Vacuum Oscillation Solution Research Articles

Symmetric textures inSO(10)and large mixing angle solution for solar neutrinos

We analyze a model based on SUSY SO(10) combined with SU(2) family symmetry and symmetric mass matrices constructed by the authors recently. Previously, only the parameter space for the LOW and vacuum oscillation (VO) solutions was investigated. We indicate in this note the parameter space which leads to large mixing angle (LMA) solution to the solar neutrino problem with a slightly modified effective neutrino mass matrix. The symmetric mass textures arising from the left-right symmetry breaking and the SU(2) symmetry breaking give rise to very good predictions for the quark and lepton masses and mixing angles. The prediction of our model for the |U_{e\nu_{3}}| element in the Maki-Nakagawa-Sakata (MNS) matrix is close to the sensitivity of current experiments; thus the validity of our model can be tested in the near future. We also investigate the correlation between the |U_{e\nu_{3}}| element and \tan^{2}\theta_{\odot} in a general two-zero neutrino mass texture.

Constraints on decay plus oscillation solutions of the solar neutrino problem

We examine the constraints on the nonradiative decay of neutrinos from the observations of solar neutrino experiments. The standard oscillation hypothesis among three neutrinos solves the solar and atmospheric neutrino problems. The decay of a massive neutrino mixed with the electron neutrino results in the depletion of the solar neutrino flux. We introduce neutrino decay in the oscillation hypothesis and demand that decay does not spoil the successful explanation of solar and atmospheric observations. We obtain a lower bound on the ratio of the lifetime over the mass of ${\ensuremath{\nu}}_{2},$ ${\ensuremath{\tau}}_{2}{/m}_{2}>22.7\mathrm{s}/\mathrm{MeV}$ for the Mikheyev-Smirnov-Wolfenstein solution of the solar neutrino problem and ${\ensuremath{\tau}}_{2}{/m}_{2}>27.8\mathrm{s}/\mathrm{MeV}$ for the vacuum oscillation solution (at $99%$ C.L.).

Solar neutrino oscillations and bounds on neutrino magnetic moment and solar magnetic field

If the observed deficit of solar neutrinos is due to neutrino oscillations, neutrino conversions caused by the interaction of their transition magnetic moments with the solar magnetic field (spin-flavour precession) can still be present at a subdominant level. In that case, the combined action of neutrino oscillations and spin-flavour precession can lead to a small but observable flux of electron antineutrinos coming from the sun. Non-observation of these ν̄e's could set limits on neutrino transition moment μ and the strength and coordinate dependence of the solar magnetic field B⊥. The sensitivity of the ν̄e flux to the product μB⊥ is the strongest in the case of the vacuum oscillation (VO) solution of the solar neutrino problem; in the case of the LOW solution, it is weaker, and it is the weakest for the LMA solution. For different solutions, different characteristics of the solar magnetic field B⊥(r) are probed: for the VO solution, the ν̄e flux is determined by the integral of B⊥(r) over the solar convective zone, for LMA it is determined by the magnitude of B⊥ in the neutrino production region, and for LOW it depends on the competition between this magnitude and the derivative of B⊥(r) at the surface of the sun.

