A new parametrization of the neutrino mixing matrix for neutrino oscillations

In this paper we study three active neutrino oscillations, favored by recent data from SuperK and SNO, using a new parametrization of the lepton mixing matrix $V$ constructed from a linear combination of the unit matrix $I$, and a hermitian unitary matrix $U$, that is, $V = \cos\theta I + i\sin \theta U$. There are only three real parameters in $V$ including the parameter $\theta$. It is interesting to find that experimental data on atmospheric neutrino dictates the angle $\theta$ to be $\pi/4$ such that the $\nu_\mu$ and $\nu_\tau$ mixing is maximal. The solar neutrino problem is solved via the MSW effect with a small mixing angle, with $U$ depending on one small parameter $\epsilon$. The resulting mixing matrix with just two parameters ($\theta$ and $\epsilon$) predicts that the oscillating probabilities for $\nu_e\to \nu_\mu$ and $\nu_e \to \nu_\tau$ to be equal and of the order $2\epsilon^2 = (0.25\sim 2.5)\times 10^{-3}$. The measurement of CP asymmetries at the proposed Neutrino Factories would also provide a test of our parametrization.Comment: 10 pages, Retex, no figure

Searches for neutrinoless double beta decay

Neutrinoless double beta decay is a lepton number violating process whose observation would also establish that neutrinos are their own anti-particles. There are many experimental efforts with a variety of techniques. Some (EXO, Kamland-Zen, GERDA phase I and CANDLES) started take data in 2011 and EXO has reported the first measurement of the half life for the double beta decay with two neutrinos of $^{136}$Xe. The sensitivities of the different proposals are reviewed.Comment: 8 pages, prepared for TAUP 201

Searches for neutrinoless double beta decay

Neutrinoless double beta decay is a lepton number violating process whose observation would also establish that neutrinos are their own anti-particles. There are many experimental efforts with a variety of techniques. Some (EXO, Kamland-Zen, GERDA phase I and CANDLES) started take data in 2011 and EXO has reported the first measurement of the half life for the double beta decay with two neutrinos of $^{136}$Xe. The sensitivities of the different proposals are reviewed.Comment: 8 pages, prepared for TAUP 201

Searches for neutrinoless double beta decay

Neutrinoless double beta decay is a lepton number violating process whose observation would also establish that neutrinos are their own anti-particles. There are many experimental efforts with a variety of techniques. Some (EXO, Kamland-Zen, GERDA phase I and CANDLES) started take data in 2011 and EXO has reported the first measurement of the half life for the double beta decay with two neutrinos of $^{136}$Xe. The sensitivities of the different proposals are reviewed.Comment: 8 pages, prepared for TAUP 201

A Mass Matrix for Atmospheric, Solar, and LSND Neutrino Oscillations

We construct a mass matrix for the four neutrino flavors, three active and one sterile, needed to fit oscillations in all three neutrino experiments: atmospheric, solar, and LSND, simultaneously. It organizes the neutrinos into two doublets whose central values are about 1 eV apart, and whose splittings are of the order of 10^(-3) eV. Atmospheric neutrino oscillations are described as maximal mixing within the upper doublet, and solar as the same within the lower doublet. Then LSND is a weak transition from one doublet to the other. We comment on the Majorana versus Dirac nature of the active neutrinos and show that our mass matrix can be derived from an S_2 x S_2 permutation symmetry plus an equal splitting rule.Comment: 4 pages, 0 figures, minor text change

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

Solar neutrino-electron scattering as background limitation for double beta decay

The background on double beta decay searches due to elastic electron scattering of solar neutrinos of all double beta emitters with Q-value larger than 2 MeV is calculated, taking into account survival probability and flux uncertainties of solar neutrinos. This work determines the background level to be [1-2]E-7 counts /keV/kg/yr, depending on the precise Q-value of the double beta emitter. It is also shown that the background level increases dramatically if going to lower Q-values. Furthermore, studies are done for various detector systems under consideration for next generation experiments. It was found that experiments based on loaded liquid scintillator have to expect a higher background. Within the given nuclear matrix element uncertainties any approach exploring the normal hierarchy has to face this irreducible background, which is a limitation on the minimal achievable background for purely calorimetric approaches. Large scale liquid scintillator experiments might encounter this problem already while exploring the inverted hierarchy. Potential caveats by using more sophisticated experimental setups are also discussed

Is CP Violation Observable in Long Baseline Neutrino Oscillation Experiments ?

