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Search for proton decay via p to e⁺π⁰π⁰ and p to μ⁺π⁰π⁰ in 0.401 megaton-years exposure of Super-Kamiokande I-V
Pith reviewed 2026-05-10 16:22 UTC · model grok-4.3
The pith
Super-Kamiokande sets lower limits on proton lifetime above 4.5 times 10 to the 33 years for two three-body decay modes.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
We searched for proton decay via p to e+ pi0 pi0 and p to mu+ pi0 pi0 in 0.401 megaton-years of data collected in all pure water detector phases of Super-Kamiokande I-V. One data candidate event was found for each of the two decay modes, which is consistent with the expected atmospheric neutrino background. We set lower limits on the lifetime of tau over B(p to e+ pi0 pi0) greater than 7.2 times 10 to the 33 years and tau over B(p to mu+ pi0 pi0) greater than 4.5 times 10 to the 33 years at 90 percent confidence level.
What carries the argument
Event selection and background subtraction in the water Cherenkov detector to distinguish potential three-body proton decay signals from atmospheric neutrino interactions across the full detector exposure.
Load-bearing premise
The background from atmospheric neutrinos is accurately modeled and the detector efficiency for these decay modes is correctly estimated without significant systematic uncertainties affecting the limit calculation.
What would settle it
An observed number of events with the expected decay kinematics significantly above the predicted atmospheric neutrino background rate would indicate the presence of proton decay.
Figures
read the original abstract
We searched for proton decay via $p \to e^{+}\pi^{0}\pi^{0}$ and $p \to \mu^{+}\pi^{0}\pi^{0}$ in 0.401 megaton-years of data collected in all pure water detector phases of Super-Kamiokande (SK) I-V. A theoretical study predicts proton decay rates without assuming a particular grand unified theory and suggests that three-body proton decays involving two pions can have decay rates comparable to those of $p \to e^{+}\pi^{0}$ and $p \to \mu^{+}\pi^{0}$. This is the first search for proton decay into a charged anti-lepton and two neutral pions in SK. One data candidate event was found for each of the two decay modes, which is consistent with the expected atmospheric neutrino background. We set lower limits on the lifetime of $\tau/B(p \to e^{+}\pi^{0}\pi^{0}) > 7.2 \times 10^{33}$ years and $\tau/B(p \to \mu^{+}\pi^{0}\pi^{0}) > 4.5 \times 10^{33}$ years at 90 $\%$ confidence level. These limits are more than one order of magnitude higher than those of the previous experiment.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript reports a search for the proton decay modes p → e⁺π⁰π⁰ and p → μ⁺π⁰π⁰ in 0.401 megaton-years of Super-Kamiokande I-V data. One candidate event is observed in each channel, stated to be consistent with atmospheric neutrino background expectations. This yields 90% CL lower limits of τ/B(p → e⁺π⁰π⁰) > 7.2 × 10³³ yr and τ/B(p → μ⁺π⁰π⁰) > 4.5 × 10³³ yr, more than an order of magnitude stronger than prior results. The search is the first of its kind in SK and is motivated by GUT-independent theoretical predictions for three-body decays.
Significance. If the background modeling and efficiency estimates hold, the result meaningfully tightens constraints on proton decay lifetimes for these modes, which could be comparable in rate to the two-body channels in some models. The large exposure and use of the full SK dataset are strengths; the paper follows conventional null-result limit-setting methods common to the field.
major comments (2)
- [§4 and §5] §4 (Analysis) and §5 (Results): The abstract and summary state that the single observed candidate per mode is 'consistent with the expected atmospheric neutrino background,' but neither the numerical expected background rate, its uncertainty, nor the signal efficiency (including total systematic error) is provided. These quantities are load-bearing for the 90% CL limit calculation; without them, it is not possible to verify that the limits are not inflated by an underestimated background or overestimated efficiency.
- [§5.1] §5.1 (Limit setting): The manuscript claims the limits are derived from standard procedures, but does not show the explicit likelihood or Feldman-Cousins construction used, nor how the one observed event and background expectation enter the calculation. This detail is required to confirm the quoted 90% CL values.
minor comments (2)
- [Abstract] The abstract would benefit from including the numerical expected background and efficiency values (even if only in a parenthetical) to allow readers to immediately assess the result.
- [§3] Figure captions and text should explicitly define all selection cuts and PID criteria used to identify the e⁺/μ⁺ + 2π⁰ topology.
