The Complementarity of Eastern and Western Hemisphere Long-Baseline Neutrino Oscillation Experiments

We present a general formalism for extracting information on the fundamental parameters associated with neutrino masses and mixings from two or more long baseline neutrino oscillation experiments. This formalism is then applied to the current most likely experiments using neutrino beams from the Japan Hadron Facility (JHF) and Fermilab's NuMI beamline. Different combinations of muon neutrino or muon anti-neutrino running are considered. To extract the type of neutrino mass hierarchy we make use of the matter effect. Contrary to naive expectation, we find that both beams using neutrinos is more suitable for determining the hierarchy provided that the neutrino energy divided by baseline ($E/L$) for NuMI is smaller than or equal to that of JHF. Whereas to determine the small mixing angle, $\theta_{13}$, and the CP or T violating phase $\delta$, one neutrino and the other anti-neutrino is most suitable. We make extensive use of bi-probability diagrams for both understanding and extracting the physics involved in such comparisons.Comment: 21 pages, Latex, 3 postscript figure

Is bi-maximal mixing compatible with the large angle MSW solution of the solar neutrino problem?

It is shown that the large angle MSW solution of the solar neutrino problem with a bi-maximal neutrino mixing matrix implies an energy-independent suppression of the solar nu_e flux. The present solar neutrino data exclude this solution of the solar neutrino problem at 99.6% CL.Comment: 6 pages. No figure

Solar Neutrino Rates, Spectrum, and its Moments : an MSW Analysis in the Light of Super-Kamiokande Results

We re-examine MSW solutions of the solar neutrino problem in a two flavor scenario taking (a) the results on total rates and the electron energy spectrum from the 1117-day SuperKamiokande (SK) data and (b) those on total rates from the Chlorine and Gallium experiments. We find that the SMA solution gives the best fit to the total rates data from the different experiments. One new feature of our analysis is the use of the moments of the SK electron spectrum in a $\chi^2$ analysis. The best-fit to the moments is broadly in agreement with that obtained from a direct fit to the spectrum data and prefers a $\Delta m^2$ comparable to the SMA fit to the rates but the required mixing angle is larger. In the combined rate and spectrum analysis, apart from varying the normalization of the $^8$B flux as a free parameter and determining its best-fit value we also obtain the best-fit parameters when correlations between the rates and the spectrum data are included and the normalization of the $^8$B flux held fixed at its SSM value. We observe that the correlations between the rates and spectrum data are important and the goodness of fit worsens when these are included. In either case, the best-fit lies in the LMA region.Comment: 17 pages, 4 figure

Deviation of Neutrino Mixing from Bi-maximal

We have studied how observables of the neutrino mixing matrix can link up with the ones in the quark sector. The deviation from the bi-maximal flavor mixing is parameterized using a 3 x 3 unitary matrix. The neutrino mixings are investigated supposing this unitary matrix to be hierarchical like the quark mixing matrix. We obtain the remarkable prediction |U_{e3}| >= 0.03 from the experimentally allowed range tan^2 theta_{sol} = 0.24 ~ 0.89. The CP violation in neutrino oscillations is expected to be very small.Comment: Some references are adde

Spontaneous Breaking of Flavor Symmetry and Naturalness of Nearly Degenerate Neutrino Masses and Bi-maximal Mixing

The gauge model with $SO(3)_{F}$ flavor symmetry and three Higgs triplets is studied. We show how the intriguing nearly degenerate neutrino mass and bi-maximal mixing scenario comes out naturally after spontaneous breaking of the symmetry. The hierarchy between the neutrino mass-squared differences, which is needed for reconciling both solar and atmospheric neutrino data, is naturally resulted from an approximate permutation symmetry. The model can also lead to interesting phenomena on lepton-flavor violations via the $SO(3)_{F}$ gauge interactions.Comment: 13 pages, latex, no figures, the version appearing in SCIENCE IN CHINA (Series A), Vol.35 No.9 (2000

