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A Measurement of Atmospheric Neutrino Oscillation Parameters by Super-Kamiokande I

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Super-Kamiokande Collaboration

High Energy Physics - Experiment · Submitted 25 Jan 2005 · 86 references

Pith's verdict: The SK-I combined fit is the reference measurement it claims to be; the one thing to press on is that the text's claim about nuisance-parameter pulls is contradicted by its own tables, which slightly oversells the precision of the quoted Δm² window.

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arXiv IDhep-ex/0501064 (version 2)
Pith ID2E54I5XF, Pith's permanent record of this paper and its review
CitationSuper-Kamiokande Collaboration. "A Measurement of Atmospheric Neutrino Oscillation Parameters by Super-Kamiokande I." arXiv:hep-ex/0501064 (2005). https://pith.science/paper/2E54I5XF
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The paper

The paper claims

Super-Kamiokande reports that muon neutrinos disappear in proportion to how far they travel, and fits the disappearance with a single two-flavour oscillation.

The reading

Super-Kamiokande is trying to establish that the shortfall of muon neutrinos in its atmospheric data is a genuine quantum-mechanical disappearance of one neutrino flavour into another over distance, not a miscalculation of the atmospheric flux. The detector watched 22.5 kilotons of water for 1489 live days and sorted roughly 15,000 candidate events into fully contained, partially contained, and upward-going muon samples, spanning neutrino energies from 100 MeV to 10 TeV and flight paths from about 15 km to the diameter of the Earth. The claim is that one two-flavour $v_mu leftrightarrow v_tau$ formula, with a single mixing angle and a single mass-squared difference, reproduces the observed zenith-angle and energy dependence across that entire range, while the electron-flavour sample stays where the no-oscillation prediction puts it. If that holds, the deficit is a property of neutrino propagation rather than of the atmosphere, and $sin^2 2 heta$ and $Delta m^2$ become measured quantities rather than fitted preferences. The paper's own summary numbers are $sin^2 2 heta > 0.92$ and $1.5 imes 10^{-3} < Delta m^2 < 3.4 imes 10^{-3}~mathrm{eV}^2$ at 90% confidence.

What carries the argument

The machinery is a forward-folding fit rather than an event-by-event reconstruction of energy and path length. Each simulated event carries its true neutrino energy $E_v$ and flight distance $L$ from the Monte Carlo, and is reweighted by the two-flavour survival probability $P = 1 - sin^2 2 heta , sin^2(1.27 Delta m^2 L / E_v)$ before binning, so that the oscillation parameters enter as a smooth reweighting of a fixed simulated sample. The reweighted prediction is compared with data in 180 bins: 150 for fully contained events split by particle identification and logarithmically spaced momentum, 10 for partially contained events, and 10 each for upward stopping and upward through-going muons, all divided into ten zenith-angle bins. Thirty-nine systematic parameters are floated in the fit, of which thirty-eight are constrained by Gaussian penalty terms and one — the absolute normalization — is left free, so the fit is effectively a constrained $chi^2$ minimization in which flux, cross-section, and detector uncertainties are pulled to their best-fit values rather than fixed. The zenith-angle asymmetry is what carries the argument: because the unoscillated flux is predicted to be nearly up-down symmetric above a few GeV, any measured asymmetry is read as oscillation.

Extended reading notes

Core claim

The central claim is that the full Super-Kamiokande I atmospheric data set is consistent with $v_mu leftrightarrow v_tau$ oscillations and inconsistent with no oscillation at overwhelming significance. Fitting 180 bins of lepton flavour, momentum, and zenith angle, the best fit sits at $sin^2 2 heta = 1.00$ and $Delta m^2 = 2.1 imes 10^{-3}~mathrm{eV}^2$ with $chi^2_{min} = 174.8$ for 177 degrees of freedom, against $chi^2 = 478.7$ for 179 degrees of freedom when oscillations are switched off. The shape of the evidence is an up-down asymmetry that appears in muon-like events and not in electron-like ones: the ratio of upward to downward multi-GeV single-ring muon events plus partially contained events is $0.551^{+0.035}_{-0.033}$, more than twelve standard deviations from unity, while the corresponding electron-like ratio is $0.961^{+0.086}_{-0.079}$. The upward-going muon samples show the same pattern in a different energy regime, with a stopping-to-through-going ratio of $0.229 pm 0.015$ against a prediction of $0.430 pm 0.065$. The quoted 90% confidence intervals, $sin^2 2 heta > 0.92$ and $1.5 imes 10^{-3} < Delta m^2 < 3.4 imes 10^{-3}~mathrm{eV}^2$, are the paper's headline result.

Load-bearing premise

The fit treats the unoscillated atmospheric neutrino flux as up-down symmetric and known in shape to the roughly 1 to 2 percent precision assigned to it, so an intrinsic asymmetry of that size in the real flux would be absorbed into the fitted $Delta m^2$.

