Parametric Resonance in Neutrino Oscillation: A Guide to Control the Effects of Inhomogeneous Matter Density

Effects of the inhomogeneous matter density on the three-generation neutrino oscillation probability are analyzed. Realistic profile of the matter density is expanded into a Fourier series. Taking in the Fourier modes one by one, we demonstrate that each mode has its corresponding target energy. The high Fourier mode selectively modifies the oscillation probability of the low-energy region. This rule is well described by the parametric resonance between the neutrino oscillation and the matter effect. The Fourier analysis gives a simple guideline to systematically control the uncertainty of the oscillation probability caused by the uncertain density of matter. Precise analysis of the oscillation probability down to the low-energy region requires accurate evaluation of the Fourier coefficients of the matter density up to the corresponding high modes.Comment: 7 pages, 5 eps figure

CP and T violation in long baseline experiments with low energy neutrino from muon storage ring

Stimulated by the idea of PRISM, a very high intensity muon ring with rather low energy, we consider possibilities of observing CP-violation effects in neutrino oscillation experiments. More than 10% of CP-violation effect can be seen within the experimentally allowed region. Destructive sum of matter effect and CP-violation effect can be avoided with use of initial nu_e beam. We finally show that the experiment with (a few) x 100 MeV of neutrino energy and (a few) x 100 km of baseline length, which is considered in this paper, is particularly suitable for a search of CP violation in view of statistical error.Comment: 12 pages, 3 eps figures included, LaTeX. A new section is added (v2). Errors in Table 2 and reference are corrected (v3

Peak loops untying the degeneracy of the neutrino parameters

Systematic analysis of the determination of the value of leptonic CP-violating angle delta and the neutrino mass hierarchy sgn(delta m^2_31) by long baseline neutrino oscillation experiments is presented. We note the difficulty to distinguish a pair of oscillation probability spectra that are peaked at the same energy and have the same probability at that energy. We thereby set forth the peak-matching condition as a criterion of the presence of degeneracy, and visualize it by intersections of the trajectories drawn by a peak of an oscillation spectrum while the value of delta is varied from 0 to 2pi. We numerically calculate the pairs of the trajectories for both hierarchies and show that the pair becomes disjoint as the baseline gets longer than a critical length, indicating the matter effect resolving the degeneracy on the hierarchy. We formulate the trajectories into analytic expressions and evaluate the critical length. We provide prospects of the following four approaches of resolving the hierarchy: making the baseline longer than the critical length, using both neutrinos and anti-neutrinos, combining experiments with different baseline lengths, and observing two or more oscillation peaks.Comment: ReVTeX4, 9 pages, 6 Figures. Prepared for the proceedings of "International Workshop on Neutrino Masses and Mixings -- Toward Unified Understanding of Quark and Lepton Mass Matrices --" at University of Shizuoka on December 17-19, 200

An illustration and analysis of the degeneracy in the search for the leptonic CP-violating angle and the neutrino mass hierarchy

Determination of the value of the leptonic CP-violating phase deltaand the neutrino mass hierarchy sgn(dm2_31) through long baselineneutrino oscillation experiments is systematically analyzed. We notethat the two oscillation spectra are difficult to discriminate andlead to the degeneracy when they are peaked at the same energy andhave the same peak probability. The condition of peak-matching istherefore introduced as a criterion for the presence of degeneracy.The matching of peaks is visualized as an intersection of trajectoriestraced by the peak of an oscillation spectrum while the value of deltais varied from 0 to 2pi. We numerically calculate a pair oftrajectories for a pair of hierarchies and examine the degeneracy,especially that concerning the hierarchy. We formulate the trajectoryin terms of analytic expressions and evaluate the critical length,which is shown to be proportional to 1/sin(theta_13). In view of ouranalysis, we discuss future prospects to solve the hierarchydegeneracy with regard to the following four approaches: elongatingthe baseline length sufficiently, using both neutrinos andanti-neutrinos, combining experiments with different baseline lengths,and observing two or more oscillation peaks.Comment: PTPTeX, 23 pages, 11 figures. Minor updates in accordance with the published versio

Leptonic CP Violation Search and the Ambiguity of dm^2_31

We consider a search for the CP-violating angle deltaCP in long baseline neutrino oscillation experiments. We show that the subleading deltaCP-dependent terms in the nu_mu -> nu_e oscillation probability can be easily obscured by the ambiguity of the leading term which depends on |dm^2_31|. It is thus necessary to determine the value of dm^2_31 with a sufficient accuracy. The nu_mu survival events, which can be accumulated simultaneously with the nu_e appearance events, can serve for this purpose owing to its large statistics. Therefore, the combined analysis of nu_e appearance and nu_mu survival events is crucial to provide a restrictive constraint on deltaCP. Taking a test experimental setup, we demonstrate in the deltaCP-dm^2_31 plane that the analysis of nu_e appearance events leads to less restrictive constraints on the value of deltaCP due to the ambiguity of dm^2_31 and that the combined analysis efficiently improves the constraints.Comment: ReVTeX file, 9 pages, 7 figures. Discussions added in Sections 1, 2, and 4; Reference expande