Global analysis with SNO: Toward the solution of the solar neutrino problem

We perform a global analysis of the latest solar neutrino data including the Solar Neutrino Observatory (SNO) result on the charged current (CC) event rate. This result further favors the large mixing angle (LMA) Mikheyev-Smirnov-Wolfenstein (MSW) solution of the solar neutrino problem. The best fit values of parameters we find are $\ensuremath{\Delta}{m}^{2}=(4.8--5.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5} {\mathrm{eV}}^{2},$ ${\mathrm{tan}}^{2}\ensuremath{\theta}=0.35--0.38,$ ${f}_{\mathrm{B}}=1.08--1.12,$ and ${f}_{\mathrm{hep}}=1--4,$ where ${f}_{\mathrm{B}}$ and ${f}_{\mathrm{hep}}$ are the boron and ${}^{3}\mathrm{He}+p$ (hep) neutrino fluxes in units of the corresponding fluxes in the standard solar model (SSM). With respect to this best fit point the low $\ensuremath{\Delta}{m}^{2}$ (LOW) MSW solution is accepted at 90% C.L. The vacuum oscillation solution (VAC) with $\ensuremath{\Delta}{m}^{2}=1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10} {\mathrm{eV}}^{2},$ gives a good fit to the data provided that the boron neutrino flux is substantially smaller than the SSM flux ${(f}_{\mathrm{B}}\ensuremath{\sim}0.5).$ The small mixing angle (SMA) solution is accepted at about the $3\ensuremath{\sigma}$ level. We find that vacuum oscillations to a sterile neutrino, VAC(sterile), with ${f}_{\mathrm{B}}\ensuremath{\sim}0.5$ also give a rather good global fit to the data. All other sterile neutrino solutions are strongly disfavored. We check the quality of the fit by constructing the pull-off diagrams of observables for the global solutions. Maximal mixing is allowed at the $3\ensuremath{\sigma}$ level in the LMA region and at 95% C.L. in the LOW region. Predictions for the day-night asymmetry, spectrum distortion, and ratio of the neutral to charged current event rates [NC]/[CC] at SNO are calculated. In the best fit points of the global solutions we find ${A}_{\mathrm{DN}}^{\mathrm{CC}}\ensuremath{\approx}7--8%$ for the LMA, $\ensuremath{\sim}3%$ for the LOW, and $2\ensuremath{-}3%$ for the SMA regions. In the LMA region the asymmetry can be as large as $15--20%.$ Observation of ${A}_{\mathrm{DN}}^{\mathrm{CC}}>5%$ will further favor the LMA solution. It will be difficult to see the distortion of the spectrum expected for LMA as well as LOW solutions. However, future SNO spectral data can significantly affect the VAC and SMA solutions. We present the expected values of the BOREXINO event rate for global solutions.

Erratum: Three flavor long-wavelength vacuum oscillation solution to the solar neutrino problem [Phys. Rev. D63, 013005 (2001)

We investigate the current status of the long-wavelength vacuum oscillation solution to the solar neutrino problem and to what extent the presence of a third neutrino can affect and modify it. Assuming that the smaller mass squared difference that can induce such oscillations, $\Delta m^2_{12}$, is in the range $10^{-11}-10^{-8}$ eV$^2$ and the larger one, $\Delta m^2_{23}$, in the range relevant to atmospheric neutrino observations, we analyze the most recent solar neutrino data coming from Homestake, SAGE, GALLEX, GNO and Super-Kamiokande experiments in the context of three neutrino generations. We include in our vacuum oscillation analysis the MSW effect in the Sun, which is relevant for some of the parameter space scrutinized. We have also performed, as an extreme exercise, the fit without Homestake data. % While we found that the MSW effect basically does not affect the best fitted parameters, it significantly modifies the allowed parameter space for $\Delta m^2_{12}$ larger than $\sim 3 \times 10^{-10}$ eV$^2$, in good agreement with the result obtained by A. Friedland in the case of two generations. % Although the presence of a third neutrino does not essentially improve the quality of the fit, the solar neutrino data alone can give an upper bound on $\theta_{13}$, which is constrained to be less than $\sim 60^\circ$ at 95 % C.L.

From CKM Matrix to MNS Matrix: A Model Based on SUSY SO(10) × U(2)F Symmetry

We construct a realistic model based on SUSY SO(10) with U(2) flavor symmetry. A set of symmetric mass textures give rise to very good predictions; 15 masses and 6 mixing angles are predicted by 11 parameters. Both the vacuum oscillation and LOW solutions are favored for the solar neutrino problem.

Solar neutrinos: global analysis and implications for SNO

We present a global analysis of all the available solar neutrino data treating consistently the 8B and hep neutrino fluxes as free parameters. The analysis reveals at 99.7% C.L. eight currently-allowed discrete regions in two-neutrino oscillation space, five regions corresponding to active neutrinos and three corresponding to sterile neutrinos. Most of the allowed solutions are robust with respect to changes in the analysis procedure, but the traditional vacuum solution is fragile. The globally-permitted range of the 8B neutrino flux, 0.45 to 1.95 in units of the BP2000 flux, is comparable to the 3 sigma range allowed by the standard solar model. We discuss the implications for SNO of a low mass, Delta m^2 ~ 6 times 10^{-12} eV^2, vacuum oscillation solution, previously found by Raghavan, and by Krastev and Petcov, but absent in recent analyses that included Super-Kamiokande data. For the SNO experiment, we present refined predictions for the charged-current rate and the ratio of the neutral-current rate to charged-current rate. The predicted charged-current rate can be clearly distinguished from the no-oscillation rate only for the LMA solution. The predicted ratio of the neutral-current rate to charged-current rate is distinguishable from the no-oscillation ratio for the LMA, SMA, LOW, and VAC solutions for active neutrinos.

