Analytic Approximations for Three Neutrino Oscillation Parameters and Probabilities in Matter

The corrections to neutrino mixing parameters in the presence of matter of constant density are calculated systematically as series expansions in terms of the mass hierarchy \dm{21}/\dm{31}. The parameter mapping obtained is then used to find simple, but nevertheless accurate formulas for oscillation probabibilities in matter including CP-effects. Expressions with one to one correspondence to the vacuum case are derived, which are valid for neutrino energies above the solar resonance energy. Two applications are given to show that these results are a useful and powerful tool for analytical studies of neutrino beams passing through the Earth mantle or core: First, the ``disentanglement problem'' of matter and CP-effects in the CP-asymmetry is discussed and second, estimations of the statistical sensitivity to the CP-terms of the oscillation probabilities in neutrino factory experiments are presented.Comment: 17 pages, 3 figure

Analytical description of quasivacuum oscillations of solar neutrinos

We propose a simple prescription to calculate the solar neutrino survival probability P_{ee} in the quasivacuum oscillation (QVO) regime. Such prescription is obtained by matching perturbative and exact analytical results, which effectively take into account the density distribution in the Sun as provided by the standard solar model. The resulting analytical recipe for the calculation of P_{ee} is shown to reach its highest accuracy |\Delta P_{ee}| < 2.6 x 10^{-2} in the whole QVO range) when the familiar prescription of choosing the solar density scale parameter r_0 at the Mikheyev-Smirnov-Wolfenstein (MSW) resonance point is replaced by a new one, namely, when r_0 is chosen at the point of ``maximal violation of adiabaticity'' (MVA) along the neutrino trajectory in the Sun. The MVA prescription admits a smooth transition from the QVO regime to the MSW transition one. We discuss in detail the phase acquired by neutrinos in the Sun, and show that it might be of relevance for the studies of relatively short timescale variations of the fluxes of the solar \nu lines in the future real-time solar neutrino experiments. Finally, we elucidate the role of matter effects in the convective zone of the Sun.Comment: 25 pages (RevTeX) + 11 figures (postscript

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

Unity of CP and T Violation in Neutrino Oscillations

In a previous work a simultaneous P- CP[P] and P- T[P] bi-probability plot was proposed as a useful tool for unified graphical description of CP and T violation in neutrino oscillation. The ``baseball diamond'' structure of the plot is understood as a consequence of the approximate CP-CP and the T-CP relations obeyed by the oscillation probabilities. In this paper, we make a step forward toward deeper understanding of the unified graphical representation by showing that these two relations are identical in its content, suggesting a truly unifying view of CP and T violation in neutrino oscillations. We suspect that the unity reflects the underlying CPT theorem. We also present calculation of corrections to the CP-CP and the T-CP relations to leading order in Delta m^2_{21} / Delta m^2_{31} and s^2_{13}.Comment: 20 references added, version to appear in "Focus Issue on Neutrino Physics" of New Journal of Physic

Dislocation loops in overheated free-standing smectic films

Static and dynamic phenomena in overheated free-standing smectic-A films are studied using a generalization of de Gennes' theory for a confined presmectic liquid. A static application is to determine the profile of the film meniscus and the meniscus contact angle, the results being compared with those of a recent study employing de Gennes' original theory. The dynamical generalization of the theory is based on on a time-dependent Ginzburg-Landau approach. This is used to compare two modes for layer-thinning transitions in overheated films, namely "uniform thinning" vs. nucleation of dislocation loops. Properties such as the line tension and velocity of a moving dislocation line are evaluated self-consistently by the theory.Comment: 16 pages, 8 figure

Solar Neutrinos and the Principle of Equivalence

We study the proposed solution of the solar neutrino problem which requires a flavor nondiagonal coupling of neutrinos to gravity. We adopt a phenomenological point of view and investigate the consequences of the hypothesis that the neutrino weak interaction eigenstates are linear combinations of the gravitational eigenstates which have slightly different couplings to gravity, $f_1G$ and $f_2G$, $|f_1-f_2| << 1$, corresponding to a difference in red-shift between electron and muon neutrinos, $\Delta z/(1+z) \sim |f_1 - f_2|$. We perform a $\chi^2$ analysis of the latest available solar neutrino data and obtain the allowed regions in the space of the relevant parameters. The existing data rule out most of the parameter space which can be probed in solar neutrino experiments, allowing only $|f_1 - f_2| \sim 3 \times 10^{-14}$ for small values of the mixing angle ($2 \times 10^{-3} \le \sin^2(2\theta_G) \le 10^{-2}$) and $10^{-16} \stackrel{<}{\sim} |f_1 - f_2| \stackrel{<}{\sim}10^{-15}$ for large mixing ($0.6 \le \sin^2(2\theta_G) \le 0.9$). Measurements of the $^8{\rm B}$-neutrino energy spectrum in the SNO and Super-Kamiokande experiments will provide stronger constraints independent of all considerations related to solar models. We show that these measurements will be able to exclude part of the allowed region as well as to distinguish between conventional oscillations and oscillations due to the violation of the equivalence principle.Comment: 20 pages + 4 figures, IASSNS-AST 94/5

