Using low energy atmospheric neutrinos for precision measurement of the mixing parameters

Use of low energy atmospheric neutrinos is considered for precision measurement of neutrino mixing parameters. At around energy $E \simeq$ a few $\times$100 MeV and baseline $L$ of a few $\times$1000 km, CP phase effect is $\sim$10 times larger than that of the conventional LBL accelerator neutrino experiments. We report here a few progresses: (1) To analyze physics in the region, a new perturbative framework at around the solar-scale enhancement is developed. (2) To know the characteristic features of CP $\delta$ dependence of the atmospheric neutrinos at low energies, we plot the ratio of the $\nu_{e}$ and $\bar{\nu}_{e}$ fluxes $F(\delta)/F(\delta=0)$ for $\delta=\pm \frac{\pi}{2}$ and $\pi$ as a function of $E$ using the Honda {\it et al.} flux. Interestingly, it shows $\delta$ dependence of $\simeq$5-10\% level, with positive (negative) sign for $\nu_{e}$ ($\bar{\nu}_{e}$). (3) To reduce the flux systematic errors, measurement of muon energy distribution around $\sim$1 GeV at high altitude may be useful. Water Cherenkov or muon range detectors may be the options with advantage in the latter if it is magnetized in view of the $\delta$ dependence of the flux.