Parameters' domain in three flavour neutrino oscillations

We consider analytically the domain of the three mixing angles $\Theta_{ij}$ and the CP phase $\delta$ for three flavour neutrino oscillations both in vacuum and matter. Similarly to the quark sector, it is necessary and sufficient to let all the mixing angles $\Theta_{12},\Theta_{13},\Theta_{23}$ and $\delta$ be in the range $$ and $0 \leq \delta < 2 \pi$, respectively. To exploit the full range of $\delta$ will be important in future when more precise fits are possible, even without CP violation measurements. With the above assumption on the angles we can restrict ourselves to the natural order of masses $m_1<m_2<m_3$. Considerations of the mass schemes with some negative $\delta m^2$'s, though for some reasons useful, are not necessary from the point of view of neutrino oscillation parametrization and cause double counting only. These conclusions are independent of matter effects.Comment: references added, to appear in PL

Generating extremal neutrino mixing angles with Higgs family symmetries

The existence of maximal and minimal mixing angles in the neutrino mixing matrix motivates the search for extensions to the Standard Model that may explain these angles. A previous study (C.I.Low and R.R.Volkas, Phys.Rev.D68,033007(2003)), began a systematic search to find the minimal extension to the Standard Model that explains these mixing angles. It was found that in the minimal extensions to the Standard Model which allow neutrino oscillations, discrete unbroken lepton family symmetries only generate neutrino mixing matrices that are ruled out by experiment. This paper continues the search by investigating all models with two or more Higgs doublets, and an Abelian family symmetry. It is found that discrete Abelian family symmetries permit, but cannot explain, maximal atmospheric mixing, however these models can ensure theta_{13}=0.Comment: Minor modifications, references added, typos corrected. LaTeX, 16 page

Super-Kamiokande atmospheric neutrino data, zenith distributions, and three-flavor oscillations

We present a detailed analysis of the zenith angle distributions of atmospheric neutrino events observed in the Super-Kamiokande (SK) underground experiment, assuming two-flavor and three-flavor oscillations (with one dominant mass scale) among active neutrinos. In particular, we calculate the five angular distributions associated to sub-GeV and multi-GeV \mu-like and e-like events and to upward through-going muons, for a total of 30 accurately computed observables (zenith bins). First we study how such observables vary with the oscillation parameters, and then we perform a fit to the experimental data as measured in SK for an exposure of 33 kTy (535 days). In the two-flavor mixing case, we confirm the results of the SK Collaboration analysis, namely, that \nu_\mu\nu_\tau oscillations are preferred over \nu_\mu\nu_e, and that the no oscillation case is excluded with high confidence. In the three-flavor mixing case, we perform our analysis with and without the additional constraints imposed by the CHOOZ reactor experiment. In both cases, the analysis favors a dominance of the \nu_\mu\nu_\tau channel. Without the CHOOZ constraints, the amplitudes of the subdominant \nu_\munu_e and \nu_e\nu_\tau transitions can also be relatively large, indicating that, at present, current SK data do not exclude sizable \nu_e mixing by themselves. After combining the CHOOZ and SK data, the amplitudes of the subdominant transitions are constrained to be smaller, but they can still play a nonnegligible role both in atmospheric and other neutrino oscillation searches. In particular, we find that the \nu_e appearance probability expected in long baseline experiments can reach the testable level of ~15%.Comment: 35 pages (RevTeX), including 20 ps figures (with epsfig.sty

Day-night asymmetry of high and low energy solar neutrino events in Super-Kamiokande and in the Sudbury Neutrino Observatory

In the context of solar neutrino oscillations among active states, we briefly discuss the current likelihood of Mikheyev-Smirnov-Wolfenstein (MSW) solutions to the solar neutrino problem, which appear to be currently favored at large mixing, where small Earth regeneration effects might still be observable in Super-Kamiokande (SK) and in the Sudbury Neutrino Observatory (SNO). We point out that, since such effects are larger at high (low) solar neutrino energies for high (low) values of the mass square difference \delta m^2, it may be useful to split the night-day rate asymmetry in two separate energy ranges. We show that the difference \Delta of the night-day asymmetry at high and low energy may help to discriminate the two large-mixing solutions at low and high \delta m^2 through a sign test, both in SK and in SNO, provided that the sensitivity to \Delta can reach the (sub)percent level.Comment: 6 pages (RevTeX) + 4 figures (PostScript). Final version, to appear in Phys. Rev.

