L/E-flatness of the electron-like event ratio, in Super-Kamiokande and a degeneracy, in neutrino masses

We show that the L/E-flatness of the electron-like event ratio in the Super-Kamiokande atmospheric neutrino data implies the equality of the expectation values for the muon and tau neutrino masses. We establish this result by obtaining a set of three constraints on the neutrino-oscillation mixing matrix as contained in the indicated flatness. The resulting 3×3 neutrino-oscillation matrix depends only on one angle. A remarkable result that follows directly from this matrix is the consistency between the mixing angles observed by LSND and Super-Kamiokande.     

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     

Impact of two mass scale oscillations on the analysis of atmospheric and reactor neutrino data

We study the stability of the results of the three-neutrino oscillation analysis of atmospheric and reactor neutrino data under departures of the one dominant mass scale approximation. In order to do so we perform the analysis of atmospheric and reactor neutrino data in terms of three-neutrino oscillations where the effect of both mass differences is explicitly considered. We study the allowed parameter space resulting from this analysis as a function of the mass splitting hierarchy parameter which parameterizes the departure from the one dominant mass scale approximation. We consider schemes with both direct and inverted mass ordering. Our results show that in the analysis of the atmospheric data the derived range of the largest mass splitting, , is stable, while the allowed ranges of mixing angles and are wider than those obtained in the one dominant mass scale approximation. Inclusion of the CHOOZ reactor data in the analysis results in the reduction of the parameter space in particular for the mixing angles. As a consequence the final allowed ranges of the parameters from the combined analysis are only slightly broader than when obtained in the one dominant mass scale approximation. Received: 31 May 2002 / Revised version: 10 July 2002 / Published online: 31 October 2002     

On vacuum oscillations solution of the solar neutrino problem

Experimental signatures of vacuum oscillations solution of the solar neutrino problem are considered. This solution predicts a strict correlation between a distortion of the neutrino energy spectrum and an amplitude of seasonal variations of the neutrino flux. The slope parameter which characterizes a distortion of the recoil electron energy spectrum in the Super-Kamiokande experiment and the seasonal asymmetry of the signal have been calculated in a wide range of oscillation parameters. The correlation of the slope and asymmetry gives crucial criteria for identification or exclusion of this solution. For the positive slope indicated by preliminary Super-Kamiokande data we predict (40 – 60) % enhancement of the seasonal variations.     

Stability of the lepton-flavor mixing matrix against quantum corrections

Recent neutrino experiments suggest strong evidence of tiny neutrino masses and the lepton-flavor mixing. Neutrino-oscillation solutions for the atmospheric neutrino anomaly and the solar neutrino deficit can determine the texture of the neutrino mass matrix according to the neutrino mass hierarchies as Type A: , Type B: , and Type C: , where is the i-th generation neutrino mass. In this paper we study the stability of the lepton-flavor mixing matrix against quantum corrections for all three types of mass hierarchy in the minimal supersymmetric Standard Model with an effective dimension-five operator which gives the Majorana masses of neutrinos. The relative sign assignments of neutrino masses in each type play crucial role for the stability against quantum corrections. We find that the lepton-flavor mixing matrix of Type A is stable against quantum corrections, and that of Type B with the same (opposite) signs of and are unstable (stable). For Type C, the lepton-flavor-mixing matrix approaches the definite unitary matrix according to the relative sign assignments of the neutrino mass eigenvalues as the effects of quantum corrections become large enough to neglect the squared mass differences of neutrinos. Received: 24 June 1999 / Revised version: 23 December 1999 / Published online: 17 March 2000     

Vacuum solutions of neutrino anomalies through a softly broken U(1) symmetry

We discuss an extended model which naturally leads to mass scales and mixing angles relevant for understanding both the solar and atmospheric neutrino anomalies in terms of the vacuum oscillations of the three known neutrinos. The model uses a softly broken –– symmetry and contains a heavy scale GeV. The –– symmetric neutrino masses solve the atmospheric neutrino anomaly while breaking of –– generates the highly suppressed radiative mass scale needed for the vacuum solution of the solar neutrino problem. All the neutrino masses in the model are inversely related to , thus providing seesaw-type of masses without invoking any heavy right-handed neutrinos. The possible embedding of the model into an SU(5) grand unified theory is discussed. Received: 5 August 1999 / Revised version: 18 November 1999 / Published online: 6 April 2000     

CP Phase Effects in Long Baseline Neutrino Experiments

Neutrino oscillation experiments are analyzed within the two-flavor frame work which is defined by 1 mass-squared difference and 1 mixing angle. In three flavor neutrino oscillation, there are 6 parameter, 2 mass squared differences, 3 mixing angle and 1 CP phase. In this article, we give the observing CP violating phase effects in neutrino oscillation probability in long baseline neutrino experiments.     

