Measuring CP violation by low-energy medium-baseline neutrino oscillation experiments

In this talk we discuss the possibility to measure CP violation in neutrino oscillation experiments using the neutrino beam with energy which is lower (E_\nu \gsim 100 MeV) than the one usually considered (typically > 1 GeV) in accelerator experiments. The advantage of using such lower energy neutrino beam is that despite the smaller detection cross sections, the effect of CP violation is larger and the optimal length of baseline can be rather short, 30-50 km, being free from matter effect contamination.Comment: 5 pages with 2 postscript figures, uses espcrc2.sty, Talk presented by H. Nunokawa at ``NuFact'00'' workshop, Monterey, CA, USA, May 22-26, 200

CP Trajectory Diagram; A tool for pictorial representation of CP and matter effects in neutrino oscillations

We introduce "CP trajectory diagram in bi-probability space" as a powerful tool for pictorial representation of the genuine CP and the matter effects in neutrino oscillations. Existence of the correlated ambiguity in a determination of CP violating phase \delta and the sign of \Delta m^2_{13} is uncovered. Principles of tuning beam energy for a given baseline distance are proposed to resolve the ambiguity and to maximize the CP-odd effect. We finally point out, quite contrary to what is usually believed, that the ambiguity may be resolved with 50 % chance in the super-JHF experiment despite its relatively short baseline of 300 km.Comment: 6 pages with 2 postscript figures. Talk presented at The 3rd International Workshop on Neutrino Factories Based on Muon Storage Rings (NuFACT01), Tsukuba, Japan, May 24-30, 200

How to Measure CP Violation in Neutrino Oscillation Experiments?

We propose a new method for measuring CP violation in neutrino oscillation experiments. The idea is to isolate the term due to the CP-violating phase out of the oscillation probability by taking difference between yields of two (or three) detectors at path-lengths $L = 250 (\frac{E}{1.35 {GeV}}) (\frac{\Delta m^2}{10^{-2}{eV}^2})^{-1} {km}$ and at $L/3$ (and also at $2L/3$ in the case of three detectors). We use possible hierarchies in neutrino masses suggested by the astrophysical and the cosmological observations to motivate the idea and to examine how the method works.Comment: RevTex, 17 pages including 4 ps figure

Method for Determination of ∣Ue3∣|U_{e3}| in Neutrino Oscillation Appearance Experiments

We point out that determination of the MNS matrix element |U_{e3}| = s_{13} in long-baseline \nu_{\mu} \to \nu_e neutrino oscillation experiments suffers from large intrinsic uncertainty due to the unknown CP violating phase \delta and sign of \Delta m^2_{13}. We propose a new strategy for accurate determination of $\theta_{13}$; tune the beam energy at the oscillation maximum and do the measurement both in neutrino and antineutrino channels. We show that it automatically resolves the problem of parameter ambiguities which involves \delta, \theta_{13}, and the sign of \Delta m^2_{13}.Comment: 15 pages, 3 figures, minor corrections, final version to appear in PL

An Effective Two-Flavor Approximation for Neutrino Survival Probabilities in Matter

It is known in vacuum that the three-flavor neutrino survival probability can be approximated by the effective two-flavor form to first orders in $\epsilon \equiv \Delta m^2_{21} / \Delta m^2_{31}$, with introduction of the effective $\Delta m^2_{\alpha \alpha}$ ($\alpha = e, \mu, \tau$), in regions of neutrino energy $E$ and baseline $L$ such that $\Delta m^2_{31} L / 2E \sim \pi$. Here, we investigate the question of whether the similar effective two-flavor approximation can be formulated for the survival probability in matter. Using a perturbative framework with the expansion parameters $\epsilon$ and $s_{13} \propto \sqrt{\epsilon}$, we give an affirmative answer to this question and the resultant two-flavor form of the probability is valid to order $\epsilon$. However, we observe a contrived feature of the effective $\Delta m^2_{\alpha \alpha} (a)$ in matter. It ceases to be a combination of the fundamental parameters and has energy dependence, which may be legitimate because it comes from the matter potential. But, it turned out that $\Delta m^2_{\mu \mu} (a)$ becomes $L$-dependent, though $\Delta m^2_{ee} (a)$ is not, which casts doubt on adequacy of the concept of effective $\Delta m^2$ in matter. We also find that the appearance probability in vacuum admits, to order $\epsilon$, the similar effective two-flavor form with a slightly different effective $\Delta m^2_{\beta \alpha}$ from the disappearance channel. A general result is derived to describe suppression of the matter effect in the oscillation probability.Comment: Discussion on appearance effective $\Delta m^2$ added. Version to appear in JHEP. 26 pages, 3 figure