The all-particle cosmic-ray spectrum steepens sharply at about 3 PeV (the 'knee') and flattens again near 3 EeV (the 'ankle'). Whether the knee is the rigidity-dependent cutoff of ordinary nuclear primaries or marks the appearance of a new, non-nuclear component is unsettled. From X-ray-emulsion-chamber measurements of extensive-air-shower (EAS) cores at the Tien Shan station, Shaulov et al. (2022) report anomalous effects beginning at 3 PeV — violation of scaling in secondary-hadron spectra at 3–200 PeV and a rise of muon content in hadron-rich showers — that no hadronic interaction model predicts, and, following the Tibet ASγ inference of a proton spectral cutoff at magnetic rigidity R≈0.1R\approx0.1 PV (in conflict with the electromagnetic-component-only KASCADE value of a few PV), they propose that strangelets — stable lumps of strange quark matter with baryon number A∼103A\sim10^3–10810^8 and charge Z∼30Z\sim30–10310^3 — dominate the cosmic-ray flux between the knee and the ankle. The problem asks for a determination of the primary composition over roughly 1–200 PeV with quantified interaction-model dependence; a test of whether strangelets form part of the cosmic-ray flux between the knee and the ankle, including their abundance, charge-to-mass distribution, and stability; and, as a special question explicitly deferred by the source, an answer to whether strangelets, if present, also contribute to the extragalactic population above the ankle.

Background

Cosmic rays are charged particles — overwhelmingly atomic nuclei — arriving at Earth from Galactic accelerators such as supernova-remnant shock waves. Their all-particle energy spectrum falls as a power law E−2.7E^{-2.7}, steepens to roughly E−3.1E^{-3.1} above about 3 PeV (the 'knee', with 1 PeV =1015=10^{15} eV), and flattens again above a few EeV (the 'ankle'). The origin of the knee is one of the oldest open problems of cosmic-ray astrophysics. The two competing classes of explanation are (i) acceleration or propagation cutoffs that act on nuclear magnetic rigidity R=E/ZR=E/Z, where ZZ is nuclear charge, so that light species drop out first and the mean mass of the flux grows above the knee; and (ii) particle-physics explanations in which a new interaction or a new primary species appears at PeV energies. Mass composition is therefore the decisive observable.

At PeV energies the flux is too low for direct satellite measurement, so composition is inferred from extensive air showers (EAS), the cascades that primaries initiate in the atmosphere. Ground arrays measure the electromagnetic component (electrons and photons) and the muon content; the EAS core, the dense central region containing the most energetic secondary hadrons, requires dedicated calorimetry, historically performed with X-ray emulsion chambers at high-altitude stations such as Pamir and Tien Shan. Composition inference from any single shower component depends on hadronic interaction models (shower-simulation codes such as QGSJET and SIBYLL), and it is a recognized systematic that current simulations underpredict the muon content of observed showers — the 'muon puzzle'.

The experimental situation that motivates the source paper is a discrepancy between two air-shower inferences of the proton cutoff rigidity. The KASCADE experiment at sea level, analyzing the electromagnetic and muon components, placed the proton cutoff at a rigidity of a few PV (about 3 PV), with composition becoming heavier through the knee (Haungs et al. 2004). The Tibet ASγ experiment at 4300 m, using emulsion chambers and burst detectors together with the shower array — i.e. including core information — reported instead that the proton spectrum steepens above about 100 TeV, implying a cutoff rigidity near 0.1 PV (Amenomori et al. 2006). If the proton cutoff were really at 0.1 PV, all nuclear species up to the iron group would end by about 3 PeV, leaving the observed flux between the knee and the ankle without a nuclear explanation.

Shaulov et al. (2022) add EAS-core evidence for such a gap. In data from the HADRON installation at Tien Shan, the normalized spectra of the most energetic hadrons in shower cores keep a constant slope up to E0∼3E_0\sim3 PeV and then harden (a 4.5 sigma 'scaling violation') over E0≈3E_0\approx3–200 PeV, while collider forward-physics experiments show scaling behavior at laboratory-equivalent energies of 1–100 PeV; simultaneously, the muon content of hadron-rich showers rises just above 3 PeV (Shepetov et al. 2021). Since a growing hadron energy together with a growing muon number cannot be produced by any change of nuclear composition under standard interactions, the authors attribute both anomalies to a new, highly penetrating primary. Invoking Witten's (1984) hypothesis that strange quark matter (deconfined matter made of up, down, and strange quarks) may be absolutely stable, and that disruptions of strange stars would eject 'strangelets' — quasi-nuclei with baryon number A∼103A\sim10^3–10810^8 and positive charge Z∼30Z\sim30–10310^3, hence a charge-to-mass ratio far below that of ordinary nuclei — they propose that strangelets are accelerated by the same shock waves as nuclei but, being far heavier, cut off at proportionally higher energy, so that strangelets dominate the flux from the knee to the ankle.

Whether strangelets exist in the cosmic-ray flux at all is untested at the relevant rigidities. Strange quark matter is a long-standing theoretical possibility (Witten 1984); balloon-borne and spectrometer searches have produced no confirmed strangelet (e.g. the claimed candidates of Saito et al. 1990 were never confirmed, and the SLIM mountain-altitude search found none), and predicted strangelet fluxes in the solar neighborhood span orders of magnitude (Madsen 2005). No existing direct search reaches PeV rigidity, so the hypothesis of strangelet dominance above the knee can currently only be tested indirectly, through air-shower composition measurements.

Problem Statement

Determine the nature of the primary cosmic-ray flux that forms the knee, and test the strange quark matter explanation of the knee, by answering two jointly linked questions whose common objective is a physically identified composition of the cosmic-ray flux from roughly 1 PeV to 200 PeV, together with one related special question that the source explicitly defers:

  1. Does a mass-composition analysis of PeV extensive air showers that simultaneously uses EAS-core (energetic-hadron) observables, muon content, and the electromagnetic component — with interaction-model dependence quantified — require a non-nuclear component appearing at E0≈3E_0\approx3 PeV? This question comprises two parts: (a) whether the anomalous observations claimed at 3–200 PeV — the scaling violation in core-hadron energy spectra, the rise of muon content in hadron-rich showers and in gamma families (clusters of cascade gamma rays recorded by emulsion chambers) above the knee, and the discrepancy between the core-inclusive Tibet ASγ inference of the proton cutoff rigidity (R≈0.1R\approx0.1 PV) and the electromagnetic-only KASCADE inference (R≈3R\approx3–44 PV) — are fully reconcilable with a purely nuclear composition and its propagation under improved hadronic interaction models, or require a new primary species; and (b) whether the all-particle spectrum between the knee and the ankle can be constructed entirely from nuclear species.

  2. Do strangelets — stable lumps of strange quark matter with baryon number A∼103A\sim10^3–10810^8 and positive charge Z∼30Z\sim30–10310^3 — form a component of the cosmic-ray flux between the knee and the ankle, as the source hypothesis requires; and if so, with what abundance, charge-to-mass distribution, and stability lifetimes?

  3. Special question, explicitly deferred by the source: if strangelets exist in the Galaxy, do they also contribute to the extragalactic cosmic-ray population above the ankle?

The questions are linked because the strangelet hypothesis was constructed precisely to accommodate existing single-observable inferences: a measurement of any single observable (for example, the proton spectrum alone) bears on the objective but does not by itself identify the composition.

References

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