned through the DCO and polarization measurements. The level structures observed in ¹⁰⁷In have been interpreted in the framework of a microscopic theory based on the deformed Hartree-Fock (HF) and angular-momentum projection techniques. Various bands are reproduced in band mixing calculations with the configurations involving high-W \Omega p \pi g _9/2 and n \nu d _5/2 orbits, and low-W \Omega p \pi g _7/2 , n \nu g _7/2 and n \nu h _11/2 orbits.     

Constraining the lightest neutrino mass and <Emphasis Type="BoldItalic">m</Emphasis> <Subscript> <Emphasis Type="BoldItalic">ee</Emphasis> </Subscript> from general lepton mass matrices

Despite spectacular advances in fixing the neutrino mass and mixing parameters through various neutrino oscillation experiments, we still have little knowledge about the magnitudes of some vital parameters in the neutrino sector such as the absolute neutrino mass scale, effective Majorana mass m_ee measured in neutrinoless double beta decay. In this context, the present work aims to make an attempt to obtain some bounds for m_ee and the lightest neutrino mass using fairly general lepton mass matrices in the Standard Model.     

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     

A systematic study of neutrino mixing and <Emphasis Type="Italic">CP</Emphasis>-violationfrom lepton mass matrices with six texture zeros

We present a systematic study of 400 combinations of the charged lepton and neutrino mass matrices with six vanishing entries or texture zeros. Only 24 of them, which can be classified into a few distinct categories, are found to be compatible with current neutrino oscillation data at the level. A peculiar feature of the lepton mass matrices in each category is that they have the same phenomenological consequences. Taking account of a simple seesaw scenario for six parallel patterns of the charged lepton and Dirac neutrino mass matrices with six zeros, we show that it is possible to fit the experimental data at or below the level. In particular, the maximal atmospheric neutrino mixing can be reconciled with a strong neutrino mass hierarchy in the seesaw case. Numerical predictions are also obtained for the neutrino mass spectrum, flavor mixing angles, CP-violating phases and effective masses of the tritium beta decay and the neutrinoless double beta decay.Received: 28 September 2004, Revised: 14 October 2004, Published online: 1 December 2004PACS: 12.15.Ff, 12.10.Kt     

Possible alternatives to tri-bimaximal mixing

Possible alternatives to tri-bimaximal mixing are presented based on other symmetry principles, and their predictions for |U _e3|, sin ² θ ₁₂ and sin ² θ ₂₃ are compared to the present neutrino mixing data. In some cases perturbations are required to give better agreement with the data, and the use of a minimal approach is illustrated. Precise experimental determinations of the mixing parameters will be required to decipher the correct mixing pattern and to pin down the appropriate flavor symmetry.     

μ–τ symmetry in Zee–Babu model

We study the Zee–Babu two-loop neutrino mass generation model and look for a possible flavor symmetry behind the tri-bimaximal neutrino mixing. We find that there probably exists the μ–τ   symmetry in the case of the normal neutrino mass hierarchy, whereas there may not be in the inverted hierarchy case. We also propose a specific model based on a Froggatt–Nielsen-like Z₅$Z_5$ symmetry to naturally accomplish the μ–τ symmetry on the neutrino mass matrix for the normal hierarchy case.     

Model-independent analysis of tri-bimaximal mixing: A softly-broken hidden or an accidental symmetry?

To address the issue of whether tri-bimaximal mixing (TBM) is a softly-broken hidden or an accidental symmetry, we adopt a model-independent analysis in which we perturb a neutrino mass matrix leading to TBM in the most general way but leave the three texture zeros of the diagonal charged lepton mass matrix unperturbed. We compare predictions for the perturbed neutrino TBM parameters with those obtained from typical SO(10) grand unified theories with a variety of flavor symmetries. Whereas SO(10) GUTs almost always predict a normal mass hierarchy for the light neutrinos, TBM has a priori no preference for neutrino masses. We find, in particular for the latter, that the value of |U_e3| is very sensitive to the neutrino mass scale and ordering. Observation of |U_e3|²>0.001 to 0.01 within the next few years would be incompatible with softly-broken TBM and a normal mass hierarchy and would suggest that the apparent TBM symmetry is an accidental symmetry instead. No such conclusions can be drawn for the inverted and quasi-degenerate hierarchy spectra.     

What can we learn from high precision measurements of neutrino mixing angles?

