Statistical treatment of detection cross-section uncertainties in the analysis of solar neutrino data

We propose a modification to the standard statistical treatment of the detection cross-section uncertainties in the analysis of solar neutrino data. We argue that the uncertainties of the energy-averaged cross sections of the different neutrino fluxes in the same experiment should be treated as correlated. We show that the resulting allowed regions for the neutrino oscillation parameters are significantly larger than the ones obtained with uncorrelated uncertainties.Comment: 12 pages. Corrected Figures 4 and 5 (vacuum oscillations

A frequentist analysis of solar neutrino data

We calculate with Monte Carlo the goodness of fit and the confidence level of the standard allowed regions for the neutrino oscillation parameters obtained from the fit of solar neutrino data. We show that the values of the goodness of fit and of the confidence level of the allowed regions are significantly smaller than the standard ones. Using Neyman's method, we also calculate exact allowed regions with correct frequentist coverage. We show that the standard allowed region around the global minimum of the least-squares function is a reasonable approximation of the exact one, whereas the size of the other regions is dramatically underestimated in the standard method.Comment: 19 page

Model Independent Information On Solar Neutrino Oscillations

We present the results of a Bayesian analysis of solar neutrino data in terms of nu_e->nu_{mu,tau} oscillations, independent from the Standard Solar Model predictions for the solar neutrino fluxes. We show that such a model independent analysis allows to constraint the values of the neutrino mixing parameters in limited regions around the usual SMA, LMA, LOW and VO regions. Furthermore, there is a strong indication in favor of large neutrino mixing and large values of Delta m^2 (LMA region). We calculate also the allowed ranges of the neutrino fluxes and we show that they are in good agreement with the Standard Solar Model prediction. In particular, the ratio of the 8B flux with its Standard Solar Model prediction is constrained in the interval [0.45,1.42] with 99.73% probability. Finally, we show that the hypothesis of no neutrino oscillations is strongly disfavored in a model independent way with respect to the hypothesis of neutrino oscillations.Comment: 40 pages, 20 figures. Added references and improved figure

Nonlinear Lattice Waves in Random Potentials

Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field. We will discuss recent advances in the dynamics of nonlinear lattice waves in random potentials. In the absence of nonlinear terms in the wave equations, Anderson localization is leading to a halt of wave packet spreading. Nonlinearity couples localized eigenstates and, potentially, enables spreading and destruction of Anderson localization due to nonintegrability, chaos and decoherence. The spreading process is characterized by universal subdiffusive laws due to nonlinear diffusion. We review extensive computational studies for one- and two-dimensional systems with tunable nonlinearity power. We also briefly discuss extensions to other cases where the linear wave equation features localization: Aubry-Andre localization with quasiperiodic potentials, Wannier-Stark localization with dc fields, and dynamical localization in momentum space with kicked rotors.Comment: 45 pages, 19 figure

Deviation of Atmospheric Mixing from Maximal and Structure in the Leptonic Flavor Sector

I attempt to quantify how far from maximal one should expect the atmospheric mixing angle to be given a neutrino mass-matrix that leads, at zeroth order, to a nu_3 mass-eigenstate that is 0% nu_e, 50% nu_mu, and 50% nu_tau. This is done by assuming that the solar mass-squared difference is induced by an "anarchical" first order perturbation, an approach than can naturally lead to experimentally allowed values for all oscillation parameters. In particular, both |cos 2theta_atm| (the measure for the deviation of atmospheric mixing from maximal) and |U_e3| are of order sqrt(Delta m^2_sol/Delta m^2_atm) in the case of a normal neutrino mass-hierarchy, or of order Delta m^2_sol/Delta m^2_atm in the case of an inverted one. Hence, if any of the textures analyzed here has anything to do with reality, next-generation neutrino experiments can see a nonzero cos 2theta_atm in the case of a normal mass-hierarchy, while in the case of an inverted mass-hierarchy only neutrino factories should be able to see a deviation of sin^2 2theta_atm from 1.Comment: 12 pages, no figures, references and acknowledgments adde

Quasi-energy-independent solar neutrino transitions

Current solar, atmospheric, and reactor neutrino data still allow oscillation scenarios where the squared mass differences are all close to 10^-3 eV^2, rather than being hierarchically separated. For solar neutrinos, this situation (realized in the upper part of the so-called large-mixing angle solution) implies adiabatic transitions which depend weakly on the neutrino energy and on the matter density, as well as on the ``atmospheric'' squared mass difference. In such a regime of ``quasi-energy-independent'' (QEI) transitions, intermediate between the more familiar ``Mikheyev-Smirnov-Wolfenstein'' (MSW) and energy-independent (EI) regimes, we first perform analytical calculations of the solar nu_e survival probability at first order in the matter density, beyond the usual hierarchical approximations. We then provide accurate, generalized expressions for the solar neutrino mixing angles in matter, which reduce to those valid in the MSW, QEI and EI regimes in appropriate limits. Finally, a representative QEI scenario is discussed in some detail.Comment: Title changed; text and acronyms revised; results unchanged. To appear in PR

