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 ∆m 2 21 /∆m 2 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.

Assuming three-neutrino mixing, we study the capabilities of very long baseline neutrino oscillation experiments to verify and test the MSW effect and to measure the lepton mixing angle θ 13 . We suppose that intense neutrino and antineutrino beams will become available in so-called neutrino factories. We find that the most promising and statistically significant results can be obtained by studying ν e → ν µ andν e →ν µ oscillations which lead to matter enhancements and suppressions of wrong sign muon rates. We show the θ 13 ranges where matter effects could be observed as a function of the baseline. We discuss the scaling of rates, significances and sensitivities with the relevant mixing angles and experimental parameters. Our analysis includes fluxes, event rates and statistical aspects so that the conclusions should be useful for the planning of experimental setups. We discuss the subleading ∆m 2 21 effects in the case of the LMA MSW solution of the solar problem, showing that they are small for L 7000 km. For shorter baselines, ∆m 2 21 effects can be relevant and their dependence on L offers a further handle for the determination of the CP-violation phase δ. Finally we comment on the possibility to measure the specific distortion of the energy spectrum due to the MSW effect.

We discuss in a systematic way the extraction of neutrino masses, mixing angles and leptonic CP violation at neutrino factories. Compared to previous studies we put a special emphasis on improved statistical methods and on the multidimensional nature of the combined fits of the ν e → ν µ ,ν e →ν µ appearance and ν µ → ν µ ,ν µ →ν µ disappearance channels. Uncertainties of all involved parameters and statistical errors are included. We find previously ignored correlations in the multidimensional parameter space, leading to modifications in the physics reach, which amount in some cases to one order of magnitude. Including proper statistical errors we determine for all parameters the improved sensitivity limits for various baselines, beam energies, neutrino fluxes and detector masses. Our results allow a comparison of the physics potential for different choices of baseline and beam energy with regard to all involved parameters. In addition we discuss in more detail the problem of parameter degeneracies in measurements of δ CP .

We study in a quantitative way CP-violating effects in neutrino oscillation experiments in the light of current and future data. Different scenarios with three and four neutrinos are worked out in detail including matter effects in long baseline experiments and it is shown that in some cases CP-violating effects could affect the analysis of a possible measurement. In particular in the three neutrino case we find that the effects can be larger than expected, at least in long-baseline $\nu_\mu\to\nu_e$. Moreover, measuring these effects could give useful information on the solar oscillation frequency. In four neutrino scenarios large effects are possible both in the $\nu_\mu\to\nu_\tau$ and $\nu_\mu\to\nu_e$ channels of long-baseline experiments, whereas short-baseline experiments are affected only marginally.Comment: 30 pages, 6 figures. Final version to appear in Nuclear Physics

We discuss and quantify different possibilities to determine matter effects, the value and the sign of ∆m 2 31 , as well as the magnitude of sin 2 2θ 13 in very long baseline neutrino oscillation experiments. We study neutrino oscillation at a neutrino factory in the ν µ → ν µ disappearance and ν e → ν µ appearance channels with and without muon charge identification. One possibility is to analyze the ν e → ν µ appearance channels leading to wrong sign muon events, which requires however very good muon charge identification. Without charge identification it is still possible to operate the neutrino factory both with µ − and µ + beams and to analyze the differences in the total neutrino event rate spectra. We show that this leads already to a quite good sensitivity, which may be important if right sign charge rejection capabilities are insufficient. With muon charge identification one can study the ν µ → ν µ disappearance and the ν e → ν µ appearance channels independently. The best method is finally achieved by combining all available information of the ν µ → ν µ disappearance and ν e → ν µ appearance channels with charge identification and we show the sensitivity which can be achieved.