Editorial extensions

If this is right

  • The mass-squared splitting is pinned to a narrow window, $1.5 imes 10^{-3} < Delta m^2 < 3.4 imes 10^{-3}~mathrm{eV}^2$ at 90% confidence, which fixes the distance scale over which muon neutrinos convert and sets the target for long-baseline beam experiments.
  • The mixing angle is near maximal, $sin^2 2 heta > 0.92$, meaning the muon neutrino is close to an equal mixture of two mass states and its disappearance can be nearly complete at the right distance-to-energy ratio.
  • Because the electron-flavour zenith distribution matches the no-oscillation prediction while the muon-flavour one does not, the data single out muon-neutrino disappearance rather than an electron-neutrino appearance channel, which excludes a two-flavour $v_mu leftrightarrow v_e$ explanation by a $chi^2$ difference of more than 100.
  • Six independent subsamples — low- and high-momentum sub-GeV single-ring, multi-GeV single-ring, partially contained, multi-ring, and upward-going muon — each fit to consistent parameter regions, so the result does not rest on any one event class.
  • The result is stable against swapping the atmospheric flux calculation and against swapping the neutrino interaction Monte Carlo, which bounds how much of the fitted parameter region is an artifact of a single simulation chain.

Reading between the lines

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

  • The paper's exclusion of the sterile-neutrino alternative is argued from the absence of matter-induced suppression and from the up-down symmetry of the multi-ring sample, but the quantitative fit for that alternative is deferred to later publications; a reader wanting the actual $chi^2$ comparison will not find it here.
  • Because all three flux calculations compared in the paper draw on much of the same primary cosmic-ray data, the agreement among them bounds hadronic-interaction modelling more than it bounds the primary spectrum; an independent cosmic-ray measurement at the relevant rigidities would test the assumption more sharply than a fourth flux model would.
  • The slight excess of partially contained events at the highest visible energies, noted by the authors as possibly indicating a neutrino spectrum that is too soft around 100 GeV, is a residual that a future flux calculation with a harder high-energy tail could absorb — and that would in turn shift the upward through-going muon prediction.
  • The quoted $Delta m^2$ window is broad enough that the same data are consistent with any value between roughly 2.0 and $2.5 imes 10^{-3}~mathrm{eV}^2$ almost equally well, so the practical precision on the splitting comes from the separate $L/E$ analysis rather than from this zenith-angle fit.
Original abstract

We present a combined analysis of fully-contained, partially-contained and upward-going muon atmospheric neutrino data from a 1489 day exposure of the Super--Kamiokande detector. The data samples span roughly five decades in neutrino energy, from 100 MeV to 10 TeV. A detailed Monte Carlo comparison is described and presented. The data is fit to the Monte Carlo expectation, and is found to be consistent with neutrino oscillations of $\nu_\mu \leftrightarrow \nu_\tau$ with $\sin^22\theta > 0.92$ and $1.5\times 10^{-3} < \Delta m^2 < 3.4\times 10^{-3}{\rm eV}^2$ at 90% confidence level.

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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,774 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.17 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.31 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We present a combined analysis of fully-contained, partially-contained and upward-going muon atmospheric neutrino data from a 1489 day exposure of the Super--Kamiokande detector. The data samples span roughly five decades in neutrino energy, from 100 MeV to 10 TeV. A detailed Monte Carlo comparison is described and presented. The data is fit to the Monte Carlo expectation, and is found to be consistent with neutrino oscillations of $\nu_\mu \leftrightarrow \nu_\tau$ with $\sin^22\theta > 0.92$ and $1.5\times 10^{-3} < \Delta m^2 < 3.4\times 10^{-3}{\rm eV}^2$ at 90% confidence level.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present a combined analysis of fully-contained, partially-contained and upward-going muon atmospheric neutrino data from a 1489 day exposure of the Super--Kamiokande detector. contribution 0.58 0.96 0.03 asserted 0.96
s1 The data samples span roughly five decades in neutrino energy, from 100 MeV to 10 TeV. method 0.95 0.80 0.02 asserted 0.98
s2 A detailed Monte Carlo comparison is described and presented. method 0.97 0.87 0.02 asserted 0.81
s3 The data is fit to the Monte Carlo expectation, and is found to be consistent with neutrino oscillations of $\nu_\mu \leftrightarrow \nu_\tau$ with $\sin^22\theta > 0.92$ and $1.5\times 10^{-3} < \Delta m^2 < 3.4\times 10^{-3}{\rm eV}^2$ at 90% confidence level. result 1.00 0.96 0.95 hedged possibility 0.75

