Measuring Oscillations with a Million Atmospheric Neutrinos

After two decades of measurements, neutrino physics is now advancing into the precision era. With the long-baseline experiments designed to tackle current open questions, a new query arises: Can atmospheric neutrino experiments also play a role? To that end, we analyze the expected sensitivity of current and near-future water(ice)-Cherenkov atmospheric neutrino experiments in the context of standard three-flavor neutrino oscillations. In this first in-depth combined atmospheric neutrino analysis, we analyze the current shared systematic uncertainties arising from the common flux and neutrino-water interactions. We then implement the systematic uncertainties of each experiment in detail and develop the atmospheric neutrino simulations for Super-Kamiokande, with and without neutron-tagging capabilities, IceCube Upgrade, ORCA, and Hyper-Kamiokande detectors. We carefully review the synergies and features of these experiments to examine the potential of a joint analysis of these atmospheric neutrino data in resolving the ${\theta }_{23}$ octant at 99% confidence level (CL), and determining the neutrino mass ordering above $5\sigma$ by 2030. Additionally, we assess the capability to constrain ${\theta }_{13}$ and the $CP$-violating phase (${\delta }_{CP}$) in the leptonic sector independently from reactor and accelerator neutrino data. A combination of the atmospheric neutrino measurements will enhance the sensitivity to a greater extent than the simple sum of individual experiment results reaching more than $3\sigma$ for some values of ${\delta }_{CP}$. These results will provide vital information for next-generation accelerator neutrino oscillation experiments such as DUNE and Hyper-Kamiokande.

Popular Summary

Atmospheric neutrinos have played a key role in discovering and understanding neutrino oscillations, a milestone in physics wherein neutrinos evolve from one “flavor” state to another. In the last two decades, the neutrino community has developed a vast program using accelerator, reactor, and solar neutrinos to measure their evolution, leading to the conclusion that atmospheric measurements will not contribute to precision neutrino physics. In this article, we change that paradigm, showing that atmospheric neutrinos will improve our knowledge of some of the largest unknowns describing the evolution of neutrino states.

Neutrinos have some notable differences compared to other particles. When an electron, for example, interacts with materials, it acts like an electron, and when it travels, its mass is that of an electron. That is not the case for neutrinos: Their interaction, or flavor, states are distinct from their mass ones. This “misalignment” is related to a parameter known as the mixing angle. One of the least-known neutrino parameters is the mixing angle between the heaviest and second-heaviest neutrino types. Other missing pieces include the neutrino mass ordering and whether the particles violate charge-parity, or CP, symmetry.

Our work provides the first in-depth analysis of how the three most relevant atmospheric neutrino experiments—Super-Kamiokande, IceCube, and ORCA—can contribute to these questions. Our results indicate that by the end of this decade, it will be possible to resolve the mixing angle’s octant—a parameter related to how the flavor states comprise the mass states. The experiments will also reach a six-sigma sensitivity on the neutrino mass ordering and be able to exclude a significant fraction of the allowed CP-phase values at a 90% confidence level.

A global neutrino analysis that properly includes atmospheric neutrinos has been a long-standing issue and is the final requirement for a complete description of neutrino mixing. This work is the first and crucial step in that direction.

Figure 1

Illustration of this analysis. Locations of experiments used in this work are shown. Note that Hyper-Kamiokande has roughly the same location as Super-Kamiokande.

Figure 2

Comparison between the present and future projected sensitivities for the oscillation parameters. This figure showcases the power of atmospheric combined neutrino experiments, as they have smaller or comparable errors on these parameters than accelerator neutrino experiments also shown in this figure. Oscillation parameters that can be measured by atmospheric experiments are arranged in the vertical axis, while their measured precision is quantified in the horizontal axis. The present (1σ) region allowed by fit to data from T2K [24] (green), $\mathrm{NO}\nu \mathrm{A}$ [25] (light orange), SuperK atmospheric neutrinos [26] (light red), DeepCore atmospheric neutrinos [27] (turquoise), the reactor experiments (gray), and the projected sensitivity of Hyper-Kamiokande’s accelerator program (blue) for 2030 [28] is compared with the expected (1σ) region from a combined atmospheric neutrino analysis (this work in red-violet). The sensitivity from DUNE is excluded due to the low significance achievable by this experiment for 2030 assuming a 2029 starting date [29].

