The Moon as a searching ground for proton decay: validating the lunar low-background advantage and the feasibility of a beyond-terrestrial proton-decay experiment

In 1986 Pati, Salam and Sreekantan proposed the Moon as a searching ground for proton decay: with no atmosphere, cosmic-ray secondaries on the Moon interact in the dense regolith before decaying, so the atmospheric-neutrino background that irreducibly limits terrestrial proton-decay searches is strongly suppressed; they estimated a net background reduction of at least $\sim200\times$ for a detector under $\gtrsim100$ m of lunar rock and projected unambiguous sensitivity to nucleon lifetimes up to $\sim10^{34}$ years for a 10–20 kton detector whose equipment (of order 50–150 metric tons) would be transported from Earth. No lunar proton-decay experiment was ever built or designed in detail, and the proposal accumulated almost no citations. Independent modern work has confirmed the core physics — calculations of the cosmic-ray-induced neutrino flux from the Moon find it suppressed by one to four orders of magnitude relative to Earth's atmospheric flux in the relevant energy range — and a 2024 concept proposes lunar paleo-detectors (billion-year-old minerals read out for kaon-endpoint tracks from $p\to\bar\nu K^{+}$ decay) that could probe beyond Super-Kamiokande's current limit and be competitive with the projected reach of Hyper-Kamiokande and DUNE. The open problem is to convert this qualitative lunar advantage into a validated experimental program: establishing the residual neutrino, muon and neutron backgrounds at a lunar underground site with controlled uncertainties (modern flux calculations still disagree at the factor-of-few to order-of-magnitude level), demonstrating the enabling technology (for the paleo route, track formation and billion-year retention of lattice damage at $10^{2}$–$10^{3}$ MeV/cm stopping powers plus readout with particle identification; for the active route, transport, assembly and long-term detector operation on the Moon), and delivering a technically credible design whose sensitivity projection for proton lifetimes in the $\sim10^{34}$–$10^{35}$-year regime either justifies or rules out a lunar proton-decay experiment.