Constraints on Exotic Mixing of Three Neutrinos

Exotic explanations are considered for atmospheric neutrino observations. Our analysis includes matter effects and the mixing of all three neutrinos under the simplifying assumption of only one relevant mixing scale. Constraints from accelerator, reactor and solar neutrinos are included. We find that the proposed mixing mechanisms based on violations of Lorentz invariance or on violations of the equivalence principle cannot explain the recent observations of atmospheric neutrino mixing. However the data still allow a wide range of energy dependences for the vacuum mixing scale, and also allow large electron-neutrino mixing of atmospheric neutrinos. Next generation long baseline experiments will constrain these possibilities.Comment: 27 pages, 4 figure

Renormalizability of the local composite operator A^2 in linear covariant gauges

The local composite operator $A_{\mu}^{2}$ is analysed within the algebraic renormalization in Yang-Mills theories in linear covariant gauges. We establish that it is multiplicatively renormalizable to all orders of perturbation theory. Its anomalous dimension is computed to two-loops in the MSbar scheme.Comment: 10 pages, LaTeX, final version to appear in Phys. Lett.

Homestake result, sterile neutrinos and low energy solar neutrino experiments

The Homestake result is about ~ 2 \sigma lower than the Ar-production rate, Q_{Ar}, predicted by the LMA MSW solution of the solar neutrino problem. Also there is no apparent upturn of the energy spectrum (R \equiv N_{obs}/N_{SSM}) at low energies in SNO and Super-Kamiokande. Both these facts can be explained if a light, \Delta m^2_{01} ~ (0.2 - 2) \cdot 10^{-5} eV^2, sterile neutrino exists which mixes very weakly with active neutrinos: \sin^2 2\alpha ~ (10^{-5} - 10^{-3}). We perform both the analytical and numerical study of the conversion effects in the system of two active neutrinos with the LMA parameters and one weakly mixed sterile neutrino. The presence of sterile neutrino leads to a dip in the survival probability in the intermediate energy range E = (0.5 - 5) MeV thus suppressing the Be, or/and pep, CNO as well as B electron neutrino fluxes. Apart from diminishing Q_{Ar} it leads to decrease of the Ge-production rate and may lead to decrease of the BOREXINO signal and CC/NC ratio at SNO. Future studies of the solar neutrinos by SNO, SK, BOREXINO and KamLAND as well as by the new low energy experiments will allow us to check this possibility. We present a general analysis of modifications of the LMA energy profile due to mixing with new neutrino states.Comment: Figures 5 and 6 modified, shorter version will be published in PR

Possible Flavor Mixing Structures of Lepton Mass Matrices

To search for possible textures of lepton mass matrices, we systematically examine flavor mixing structures which can lead to large lepton mixing angles. We find out 37 mixing patterns are consistent with experimental data, taking into account phase factors in the mixing matrices. Only six of the patterns can explain the observed data without any tuning of parameters, while the others need particular choices for the phase values. It is found that these six mixing patterns are those predicted by the models which have been proposed to account for fermion mass hierarchies. On the other hand, the others may give new flavor mixing structures of lepton mass matrices and therefore new possibilities of model construction.Comment: 21 page

Second-order corrections to neutrino two-flavor oscillation parameters in the wave packet approach

We report about an analytic study involving the {\em intermediate} wave packet formalism for quantifying the physically relevant information which appear in the neutrino two-flavor conversion formula and help us to obtain more precise limits and ranges for neutrino flavor oscillation. By following the sequence of analytic approximations where we assume a strictly peaked momentum distribution and consider the second-order corrections in a power series expansion of the energy, we point out a {\em residual} time-dependent phase which, coupled with the {\em spreading/slippage} effects, can subtly modify the neutrino oscillation parameters and limits. Such second-order effects are usually ignored in the relativistic wave packet treatment, but they present an evident dependence on the propagation regime so that some small modifications to the oscillation pattern, even in the ultra-relativistic limit, can be quantified. These modifications are implemented in the confront with the neutrino oscillation parameter range (mass-squared difference \Delta m^{\2} and the mixing-angle $\theta$) where we assume the same wave packet parameters previously noticed in the literature in a kind of {\em toy model} for some reactor experiments. Generically speaking, our analysis parallels the recent experimental purposes which concern with higher precision parameter measurements. To summarize, we show that the effectiveness of a more accurate determination of \Delta m^{\2} and $\theta$ depends on the wave packet width $a$ and on the averaged propagating energy flux $\bar{E}$ which still correspond to open variables for some classes of experiments. \Comment: 25 pages, 5 figure