Neutrino textures in light of Super-Kamiokande data and a realistic string model

Motivated by the Super-Kamiokande atmospheric neutrino data, we discuss possible textures for Majorana and Dirac neutrino masses within the see-saw framework. There are two main purposes of this paper: first, to gain intuition into this area from a purely phenomenological analysis, and second, to explore to what extent it may be realized in a specific model. We comment initially on the simplified two-generation case, emphasizing that large mixing is not incompatible with a large hierarchy of mass eigenvalues. We also emphasize that renormalization-group effects may amplify neutrino mixing, and we present semi-analytic expressions for estimating this amplification. Several examples are then given of three-family neutrino mass textures, which may also accommodate the persistent solar neutrino deficit, with different assumptions for the neutrino Dirac mass matrices. We comment on a few features of neutrino mass textures arising in models with a U(1) flavour symmetry. Finally, we discuss the possible pattern of neutrino masses in a “realistic” flipped SU(5) model derived from string theory, illustrating how a desirable pattern of mixing may emerge. Both small- or large-angle MSW solutions are possible, while a hierarchy of neutrino masses appears more natural than near-degeneracy. This model contains some unanticipated features that may be relevant in other models also: The neutrino Dirac matrices may not be related closely to the quark mass matrices, and the heavy Majorana states may include extra gauge-singlet fields. Received: 6 November 1998 / Published online: 18 June 1999     

Phenomenological analysis of hybrid textures of neutrinos

We present a comprehensive phenomenological analysis of the allowed hybrid textures of neutrinos. Out of a total of sixty hybrid textures with one equality between the elements of neutrino mass matrix and one texture zero only twenty three are found to be viable at 99% C.L. whereas the earlier analysis found fifty four to be viable. We examine the phenomenological implications of the allowed hybrid textures including Majorana type CP-violating phases, 1–3 mixing angle and Dirac type CP-violating phase, δ. We, also, obtain lower bound on effective Majorana mass for all the allowed hybrid textures.     

Limits of Majorana neutrino mass from combined analysis of data from <Superscript>76</Superscript>Ge and <Superscript>136</Superscript>Xe neutrinoless double beta decay experiments

We present effective Majorana neutrino mass limits <m _ββ> obtained from the joint analysis of the recently published results of ⁷⁶Ge and ¹³⁶Xe neutrinoless double beta decay (0νββ) experiments, which was carried out by using the Bayesian calculations. Nuclear matrix elements (NMEs) used for the analysis are taken from the works, in which NMEs of ⁷⁶Ge and ¹³⁶Xe were simultaneously calculated. This reduced systematic errors connected with NME calculation techniques. The new effective Majorana neutrino mass limits <m _ββ> less than [85.4–197.0] meV are much closer to the inverse neutrino mass hierarchy region.     

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.     

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.     

Majorana neutrinos, <Emphasis Type="Italic">CP</Emphasis> violation,neutrinoless double beta and tritium beta decays

If the present or upcoming searches for neutrinoless double beta ((ββ)_0ν) decay give a positive result, the Majorana nature of massive neutrinos will be established. From the determination of the value of the (ββ)_0ν-decay effective Majorana mass parameter (|〈m〉|), it would be possible to obtain information on the type of neutrino mass spectrum. Assuming 3-ν mixing and massive Majorana neutrinos, we discuss the information that a measurement of, or an upper bound on, |〈m〉| can provide on the value of the lightest neutrino mass m₁. With additional data on the neutrino masses obtained in ³H β-decay experiments, it might be possible to establish whether the CP symmetry is violated in the lepton sector. This would require very high precision measurements. If CP invariance holds, the allowed patterns of the relative CP parities of the massive Majorana neutrinos would be determined.     

Hybrid textures in minimal seesaw mass matrices

In the context of the minimal seesaw framework, we discuss the implications of Dirac and Majorana mass matrices in which two properties coexist, namely, equalities among matrix elements and texture zeros. Among the large number of general possibilities, only 12 patterns are found to be consistent with the global neutrino oscillation data at the level of the most minimal number of free parameters. The predictions of the allowed textures for mass hierarchy, θ₁₃${\theta }_{13}$ and effective mass governing neutrino-less double beta decay are discussed. We also explore the possibility of having non-zero CP violation for each allowed solution. We find that only one allowed solution can accommodate both low and high energy CP violation. We discuss the prediction of this solution for leptogenesis and explore the correlation, between leptogenesis and low energy CP violation.     

Effective Majorana mass and neutrinoless double beta decay

The probability distribution for the effective Majorana mass as a function of the lightest neutrino mass in the standard three neutrino scheme is computed via a random sampling from the distributions of the involved mixing angles and squared mass differences. A flat distribution in the \([0,2\pi ]\) range for the Majorana phases is assumed, and the dependence of small values of the effective mass on the Majorana phases is highlighted. The study is then extended with the addition of the cosmological bound on the sum of the neutrino masses. Finally, the prospects for \(0\nu \beta \beta \) decay search with \(^{76}\)Ge, \(^{130}\)Te and \(^{136}\)Xe are discussed, as well as those for the measurement of the electron neutrino mass.     

Effect of Majorana Phases in Neutrino Oscillation

Quantum gravity (Planck scale effects) lead to an effective SU(2) _L ×U(1) invariant dimension-5 Lagrangian involving neutrino and Higgs fields. On symmetry breaking, this operator gives rise to correction to the above masses and mixing. The gravitational interaction M _X =M _pl , we find that for degenerate neutrino mass spectrum, it is shown that the Majorana phase of the neutrino mixing matrix can effects in neutrino oscillation probability.     