We have studied CP violation originated by the phase of the neutrino mixing matrix in the long baseline neutrino oscillation experiments. The direct measurements of CP violation is the difference of the transition probabilities between CP-conjugate channels. In those experiments, the CP violating effect is not suppressed if the highest neutrino mass scale is taken to be 1\sim 5 \eV, which is appropriate for the cosmological hot dark matter. Assuming the hierarchy for the neutrino masses, the upper bounds of CP violation have been caluculated for three cases, in which mixings are constrained by the recent short baseline ones. The calculated upper bounds are larger than $10^{-2}$, which will be observable in the long baseline accelerator experiments. The matter effect, which is not CP invariant, has been also estimated in those experiments.Comment: 28 pages, LaTex file, 6 figures included using epsfig Matter effect is estimated(Figs.3(a) (b)). Physical parameters are change

CP violation effect in long-baseline neutrino oscillation in the four-neutrino model

We investigate CP-violation effect in the long-baseline neutrino oscillation in the four-neutrino model with mass scheme of the two nearly degenerate pairs separated with the order of 1 eV, by using the data from the solar neutrino deficit, the atmospheric neutrino anomaly and the LSND experiments along with the other accelerator and reactor experiments. By use of the most general parametrization of the mixing matrix with six angles and six phases, we show that the genuine CP-violation effect could attain as large as 0.3 for $\Delta P(\nu_\mu\to\nu_\tau) \equiv P(\nu_\mu\to\nu_\tau) - P(\bar{\nu_\mu}\to\bar{\nu_\tau})$ and that the matter effect is negligibly small such as at most 0.01 for $\Delta P(\nu_\mu\to\nu_\tau)$ for $\Delta m^2 = (1-5)\times 10^{-3} {\rm eV}^2$, which is the mass-squared difference relevant to the long-baseline oscillation.Comment: 21 pages in LaTeX, 9 ps figures. Some changes in the Introduction and Reference

Three-flavor atmospheric neutrino anomaly

We investigate the indications of flavor oscillations that come from the anomalous flavor composition of the atmospheric neutrino flux observed in some underground experiments. We study the information coming from the neutrino-induced $\mu$-like and $e$-like events both in the sub-GeV energy range (Kamiokande, IMB, Fr{\'e}jus, and NUSEX experiments) and in the multi-GeV energy range (Kamiokande experiment). First we analyze all the data in the limits of pure $\nu_\mu\leftrightarrow\nu_\tau$ and $\nu_\mu\leftrightarrow\nu_e$ oscillations. We obtain that $\nu_\mu\leftrightarrow\nu_e$ oscillations provide a better fit, in particular to the multi-GeV data. Then we perform a three-flavor analysis in the hypothesis of dominance of one neutrino square mass difference, $m^2$, implying that the neutrino mixing is parametrized by two angles, $(\psi,\,\phi)\in[0,\,\pi/2]$. We explore the space $(m^2,\,\psi,\,\phi)$ exhaustively, and find the regions favored by the oscillation hypothesis. The results are displayed in a form suited to the comparison with other flavor oscillation searches at accelerator, reactor, and solar $\nu$ experiments. In the analysis, we pay particular attention to the earth matter effects, to the correlation of the uncertainties, and to the symmetry properties of the oscillation probability.Comment: 25 pages (RevTeX) + 12 figures, requires epsfig.sty. All the figures are bitmapped. Postscript figures with full resolution are available at ftp://ftp.sns.ias.edu/pub/lisi/atmpaper