The all-particle cosmic-ray spectrum steepens at the knee (E0≃3E_0\simeq 3 PeV) and flattens again at the ankle (≃3×1018\simeq 3\times10^{18} eV); the origin of the knee is a decades-old open problem tied to the unknown mass composition of the primaries. Shaulov, Ryabov, Pyatovsky, Shepetov and Zhukov (SciPost Phys. Proc. 13, 014 (2023); arXiv:2206.12165) argued from extensive-air-shower (EAS) core data — scaling violation in secondary-hadron spectra and a muon excess starting exactly at the knee — together with the Tibet ASγ\gamma proton cutoff at rigidity R≃0.1R\simeq 0.1 PV that the flux between knee and ankle must be dominated by a non-nuclear component: stable strangelets (hypothetical strange-quark-matter particles with baryon number A∼103A\sim 10^3–10810^8 and charge Z∼30Z\sim 30–10001000). The open problem is to determine observationally whether such a component exists in the 33 PeV–33 EeV flux with the required abundance, to establish the actual rigidity scale of the nuclear spectral cutoffs (≃0.1\simeq 0.1 PV versus ≃3\simeq 3 PV, a discrepancy entangled with hadronic-interaction-model choices), and to decide, if strangelets are present, whether they also contribute to the extragalactic flux above the ankle; mass-composition information at E0≃1E_0\simeq 1–200200 PeV serves as the observational input to this adjudication. No direct experimental test of the strangelet hypothesis in the relevant charge, mass, and energy regime is known to date; existing strangelet searches cover only Z≤8Z\leq 8 and rigidity ≤103\leq 10^3 GV. The problem is open.

Background

Cosmic rays are atomic nuclei (and electrons) arriving at Earth from astrophysical accelerators. Their all-particle energy spectrum falls as a power law but steepens abruptly at the knee, E0≃3E_0\simeq 3 PeV (the power-law index changes from about −2.7-2.7 to about −3.1-3.1), and flattens again at the ankle, ≃3×1018\simeq 3\times10^{18} eV, conventionally taken as the transition to extragalactic sources. Explaining the knee is one of the classic problems of cosmic-ray astrophysics, and it is inseparable from the question of the mass composition of the primaries: direct magnetic spectrometers reach only the TeV scale, so at PeV energies the primary mass must be inferred indirectly, from extensive air showers (EAS) — the cascades of electrons, photons, muons, and hadrons that a primary initiates in the atmosphere.

Air-shower observables and their model dependence. Detectors at ground level register the electromagnetic component (electrons and photons, spread over hundreds of meters), the muon component (penetrating, detected also underground), and — with specialized instruments — the hadrons concentrated within tens of meters of the shower axis, the EAS core. Because a primary nucleus of mass number AA and charge ZZ produces a shower whose shape depends on AA, shower observables can be inverted into composition estimates, but only through hadronic interaction models such as QGSJET, SIBYLL, or EPOS — Monte Carlo event generators tuned to accelerator data. A key diagnostic is magnetic rigidity, R=E/ZR=E/Z: diffusive shock acceleration at supernova remnants, the standard Galactic acceleration mechanism, implies that spectra of different nuclei cut off at approximately the same rigidity, so the all-particle knee should be built from a sequence of elemental knees at Eknee(Z)∝ZE_{\rm knee}(Z)\propto Z.

The rigidity controversy. The KASCADE experiment (sea level, Germany) analyzed essentially only the electromagnetic component and, using the QGSJET model, obtained a proton knee at rigidity Rmax⁡≃3R_{\max}\simeq 3 PV — the generally accepted value. The Tibet ASγ\gamma hybrid experiment (4300 m altitude; air-shower array plus emulsion chambers and burst detectors, i.e. core-inclusive instrumentation) instead found the proton spectrum steepening above ≃100\simeq 100 TeV, i.e. a proton cutoff at Rp≃0.1R_p\simeq 0.1 PV =100=100 TV, roughly thirty times lower. Shaulov et al. stress that analyses including core information are far less dependent on the choice of interaction model than electromagnetic-component-only analyses (the KASCADE results themselves differ by factors depending on whether QGSJET or SIBYLL is used). If the true cutoff rigidity is ≃0.1\simeq 0.1 PV, then all nuclear species — including the iron group at Z=26Z=26 — end by E0≃3E_0\simeq 3 PeV, and the sizeable observed flux above the knee requires primaries that are not ordinary nuclei.