Neutrino physics with cryogenic detectors

The recent results on neutrino oscillations and the consequent need to measure the value of the neutrino mass are briefly discussed. The operating principle of cryogenic detectors working at low temperatures, where the small heat capacity allows one to record and measure the temperature increase due to the tiny energy lost by a particle in form of heat is described. An application of these detectors is the measurement, or at least an upper constraint, of the neutrino mass in β decay. This approach is complementary and can, in the future, be competitive with experiments based on the spectrometric measurement of the electron energy. The search for neutrinoless double beta decay could reach a better sensitivity on the mass if a neutrino is a Majorana particle. A large cryogenic detector, named CUORICINO, on neutrinoless double beta decay (DBD) of ¹³⁰Te already yields the best constraint on the absolute value of the Majorana neutrino mass. A much larger detector, named CUORE, for Cryogenic Underground Observatory for Rare Events, is currently under construction. With its active mass of 750 kg of natural TeO₂ it aims to reach the sensitivity in the determination of the Majorana neutrino mass suggested by the results of neutrino oscillation under the inverse hierarchy hypothesis. The problem is closely connected with what I call “the second mystery of Ettore Majorana” who suggested a particle that would violate the lepton number.     

On the oscillations of neutrinos with Dirac and Majorana masses

Pontecorvo neutrino oscillations are discussed in the case of Dirac as well as Majorana neutrino mass terms. We prove that none of the possible experiments on neutrino oscillations including those on CP nonconservation, can distinguish between these two possibilities. Oscillations of neutrinos having both Dirac and Majorana mass terms also considered.     

Majorana neutrinos and same-sign dilepton production at LHC and in rare meson decays

We discuss same-sign dilepton production mediated by Majorana neutrinos in high-energy proton–proton collisions for at the LHC energy TeV, and in the rare decays of the , and B mesons of the type . For the pp reaction, assuming one heavy Majorana neutrino of mass , we present discovery limits in the plane where are the mixing parameters. Taking into account the present limits from low-energy experiments, we show that at LHC one has sensitivity to heavy Majorana neutrinos up to a mass TeV in the dilepton channels , and , but the dilepton states will not be detectable due to the already existing constraints from neutrinoless double beta decay. We work out a large number of rare meson decays, both for the light and heavy Majorana neutrino scenarios, and argue that the present experimental bounds on the branching ratios are too weak to set reasonable limits on the effective Majorana masses. Received: 24 April 2001 / Published online: 29 June 2001     

Radiative transmission of lepton flavor hierarchies

We discuss a one loop model for neutrino masses which leads to a seesaw-like formula with the difference that the charged lepton masses replace the unknown Dirac mass matrix present in the usual seesaw case. This is a considerable reduction of parameters in the neutrino sector and predicts a strong hierarchical pattern in the right handed neutrino mass matrix that is easily derived from a U(1)_H family symmetry. The model is based on the left–right gauge group with an additional Z₄ discrete symmetry which gives vanishing neutrino Dirac masses and finite Majorana masses arising at the one loop level. Furthermore, it is one of the few models that naturally allow for large (but not necessarily maximal) mixing angles in the lepton sector. A generalization of the model to the quark sector requires three iso-spin singlet vector-like down type quarks, as in E₆. The model predicts an inert doublet type scalar dark matter.     

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     

Is the magic texture of Majorana neutrinos immanent in Dirac nature?

Magic textures are successful candidates of the correct texture for Majorana neutrinos. In this study, we demonstrate that several types of magic textures of Majorana neutrinos are approximately immanent in the flavor mass matrix of Dirac neutrinos. In addition, the normal mass ordering of Dirac neutrino masses is slightly preferable to inverted mass ordering in the context of magic textures.     

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     

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.     

Angular distribution of electrons in neutrinoless double-beta decay and new physics

For neutrinoless double-beta decay caused by the exchange of light Majorana neutrinos, an expression for the differential width with respect to the angle between the final-electron momenta is obtained on the basis of a Lorentz-invariant effective Lagrangian of the general form. The shape of this angular distribution is analyzed within various extensions of the Standard Model that allow this process—in particular, within theories that involve Majorana super partners and (or) right-handed currents. The angular correlation coefficient for electrons as a function of the mass of the right-handed W boson and the effective Majorana neutrino mass in the decay of the ⁷⁶Ge nucleus is considered within the model involving left—right symmetry.     

Texture zeros and majorana phases of the neutrino mass matrix

We present the generic formulas to calculate the ratios of neutrino masses and the Majorana phases of CP violation from the neutrino mass matrix with two independent vanishing entries in the flavor basis where the charged lepton mass matrix is diagonal. An order-of-magnitude illustration is given for seven experimentally acceptable textures of the neutrino mass matrix, and some analytical approximations are made for their phenomenological consequences at low energy scales.     

Present and future strategies for neutrinoless double beta decay searches

The renewed interest shown in these days towards neutrinoless double beta decay, a lepton number violating process which can take place only if neutrinos are Majorana particles (ν = \(\bar \nu \)) with a nonvanishing mass, is justified by the fact that the Majorana nature of neutrinos is expected in many theories beyond the Standard Model. We also now know, thanks to the neutrino oscillation experiments, that neutrinos are in fact massive, as expected in these theories and not requested in the Standard Model. Moreover, since neutrino oscillation experiments measure only the absolute value of the difference of the square of the neutrino masses, the discovery of neutrinoless double beta decay would help to disentangle questions that still remain unsolved: what is the absolute mass scale of the neutrinos and which mass hierarchy (normal, inverted or quasi-degenerate) is the correct one?The scope of this paper is not only to review the present results reached in the field by the different groups and technologies worldwide, but also to illustrate and comment on the (near and long-term) future strategies that experimentalists are trying to pursue to reach the needed sensitivity required to explore the inverted hierarchy neutrino mass scale.