Three Generation Neutrino Oscillation Parameters after SNO

We examine the solar neutrino problem in the context of the realistic three neutrino mixing scenario including the SNO charged current (CC) rate. The two independent mass squared differences $\Delta m^2_{21}$ and $\Delta m^2_{31} \approx \Delta m^2_{32}$ are taken to be in the solar and atmospheric ranges respectively. We incorporate the constraints on $\Delta$m$^2_{31}$ as obtained by the SuperKamiokande atmospheric neutrino data and determine the allowed values of $\Delta m^2_{21}$, $\theta_{12}$ and $\theta_{13}$ from a combined analysis of solar and CHOOZ data. Our aim is to probe the changes in the values of the mass and mixing parameters with the inclusion of the SNO data as well as the changes in the two-generation parameter region obtained from the solar neutrino analysis with the inclusion of the third generation. We find that the inclusion of the SNO CC rate in the combined solar + CHOOZ analysis puts a more restrictive bound on $\theta_{13}$. Since the allowed values of $\theta_{13}$ are constrained to very small values by the CHOOZ experiment there is no qualitative change over the two generation allowed regions in the $\Delta m^2_{21} - \tan^2 \theta_{12}$ plane. The best-fit comes in the LMA region and no allowed area is obtained in the SMA region at 3$\sigma$ level from combined solar and CHOOZ analysis.Comment: One reference added. Version to apprear in PR

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 SNO result on the CC-event rate. This result further favors the LMA solution of the solar neutrino problem. The best fit values of parameters we find are: \Delta m^2 = (4.8 - 5.0)10^{-5} eV^2, tan^2 \theta = 0.35 - 0.38, f_B = 1.08 - 1.12, and f_{hep} = 1 - 4. With respect to this best fit the LOW solution is accepted at 90% C.L.. The Vacuum oscillation solution with \Delta m^2 = 1.4 10^{-10} eV^2, gives good fit of the data provided that the boron neutrino flux is substantially smaller than the SSM flux (f_B \sim 0.5). The SMA solution is accepted only at 3\sigma level. We find that vacuum oscillations to sterile neutrino, VAC(sterile), with f_B \sim 0.5 also give rather good global fit of the data. All other sterile solutions are strongly disfavored. We check the quality of the fit by constructing the pull-off diagrams of observables. Predictions for the day-night asymmetry, spectrum distortion and NC/CC ratio at SNO are calculated. In the best fit points of the global solutions we find: A_{DN}^{CC} \approx (7 - 8)% for LMA, \sim 3% for LOW, and (2 - 3)% for SMA. 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 also calculate expectations for the BOREXINO rate.Comment: 35 pages, latex, 9 figures; results of analysis slightly changed due to different treatment of the hep neutrino flux; predictions for NC/CC ratio and Borexino rate adde

Three-Neutrino Mixing after the First Results from K2K and KamLAND

We analyze the impact of the data on long baseline \nu_\mu disappearance from the K2K experiment and reactor \bar\nu_e disappearance from the KamLAND experiment on the determination of the leptonic three-generation mixing parameters. Performing an up-to-date global analysis of solar, atmospheric, reactor and long baseline neutrino data in the context of three-neutrino oscillations, we determine the presently allowed ranges of masses and mixing and we consistently derive the allowed magnitude of the elements of the leptonic mixing matrix. We also quantify the maximum allowed contribution of \Delta m^2_{21} oscillations to CP-odd and CP-even observables at future long baseline experiments.Comment: Some typos correcte

Status of four-neutrino mass schemes: a global and unified approach to current neutrino oscillation data

We present a unified global analysis of neutrino oscillation data within the framework of the four-neutrino mass schemes (3+1) and (2+2). We include all data from solar and atmospheric neutrino experiments, as well as information from short-baseline experiments including LSND. If we combine only solar and atmospheric neutrino data, (3+1) schemes are clearly preferred, whereas short-baseline data in combination with atmospheric data prefers (2+2) models. When combining all data in a global analysis the (3+1) mass scheme gives a slightly better fit than the (2+2) case, though all four-neutrino schemes are presently acceptable. The LSND result disfavors the three-active neutrino scenario with only $\Delta m^2_{sol}$ and $\Delta m^2_{atm}$ at 99.9% CL with respect to the four-neutrino best fit model. We perform a detailed analysis of the goodness of fit to identify which sub-set of the data is in disagreement with the best fit solution in a given mass scheme.Comment: 32 pages, 8 Figures included, REVTeX4.Improved discussion in sec. XI, references added, version accepted by Phys. Rev.