A question of hierarchy: matter effects with atmospheric neutrinos and anti-neutrinos

It is by now established that neutrinos mix, have (different) non-zero masses, and therefore oscillate. The oscillation parameters themselves, however, are not all well-known. An open problem is that of the neutrino mass hierarchy. We study the possibility of determining the neutrino mass hierarchy with atmospheric neutrinos using an iron calorimeter detector capable of charge identification such as the proposed monolith and ical/ino detectors. We find that such detectors are sensitive to the sign of the mass-squared difference, δ32 = m 2 3 −m2, provided the as-yet unknown mixing angle between the first and third generations, θ13, is greater than 5 ◦ (sin 2θ13 > 0.03). The exposure required is at least about 500 kton-years in such a case; in contrast, such detectors can establish a clear oscillation pattern in atmospheric neutrinos in about 150 kton-years, therefore determining the absolute value of δ32 and sin 2θ23 to within 10%. Typeset using REVTEX