Solar neutrino problem accounting for self-consistent magnetohydrodynamics solution for solar magnetic fields

The analysis of the resonant spin-flavour (RSF) solutions to the solar neutrino problem in the framework of simplest analytic solutions to the solar magneto-hydrodynamics (MHD) equations is presented. We performed the global fit of the recent solar neutrino data, including event rates as well as zenith angle distributions and recoil electron spectra induced by solar neutrino interactions in SuperKamiokande. We compare quantitatively our simplest MHD-RSF fit with vacuum oscillation (VAC) and MSW-type (SMA, LMA and LOW) solutions to the solar neutrino problem using a common well-calibrated theoretical calculation and fit procedure and find MHD-RSF fit to be somewhat better than those obtained for the favored neutrino oscillation solutions. We made the predictions for future experiments to disentangle the MHD-RSF scenario from other scenarios.

Correlations of solar neutrino observables for SNO

Neutrino oscillation scenarios predict correlations, and zones of avoidance, among measurable quantities such as spectral energy distortions, total fluxes, time dependences, and flavor content. The comparison of observed and predicted correlations will enhance the diagnostic power of solar neutrino experiments. A general test of all presently-allowed (two neutrino) oscillation solutions is that future measurements must yield values outside the predicted zones of avoidance. To illustrate the discriminatory power of the simultaneous analysis of multiple observables, we map currently allowed regions of neutrino masses and mixing angles onto planes of quantities measurable with the Sudbury Neutrino Observatory (SNO). We calculate the correlations that are predicted by vacuum and MSW (active and sterile) neutrino oscillation solutions that are globally consistent with all available neutrino data. We derive approximate analytic expressions for the dependence of individual observables and specific correlations upon neutrino oscillations parameters. We also discuss the prospects for identifying the correct oscillation solution using multiple SNO observables.

The simplest resonant spin-flavour solution to the solar neutrino problem

We re-analyse the resonant spin-flavour (RSF) solutions to the solar neutrino problem in the framework of analytic solutions to the solar magneto-hydrodynamics (MHD) equations. By substantially eliminating the arbitrariness associated to the magnetic field profile due to both mathematical consistency and physical requirements we propose the simplest scheme (MHD-RSF, for short) for solar neutrino conversion using realistic static MHD solutions. Using such effective two-parameter scheme we perform the first global fit of the recent solar neutrino data, including event rates as well as zenith angle distributions and recoil electron spectra induced by solar neutrino interactions in Superkamiokande. We compare quantitatively our simplest MHD-RSF fit with vacuum oscillation (VAC) and MSW-type (SMA, LMA and LOW) solutions to the solar neutrino problem using a common well-calibrated theoretical calculation and fit procedure. We find our MHD-RSF fit to be somewhat better than those obtained for the favored neutrino oscillation solutions, though not in a statistically significant way. We briefly discuss the prospects to disentangle our MHD-RSF scenario at future solar neutrino experiments, giving some predictions for the SNO experiment.

Three flavor long-wavelength vacuum oscillation solution to the solar neutrino problem

We investigate the current status of the long-wavelength vacuum oscillation solution to the solar neutrino problem and to what extent the presence of a third neutrino can affect and modify it. Assuming that the smaller mass squared difference that can induce such oscillations $\ensuremath{\Delta}{m}_{12}^{2}$ is in the range ${10}^{\ensuremath{-}11}\ensuremath{-}{10}^{\ensuremath{-}8} {\mathrm{eV}}^{2}$ and the larger one, $\ensuremath{\Delta}{m}_{23}^{2},$ in the range relevant to atmospheric neutrino observations, we analyze the most recent solar neutrino data coming from Homestake, SAGE, GALLEX, GNO, and Super-Kamiokande experiments in the context of three neutrino generations. We include in our vacuum oscillation analysis the Mikheyev-Smirnov-Wolfenstein (MSW) effect in the Sun, which is relevant for some of the parameter space scrutinized. We have also performed, as an extreme exercise, the fit without Homestake data. While we found that the MSW effect basically does not affect the best fitted parameters, it significantly modifies the allowed parameter space for $\ensuremath{\Delta}{m}_{12}^{2}$ larger than $\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10} {\mathrm{eV}}^{2},$ in good agreement with the result obtained by Friedland in the case of two generations. Although the presence of a third neutrino does not essentially improve the quality of the fit, the solar neutrino data alone can give an upper bound on ${\ensuremath{\theta}}_{13},$ which is constrained to be less than $\ensuremath{\sim}60\ifmmode^\circ\else\textdegree\fi{}$ at 95 % C.L.