The EAS-core anomalies. The HADRON installation at Tien-Shan (3330 m) combined a scintillator shower array, a 162 m2^2 X-ray emulsion chamber (XREC — lead plates interleaved with photographic emulsion, registering the highly energetic hadrons of the core), and an underground muon hodoscope (a tracking detector recording the arrival positions and directions of muons). Its data show two effects concentrated at the knee: first, scaling violation — the energy spectra of individual hadrons in shower cores, which at lower energies follow a scaling form with slope ≃−1.9\simeq -1.9, harden to ≃−1.2\simeq -1.2 over E0=3E_0=3–200200 PeV (a 4.5σ4.5\sigma effect), whereas forward-region collider experiments (LHCf at the LHC, experiments at RHIC) show scaling behavior at equivalent lab energies 11–100100 PeV, and QCD-based simulations predict no comparable change in nuclear interactions; second, a rise of the muon content of showers containing energetic core hadrons, starting exactly at E0≃3E_0\simeq 3 PeV. A new proton component would raise hadron energies but lower muon numbers; heavier nuclei fit neither. The authors conclude that a highly penetrating non-nuclear component appears at the knee.

Strangelets. Strange quark matter (SQM) is hypothetical matter containing roughly equal numbers of up, down, and strange quarks, proposed by Witten (1984) and studied by Farhi and Jaffe (1984) as a possibly stable (or absolutely stable) form of dense matter; if strange stars exist, their debris could include strangelets — stable or quasi-stable lumps with baryon number A∼103A\sim 10^3–10810^8 and positive electric charge Z∼30Z\sim 30 up to thousands, effectively very heavy quasi-nuclei. Being charged, strangelets are accelerated by the same shock waves as nuclei; at a given rigidity their much larger mass means much larger total energy. Shaulov et al. therefore propose that the knee is the onset of a strangelet component that dominates the cosmic-ray flux from the knee to the ankle — in their words the only knee model compatible with a nuclear-cutoff rigidity R=100R=100 TV — and they pose the presence of strangelets in the extragalactic flux above the ankle as a separate open ('special') question.

Current context. The mainstream picture explains the knee by rigidity-dependent cutoffs of ordinary nuclei with the composition becoming heavier above it; the new measurement by LHAASO-KM2A (the square-kilometer surface array of the Large High Altitude Air Shower Observatory, a hybrid air-shower detector at 4410 m altitude in Sichuan, China; Phys. Rev. Lett. 132, 131002 (2024)) locates the knee at 3.673.67 PeV and finds the mean logarithmic mass — the event-averaged natural logarithm of the primary mass number AA — of ⟨ln⁡A⟩˚≃1.3\langle\ln A\r\rangle\simeq 1.3–1.71.7 over 0.30.3–3030 PeV (i.e. predominantly light, helium-like primaries), rising above the knee, attributing the knee to the light component. The muon excess relative to simulations ('muon puzzle') is being pursued as a deficiency of hadronic interaction models. Neither line has tested the strangelet hypothesis in its own regime: existing strangelet searches cover only low charges and rigidities, so whether the PeV flux is nuclear or contains a dominant non-nuclear component remains an open empirical question.

Problem Statement

Determine, observationally, whether the knee of the cosmic-ray spectrum at E0≃3E_0\simeq 3 PeV marks the appearance of a non-nuclear primary component — stable strangelets (strange-quark-matter particles with baryon number A∼103A\sim 10^3–10810^8 and positive charge Z∼30Z\sim 30–10001000) — that dominates the flux between the knee and the ankle (≃3×1018\simeq 3\times10^{18} eV), or whether ordinary nuclei with rigidity-dependent cutoffs suffice. This overarching objective decomposes into three scientifically linked questions, as posed by Shaulov et al. (2022): (1) Do strangelets exist in the primary cosmic-ray flux at E0≃3E_0\simeq 3 PeV–33 EeV with the abundance, charge-to-mass distribution, and stability lifetimes required to dominate it — established by direct or targeted detection (anomalously large mass-to-charge ratio, or anomalous shower development such as the observed core-hadron scaling violation and muon excess), or excluded by flux limits covering that charge, mass, and energy regime? (2) What is the magnetic rigidity scale of the cutoffs in the individual nuclear spectra — ≃0.1\simeq 0.1 PV, as indicated by core-inclusive Tibet ASγ-type analyses, or ≃3\simeq 3 PV, as indicated by electromagnetic-component KASCADE analyses with QGSJET — and, given that scale, does the observed all-particle spectrum above the knee require a non-nuclear component at all? (3) If strangelets are present, do they also contribute to the extragalactic cosmic-ray population above the ankle? Adjudicating (1)–(2) requires mass-composition information over E0≃1E_0\simeq 1–200200 PeV. The nature and composition of the primary flux across the knee is established observationally by confirming the strangelet component (detection with established signatures), by excluding it at the abundance required to dominate the observed all-particle flux between the knee and the ankle (a strangelet flux comparable to the measured all-particle flux over E0≃3E_0\simeq 3 PeV–3×10183\times10^{18} eV), or by demonstrating that the EAS-core anomalies (scaling violation and muon excess) are fully accounted for by nuclear primaries within validated interaction models at the resolved rigidity scale. Questions (1)–(2) are jointly posed; question (3) — whether a confirmed strangelet component also contributes to the extragalactic flux above the ankle — is moot unless the strangelet component is confirmed.

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