Many experiments are being planned to measure the neutrino mixing angles more precisely. In this note, the theoretical significance of a high precision measurement of these parameters is discussed. It is emphasized that they can provide crucial information about different ways to understand the origin of large atmospheric neutrino mixing and move us closer towards determining the neutrino mass matrix. They may also be able to throw light on the question of lepton-quark unification as well as the existence of any leptonic symmetries. For instance if exact μ↔ τ symmetry in the neutrino mass matrix is assumed to be the reason for maximalv _μ-v_gt mixing, one gets θ₁₃ = 0 and {ie1295-01} can provide information about the way the μ↔ τ symmetry breaking manifests in the case of normal hierarchy.     

Neutrino hierarchy from CP-blind observables with high density magnetized detectors

High density magnetized detectors are well suited to exploit the outstanding purity and intensities of novel neutrino sources like neutrino factories and beta beams. They can also provide independent measurements of leptonic mixing parameters through the observation of atmospheric muon-neutrinos. In this paper, we discuss the combination of these observables from a multi-kT iron detector and a high energy beta beam; in particular, we demonstrate that even with moderate detector granularities the neutrino mass hierarchy can be determined for θ₁₃ values greater than 4°. PACS 14.60.Pq; 14.60.Lm     

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.     

<Emphasis Type="Italic">SU</Emphasis><Subscript><Emphasis Type="Italic">L</Emphasis></Subscript>(4)×<Emphasis Type="Italic">U</Emphasis>(1) model for electroweak unification and sterile neutrinos

Some of the basic problems in neutrino physics, such as new energy scales, the enormous gap between the neutrino masses and the lightest charged fermion mass, and the possible existence of sterile neutrinos in the eV mass range are studied in the local gauge group SU _L (4)×U(1) for electroweak unification, which does not contain fermions with exotic electric charges. It is shown that the neutrino mass spectrum can be decoupled from that of the other fermions. The further normal seesaw mechanism for neutrinos, with right-handed neutrino Majorana masses of order M≫M _weak as well a new eV-scale can be accommodated. The eV-scale seesaw may manifest itself in experiments like the Liquid Scintillation Neutrino Detector (LSND) and MiniBooNE (MB) experimental results and future neutrino experiments.     

On the magnetism of Ln<Subscript>2/3</Subscript>Cu<Subscript>3</Subscript>Ti<Subscript>4</Subscript>O<Subscript>12</Subscript> (Ln = lanthanide)

The magnetic and thermodynamic properties of the complete Ln_2/3Cu₃Ti₄O₁₂ series were investigated. Here Ln stands for the lanthanides La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb. All the samples investigated crystallize in the space group Im[`3]Im\bar{3} with lattice constants that follow the lanthanide contraction. The lattice constant of the Ce compound reveals the presence of Ce⁴⁺ leading to the composition Ce_1/2Cu₃Ti₄O₁₂. From magnetic susceptibility and electron-spin resonance experiments it can be concluded that the copper ions always carry a spin S = 1/2 and order antiferromagnetically close to 25 K. The Curie-Weiss temperatures can approximately be calculated assuming a two-sublattice model corresponding to the copper and lanthanide ions, respectively. It seems that the magnetic moments of the heavy rare earths are weakly coupled to the copper spins, while for the light lanthanides no such coupling was found. The 4f moments remain paramagnetic down to the lowest temperatures, with the exception of the Tm compound, which indicates enhanced Van-Vleck magnetism due to a non-magnetic singlet ground state of the crystal-field split 4f manifold. From specific-heat measurements we accurately determined the antiferromagnetic ordering temperature and obtained information on the crystal-field states of the rare-earth ions.     

Magnetic state of the structural separated anion-deficient La<Subscript>0.70</Subscript>Sr<Subscript>0.30</Subscript>MnO<Subscript>2.85</Subscript> manganite

The results of neutron diffraction studies of the La_0.70Sr_0.30MnO_2.85 compound and its behavior in an external magnetic field are stated. It is established that in the 4–300 K temperature range, two structural perovskite phases coexist in the sample, which differ in symmetry (groups R[`3]cR\bar 3c and I4/mcm). The reason for the phase separation is the clustering of oxygen vacancies. The temperature (4–300 K) and field (0–140 kOe) dependences of the specific magnetic moment are measured. It is found that in zero external field, the magnetic state of La_0.70Sr_0.30MnO_2.85 is a cluster spin glass, which is the result of frustration of Mn³⁺-O-Mn³⁺ exchange interactions. An increase in external magnetic field up to 10 kOe leads to fragmentation of ferromagnetic clusters and then to an increase in the degree of polarization of local spins of manganese and the emergence of long-range ferromagnetic order. With increasing magnetic field up to 140 kOe, the magnetic ordering temperature reaches 160 K. The causes of the structural and magnetic phase separation of this composition and formation mechanism of its spin-glass magnetic state are analyzed.