Figure 3

Neutrino mass ordering sensitivity as a function of years in operation. The cyan (orange) band shows the sensitivity for rejecting the wrong ordering hypothesis for true normal (inverted) ordering, assuming fixed ${\sin }^2{\theta }_{13}=0.022$. The width of the bands covers the allowed values for ${\sin }^2{\theta }_{23}$ from 0.45 to 0.6. The black dot corresponds to the last reported SuperK neutrino mass ordering analysis [43]. For comparison, we also include the prediction of the next-generation long-baseline neutrino experiments that are supposed to start in mid-2027 in the case of HyperK and 2029 in the case of DUNE [44].

Figure 4

Measurements of the atmospheric neutrino flux as a function of the energy. The total neutrino flux measured by different experiments [57, 58, 59] together with the energy range covered by the four experiments (SuperK, IceCube Upgrade, ORCA, and HyperK) considered in this analysis are shown in the lower panel. In the lower panel, we also include the flux prediction from the HKKM2014 model [55]. In the top panel, we have the effective volume for the three experiments as a function of the neutrino energy.

Figure 5

Energy (left) and zenith (right) distribution of the atmospheric neutrino flux. The flux is based on the Honda et al. [55] calculation. Around the prediction for each flavor component of the flux at the detector, we show the $1\sigma$ uncertainty band.

Figure 6

Charged-current ${\nu }_{\mu }$ cross section per nucleon as a function of the energy split by its main contributions, QE, RES, and DIS. The cross-section models used are from GENIE precomputed splines, shaded regions correspond to the $1\sigma$ priors assumed in Table 2, and data points correspond to the most relevant inclusive cross-section measurements for this work.

Figure 7

Diagram showing neutron tagging on gadolinium in an inverse-$\beta$ interaction.

Figure 8

Muon-disappearance probability. For energies above 1 GeV and all the trajectories crossing Earth [$-1<\cos ({\theta }_{\mathrm{zen}})<0$], we compute $P({\nu }_{\mu }\to {\nu }_{\mu })$ for normal (left) and inverted (right) mass ordering. We consider the PREM for Earth matter distribution.

Figure 9

Electron-appearance probability. Similar to Fig. 8, we compute $P({\nu }_{\mu }\to {\nu }_e)$ for both mass orderings, normal (left) and inverted (right). In this case, we consider neutrinos with energies between 0.1 and 15 GeV.

Figure 10

Electron- (top) and muon- (bottom) appearance probabilities for $\cos ({\theta }_{\mathrm{zen}})=-0.85$. We show the impact of ${\delta }_{CP}$ in both oscillation channels. The fast oscillations are smeared assuming a Gaussian uncertainty of 5% $E/\mathrm{GeV}$.

Figure 11

Electron-appearance probability for different values of ${\sin }^2{\theta }_{13}$. The neutrino direction is fixed to $\cos ({\theta }_{\mathrm{zen}})=-0.85$. The fast oscillations that happen for $E\sim \mathrm{GeV}$ are smeared assuming a Gaussian uncertainty of 5% $E/\mathrm{GeV}$.

Figure 12

Electron-appearance (left) and muon-disappearace (right) probabilities for $\cos ({\theta }_{\mathrm{zen}})=-0.85$. We show the impact of ${\sin }^2{\theta }_{13}$ in both oscillation channels. The fast oscillations are smeared assuming a Gaussian uncertainty of 5% $E/\mathrm{GeV}$.

