Determining neutrino mass hierarchy from electron disappearance at a low energy neutrino factory

Recent measurements of large ${\theta }_{13}$ by the reactor experiments have opened up the possibility of determining the neutrino mass hierarchy, i.e., the sign of the mass squared splitting $\mathrm{\Delta }{m}_{31}^2$, the $CP$-violating phase ${\delta }_{CP}$, and the octant of ${\theta }_{23}$. In light of this result, we study the performance of a low energy neutrino factory (LENF) for determination of the mass hierarchy. In particular, we explore the potential of the ${\nu }_e$ and ${\overline{\nu }}_e$ disappearance channels at LENF to determine the neutrino mass hierarchy, that is free from the uncertainties arising from the unknown ${\delta }_{CP}$ phase and the ${\theta }_{23}$ octant. We find that using these electron neutrino (antineutrino) disappearance channels with a standard LENF, it is possible to exclude the wrong hierarchy at $5\sigma$ with only 2 years of running, with a muon beam energy above $\sim 3.5(5.0–10.0)\mathrm{GeV}$ and baseline longer than $\sim 1400(1900–2400)\mathrm{km}$ for an optimistic (conservative) systematic error of 2% (5%).

Figure 1

Electron/positron event rates per bin (0.05 GeV) for ${\sin }^{2}2{\theta }_{13}=0.1$, as a function of the observed lepton energy at a LENF corresponding to NH (red/solid curve) and IH (blue/dashed curve). The events are for a 2 year exposure of a 20 kton detector at a baseline of $L=1300\mathrm{km}$, for neutrinos from 4.5 GeV muon beams with $1.4\times {10}^{21}$ useful muon decays per year per polarity. The other detector specifications are as mentioned in Sec. 2.

Figure 2

Electron/positron event rates per bin (1.0 GeV) for ${\sin }^2(2{\theta }_{13})=0.01$ (Left) and 0.1 (Right) as a function of the observed lepton energy at a LENF with an optimistic systematic error of 2% (Upper panel) and a conservative systematic error of 5% (Lower panel) for the signal. The bands around each of the curves denote the combination of statistical and systematic errors added in quadrature. All other specifications are similar to that in Fig. 1.

Figure 3

${\chi }^2$ as a function of the baseline $L$ for different values of the muon beam energy $E_{\mu }$ at a LENF over a 2 year (Left) and 5 year (Right) exposure for input ${\sin }^{2}2{\theta }_{13}=0.1$ and ${\delta }_{CP}=90°$ with an optimistic systematic error of 2% for the signal. We keep all other oscillation parameters fixed at their central values and assume normal hierarchy (NH) to be true hierarchy.

Figure 4

${\chi }^2$ as a function of the baseline $L$ for different values of the muon beam energy $E_{\mu }$ at a LENF over a 2 year (Left) and 5 year (Right) exposure for input ${\sin }^{2}2{\theta }_{13}=0.1$ and ${\delta }_{CP}=90°$ with a conservative systematic error of 5% for the signal. We keep all other oscillation parameters fixed at their central values and assume normal hierarchy (NH) to be true hierarchy.

Figure 5

$3\sigma$ and $5\sigma$ contours in $L-E_{\mu }$ plane at a LENF over a 2 year (red/solid curves) and a 5 year (blue/dashed curves) exposure for input ${\sin }^2(2{\theta }_{13})=0.1$ with a systematic error of 2% (Left) and 5% (Right) for the signal. We have assumed normal hierarchy (NH) to be the true hierarchy.