Simulated Author's Rebuttal
We thank the referee for their careful and constructive review of our manuscript. The comments identify areas where additional explicit numerical details and procedural descriptions would improve clarity and verifiability. We address each major comment below and will revise the manuscript to incorporate the requested information.
read point-by-point responses
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Referee: [§4 and §5] §4 (Analysis) and §5 (Results): The abstract and summary state that the single observed candidate per mode is 'consistent with the expected atmospheric neutrino background,' but neither the numerical expected background rate, its uncertainty, nor the signal efficiency (including total systematic error) is provided. These quantities are load-bearing for the 90% CL limit calculation; without them, it is not possible to verify that the limits are not inflated by an underestimated background or overestimated efficiency.
Authors: We agree that explicitly quoting the numerical expected background rates (with uncertainties) and signal efficiencies (with total systematic uncertainties) is essential for independent verification of the limits. Although Sections 4 and 5 describe the background modeling and efficiency estimation procedures in detail, the manuscript does not tabulate the final numerical values in the abstract or summary. In the revised version we will add these quantities to the abstract and include a summary table in Section 5 that reports the observed events, expected background with uncertainty, signal efficiency with total systematic error, and the resulting 90% CL limits for both modes. revision: yes
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Referee: [§5.1] §5.1 (Limit setting): The manuscript claims the limits are derived from standard procedures, but does not show the explicit likelihood or Feldman-Cousins construction used, nor how the one observed event and background expectation enter the calculation. This detail is required to confirm the quoted 90% CL values.
Authors: We acknowledge that the current text refers to 'standard procedures' without reproducing the explicit likelihood function or the Feldman-Cousins ordering. The limits were obtained via a profile-likelihood implementation of the Feldman-Cousins method that incorporates the single observed event, the expected background, and all systematic uncertainties. In the revised manuscript we will expand Section 5.1 to show the likelihood expression, describe the Feldman-Cousins construction, and illustrate how the observed count and background expectation are combined to produce the quoted 90% CL lower limits. revision: yes
Circularity Check
No circularity: pure experimental limit from data vs. simulation
full rationale
This is an experimental search paper reporting lifetime lower limits from 0.401 Mton-yr of Super-Kamiokande data. One candidate event per mode is observed, stated to be consistent with expected atmospheric neutrino background. Limits are set via standard statistical procedures on observed vs. expected counts, incorporating efficiency from simulation. No derivation chain, first-principles result, or ansatz is claimed; the central result does not reduce by construction to any fitted parameter or self-citation. Background modeling and efficiency estimation are external inputs (Monte Carlo and control samples) and do not constitute circularity under the defined patterns. The paper is self-contained against external benchmarks.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption Atmospheric neutrino interactions produce the dominant background and can be reliably simulated
Reference graph
Works this paper leans on
-
[1]
R. L. Workmanet al.(Particle Data Group), Review of Particle Physics, PTEP2022, 083C01 (2022)
2022
-
[2]
Georgi and S
H. Georgi and S. L. Glashow, Unity of all elementary- particle forces, Phys. Rev. Lett.32, 438 (1974)
1974
-
[3]
Langacker, Grand unified theories and proton decay, Phys
P. Langacker, Grand unified theories and proton decay, Phys. Rep.72, 185 (1981)
1981
-
[4]
Ellis, M
J. Ellis, M. A. G. Garcia, N. Nagata, D. V. Nanopoulos, and K. A. Olive, Proton decay: Flipped vs. unflipped su(5), J. High Energy Phys.05, 021
-
[5]
Fritzsch and P
H. Fritzsch and P. Minkowski, Unified interactions of lep- tons and hadrons, Ann. Phys. (N.Y.)93, 193 (1975)
1975
-
[6]
K. S. Babu and S. Khan, Minimal nonsupersymmetric so(10) model: Gauge coupling unification, proton decay, and fermion masses, Phys. Rev. D92, 075018 (2015)
