Search for CP Violation at a Neutrino Factory in a Four-Neutrino Model

The CP violation effects in long baseline neutrino oscillations are studied in the framework of a four-neutrino model (three active neutrinos and one sterile neutrino). It is assumed that neutrino masses are devided into two nearly degenerate pairs, as indicated by the oscillation data. Approximative analytic expressions are derived for the probability differences \Delta P_{\a\b} \equiv P(\nu_\alpha \to \nu_\beta)- P(\bar\nu_\alpha \to \bar\nu_\beta) taking into account the CP violation effect of the Earth's crust. The matter effect is found to be small compared with the genuine CP violation term, in contrast with the three-neutrino model.Comment: 16 pages, latex, no figures, minor correction

Search for CP Violation with a Neutrino Factory

We have discussed the search of the genuine CP violation in a neutrino factory, in which well known neutrino beams are provided by a high intensity muon storage ring. Both \Delta P(\n_\a \Ar \n_\b) and CP odd asymmetry $A_{CP}$ in neutrino oscillations are investigated by taking account of the atmospheric neutrino data and the solar neutrino data. If the large mixing angle MSW solution is taken, the magnitude of \Delta P(\n_e \Ar \n_\m) could be 1%. If $s_{13}$ is lower than 0.05 with the maximal CP violating phase, the matter effect is negligible in \Delta P(\n_e \Ar \n_\m) and $A_{CP}$. We have proposed how to extract the genuine CP violation effect in the three family scheme from the neutrino oscillation data \Delta P(\n_e \Ar \n_\m), \Delta P(\n_\m \Ar \n_e) and \Delta P(\n_e \Ar \n_\tau).Comment: LaTeX, 16 pages, 5 figures, Added references, A comment about matter density is adde

Dynamical behaviour of cyclic production lines under instationary conditions with a system dynamics approach

In this paper, we investigate the dynamical behaviour of cyclic production lines under the presence of stochasticity An approach is presented which allows the modeling of a large part of the production line as a single module, which is characterized by a holistic description covering the effective dynamical behaviour by means of a system dynamics approach. To this aim, a module is viewed as a system which is described by two binary random variables describing the modules’ behaviour at its beginning and its end. These random variables are controlled by a state variable N(t) which denotes the mean number of items in the module. The dynamics of the module is then given by a system dynamics approach where the change of stock equals the difference of incoming and outgoing flow. It is shown by a simulation study that this simple approximate model is able to reproduce correctly typical dynamical features of the filling-up process of a production line

Neutrino oscillations with three flavors in matter: Applications to neutrinos traversing the Earth

Analytic formulas are presented for three flavor neutrino oscillations in matter in the plane wave approximation. We calculate in particular the time evolution operator in both mass and flavor bases. We also find the transition probabilities expressed as functions of the vacuum mass squared differences, the vacuum mixing angles, and the matter density parameter. The application of this to neutrino oscillations for both atmospheric and long baseline neutrinos in a mantle-core-mantle step function model of the Earth's matter density profile is discussed.Comment: 14 pages, 4 figures (PostScript), Elsevier LaTe

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

Neutrino mixing in matter

Three-neutrino mixing in matter is studied through a set of evolution equations which are based on a rephasing invariant parametrization. Making use of the known properties of measured neutrino parameters, analytic, approximate, solutions are obtained. Their accuracy is confirmed by comparison with numerical integration of these equations. The results, when expressed in the elements squared of the mixing matrix, exhibit striking patterns as the matter density varies.Comment: Revised, 5 pages, 3 figures, references added

Mass or Gravitationally Induced Neutrino Oscillations? -- A Comparison of \B Neutrino Flux Spectra in a Three--Generation Framework

Both gravitational and mass induced neutrino oscillation mechanisms provide possible resolutions to the Solar Neutrino Problem. The distinguishing feature between the two mechanisms is their dependence on the neutrino energy. We investigate the implications of this by computing the \B neutrino spectrum as determined from each mechanism using a realistic three--flavor evolution model. We find that in the limit of small \tetau mixing angle, the differences are significant enough to observe in future solar neutrino experiments.Comment: 14 pages, latex, epsf, 5 figures; to appear in Phys Lett

Untangling CP Violation and the Mass Hierarchy in Long Baseline Experiments

In the overlap region, for the normal and inverted hierarchies, of the neutrino-antineutrino bi-probability space for $\nu_\mu \to \nu_e$ appearance, we derive a simple identity between the solutions in the ($\sin^2 2\theta_{13}$, $\sin \delta$) plane for the different hierarchies. The parameter $\sin^2 2\theta_{13}$ sets the scale of the $\nu_\mu \to \nu_e$ appearance probabilities at the atmospheric $\delta m^2_{atm} \approx 2.4 \times 10^{-3}$ eV$^2$ whereas $\sin \delta$ controls the amount of CP violation in the lepton sector. The identity between the solutions is that the difference in the values of $\sin \delta$ for the two hierarchies equals twice the value of $\sqrt{\sin^2 2\theta_{13}}$ divided by the {\it critical} value of $\sqrt{\sin^2 2\theta_{13}}$. We apply this identity to the two proposed long baseline experiments, T2K and NO$\nu$A, and we show how it can be used to provide a simple understanding of when and why fake solutions are excluded when two or more experiments are combined. The identity demonstrates the true complimentarity of T2K and NO$\nu$A.Comment: 15 pages, Latex, 4 postscript figures. Submitted to New Journal of Physics, ``Focus on Neutrino Physics'' issu