Exact Formulas and Simple CP dependence of Neutrino Oscillation Probabilities in Matter with Constant Density

We investigate neutrino oscillations in constant matter within the context of the standard three neutrino scenario. We derive an exact and simple formula for the oscillation probability applicable to all channels. In the standard parametrization, the probability for $\nu_e$ $\to$ $\nu_{\mu}$ transition can be written in the form $P(\nu_e \to \nu_{\mu})=A_{e\mu}\cos\delta+B_{e\mu}\sin\delta+C_{e\mu}$ without any approximation using CP phase $\delta$. For $\nu_{\mu}$ $\to$ $\nu_{\tau}$ transition, the linear term of $\cos 2\delta$ is added and the probability can be written in the form $P(\nu_{\mu} \to \nu_{\tau})=A_{\mu\tau}\cos\delta+B_{\mu\tau} \sin\delta+C_{\mu\tau}+D_{\mu\tau}\cos 2\delta$. We give the CP dependences of the probability for other channels. We show that the probability for each channel in matter has the same form with respect to $\delta$ as in vacuum. It means that matter effects just modify the coefficients $A$, $B$, $C$ and $D$. We also give the exact expression of the coefficients for each channel. Furthermore, we show that our results with respect to CP dependences are reproduced from the effective mixing angles and the effective CP phase calculated by Zaglauer and Schwarzer. Through the calculation, a new identity is obtained by dividing the Naumov-Harrison-Scott identity by the Toshev identity.Comment: 12 pages, RevTeX4 style, changed title, minor correction

Extrinsic CPT Violation in Neutrino Oscillations in Matter

We investigate matter-induced (or extrinsic) CPT violation effects in neutrino oscillations in matter. Especially, we present approximate analytical formulas for the CPT-violating probability differences for three flavor neutrino oscillations in matter with an arbitrary matter density profile. Note that we assume that the CPT invariance theorem holds, which means that the CPT violation effects arise entirely because of the presence of matter. As special cases of matter density profiles, we consider constant and step-function matter density profiles, which are relevant for neutrino oscillation physics in accelerator and reactor long baseline experiments as well as neutrino factories. Finally, the implications of extrinsic CPT violation on neutrino oscillations in matter for several past, present, and future long baseline experiments are estimated.Comment: 47 pages, 7 figures, RevTeX4. Final version to be published in Phys. Rev.

Energy-dependent solar neutrino flux depletion in the Exact Parity Model and implications for SNO, SuperKamiokande and BOREXINO

Energy-dependent solar neutrino flux reduction caused by the Mikheyev-Smirnov-Wolfenstein (MSW) effect is applied to the Exact Parity Model. Several scenarios are possible, depending on the region of parameter space chosen. The interplay between intergenerational MSW transitions and vacuum ``intragenerational'' ordinary-mirror neutrino oscillations is discussed. Expectations for the ratio of charged to neutral current event rates at the Sudbury Neutrino Observatory (SNO) are estimated. The implications of the various scenarios for the Boron neutrino energy spectrum and BOREXINO are briefly discussed. The consequences of MSW-induced solar neutrino depletion within the Exact Parity Model differ in interesting ways from the standard $\nu_e - \nu_{\mu, \tau}$ and $\nu_e - \nu_s$ cases. The physical causes of these differences are determined.Comment: 43 pages, 8 figures, RevTeX; to appear in Phys. Rev. D, accepted versio

Radiatively Induced Neutrino Masses and Oscillations in an SU(3)_LxU(1)_N Gauge Model

We have constructed an $SU(3)_L \times U(1)_N$ gauge model utilizing an $U(1)_{L^\prime}$ symmetry, where $L^\prime$ = $L_e-L_\mu-L_\tau$, which accommodates tiny neutrino masses generated by $L^\prime$-conserving one-loop and $L^\prime$-breaking two-loop radiative mechanisms. The generic smallness of two-loop radiative effects compared with one-loop radiative effects describes the observed hierarchy of $\Delta m_{atm}^2$ $\gg$ $\Delta m_\odot^2$. A key ingredient for radiative mechanisms is a charged scalar ($h^+$) that couples to charged lepton-neutrino pairs and $h^+$ together with the standard Higgs scalar ($\phi$) can be unified into a Higgs triplet as ($\phi^0$, $\phi^-$, $h^+$)$^T$. This assignment in turn requires lepton triplets ($\psi_L^i$) with heavy charged leptons ($\kappa_L^{+i}$) as the third member: $\psi_L^i=(\nu^i_L,\ell^i_L,\kappa^{+i}_L)^T$, where $i$ ($=1,2,3$) denotes three families. It is found that our model is relevant to yield quasi-vacuum oscillations for solar neutrinos.Comment: 11 pages, revtex, including 2 figures, accepted for publication in Phys. Rev. D with minor modification of our resul