A 4-neutrino model with a Higgs triplet

We take as a starting point the Gelmini–Roncadelli model enlarged by a term with explicit lepton number violation in the Higgs potential and add a neutrino singlet field that is coupled via a scalar doublet to the usual leptons. This scenario allows us to take into account all three present indications in favor of neutrino oscillations provided by the solar, atmospheric, and LSND neutrino oscillation experiments. Furthermore, it suggests a model which reproduces naturally one of the two 4-neutrino mass spectra favored by the data. In this model, the solar neutrino problem is solved by large mixing MSW transitions, and the atmospheric neutrino problem by transitions of into a sterile neutrino. Received: 11 May 1999 / Published online: 3 February 2000     

Charged-Lepton-Flavour Violation in the light of the Super-Kamiokande data

Motivated by the data from Super-Kamiokande and elsewhere indicating oscillations of atmospheric and solar neutrinos, we study charged-lepton-flavour violation, in particular the radiative decays and , but also commenting on and decays, as well as conversion on nuclei. We first show how the renormalization group may be used to calculate flavour-violating soft supersymmetry-breaking masses for charged sleptons and sneutrinos in models with universal input parameters. Subsequently, we classify possible patterns of lepton-flavour violation in the context of phenomenological neutrino mass textures that accommodate the Super-Kamiokande data, giving examples based on Abelian flavour symmetries. Then we calculate in these examples rates for and , which may be close to the present experimental upper limits, and show how they may distinguish between the different generic mixing patterns. The rates are promisingly large when the soft supersymmetry-breaking mass parameters are chosen to be consistent with the cosmological relic-density constraints. In addition, we discuss conversion on Titanium, which may also be accessible to future experiments. Received: 18 December 1999 / Published online: 6 March 2000     

The Earth effects on the supernova neutrino spectra

The Earth effects on the energy spectra of supernova neutrinos are studied. We analyze numerically the time-integrated energy spectra of neutrino in a mantle–core–mantle step function model of the Earth's matter density profile. We consider a realistic frame-work in which there are three active neutrinos whose mass squared differences and mixings are constrained by the present understanding of solar and atmospheric neutrinos. We find that the energy spectra change for some allowed mixing parameters. Especially, the expected number of events at SNO shows characteristic behavior with respect to energy, i.e., a great dip and peak. We show that observations of the Earth effect allow us to identify the solar neutrino solution and to probe the mixing angle θ₂.     

Neutrino masses, mixing angles and the unification of couplings in the MSSM

In the light of the gathering evidence for neutrino oscillations, coming in particular from the Super-Kamiokande data on atmospheric neutrinos, we re-analyze the unification of gauge and Yukawa couplings within the minimal supersymmetric extension of the Standard Model (MSSM). Guided by a range of different grand-unified models, we stress the relevance of large mixing in the lepton sector for the question of bottom-tau Yukawa coupling unification. We also discuss the dependence of the favoured value of on the characteristics of the high-energy quark and lepton mass matrices. In particular, we find that, in the presence of large lepton mixing, Yukawa unification can be achieved for intermediate values of that were previously disfavoured. The renormalization-group sensitivity to the structures of different mass matrices may enable Yukawa unification to serve as a useful probe of GUT models. Received: 22 June 1999 / Published online: 10 December 1999     

Results from solar, atmospheric and K2K experiments and future possibilities with T2K

Recent results from solar, reactor, atmospheric and long baseline (K2K) experiments are discussed. With the improved data statistics and analyses, our knowledge on the neutrino masses and mixing angles are steadily improving. T2K is the next generation neutrino oscillation experiment between J-PARC in Tokai and Super-Kamiokande. This experiment will start in 2009. This experiment is expected to improve the current knowledge on the neutrino masses and mixings substantially.     

Progress in neutrino oscillation searches and their implications

Neutrino oscillation, in which a given flavor of neutrino transforms into another is a powerful tool for probing small neutrino masses. The intrinsic neutrino properties involved are neutrino mass squared difference Δm ² and the mixing angle in vacuum θ. In this paper I will summarize the progress that we have achieved in our search for neutrino oscillation with special emphasis on the recent results from the Sudbury Neutrino Observatory (SNO) on the measurement of solar neutrino fluxes. I will outline the current bounds on the neutrino masses and mixing parameters and discuss the major physics goals of future neutrino experiments in the context of the present picture.     

Neutrino Mixing in Matter at Extreme High Energy

We have studied neutrino mixing at extreme high energy considering two flavour framework with matter effects. We analyze the atmospheric neutrino data within the simplest scheme of two neutrino oscillation. We consider as special case of matter density profile, which are relevant for neutrino oscillations. In particular, we compute to constrain a specific from of neutrino mass square difference and mixing in extreme high energy in matter. The dispersion relation for the neutrino mixing in neutrino oscillation in matter are discussed.     

