Evidence for Normal Neutrino Ordering with Combined Atmospheric Neutrino Experiments

Carlos A. Arg\"uelles; Iv\'an Mart\'inez-Soler; Miaochen Jin; Pablo Fern\'andez-Men\'endez

REVIEW

Evidence for Normal Neutrino Ordering with Combined Atmospheric Neutrino Experiments

Miaochen Jin, Carlos A. Argüelles, Pablo Fernández-Menéndez, Iván Martínez-Soler

High Energy Physics - Experiment · Submitted 8 Oct 2026

Pith's verdict: First real-data combined fit of three atmospheric neutrino experiments, giving 3.3σ evidence for normal ordering; stress-test concern about the SK tune kernel is reasonable but likely minor—the paper deserves a serious referee.

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arXiv ID2610.12208 (version 2)

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CitationCarlos A. Arg\"uelles, Iv\'an Mart\'inez-Soler, Miaochen Jin, Pablo Fern\'andez-Men\'endez. "Evidence for Normal Neutrino Ordering with Combined Atmospheric Neutrino Experiments." arXiv:2610.12208 (2026). https://pith.science/paper/BTFVWBI2

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Editor's note

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This is a well-executed paper that does what the same group forecast in 2023: combine the public data sets of Super-Kamiokande, IceCube-DeepCore, and KM3NeT/ORCA6 with correlated systematics. The result—3.3σ preference for normal ordering from atmospheric neutrinos alone—is new and comes with honest caveats. The statistical methodology is rigorous (binned Poisson, pseudoexperiments for the mass-ordering test, parameter goodness-of-fit), and the authors have done the hard work of building an independent SK MC, fixing a bug in the SK public release, and validating their single-experiment fits against the official contours.

The stress-test concern about the SK tune kernel—anchored at the NO best fit and then used for IO fits—is not addressed in the current version. The authors state in Appendix A that the tune is normalization-preserving and that the physics dependence is retained, but they do not quantify how large a Δχ² shift this choice could produce. Since SK contributes Δχ² = 6.2 to the combined 11.0, a kernel-induced bias of even 1–2 units would move the combined significance. I think the effect is probably small, because the tune is a per-bin normalization that is already cross-checked in the single-experiment contours (Fig. 7), and the pseudoexperiment calibration would partially absorb any mismodelling. But the authors should either test this by re-running the fit with the tune fixed at a different point, or at minimum state that the effect has been checked and is negligible. Without that check, the central claim is slightly less robust than the paper implies.

Other soft spots are minor: the missing ORCA energy-scale nuisance is a known limitation, and the combined goodness-of-fit p = 0.011 (driven by ORCA) becomes 0.12 when finite MC statistics are included, so there is no hidden tension. The δCP constraint is new but still broad.

Who is this for? Neutrino oscillation phenomenologists, experimentalists working on atmospheric neutrinos, and global-fit authors. The paper is a solid step forward. I would accept it for peer review and recommend publication after the authors address the tune-kernel sensitivity or at least document its estimated impact.

Referee report

Major objections (2)

[Appendix A and Section IV.C] The Super-Kamiokande tune kernel is anchored at the official NO best-fit parameters to match reconstructed-bin counts and true-energy quantiles (Appendix A, [b295–b296]). The kernel is an artificial reweight on unoscillated true energy distributions. While the tuned MC reproduces the SK official contours in Fig. 7, the effect of this anchoring choice on the combined mass-ordering Δχ² is not tested. Since SK contributes the largest individual preference (Δχ²=6.2), any systematic bias in the kernel—potentially from the kernel being fixed to a NO-calibrated point and then applied when fitting IO—could affect the combined Δχ². The authors should either repeat the mass-ordering test using a tune kernel derived at the IO best fit (or an alternative anchor) or provide a quantitative estimate of the resulting systematic uncertainty on Δχ²(NO–IO) and on the calibrated p-value.
[Section IV.C and Appendix B] The goodness-of-fit p-values are sensitive to the inclusion of finite Monte Carlo statistics for IceCube and ORCA (Appendix B, Fig. 9): the combined p-value increases from 0.011 to 0.118 when finite MC fluctuations are included. The pseudoexperiments used to calibrate the mass-ordering test statistic (Section IV.C) are generated using only Poisson fluctuations, without accounting for finite MC statistics. If the finite MC uncertainty broadens the test statistic distribution, the calibrated p-value might become less extreme. The authors should discuss whether including finite MC fluctuations in the mass-ordering pseudoexperiments could affect the reported significance and, if feasible, quantify the size of any such effect. The authors acknowledge this: “These p-values and χ2 test statistics reported above are evaluated using the Poisson likelihood without accounting for finite MC statistical uncertainties.”