From the CKM matrix to the Maki-Nakagawa-Sakata matrix: A model based on supersymmetricSO(10)×U(2)Fsymmetry

We construct a realistic model based on SUSY SO(10) with U(2) flavor symmetry. In contrast to the commonly used effective operator approach, $126-$dimensional Higgses are used to construct the Yukawa sector. R-parity symmetry is thus preserved at low energies. The Dirac and right-handed Majorana mass matrices in our model have very small mixing, and they combine with the seesaw mechanism resulting in a large leptonic mixing. The symmetric mass textures arising from the left-right symmetry breaking chain of SO(10) give rise to very good predictions; 15 masses (including 3 right-handed Majorana neutrino masses) and 6 mixing angles are predicted by 11 parameters. Both the vacuum oscillation and LOW solutions are favored for the solar neutrino problem.

Vacuum and MSW interpretations of solar neutrino data with the LNW mass matrix

The Lehmann–Newton–Wu mass matrix, which was recently applied to neutrinos, is further investigated. The analytic results presented earlier are confirmed numerically for the solar density profile of the Standard Solar Model. The combined analysis of atmospheric and solar neutrino data favors the MSW solution over the vacuum-oscillation solution. The total rates from the solar neutrino detectors favor two regions in the ( m 1, m 2, m 3) mass space, with the heaviest one, m 3∼0.05 eV. The spectrum distortion reported by the Super-Kamiokande collaboration favors one of these two regions, which has two light ( m 1, m 2≲0.003 eV) neutrinos.

Are lepton flavor mixings in the democratic mass matrix stable against quantum corrections?

We investigate whether the lepton flavor mixing angles in the so-called democratic type of mass matrix are stable against quantum corrections or not in the minimal supersymmetric standard model with dimension five operator which induces neutrino mass matrix. By taking simple breaking patterns of S 3 L×S 3 R or O(3) L × O(3) R flavor symmetries and the scale where democratic textures are induced as O(10 13) GeV, we find that the stability of the lepton flavor mixing angles in the democratic type of mass matrix against quantum corrections depends on the solar neutrino solutions. The maximal flavor mixing of the vacuum oscillation solution is spoiled by quantum corrections in the experimental allowed region of tan β. The large angle MSW solution is spoiled by quantum corrections in the region of tan β>10. The condition of tan β≤10 is needed in order to obtain the suitable mass squared difference of the small angle MSW solution. These strong constraints must be regarded for the model building of the democratic type of mass matrix.

Neutrino oscillations in an SO(10) supersymmetric grand unified theory withU(2)×U(1)nfamily symmetry

In a previous paper we analyzed fermion masses (focusing on neutrino masses and mixing angles) in an SO(10) SUSY GUT with ${\mathrm{U}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)}^{n}$ family symmetry. The model is ``natural'' containing all operators in the Lagrangian consistent with the states and their charges. With minimal family symmetry breaking vacuum expectation values (VEVs) the model is also predictive giving a unique solution to atmospheric (with maximal ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ mixing) and solar (with SMA MSW ${\ensuremath{\nu}}_{e}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{s}$ mixing) neutrino oscillations. In this paper we analyze the case of general family breaking VEVs. We now find several new solutions for three, four, and five neutrinos. For three neutrinos we now obtain SMA MSW, LMA MSW, or vacuum oscillation solutions for solar neutrinos. In all three cases the atmospheric data are described by maximal ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\rightarrow}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ mixing. In the four and five neutrino cases, in addition to fitting atmospheric and solar data as before, we are now able to fit LSND data. All this is obtained with the additional parameters coming from the family symmetry breaking VEVs, providing only minor changes in the charged fermion fits.

