CP and T violation test in neutrino oscillation

We examine how large violation of CP and T is allowed in long base line neutrino experiments. When we attribute only the atmospheric neutrino anomaly to neutrino oscillation we may have large CP violation effect. When we attribute both the atmospheric neutrino anomaly and the solar neutrino deficit to neutrino oscillation we may have a sizable T violation effect proportional to the ratio of two mass differences; it is difficult to see CP violation since we can't ignore the matter effect. We give a simple expression for T violation in the presence of matter.Comment: 12 pages + 2 eps figures, Latex, In order to avoid misunderstanding we have refined our English and rewritten the parts which might be misleading. Several typographical errors are correcte

CP Violation and Matter Effect in Long Baseline Neutrino Oscillation Experiments

We show simple methods how to separate pure CP violating effect from matter effect in long baseline neutrino oscillation experiments with three generations of neutrinos. We give compact formulae for neutrino oscillation probabilities assuming one of the three neutrino masses (presumably tau-neutrino mass) to be much larger than the other masses and the effective mass due to matter effect. Two methods are shown: One is to observe envelopes of the curves of oscillation probabilities as functions of neutrino energy; a merit of this method is that only a single detector is enough to determine the presence of CP violation. The other is to compare experiments with at least two different baseline lengths; this has a merit that it needs only narrow energy range of oscillation data.Comment: 17 pages + 9 eps figures, LaTeX, errors are correcte

On the Evolution of the Neutrino State inside the Sun

We reexamine the conventional physical description of the neutrino evolution inside the Sun. We point out that the traditional resonance condition has physical meaning only in the limit of small values of the neutrino mixing angle, theta<<1. For large values of theta, the resonance condition specifies neither the point of the maximal violation of adiabaticity in the nonadiabatic case, nor the point where the flavor conversion occurs at the maximal rate in the adiabatic case. The corresponding correct conditions, valid for all values of theta including theta>pi/4, are presented. An adiabaticity condition valid for all values of theta is also described. The results of accurate numerical computations of the level jumping probability in the Sun are presented. These calculations cover a wide range of Delta m^2, from the vacuum oscillation region to the region where the standard exponential approximation is good. A convenient empirical parametrization of these results in terms of elementary functions is given. The matter effects in the so-called "quasi-vacuum oscillation regime" are discussed. Finally, it is shown how the known analytical results for the exponential, 1/x, and linear matter distributions can be simply obtained from the formula for the hyperbolic tangent profile. An explicit formula for the jumping probability for the distribution N_e ~ (coth(x/l) +- 1) is obtained.Comment: 34 pages, 8 figure

Exact Solutions for Matter-Enhanced Neutrino Oscillations

The analogy between supersymmetric quantum mechanics and matter-enhanced neutrino oscillations is exploited to obtain exact solutions for a class of electron density profiles. This integrability condition is analogous to the shape-invariance in supersymmetric quantum mechanics. This method seems to be the most direct way to obtain the exact survival probabilities for a number of density profiles of interest, such as linear and exponential density profiles. The resulting neutrino amplitudes can also be utilized as comparison amplitudes for the uniform semiclassical treatment of neutrino propagation in arbitrary electron density profiles.Comment: Submitted to Physical Review D. Latex file, 8 pages. This paper is also available at http://nucth.physics.wisc.edu/preprints

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

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

Nonlinear level crossing models

We examine the effect of nonlinearity at a level crossing on the probability for nonadiabatic transitions $P$. By using the Dykhne-Davis-Pechukas formula, we derive simple analytic estimates for $P$ for two types of nonlinear crossings. In the first type, the nonlinearity in the detuning appears as a {\it perturbative} correction to the dominant linear time dependence. Then appreciable deviations from the Landau-Zener probability $P_{LZ}$ are found to appear for large couplings only, when $P$ is very small; this explains why the Landau-Zener model is often seen to provide more accurate results than expected. In the second type of nonlinearity, called {\it essential} nonlinearity, the detuning is proportional to an odd power of time. Then the nonadiabatic probability $P$ is qualitatively and quantitatively different from $P_{LZ}$ because on the one hand, it vanishes in an oscillatory manner as the coupling increases, and on the other, it is much larger than $P_{LZ}$. We suggest an experimental situation when this deviation can be observed.Comment: 9 pages final postscript file, two-column revtex style, 5 figure

An exact analytic description of neutrino oscillations in matter with exponentially varying density for arbitrary number of neutrino species

Exact analytical expressions in terms of generalized confluent hypergeometric functions for the transition amplitudes of neutrino oscillations in presence of matter are computed for an arbitrary number of species. The density of matter is assumed to be exponentially decaying. The results can be used for the description of matter-induced neutrino oscillations in the Sun which can take place when the solar neutrinos propagate radially from the interior to the surface. Expressions are particularly simple in the limit of infinite propagation time as is suitable for the case of detection at Earth. PACS: 14.60.Pq, 02.30.Gp, 02.30.HqComment: 20 latex pages, 7 embedded ps uuencoded figures. final published versio

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

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