Three-flavor MSW solutions of the solar neutrino problem

We perform an updated phenomenological analysis of the Mikheyev-Smirnov-Wolfenstein (MSW) solutions of the solar neutrino problem, assuming oscillations between two and three neutrino families. The analysis includes the total rates of the Homestake, SAGE, GALLEX, Kamiokande and Super-Kamiokande experiments, as well as the day-night asymmetry and the 18-bin energy spectrum of Super-Kamiokande. Solutions are found at several values of the theta_{13} mixing angle. Among the most interesting features, we find that solar neutrino data alone put the constraint theta_{13} < 55--59 deg at 95% C.L., and that a fraction of the MSW solutions extends at and beyond maximal (nu_1,nu_2) mixing (theta_{12} > pi/4), especially if the neutrino square mass splitting is in its lower range (m^2_2-m^2_1 ~ 10^{-7} eV^2) and if theta_{13} is nonzero. In particular, bimaximal (or nearly bimaximal) mixing is possible for atmospheric and MSW solar neutrino oscillations within the stringent reactor bounds on theta_{13}.Comment: 19 pages (RevTeX) + 14 figures (PostScript

Active neutrino Oscillations and the SNO neutral Current measurement

We discuss the relation between the observed CC, ES, and NC fluxes with the flavor fractional content of the solar neutrino flux seen by SNO. By using existing estimates of the cross sections for the charged and neutral current reactions which take into account the detector resolution, we show how the forthcoming SNO rates unconstrained by the standard $^8$B shape could test the oscillations into active states. We perform a model independent analysis for the Super-K and SNO data, assuming a non distorted spectrum.Comment: 6pages, 4 figure

Oscillations of solar atmosphere neutrinos

The Sun is a source of high energy neutrinos (E > 10 GeV) produced by cosmic ray interactions in the solar atmosphere. We study the impact of three-flavor oscillations (in vacuum and in matter) on solar atmosphere neutrinos, and calculate their observable fluxes at Earth, as well as their event rates in a kilometer-scale detector in water or ice. We find that peculiar three-flavor oscillation effects in matter, which can occur in the energy range probed by solar atmosphere neutrinos, are significantly suppressed by averaging over the production region and over the neutrino and antineutrino components. In particular, we find that the relation between the neutrino fluxes at the Sun and at the Earth can be approximately expressed in terms of phase-averaged ``vacuum'' oscillations, dominated by a single mixing parameter (the angle theta_23).Comment: v2: 11 pages, 8 eps figures. Content added (Sec. III D and Fig. 6), references updated. Matches the published versio

Hints of theta_13>0 from global neutrino data analysis

Nailing down the unknown neutrino mixing angle theta_13 is one of the most important goals in current lepton physics. In this context, we perform a global analysis of neutrino oscillation data, focusing on theta_13, and including recent results [Neutrino 2008, Proceedings of the XXIII International Conference on Neutrino Physics and Astrophysics, Christchurch, New Zealand, 2008 (unpublished)]. We discuss two converging hints of theta_13>0, each at the level of ~1sigma: an older one coming from atmospheric neutrino data, and a newer one coming from the combination of solar and long-baseline reactor neutrino data. Their combination provides the global estimate sin^2(theta_13) = 0.016 +- 0.010 (1sigma), implying a preference for \theta_13>0 with non-negligible statistical significance (~90% C.L.). We discuss possible refinements of the experimental data analyses, which might sharpen such intriguing indication.Comment: Minor changes in the text. Matches published version in PR

How precisely can we reduce the three-flavor neutrino oscillation to the two-flavor one only from (\delta m^2_{12})/(\delta m^2_{13}) <~ 1/15 ?

We derive the reduction formula, which expresses the survival rate for the three-flavor neutrino oscillation by the two-flavor one, to the next-to-leading order in case there is one resonance due to the matter effect. We numerically find that the next-to-leading reduction formula is extremely accurate and the improvement is relevant for the precision test of solar neutrino oscillation and the indirect measurment of CP violation in the leptonic sector. We also derive the reduction formula, which is slightly different from that previously obtained, in case there are two resonances. We numerically verify that this reduction formula is quite accurate and is valid for wider parameter region than the previously obtained ones are.Comment: 28pages, 8figures, revtex4. to appear in PR

Muon-anti-neutrino <---> electron-anti-neutrino mixing: analysis of recent indications and implications for neutrino oscillation phenomenology

We reanalyze the recent data from the Liquid Scintillator Neutrino Detector (LSND) experiment, that might indicate anti-nu_muanti-nu_e mixing. This indication is not completely excluded by the negative results of established accelerator and reactor neutrino oscillation searches. We quantify the region of compatibility by means of a thorough statistical analysis of all the available data, assuming both two-flavor and three-flavor neutrino oscillations. The implications for various theoretical scenarios and for future oscillation searches are studied. The relaxation of the LSND constraints under different assumptions in the statistical analysis is also investigated.Comment: 17 pages (RevTeX) + 9 figures (Postscript) included with epsfig.st