Neutrino masses and mixings in a seesaw framework

Assuming the seesaw mechanism for hierarchical neutrino masses, we calculate the heavy neutrino masses under the hypotheses that the mixing in the Dirac leptonic sector is similar to the quark mixing ($V_D \sim V_{CKM}$) and that $M_{\nu} \sim M_u$ or $M_e$, where $M_{\nu}$ is the Dirac mass matrix of neutrinos. As a result we find that for $M_{\nu} \sim M_u$ the vacuum oscillation solution of the solar neutrino problem leads to a scale for the heavy neutrino mass well above the unification scale, while for the MSW solutions there is agreement with this scale. For $M_{\nu} \sim M_e$ the vacuum solution is consistent with the unification scale, and the MSW solutions with an intermediate scale. The mass of the lightest heavy neutrino can be as small as $10^5$ GeV.

Quark and lepton mass matrices in the SO(10) grand unified theory with generation flipping

We investigate the SO(10) grand unified model with generation flipping. The model contains one extra matter multiplet $\psi(10)$ and it mixes with the usual matter multiplets $\psi_i(16)$ when the SO(10) is broken down to SU(5). We find the parameter region of the model in which the observed quark masses and mixings are well reproduced. The resulting parameter region is consistent with the observation that only $\psi_i(16)$ have a source of hierarchies and indicates that the mixing between second and third generations tends to be large in the lepton sector, which is consistent with the observed maximal mixing of the atmospheric neutrino oscillation. We also show that the model can accommodate MSW and vacuum oscillation solutions to the solar neutrino deficit depending on the form of the Majorana mass matrix for the right-handed neutrinos.

Nearly degenerate neutrinos, supersymmetry and radiative corrections

If neutrinos are to play a relevant cosmological rôle, they must be essentially degenerate with a mass matrix of the bimaximal mixing type. We study this scenario in the MSSM framework, finding that if neutrino masses are produced by a see-saw mechanism, the radiative corrections give rise to mass splittings and mixing angles that can accommodate the atmospheric and the (large angle MSW) solar neutrino oscillations. This provides a natural origin for the Δm 2 sol≪ Δm 2 atm hierarchy. On the other hand, the vacuum oscillation solution to the solar neutrino problem is always excluded. We discuss also in the SUSY scenario other possible effects of radiative corrections involving the new neutrino Yukawa couplings, including implications for triviality limits on the Majorana mass, the infrared fixed point value of the top Yukawa coupling, and gauge coupling and bottom-tau unification.

Sterile neutrinos inE6and a natural understanding of the vacuum oscillation solution to the solar neutrino puzzle

If nature has chosen the vacuum oscillation solution to the solar neutrino puzzle, a key theoretical challenge is to understand the extreme smallness of the $\ensuremath{\Delta}{m}_{{\ensuremath{\nu}}_{e}\ensuremath{-}{\ensuremath{\nu}}_{X}}^{2}$ $(\ensuremath{\sim}{10}^{\ensuremath{-}10} {\mathrm{eV}}^{2})$ required for the purpose. We find that in a class of models such as $[\mathrm{SU}(3){]}^{3}$ or its parent group ${\mathrm{E}}_{6},$ which contains one sterile neutrino ${\ensuremath{\nu}}_{\mathrm{is}}$ for each family, the $\ensuremath{\Delta}{m}_{{\ensuremath{\nu}}_{i}\ensuremath{-}{\ensuremath{\nu}}_{\mathrm{is}}}^{2}$ is proportional to the cube of the lepton Yukawa coupling. Therefore fitting the atmospheric neutrino data then predicts the ${\ensuremath{\nu}}_{e}\ensuremath{-}{\ensuremath{\nu}}_{\mathrm{es}}$ mass difference square to be $\ensuremath{\sim}{(m}_{e}{/m}_{\ensuremath{\mu}}{)}^{3}\ensuremath{\Delta}{m}_{\mathrm{atmos}}^{2},$, where the atmospheric neutrino data are assumed to be solved via the ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{-}{\ensuremath{\nu}}_{\ensuremath{\mu}s}$ oscillation. This provides a natural explanation of the vacuum oscillation solution to the solar neutrino problem while simultaneously solving the atmospheric neutrino puzzle as well as the Liquid Scintillation Neutrino Detector (LSND) observations.

Bimaximal neutrino mixing pattern reexamined

I propose a simple extension of the bi-maximal neutrino mixing pattern, allowing slight coupling between solar and atmospheric neutrino oscillations as well as large CP violation. The new scenario is compatible with either the vacuum oscillation solution or the large-angle MSW solution to the solar neutrino problem.