Combined sensitivity to the neutrino mass ordering with JUNO, the IceCube Upgrade, and PINGU

The ordering of the neutrino mass eigenstates is one of the fundamental open questions in neutrino physics. While current-generation neutrino oscillation experiments are able to produce moderate indications on this ordering, upcoming experiments of the next generation aim to provide conclusive evidence. In this paper we study the combined performance of the two future multi-purpose neutrino oscillation experiments JUNO and the IceCube Upgrade, which employ two very distinct and complementary routes toward the neutrino mass ordering. The approach pursued by the 20 kt medium-baseline reactor neutrino experiment JUNO consists of a careful investigation of the energy spectrum of oscillated ${\overline{\nu }}_e$ produced by ten nuclear reactor cores. The IceCube Upgrade, on the other hand, which consists of seven additional densely instrumented strings deployed in the center of IceCube DeepCore, will observe large numbers of atmospheric neutrinos that have undergone oscillations affected by Earth matter. In a joint fit with both approaches, tension occurs between their preferred mass-squared differences $\mathrm{\Delta }{m}_{31}^2=m_3^2-m_1^2$ within the wrong mass ordering. In the case of JUNO and the IceCube Upgrade, this allows to exclude the wrong ordering at $>5\sigma$ on a timescale of 3–7 years—even under circumstances that are unfavorable to the experiments’ individual sensitivities. For PINGU, a 26-string detector array designed as a potential low-energy extension to IceCube, the inverted ordering could be excluded within 1.5 years (3 years for the normal ordering) in a joint analysis.

Figure 1

Simulation chain employed in the modeling of the event distributions in JUNO and the IceCube Upgrade and PINGU. Blue boxes represent intermediate distributions, red ones physics inputs of the two experiments (JUNO on the left, the IceCube Upgrade and PINGU on the right, shared ones centered), whereas green boxes specify the entities that transform between the intermediate distributions. See text for details.

Figure 2

Expected distribution of reconstructed energies $E_{\nu ,\text{reco}}$ of reactor ${\overline{\nu }}_e$ events in JUNO given true NO for our analysis binning after 6 years of operation (1800 days), without any background contribution. Shown is the expected spectrum assuming the nominal oscillation parameter inputs from [20] (thin orange line) and the spectrum assuming the inputs from Table 3 (thick blue line).

Figure 3

Nominal expected event distributions given true NO for our analysis binning in reconstructed neutrino cosine zenith $\cos ({\theta }_{Z,\text{reco}})$ and reconstructed neutrino energy $E_{\nu ,\text{reco}}$ for the IceCube Upgrade (top) and PINGU (bottom) after 4 years of operation.

Figure 4

$\overline{\mathrm{\Delta }{\chi }^2}$ profiles as function of the tested/fit values of $\mathrm{\Delta }{m}_{31}^2$ within the true ordering (upper panels) and the wrong ordering (lower panels) for a livetime of 6 years for both experiments. On the left (right), the NO (IO) is assumed to be true. The scans within the wrong ordering illustrate the synergy effect of performing a combined fit. Here, a tension in the best-fit values of $\mathrm{\Delta }{m}_{31}^2$ for PINGU and JUNO is visible that is greater than the “resolution” of the two experiments. Shown in addition are the hypothetical wrong-ordering profiles assuming a vanishing matter density along all neutrino trajectories in the case of PINGU (labeled “PINGU vacuum”). The line labeled “simple sum” (dashed orange) is the sum of the “JUNO” and “PINGU” curves at each tested value of $\mathrm{\Delta }{m}_{31}^2$.

Figure 5

${\theta }_{13}$ synergy effect after 6 years of livetime of both experiments, without (top) and with (bottom) a prior on the parameter, assuming true NO on the left and true IO on the right. In each case, the wrong ordering is fit to the true one. In contrast to Fig. 4, here we show the full combined fit (solid red) in addition to the “simple sum” (dashed orange).

Figure 6

Livetime evolution of the NMO sensitivity of each considered pair of experiments: stand-alone, the simple (quadratic) sum, and the combination. Results for the nominal JUNO configuration and PINGU are shown side-by-side with the 8-core JUNO configuration (labeled as “JUNO (8 cores)”) and the IceCube Upgrade. The two panels on the left assume true NO, while the two panels on the right assume true IO.

Figure 7

NMO sensitivities (combined, statistical contributions of JUNO and PINGU, JUNO stand-alone) as a function of JUNO’s true energy resolution (for true NO on the left, true IO on the right) after 6 years of operation of both experiments.

Figure 8

NMO sensitivities (combined, statistical contributions of JUNO and PINGU, PINGU stand-alone) as a function of the true value of ${\sin }^2({\theta }_{23})$ (for true NO on the left, true IO on the right) after 6 years of operation of both experiments. The lower panels show the global $\mathrm{\Delta }{\chi }^2$ constraint on ${\sin }^2({\theta }_{23})$ (relative to the ${\chi }^2$ minimum within each ordering) from [7, 8].

Figure 9

Time required for the combined analysis of the 8-core JUNO configuration and the IceCube Upgrade to attain a $5\sigma$ measurement of the NMO as a function of the true mixing angle ${\sin }^2({\theta }_{23})$ and JUNO’s energy resolution, for true NO on the left and true IO on the right. The empty square marks our nominal assumption about the two parameters. Solid contours trace parameter combinations for which the required time is 3, 4, 5, 6, and 7 years, respectively.

Figure 10

$\overline{\mathrm{\Delta }{\chi }^2}$ profiles as a function of the tested values of ${\sin }^2({\theta }_{13})$ within the true ordering for JUNO and PINGU stand-alone, their simple sum, and their combination, for a livetime of 6 years of both experiments. On the left (right), the NO (IO) is assumed to be true. The current global sensitivity to ${\sin }^2({\theta }_{13})$ is superimposed (dotted black) [7, 8].

Figure 11

$\overline{\mathrm{\Delta }{\chi }^2}$ profiles as a function of the tested values of $\mathrm{\Delta }{m}_{31}^2$ within the true ordering for JUNO and PINGU stand-alone, their simple sum, and their combination, for a livetime of 6 years of both experiments. On the left (right), the NO (IO) is assumed to be true. The current global sensitivity to $\mathrm{\Delta }{m}_{31}^2$ is superimposed (dotted black) [7, 8].