The 2-3 mixing and mass split: atmospheric neutrinos and magnetized spectrometers

Abstract

We study dependence of the atmospheric ${\nu }_{\mu }$ and ${\bar{\nu }}_{\mu }$ fluxes on the deviations of the 2-3 mixing from maximal, $|45^{\circ }-{\theta }_{23}|$, on the ${\theta }_{23}$-octant and on the neutrino mass splitting $\Delta m_{32}^2$. Analytic expressions for the ${\theta }_{23}-$deviation effect and the octant asymmetry are derived. We present conservative estimations of sensitivities of the iron (magnetized) calorimeter detectors (ICAL) to these parameters. ICAL can establish the ${\theta }_{23}$-deviation at higher than 3$\sigma$ confidence level if $|45^{\circ }-{\theta }_{23}|>6^{\circ }$ with the exposure of 1 Mton$\cdot$yr. Sensitivity to the octant is low for zero or very small 1-3 mixing, but it can be substantially enhanced for ${\theta }_{13}>3^{\circ }$. ICAL can measure the difference of $\Delta m_{32}^2$ in $\nu$ and $\bar{\nu }$ channels (the CPT test) with accuracy $0.8\times 10^{-4}$ eV${}^2$ (3$\sigma$) with 1 Mton$\cdot$yr exposure, and the present MINOS result can be excluded at $>5\sigma$ confidence level. We discuss possible ways to further improve sensitivity of the magnetized spectrometers.

Comments: 15 pages, 1 new figure added, typos corrected, discussion extended. Improvement of the ICAL sensitivities with adding the information on hadrons is studied