Background

Proton decay is the hypothetical disintegration of the proton — the lightest baryon, whose stability in the Standard Model follows only from an accidental conservation of baryon number (protons plus neutrons, minus antibaryons) — into lighter particles such as a positron plus a neutral pion ($p\to e^{+}\pi^{0}$) or an antineutrino plus a charged kaon ($p\to\bar\nu K^{+}$). Grand Unified Theories (GUTs), which embed the Standard Model's three forces into a single symmetry at very high energies, generically predict proton lifetimes between roughly $10^{32}$ and $10^{40}$ years, so proton decay is a flagship experimental test of physics beyond the Standard Model. Searches since the 1980s use massive detectors deep underground; the leading one is Super-Kamiokande, a 50-kton water-Cherenkov detector (a tank of ultra-pure water instrumented with photomultipliers that images the Cherenkov light of charged particles) in a Japanese mine, which currently bounds the partial lifetime $\tau/B(p\to e^{+}\pi^{0})>2.4\times10^{34}$ years. The next-generation detectors Hyper-Kamiokande (water Cherenkov, approximately 200 kton) and DUNE (liquid argon, 40 kton) will probe the $10^{34}$–$10^{35}$-year regime. On Earth the limiting background is atmospheric neutrinos — neutrinos produced when cosmic rays strike Earth's atmosphere. At the approximately GeV energies relevant to proton decay they cannot be shielded, and some of their interactions in or near the detector imitate proton-decay final states. Topological cuts — event selections rejecting interactions whose visible pattern is inconsistent with a two-body decay of a proton at rest — reduce this background by roughly $100\times$ in fine-grained detectors (detectors with many small sensitive cells interleaved with absorber layers), but the residual is irreducible on Earth and becomes comparable to the expected signal as the proton lifetime approaches $10^{34}$ years; scaling conventional detectors far beyond the approximately 100-kton scale is regarded as unaffordable. In 1986 Pati, Salam and Sreekantan observed that the Moon escapes this background at its origin. The Moon has essentially no atmosphere, so primary cosmic rays strike the regolith (the layer of fragmented rock covering the bedrock) directly; in the dense rock, the charged pions and kaons produced in the hadronic cascade undergo nuclear interactions (mean free path below $\sim0.5$ m) long before they can decay (a 2-GeV pion travels $\sim110$ m before decaying), so the conventional cosmic-ray-induced neutrino flux — the component from pion and kaon decay — is strongly suppressed, and muons produced at the surface range out within meters. They estimated that a detector under $\gtrsim100$ m of lunar rock would see a net neutrino background at least $\sim200\times$ smaller than at a terrestrial site, so a 10–20-kton modular fine-grain detector — modules stacked from 10-cm lunar-rock absorber slabs and gas-discharge counter layers, with only of order 50–150 metric tons of equipment to be transported from Earth and assembled in a tunnel beneath a crater — could probe nucleon lifetimes up to $\sim10^{34}$ years unambiguously in a 20-kiloton-year exposure. The authors themselves flagged what remained unresolved: the engineering, logistical and financial feasibility; the poorly known lunar subsurface geology and its secondary neutron and hadron production and transport; the practicality of detection media, counter gas supplies, reliability and maintenance on the Moon, and whether terrestrial topological rejection factors can be matched; the uncertain galactic and extragalactic neutrino fluxes entering the residual background; and the absence of the optimized designs and detailed simulations needed to validate the asserted background reductions and sensitivity. The physical premise has since been independently confirmed: modern semi-analytic and Monte-Carlo calculations find the cosmic-ray-induced neutrino flux from the Moon suppressed by one to four orders of magnitude relative to Earth's atmospheric flux over the relevant energy range — about $10\times$ and $100\times$ at 0.1 and 1 GeV in the most recent study, and approaching $10^{4}$ above 10 GeV in the earlier semi-analytic calculation — with muon fluxes similarly suppressed at depth, and the same logic now motivates proposals for lunar dark-matter detectors. In 2024 Baum, Little, Sala, Spitz and Stengel proposed a different realization for proton decay: lunar paleo-detectors, i.e. ancient minerals such as olivine that record lattice damage from charged particles over geological times, retrieved from several kilometers depth. In the $p\to\bar\nu K^{+}$ channel the charged kaon from a decay travels a few centimeters depositing too little energy to leave permanent damage, then produces a short kaon-endpoint track where its stopping power (energy loss per unit length, $dE/dx$, which rises steeply near the end of a particle's range at the Bragg peak) exceeds the threshold for damage stable on billion-year timescales. In the Moon-suppressed neutrino field they estimate $\sim0.5$ neutrino-induced kaon endpoints per 100 g of mineral per billion years, versus $\sim400$ on Earth, giving sensitivity beyond $10^{34}$ years in the kaon channel, provided samples can be retrieved from $\gtrsim5$ km depth and read out with particle-identifying microscopy. Whether either route — the original active detector in a lunar tunnel, or retrieved lunar paleo-detectors — can actually deliver a proton-decay search beyond the terrestrial program remains unestablished: the enabling track physics at low stopping powers, the readout technology, access to kilometer-scale depth, the few-GeV neutrino reactions that produce kaon backgrounds, and the exact level of the lunar neutrino flux itself are all unproven or contested.

Problem Statement

Establish, with validated calculations, demonstrated or quantitatively bounded enabling technology, and a technically credible experimental concept, whether the Moon can serve as the searching ground for proton decay that Pati, Salam and Sreekantan proposed in 1986 — that is, whether proton-lifetime sensitivity in the $\sim10^{34}$–$10^{35}$-year regime, meeting or exceeding the projected reach of the next-generation terrestrial detectors (Hyper-Kamiokande and DUNE), can actually be achieved there. As one joint scientific objective, the problem requires: (i) determining the residual cosmic-ray-induced neutrino, muon and neutron backgrounds at a lunar underground site at the depth required for shielding, with controlled uncertainties — resolving the present factor-of-few to order-of-magnitude disagreements between modern lunar neutrino-flux calculations and the poorly measured few-GeV neutrino reactions, especially those producing charged kaons, the irreducible background to the $p\to\bar\nu K^{+}$ signal; (ii) establishing the achievable signal efficiency and background rejection of candidate experimental realizations — an active detector assembled and operated in a lunar tunnel, or ancient lunar minerals read out as paleo-detectors after retrieval from kilometer-scale depth — including, for the paleo route, whether charged particles at stopping powers of $10^{2}$–$10^{3}$ MeV/cm form lattice damage stable on billion-year timescales and whether a readout with particle identification over approximately 100 g-scale mineral volumes is possible, and, for the active route, whether terrestrial topological rejection factors can be matched in a lunar implementation; and (iii) deriving from (i) and (ii) a defensible sensitivity projection, with uncertainty budget, that either establishes a concrete feasible design reaching beyond the terrestrial program, or demonstrates that the lunar advantage cannot be exploited. The observation of proton decay itself is not part of this problem.

