Mass hierarchy determination for θ₁₃ = 0 and atmospheric neutrinos

Abstract

We examine the possibility of determining the neutrino mass hierarchy in the limit θ₁₃=0 using atmospheric neutrinos as the source. In this limit, in which θ₁₃ driven matter effects are absent, independent measurements of Δ₃₁ and Δ₃₂ can, in principle, lead to hierarchy determination. Since the difference between these two is Δ₂₁, one needs an experimental arrangement where Δ₂₁ L/E ≳1 can be achieved. This condition can be satisfied by atmospheric neutrinos since they have a large range of energies and baselines. In spite of this, we find that hierarchy determination in the θ₁₃ = 0 limit with atmospheric neutrinos is not a realistic possibility, even in conjunction with an apparently synergistic beam experiment like T2K or NOνA. We discuss the reasons for this, and also in the process clarify the conditions that must be satisfied in general for hierarchy determination if θ₁₃ = 0.