Treating Solar Model Uncertainties: A Consistent Statistical Analysis of Solar Neutrino Models and Data

We describe how to consistently incorporate solar model uncertainties, along with experimental errors and correlations, when analyzing solar neutrino data to derive confidence limits on parameter space for proposed solutions of the solar neutrino problem. Our work resolves ambiguities and inconsistencies in the previous literature. As an application of our methods we calculate the masses and mixing angles allowed by the current data for the proposed MSW solution using both Bayesian and frequentist methods, allowing purely for solar model flux variations, to compare with previous work. We consider the effects of including metal diffusion in the solar models and also discuss implications for future experiments.Comment: 29 pages (incl figs), latex, 6 figures (appended as separate uuencoded file. To embed figures in text, uncomment 6 \epsfysize lines which appear before bibliography), CWRU-P5-94, CfPA-94-TTH-29, Fermilab-Pub-94/176-

Solar and atmospheric neutrino oscillations with three flavours

We analyze the solar and the atmospheric neutrino problems in the context of three flavour neutrino oscillations. We assume a mass hierarchy in the vacuum mass eigenvalues $\mu_3^2 \gg \mu_2^2 \geq \mu_1^2$, but make no approximation regarding the magnitudes of the mixing angles. We find that there are small but continuous bands in the parameter space where the constraints imposed by the current measurements of $\ {}^{71} Ga$, ${}^{37} Cl$ and Kamiokande experiments are satisfied at $1 \sigma$ level. The allowed parameter space increases dramatically if the error bars are enlarged to $1.6 \sigma$. The electron neutrino survival probability has different energy dependence in different regions of the parameter space. Measurement of the recoil electron energy spectrum in detectors that use $\nu - e$ scattering may distinguish between some of the allowed regions of parameter space. Finally we use the results for the parameter space admitted by the solar neutrinos as an input for the atmospheric neutrino problem and show that there exists a substantial region of parameter space in which both problems can be solved.Comment: 25 pages plus eight figures. Uses Revtex. Postcript files for figures sent separately as a uuencoded fil

Unified explanation of the Solar and Atmospheric neutrino Puzzles in a minimal supersymmetric SO(10) model

It was recently suggested that in a class of supersymmetric SO(10) models with Higgs multiplets in 10, and a single $126+\bar{126}$ representations, if the $\bar{126}$ contributes both to the right handed neutrino masses as well as to the charged fermion masses, one can have a complete prediction of the neutrino masses and mixings. It turns out that if one chooses only one 10, there are no regions in the parameter space where one can have a large $\nu_{\mu}-\nu_{\tau}$ mixing angle necessary to solve the atmospheric neutrino deficit while at the same time solving the solar neutrino puzzle via the $\nu_e \leftrightarrow \nu_{\mu}$ oscillation. We show that this problem can be solved in a particular class of SO(10) models with a pair of 10 multiplets if we include the additional left-handed triplet contribution to the light neutrino mass matrix. This model cannot reproduce the mass and mixing parameters required to explain the LSND observations neither does it have have a neutrino hot dark matter.Comment: 4 pages and 4 figures; Version substantially different from the original one but same conclusion

Phenomenology of Neutrino Oscillations

The phenomenology of solar, atmospheric, supernova and laboratory neutrino oscillations is described. Analytical formulae for matter effects are reviewed. The results from oscillations are confronted with neutrinoless double beta decay.Comment: 11 pages, 2 figures, latex, Plenary talk given at Workshop in High Energy Particle Physics-6, Chennai, Indi

Neutrino conversions in random magnetic fields and ν~e\tilde{\nu}_e from the Sun

The magnetic field in the convective zone of the Sun has a random small-scale component with the r.m.s. value substantially exceeding the strength of a regular large-scale field. For two Majorana neutrino flavors $\times$ two helicities in the presence of a neutrino transition magnetic moment and nonzero neutrino mixing we analyze the displacement of the allowed ($\Delta m^2- \sin^22\theta$)-parameter region reconciled for the SuperKamiokande(SK) and radiochemical (GALLEX, SAGE, Homestake) experiments in dependence on the r.m.s. magnetic field value $b$, or more precisely, on a value $\mu b$ assuming the transition magnetic moment $\mu = 10^{-11}\mu_B$. In contrast to RSFP in regular magnetic fields we find an effective production of electron antineutrinos in the Sun even for small neutrino mixing through cascade conversions $\nu_{eL}\to \nu_{\mu L}\to \tilde{\nu}_{eR}$, $\nu_{eL}\to \nu_{\mu R}\to \tilde{\nu}_{eR}$ in a random magnetic field that would be a signature of the Majorana nature of neutrino if $\tilde{\nu}_{eR}$ will be registered. Basing on the present SK bound on electron antineutrinos we have also found an excluded area in the same $\Delta m^2,~\sin^22\theta$-plane and revealed a strong sensitivity to the random magnetic field correlation length $L_0$.Comment: LaTex 36 pages including 14 PostScript figure

