Mass Hierarchy Determination for $\theta_{13}=0$ and Atmospheric Neutrinos

TL;DR

This paper investigates the potential to determine the neutrino mass hierarchy using atmospheric neutrinos when heta_{13} = 0, concluding it is not feasible despite theoretical conditions suggesting it might be possible.

Contribution

It clarifies the limitations of hierarchy determination with atmospheric neutrinos at heta_{13} = 0 and specifies the conditions needed for such measurements.

Findings

Hierarchy determination is not feasible at heta_{13} = 0 with atmospheric neutrinos.

Large rac{ ext{L}}{ ext{E}} range is necessary but insufficient for hierarchy resolution.

Synergistic beam experiments do not improve hierarchy determination in this limit.

Abstract

We examine the possibility of determining the neutrino mass hierarchy in the limit \theta_{13} = 0 using atmospheric neutrinos as the source. In this limit, in which \theta_{13} driven matter effects are absent, independent measurements of \Delta_{31} and \Delta_{32} can, in principle, lead to hierarchy determination. Since the difference between these two is \Delta_{21}, one needs an experimental arrangement where \Delta_{21} L/E \gtrsim 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 \theta_{13}=0 limit with atmospheric neutrinos is not a realistic possibility, even in conjunction with an apparently synergistic beam experiment like T2K or NOvA. We discuss the reasons for this, and also in the process clarify the conditions that must be satisfied in general for hierarchy determination if \theta_{13} = 0.