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from observation or experiment 0.78.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
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 1. FIG. 1: The parent neutrino energy distributions for the ful
Figure 2. FIG. 2: (a) The direction averaged atmospheric neutrino ene
Figure 3. FIG. 3: The flux ratio of
Figure 4. shows the calculated flux ratios of νµ to νµ and νe to νe. The calculations agree to about 5 % for both of these ratios below 10 GeV. However, the disagreement gets larger above 10 GeV as a function of neutrino energy. The sys￾tematic errors in the ν/ν ratio are assumed to be 5 % below 10 GeV and linearly increase with logEν to 10 % and 25 % at 100 GeV, for the νe to νe and νµ to νµ ratios, respectively
Figure 6. FIG. 6: The flux of upward-going atmospheric neutrinos versu
Figure 7. FIG. 7: The calculated flight length of neutrinos for vertica
Figure 8. FIG. 8: A drawing of the Super-Kamiokande detector. The cuta
Figure 11. FIG. 11: The mean reconstructed energy of cosmic ray stoppin
Figure 12. FIG. 12: The gain uniformity of the Super-Kamiokande detect
Figure 13. FIG. 13: The gain uniformity of the Super-Kamiokande detect
Figure 14. FIG. 14: The scattering angle distribution by neutrino inte
Figure 15. FIG. 15: Charged current total cross section divided by
Figure 16. FIG. 16: The number of hits in the largest outer detector clus
Figure 17. FIG. 17: The distribution of fully-contained event vertice
Figure 18. FIG. 18: The distribution of the likelihood difference betw
Figure 19. FIG. 19: The distribution of the number of identified Cherenk
Figure 22. FIG. 22: The distribution of particle identification likeli
Figure 23. FIG. 23: Particle ID likelihood distribution for sub-GeV (t
Figure 24. FIG. 24: The distribution of partially-contained event ver
Figure 25. FIG. 25: The zenith versus azimuth directions for a 641.4 day
Figure 26. FIG. 26: The zenith angle distribution of upward muon candid
Figure 27. FIG. 27: Event rates as a function of elapsed SK running time fo
Figure 29. FIG. 29: Visible energy distribution of multi-ring
Figure 30. FIG. 30: Expected
Figure 31. FIG. 31: The zenith angle distribution for fully-contained
Figure 33. FIG. 33: The azimuth distribution of the sample of events sel
Figure 35. FIG. 35: Event rates as a function of elapsed SK running time fo
Figure 36. FIG. 36: Expected ratio of vertical to horizontal upward thr
Figure 37. FIG. 37: Expected ratio of stopping to through-going upward
Figure 38. FIG. 38: Allowed oscillation parameters for
Figure 41. FIG. 41: Left: 90 % confidence level allowed oscillation para
Figure 42. FIG. 42: The 68, 90 and 99 % confidence level allowed oscilla

Showing 32 of the paper's 42 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ex/0501064 by the authors.

References
How later papers used it

129 later papers cite it

Evidence: substantial. 121 of the citing papers share no author with it, and 34 of those carry a confident label from Pith's citation classifier.

Pith read 30 of the 184 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

Uses its data or values 11 of 26 papers with this label
How the literature uses it

106 arXiv papers cite this in 154 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 85 sentences without a confident label

Uses its method or tool 8 papers
Uses its data or values 25 papers
  • The total mass target in Deep Core for incoming neutrino is taken from the effective volume estimated (for each energy) in [ref] , without online veto.

    Foreseeing Neutrino spectra in Deep Core · From the atmospheric cosmic ray to the event rate in Deep Core · 0.97

  • The effective cross-section can be estimated from Ref. [ref] by dividing the estimated rate of events by the predicted atmospheric flux, integrated over the relevant range of energies.

    Testing the Dark Matter Interpretation of the DAMA/LIBRA Result with Super-Kamiokande · Projection of Super-K Sensitivity · 0.95

  • The Super-K collaboration reports [ref] that, for $E_ν_μ 4 GeV$, they expect less than 20 fully-contained muon events (in the cone of the sun) per GeV neutrino energy bin per 1000 live days running time due to atmospheric neutrinos (the rate falls to 2 events per GeV per 1000 live days at $E_ν_μ ∼10 GeV$).

    Light Dark Matter Detection Prospects at Neutrino Experiments · Limits for a liquid scintillator detector · 1.00

Compares with it 2 papers
  • Taking into account both the absence of narrow e$^+$e$^-$ pairs pointing directly to the beam direction and the presence of several high energy charged current events (for instance, 25$±$5 events with deposited energy in excess of 25 GeV are present in Fig. [ref] against 18$±$1.3 expected), we can set the limit $δ< 2.5·10^-8$ at 90% CL for CNGS neutrinos[$δ=2.5·10^-8$ corresponds to a 10% probability of observing zero events for an exposure of $6.70 ·10^21$ t$·$pot], comparable to the limit $δ< 1.4·10^-8$ established by SuperKamiokande [ref] from the lack of depletion of atmospheric neutrinos, and somewhat larger than the lower energy velocity constraint $δ< 4·10^-9$ from SN1987a [ref] .

    A search for the analogue to Cherenkov radiation by high energy neutrinos at superluminal speeds in ICARUS · Experimental results and related constraints · 0.98

  • We show in Fig. [ref] the differential event-rate per 1000 days as a comparison between our results for fully contained electron (left) and muon (right) neutrinos, compared with the data from Fig. 1 of [ref] shown as a solid blue line.

    Searching for Sub-GeV Dark Matter in the Galactic Centre using Hyper-Kamiokande · Validation · 0.89

Cites it as background 23 papers

Discussion

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