Cold Plus Hot Dark Matter Cosmology in the Light of Solar and Atmospheric Neutrino Oscillations

We explore the implications of possible neutrino oscillations, as indicated by the solar and atmospheric neutrino experiments, for the cold plus hot dark matter scenario of large scale structure formation. We find that there are essentially three distinct schemes that can accommodate the oscillation data and which also allow for dark matter neutrinos. These include (i) three nearly degenerate (in mass) neutrinos, (ii) non-degenerate masses with $\nu_\tau$ in the eV range, and (iii) nearly degenerate $\nu_\mu-\nu_\tau$ pair (in the eV range), with the additional possibility that the electron neutrino is cosmologically significant. The last two schemes invoke a `sterile' neutrino which is light (< or ~ eV). We discuss the implications of these schemes for $\bar{\nu}_\mu - \bar{\nu}_e$ and $\nu_\mu - \nu_\tau$ oscillation, and find that scheme (ii) in particular, predicts them to be in the observable range. As far as structure formation is concerned, we compare the one neutrino flavor case with a variety of other possibilities, including two and three degenerate neutrino flavors. We show, both analytically and numerically, the effects of these neutrino mass scenarios on the amplitude of cosmological density fluctuations. With a Hubble constant of 50 km s$^{-1}$ Mpc$^{-1}$, a spectral index of unity, and $\Omega_{baryon} = 0.05$, the two and three flavor scenarios fit the observational data marginally better than the single flavor scheme. However, taking account of the uncertainties in these parameters, we show that it is premature to pick a clear winner.Comment: 1 LaTEX file plus 1 uuencoded Z-compressed tar file with 3 postscript figure

Neutrinos from the Sun: experimental results confronted with solar models

For standard neutrinos, recent solar neutrino results together with the assumption of a nuclearly powered Sun imply severe constraints on the individual components of the total neutrino flux: \Phi_{Be}<0.7*10^9cm^-2 s^-1, \Phi_{CNO}< 0.6*10^9 cm^-2 s^-1, and $64*10^9 cm^-2 s^-1< \Phi_{pp+pep} < 65*10^9 cm^-2 s^-1 (at 1 \sigma level). The bound on \Phi_{Be} is in strong disagreement with the standard solar model prediction \Phi_{Be}^{SSM}\approx 5*10^9 cm^-2 s^-1. We study a large variety of non-standard solar models with low inner temperature, finding that the temperature profiles T(m) follow the homology relationship: T(m)=kT^{SSM}(m), so that they are specified just by the central temperature T_c. There is no value of T_c which can account for all the available experimental results. Even if we only consider the Gallium and Kamiokande results, they remain incompatible. Lowering the cross section p+Be7 \to \gamma+B8 is not a remedy. The shift of the nuclear fusion chain towards the pp-I termination could be induced by a hypothetical low energy resonance in the He3+He3 reaction. This mechanism gives a somehow better, but still bad fit to the combined experimental data. We also discuss what can be learnt from new generation experiments about the properties of neutrinos and of the Sun.Comment: 20 pages in RevTeX 3.0 plus 14 figures in uuencoded postscript file

Accelerator, reactor, solar and atmospheric neutrino oscillation: beyond three generations

We perform a phenomenological analysis of neutrino oscillation in a four generation framework introducing an additional sterile neutrino. In such a scenario, more than one pattern is possible that can accommodate three hieararchically different mass squared differences as required by the present experiments. We considered two different spectrums. Choosing the ${\Delta{m}}^2$s in the ranges suitable for the LSND, atmospheric and solar neutrino oscillation, limits on the mixing angles are derived, consistent with the most restrictive accelerator and reactor data as well as the atmospheric and solar neutrino results. The allowed mixing angles are found to be constrained very severely in both cases. For one mass pattern in the combined allowed zone the atmospheric anomaly can be explained by $\nu_e - \nu_{\mu}$ oscillation whereas for the other the $\nu_{\mu} - \nu_{\tau}$ channel is preferred. The accelerator experiments CHORUS and NOMAD have different sensitivities in these regions and they can distinguish between the two choices.Comment: Latex, 26 pages, 6 figures, 1 included in the Latex File, remaining 5 available on reques