Figure 13

Impact of different values of ${\delta }_{CP}$ (left) and both neutrino mass orderings (right) for the most sensitive SuperK samples. On the left, ${\mathcal{R}}_{\mu /e}({\delta }_{CP};0)$ are the ratio of the number of events in sub-GeV $\mu$-like and $e$-like samples, with one and zero decay electrons, respectively, for a given value of ${\delta }_{CP}$ compared with the case of ${\delta }_{CP}=0$. On the right, we show the ratio between inverted ($N_{\mathrm{IO}}$) and normal ($N_{\mathrm{NO}}$) orderings for the number of events in SuperK single-ring and multiting multi-GeV $e$-like samples. The rest of the parameters follow Table 3.

Figure 14

Impact of different values of ${\delta }_{CP}$ (left) and both neutrino mass orderings (right) for the most relevant SKGd samples. On the left, ${\mathcal{R}}_{\mu /e}({\delta }_{CP};0)$ are the ratio of the number of events in sub-GeV $\mu$-like and $e$-like samples, with zero Gd-tagged neutrons, and one and zero decay electrons, respectively, for a given value of ${\delta }_{CP}$ compared with the case of $CP$ conservation. On the right, we show the ratio between inverted ($N_{\mathrm{IO}}$) and normal ($N_{\mathrm{NO}}$) orderings for the number of events in SKGd single-ring multi-GeV $e$-like samples. The rest of the parameters follow Table 3.

Figure 15

Event distribution for different set of values of the mixing parameters for $\cos \theta \in [-1,-0.8]$ as a function of the reconstructed neutrino energy ($E_r$). We use the IceCube upgrade MC to evaluate the neutrino reconstructed energy [201]. The cascade distribution is shown on the left and tracks on the right. The statistical $1\sigma$ error is shown as a band around the event distribution.

Figure 16

Event distribution as a function of the reconstructed energy and direction for ORCA after three years of data taking. Lines correspond to event distributions (with oscillations) for track, cascade, and intermediate morphology classes, respectively.

Figure 17

DUNE sensitivity to ${\delta }_{CP}$. We consider one year of data taking and two modules of 10 kton each.

Figure 18

Two-dimensional 90% confidence level regions for ${\sin }^2{\theta }_{23}$ and $\mathrm{\Delta }{m}_{31}^2$ for SuperK (dashed dark blue), IceCube Upgrade (dashed orange), ORCA (dashed green), HyperK (dashed cyan), and combined analysis (solid violet-red).

Figure 19

Sensitivity to ${\sin }^2{\theta }_{13}$ for SuperK (dashed dark blue), IceCube Upgrade (dashed orange), ORCA (dashed green), HyperK (dashed cyan), and combined analysis (solid violet red).

Figure 20

Sensitivity to ${\delta }_{CP}$ for SuperK (dashed dark blue), IceCube Upgrade (dashed orange), ORCA (dashed green), HyperK (dashed cyan), and combined analysis (solid violet red).

Figure 21

Excluded fraction of ${\delta }_{CP}$ as a function of the true value of ${\delta }_{CP}$. Lines correspond to exclusion at $2\sigma$ (blue), 99% (orange), and $3\sigma$ (green) for the combined fit assuming normal ordering and fixed ${\sin }^2{\theta }_{13}=0.022$. 40% of the parameter space can be excluded at 99% confidence level for the $CP$-conserving scenario. For lower confidence levels, the small deviations in the event number expectations can contribute to increase the sensitive region making the sensitivity more uniform.

Figure 22

Present sensitivity to the $3\nu$ mixing parameters Comparison between the latest results from reactor and LBL measurements, and the future prediction from the combined analysis of SuperK, IceCube upgrade, and ORCA.

Figure 23

From top to bottom, the impact of each atmospheric neutrino flux (left) and cross-section (right) systematic uncertainties on the sensitivity to ${\delta }_{CP}$, ${\sin }^2{\theta }_{23}$, and $\mathrm{\Delta }{m}_{31}^2$. For clarity, solid lines represent the most relevant systematics, while dashed lines represent the rest.

Figure 24

From top to bottom, impact of each detector’s systematic uncertainties on the sensitivity to ${\delta }_{CP}$, ${\sin }^2{\theta }_{23}$, and $\mathrm{\Delta }{m}_{31}^2$.