Minor objections (8)

[Abstract] The abstract states 'exclude the inverted ordering at 99.95% confidence level (3.3σ)'. While technically correct for a one-sided normal approximation, consider also quoting the CL_s value (given as 5.4×10⁻³ in the text) to clarify the modified frequentist interpretation.
[Section I, last paragraph] The sentence 'Our work is a significant leap forward compared to a recent work [44]' is somewhat subjective. Since [44] is a preprint, consider a less comparative phrasing, e.g., 'Our work improves upon ref. [44] by using all data simultaneously with 930 bins, an independent high-statistics SK MC, and a bug-fixed SK data release.'
[Figures 1 and 2] Some panels have very small font sizes for axis labels and legends (e.g., Fig. 2 sub-panels). Please enlarge text to ensure readability in print and at standard screen resolution.
[Table I] For IceCube-DeepCore and ORCA6, the δ_CP interval is marked '—' because the profile is flat. Consider adding a footnote explicitly stating that no constraint is obtained; the current notation '(—)' is clear but could be elaborated.
[Table II] The table of nuisance parameters is very long. Consider moving it entirely to the Supplemental Material and summarizing the most important pulls in the main text.
[Appendix A] The hypothetical discussion about NEUT cross-section simulation ([b304]) is tangential and could be shortened or removed to avoid confusion.
[Reference [90]] Reference [90] is a conference talk (NOW 2026). Please provide a DOI or ensure that the talk slides or proceedings are publicly accessible; otherwise update the reference.
[Throughout] A few typos: 'therefor' should be 'therefore' in [b296]; 'statisical' in Fig. 8 caption (check if present).

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The paper

The paper claims

Combined atmospheric neutrino data from three experiments show a 3.3σ preference for normal neutrino mass ordering over inverted ordering, with independent constraints on oscillation parameters.

The reading

This paper combines publicly available atmospheric neutrino data from Super-Kamiokande, IceCube-DeepCore, and KM3NeT/ORCA6 to measure the three-flavor neutrino oscillation parameters. By treating shared flux and cross-section uncertainties as fully correlated across experiments, the analysis achieves a precision on $\Delta m^2_{31}$ and $\sin^2\theta_{23}$ competitive with accelerator-based measurements and provides an independent constraint on the CP-violating phase $\delta_{\mathrm{CP}}$. The central result is a strong preference for the normal neutrino mass ordering over the inverted ordering, with $\Delta\chi^2 = 11.0$ between the two hypotheses. Calibrated with pseudoexperiments, the inverted ordering is excluded at $3.3\sigma$ (99.95% confidence level). This finding is driven by coherent Earth-matter effects across the three detectors and offers an independent determination of the neutrino mass ordering, a key unknown in particle physics.

What carries the argument

The analysis constructs a combined binned Poisson likelihood that simultaneously fits all event samples from the three experiments. Shared nuisance parameters for the atmospheric neutrino flux and neutrino–water cross sections are fully correlated across experiments, while detector-response uncertainties are experiment-specific. The fit uses the PyNu framework with nuSQuIDS for neutrino propagation through the Earth, and achieves a 930-bin joint fit. For Super-Kamiokande, a high-statistics Monte Carlo simulation with GENIE and tune kernels matching the official release is used; a bug in the true-energy quantiles was identified and corrected via private communication with the collaboration. The mass-ordering significance is assessed via pseudoexperiments because the two hypotheses are non-nested, and Wilks' theorem does not apply.

Extended reading notes

Core claim

The combined fit of atmospheric neutrino data from Super-Kamiokande, IceCube-DeepCore, and KM3NeT/ORCA6 yields $\Delta m^2_{31} = 2.44^{+0.06}_{-0.04} \times 10^{-3}\,\mathrm{eV}^2$, $\sin^2\theta_{23} = 0.52^{+0.03}_{-0.04}$, and $\delta_{\mathrm{CP}} = 1.30^{+0.24}_{-0.28}\,\pi$. The most significant result is the preference for the normal neutrino mass ordering over the inverted ordering, with a test statistic $\Delta\chi^2 = 11.0$ that, after calibration with pseudoexperiments, corresponds to a $p$-value for the inverted ordering of $p_{\mathrm{IO}} = 4.55 \times 10^{-4}$ ($3.3\sigma$ exclusion). This preference arises from the MSW and parametric matter-effect resonances in the Earth, which enhance neutrino conversion in the 2–10 GeV range for the normal ordering and are consistently observed by all three experiments.

Load-bearing premise

The tune kernels (artificial reweights) used to match the Super-Kamiokande Monte Carlo to the official data release leave an imprint on the unoscillated true energy distributions, and the corrected SK data release (bug-fixed via private communication) may introduce biases that affect the mass-ordering preference, especially since the tune kernels are not independently validated by the collaboration.