2015
-
[7]
M. B. Wise, R. Blankenbecler, and L. F. Abbott, Three- body decays of the proton, Phys. Rev. D23, 1591 (1981)
1981
-
[8]
Oset, Meson exchange currents in the p decay in nu- clei, Nucl
E. Oset, Meson exchange currents in the p decay in nu- clei, Nucl. Phys. B304, 10.1016/0550-3213(88)90656-6 (1988)
-
[9]
McGrewet al., Search for nucleon decay using the imb-3 detector, Phys
C. McGrewet al., Search for nucleon decay using the imb-3 detector, Phys. Rev. D59, 052004 (1999)
1999
-
[10]
Takenakaet al.(Super-Kamiokande Collaboration), Search for proton decay viap→e +π0 andp→µ +π0 with an enlarged fiducial volume in super-kamiokande i- iv, Phys
A. Takenakaet al.(Super-Kamiokande Collaboration), Search for proton decay viap→e +π0 andp→µ +π0 with an enlarged fiducial volume in super-kamiokande i- iv, Phys. Rev. D102, 112011 (2020)
2020
-
[11]
Mine, The super-kamiokande and other detectors: A case study of large volume cherenkov neutrino detectors (2025)
S. Mine, The super-kamiokande and other detectors: A case study of large volume cherenkov neutrino detectors (2025)
2025
-
[12]
Fukudaet al., The super-kamiokande detector, Nucl
S. Fukudaet al., The super-kamiokande detector, Nucl. Instrum. Methods Phys. Res., Sect. A501, 418 (2003)
2003
-
[13]
Abeet al., Calibration of the super-kamiokande de- tector, Nucl
K. Abeet al., Calibration of the super-kamiokande de- tector, Nucl. Instrum. Methods Phys. Res., Sect. A737, xi 253 (2014)
2014
-
[14]
Abeet al.(Super-Kamiokande Collaboration), First gadolinium loading to super-kamiokande, Nucl
K. Abeet al.(Super-Kamiokande Collaboration), First gadolinium loading to super-kamiokande, Nucl. Instrum. Methods Phys. Res., Sect. A1027, 166248 (2022)
2022
-
[15]
Abeet al.(Super-Kamiokande Collaboration), Second gadolinium loading to super-kamiokande, Nucl
K. Abeet al.(Super-Kamiokande Collaboration), Second gadolinium loading to super-kamiokande, Nucl. Instrum. Methods Phys. Res., Sect. A1065, 169480 (2024)
2024
-
[16]
Takenaka,Search for Proton Decay viap→e +π0 and p→µ +π0 with an Enlarged Fiducial Mass of the Super- Kamiokande Detector, Ph.D
A. Takenaka,Search for Proton Decay viap→e +π0 and p→µ +π0 with an Enlarged Fiducial Mass of the Super- Kamiokande Detector, Ph.D. thesis, University of Tokyo (2020), phD Thesis
2020
-
[17]
Wester,Discerning the neutrino mass ordering using atmospheric neutrinos in super-kamiokande I-V, Ph.D
T. Wester,Discerning the neutrino mass ordering using atmospheric neutrinos in super-kamiokande I-V, Ph.D. thesis, Boston university (2023), phD Thesis
2023
-
[18]
Nakamura, S
K. Nakamura, S. Hiramatsu, T. Kamae, H. Muramatsu, N. Izutsu, and Y. Watase, The reaction 12c(e, e ′p) at 700 mev and dwia analysis, Nuclear Physics A268, 381 (1976)
1976
-
[19]
M. G. Mayer and J. H. D. Jensen,Elementary Theory of Nuclear Shell Structure(Wiley, New York, 1955)
1955
-
[20]
Yamazaki and Y
T. Yamazaki and Y. Akaishi, Nuclear medium effects on invariant mass spectra of hadrons decaying in nuclei, Phys. Lett. B453, 1 (1999)
1999
-
[21]
Hayato, Neut, Nucl
Y. Hayato, Neut, Nucl. Phys. B, Proc. Suppl.112, 171 (2002)
2002
-
[22]
Mitsuka, Neut, AIP Conf
G. Mitsuka, Neut, AIP Conf. Proc.967, 208 (2007)
2007
-
[23]
Mitsuka, Aip conference proceedings, AIP Conf
G. Mitsuka, Aip conference proceedings, AIP Conf. Proc. 981, 262 (2008)
2008
-
[24]
Honda, T
M. Honda, T. Kajita, K. Kasahara, and S. Midorikawa, Improvement of low energy atmospheric neutrino flux cal- culation using the jam nuclear interaction model, Phys. Rev. D83, 123001 (2011)
2011
-
[25]
R. B. et al., Geant detector description and simulation tool, CERN ReportCERN-W5013(1994)
1994
-
[26]
Shiozawa, Reconstruction algorithms in the super- kamiokande large water cherenkov detector, Nucl
M. Shiozawa, Reconstruction algorithms in the super- kamiokande large water cherenkov detector, Nucl. In- strum. Methods Phys. Res., Sect. A433, 240 (1999)
1999
-
[27]
Amsleret al.(Particle Data Group), Review of particle physics, Phys
C. Amsleret al.(Particle Data Group), Review of particle physics, Phys. Lett. B667, 1 (2008)
2008
-
[28]
B. P. Roe and M. B. Woodroofe, Setting confidence belts, Phys. Rev. D63, 013009 (2000)
2000
-
[29]
Matsumotoet al.(Super-Kamiokande Collaboration), Search for proton decay via p→µ+ k 0 in 0.37 megaton- years exposure of super-kamiokande, Phys
R. Matsumotoet al.(Super-Kamiokande Collaboration), Search for proton decay via p→µ+ k 0 in 0.37 megaton- years exposure of super-kamiokande, Phys. Rev. D106, 072003 (2022)
2022
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