Domain of mixing angles in three flavor neutrino oscillations

We clarify the domain needed for the mixing angles in three flavor neutrino oscillations. By comparing the ranges of the transition probabilities as functions of the domains of the mixing angles, we show that it is necessary and sufficient to let all mixing angles be in . This holds irrespectively of any assumptions on the neutrino mass squared differences.     

The effects of Majorana phases in three-generation neutrinos

Neutrino-oscillation solutions for the atmospheric neutrino anomaly and the solar neutrino deficit can determine the texture of the neutrino mass matrix according to three types of neutrino mass hierarchy: Type A: , Type B: , and Type C: , where is the absolute mass of the ith generation neutrino. The relative sign assignments of the neutrino masses in each type of mass hierarchy play crucial roles in the stability against quantum corrections. Actually, two physical Majorana phases in the lepton flavor mixing matrix connect the relative sign assignments of the neutrino masses. Therefore, in this paper we analyze the stability of the mixing angles against quantum corrections according to three types of neutrino mass hierarchy (Type A, B, C) and two Majorana phases. The two phases play crucial roles in the stability of the mixing angles against quantum corrections. Received: 9 May 2000 / Revised version: 23 May 2000 / Published online: 8 September 2000     

Probing the neutrino mass matrix in next-generation neutrino oscillation experiments

We review the current status of the neutrino mass and mixing parameters needed to reconstruct the neutrino mass matrix. A comparative study of the precision in the measurement of oscillation parameters expected from the next-generation solar, atmospheric, reactor-and accelerator-based neutrino experiments is presented. We discuss the potential of 0νββ experiments in determining the neutrino mass hierarchy and the importance of a better ϑ ₁₂ measurement for it. The text was submitted by the author in English.     

A new three-flavor oscillation solution of the solar neutrino deficit in <Emphasis Type="Italic">R</Emphasis>-parity violating supersymmetry

We present a solution of the solar neutrino deficit using three flavors of neutrinos and R-parity non-conserving supersymmetry. In this model, in vacuum, the is massless and unmixed, mass and mixing being restricted to the - sector only, which we choose in consistency with the requirements of the atmospheric neutrino anomaly. The flavor changing and flavor diagonal neutral currents present in the model and the three-flavor picture together produce an energy dependent resonance-induced - mixing in the sun. This mixing plays a key role in the new solution to the solar neutrino problem. The best fit to the solar neutrino rates and spectrum (1258-day SK and 241-day SNO data) requires a mass square difference of eV² in vacuum between the two lightest neutrinos. This solution cannot accommodate a significant day-night effect for solar neutrinos nor CP violation in terrestrial neutrino experiments. Received: 26 December 2001 / Revised version: 16 February 2002 / Published online: 26 July 2002     

Theoretical study of lepton events in the atmospheric neutrino experiments at SuperK

Super-Kamiokande has reported the results for the lepton events in the atmospheric neutrino experiment. These results have been presented for a 22.5kT water fiducial mass on an exposure of 1489 days, and the events are divided into sub-GeV, multi-GeV and PC events. We present a study of nuclear medium effects in the sub-GeV energy region of atmospheric neutrino events for the quasielastic scattering, incoherent and coherent pion production processes, as they give the most dominant contribution to the lepton events in this energy region. We have used the atmospheric neutrino flux given by Honda et al. These calculations have been done in the local density approximation. We take into account the effects of Pauli blocking, Fermi motion, Coulomb effect, renormalization of weak transition strengths in the nuclear medium in the case of the quasielastic reactions. The inelastic reactions leading to production of leptons along with pions is calculated in a $ \Delta$ -dominance model by taking into account the renormalization of $ \Delta$ properties in the nuclear medium and the final-state interaction effects of the outgoing pions with the residual nucleus. We present the results for the lepton events obtained in our model with and without nuclear medium effects, and compare them with the Monte Carlo predictions used in the simulation and the experimentally observed events reported by the Super-Kamiokande Collaboration.     

Neutrino oscillations with three flavors in matter of varying density

In this paper, we discuss the evolution operator and the transition probabilities expressed as functions of the vacuum mass squared differences, the vacuum mixing angles, and the matter density parameter for three flavor neutrino oscillations in matter of varying density in the plane wave approximation. The applications of this to neutrino oscillations in a model of the earth's matter density profile, step function matter density profiles, constant matter density profiles, linear matter density profiles, and finally in a model of the sun's matter density profile are discussed. We show that for matter density profiles which do not fluctuate too much, the total evolution operator consisting of n operators can be replaced by one single evolution operator in the semi-classical approximation. Received: 23 March 2001 / Published online: 8 June 2001