Editorial extensions

If this is right

If the normal ordering is confirmed, it would rule out the inverted ordering with high confidence, directly impacting searches for neutrinoless double-beta decay and cosmological mass-sum constraints.
The combined $\Delta\chi^2 = 16.0$ from this atmospheric analysis and reactor experiments (JUNO, Daya Bay) would bring the mass-ordering determination close to $4\sigma$, further tightening the case.
The independent constraint on $\delta_{\mathrm{CP}}$ helps resolve tensions between T2K and NOvA, as the atmospheric data favor values around $1.3\pi$, consistent with T2K's preferred region and providing cross-checks for accelerator-based measurements.
The correlated systematic treatment improves precision on $\sin^2\theta_{23}$ and $\delta_{\mathrm{CP}}$ beyond naive combination, demonstrating a methodology valuable for future multi-experiment analyses.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The analysis suggests that a global network of atmospheric neutrino detectors, when combined with correlated systematics, can provide competitive and complementary results to long-baseline experiments, potentially reducing the need for dedicated beam-based mass-ordering measurements.
The fact that the preference for normal ordering emerges coherently from three detectors with different systematics and media implies that systematic uncertainties are well under control; future data from JUNO, IceCube Upgrade, and full ORCA will likely further strengthen this conclusion.

Original abstract

We present a combined analysis of the latest publicly available atmospheric neutrino data from Super-Kamiokande including all data-taking stages previous to the gadolinium phase, IceCube-DeepCore, and the six-detection-unit configuration of KM3NeT/ORCA. Our fit uses all event samples simultaneously and treats the systematic uncertainties shared among experiments as fully correlated, while detector-response uncertainties are modeled independently for each experiment. The combined data constrain the atmospheric oscillation parameters to $\Delta m^2_{31} = 2.44^{+0.06}_{-0.04} \times 10^{-3}\,\mathrm{eV}^2$ and $\sin^2\theta_{23} = 0.52^{+0.03}_{-0.04}$, with a precision of $2.2\%$ and $6.1\%$, respectively, which is competitive with current accelerator-based measurements, and independently constrain the $CP$-violating phase to $\delta_{CP} = 1.30^{+0.24}_{-0.28}~\pi$. Finally, comparing the orderings of the neutrino mass spectrum, we find a preference for the normal ordering with $\Delta\chi^2 = 11.0$; further calibrated with pseudoexperiments, we exclude the inverted ordering at $99.95\%$ confidence level ($3.3\sigma$). In a joint fit including 207 days of JUNO data, we further exclude the inverted ordering at $\Delta \chi^2 = 15.1$, corresponding to $3.9 \sigma$.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-10-09: 1 request, 3,333 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.19 · human participants 0.02 · controlled comparison 0.18 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.82 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We present a combined analysis of the latest publicly available atmospheric neutrino data from Super-Kamiokande including all data-taking stages previous to the gadolinium phase, IceCube-DeepCore, and the six-detection-unit configuration of KM3NeT/ORCA. Our fit uses all event samples simultaneously and treats the systematic uncertainties shared among experiments as fully correlated, while detector-response uncertainties are modeled independently for each experiment. %We measure The combined data constrain the atmospheric oscillation parameters to $\Delta m^2_{31} = 2.44^{+0.06}_{-0.04} \times 10^{-3}\,\mathrm{eV}^2$ and $\sin^2\theta_{23} = 0.52^{+0.03}_{-0.04}$, with a precision of $2.2\%$ and $6.1\%$, respectively, which is competitive with current accelerator-based measurements, and independently constrain the $CP$-violating phase to $\delta_{CP} = 1.30^{+0.24}_{-0.28}~\pi$. Finally, comparing the orderings of the neutrino mass spectrum, we find a preference for the normal ordering with $\Delta\chi^2 = 11.0$; further calibrated with pseudoexperiments, we exclude the inverted ordering at $99.95\%$ confidence level ($3.3\sigma$).

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We present a combined analysis of the latest publicly available atmospheric neutrino data from Super-Kamiokande including all data-taking stages previous to the gadolinium phase, IceCube-DeepCore, and the six-detection-unit configuration of KM3NeT/ORCA.	contribution 0.57	0.84	0.02	asserted 0.94
s1	Our fit uses all event samples simultaneously and treats the systematic uncertainties shared among experiments as fully correlated, while detector-response uncertainties are modeled independently for each experiment. %We measure The combined data constrain the atmospheric oscillation parameters to $\Delta m^2_{31} = 2.44^{+0.06}_{-0.04} \times 10^{-3}\,\mathrm{eV}^2$ and $\sin^2\theta_{23} = 0.52^{+0.03}_{-0.04}$, with a precision of $2.2\%$ and $6.1\%$, respectively, which is competitive with current accelerator-based measurements, and independently constrain the $CP$-violating phase to $\delta_{CP} = 1.30^{+0.24}_{-0.28}~\pi$.	result 0.56	0.91	0.09	asserted 0.98
s2	Finally, comparing the orderings of the neutrino mass spectrum, we find a preference for the normal ordering with $\Delta\chi^2 = 11.0$; further calibrated with pseudoexperiments, we exclude the inverted ordering at $99.95\%$ confidence level ($3.3\sigma$).	result 1.00	0.97	0.90	asserted 1.00

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from analysis of existing data 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 6.** FIG. 6. True energy distribution of high-statistics SK MC we develop after applying tune tensors to match for the SK

Showing 1 of the paper's 15 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:2610.12208 by the authors.

Discussion

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