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

We study dependence of the atmospheric ${\nu }_{\mu }$ and ${\bar{\nu }}_{\mu }$ fluxes on the deviations of the 2-3 mixing from maximal, $\mathrm{\mid }{45}^{\circ }-{\theta }_{23}\mathrm{\mid }$, on the ${\theta }_{23}$-octant and on the neutrino mass splitting $\Delta m_{32}^2$\mathrm{.}Analyticexpressionsforthe$\theta_{23}-$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 $\mathrm{\mid }{45}^{\circ }-{\theta }_{23}\mathrm{\mid }>6^{\circ }$ 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 $\theta_{13} > 3^\circ$\mathrm{.}ICALcanmeasurethedifferenceof$\Delta m_{32}^2$in$\nu$and$\bar\nu$channels(theCPTtest)withaccuracy$0.8\times 10^{-4}$eV$^2$(3$\sigma$)with1Mton$\cdot$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.