References

1. J. C. Pati, Abdus Salam, and B. V. Sreekantan, 'The Moon as the Searching Ground for Proton Decay', International Journal of Modern Physics A 1(01), 147–153 (1986), DOI: 10.1142/S0217751X86000071, https://doi.org/10.1142/s0217751x86000071.
2. J. C. Pati, Abdus Salam, and B. V. Sreekantan, 'The moon as the searching ground for proton decay', AIP Conference Proceedings 202, 297–304 (1990), workshop 'Physics and Astrophysics from a Lunar Base', Stanford, CA, DOI: 10.1063/1.39114, https://doi.org/10.1063/1.39114.
3. J. Rich, D. Lloyd Owen, and M. Spiro, 'Experimental particle physics without accelerators', Physics Reports 151, 239–364 (1987), DOI: 10.1016/0370-1573(87)90055-X, https://doi.org/10.1016/0370-1573(87)90055-X.
4. P. K. Patra and M. K. Parida, 'Spontaneous-compactification effects on SO(10) grand unification with $SU(2)_L \times SU(2)_R \times SU(4)_C$ intermediate symmetry', Physical Review D 44, 2179–2187 (1991), DOI: 10.1103/PhysRevD.44.2179, https://doi.org/10.1103/PhysRevD.44.2179.
5. D. B. Cline, 'Proton Decay and Neutrino Burst Observatory on the Moon', UCLA preprint UCLA-01-89-APH0012 (February 1990, unpublished), INSPIRE record: https://inspirehep.net/literature/294512.
6. T. L. Wilson, 'Particle astronomy and particle physics from the moon: The particle observatory', AIP Conference Proceedings 207, 608–621 (1990), workshop 'Astrophysics from the Moon', Annapolis, MD, DOI: 10.1063/1.39353, https://doi.org/10.1063/1.39353.
7. R. S. Miller and T. Cohen, 'Cosmic-ray induced neutrino fluxes at the Moon: A semi-analytic approach', Astroparticle Physics 25(6), 368–374 (2006), DOI: 10.1016/j.astropartphys.2006.03.009, https://doi.org/10.1016/j.astropartphys.2006.03.009.
8. S. Demidov and D. Gorbunov, 'Lunar neutrinos', Physical Review D 104, 043023 (2021), DOI: 10.1103/PhysRevD.104.043023, arXiv:2012.12870, https://arxiv.org/abs/2012.12870.
9. Andréa Gaspert, Pietro Giampa, Navin McGinnis, and David E. Morrissey, 'Dark matter direct detection on the Moon', Physical Review D 108, 115015 (2023), DOI: 10.1103/PhysRevD.108.115015, arXiv:2305.04943, https://arxiv.org/abs/2305.04943.
10. Sebastian Baum, Cassandra Little, Paola Sala, Joshua Spitz, and Patrick Stengel, 'The Final Frontier for Proton Decay', arXiv:2405.15845 [hep-ph] (2024), DOI: 10.48550/arXiv.2405.15845, https://arxiv.org/abs/2405.15845.
11. Xilin Zhang, Jason Detwiler, and Clint Wiseman, 'The lowest-radiation environments in the Solar System: new opportunities for underground rare-event searches', arXiv:2411.09634 [hep-ex] (2024), DOI: 10.48550/arXiv.2411.09634, https://arxiv.org/abs/2411.09634.
12. A. Takenaka et al. (Super-Kamiokande Collaboration), 'Search for proton decay via p to e+ pi0 and p to mu+ pi0 with an enlarged fiducial volume in Super-Kamiokande I-IV', Physical Review D 102, 112011 (2020), DOI: 10.1103/PhysRevD.102.112011, arXiv:2010.16098, https://arxiv.org/abs/2010.16098.