The source paper (Shaulov et al., JETP Letters 116, 1 (2022)) proposes that the 3 PeV knee of the cosmic-ray spectrum and a set of anomalous extensive-air-shower observables — scaling violation in secondary-hadron spectra, muon excess, halos, alignment, Centauro-type events, and delayed shower fronts — are produced by a nonnuclear component of cosmic rays consisting of strangelets, stable lumps of strange quark matter, and it explicitly acknowledges that calculations of strangelet interactions with air nuclei within QCD are absent, leaving all predictions of the model qualitative. The problem asks for a quantitative description of strangelet interactions with air nuclei, incorporated into air-shower simulations, that either reproduces or excludes the strangelet interpretation of the knee-region anomalies and defines the measurements needed to settle whether strange quark matter exists in nature.

Background

Cosmic rays are atomic nuclei (mostly protons through iron) arriving at Earth from Galactic sources; above roughly 0.1 PeV0.1\,\mathrm{PeV} (1 PeV=1015 eV1\,\mathrm{PeV} = 10^{15}\,\mathrm{eV}) their energies can only be inferred from extensive air showers (EAS) — avalanches of secondary particles produced when a primary particle strikes the atmosphere. The EAS all-particle spectrum steepens at E0≈3 PeVE_0 \approx 3\,\mathrm{PeV}; this bend is called the knee, and its origin has been an open question of astroparticle physics for more than half a century. In the conventional picture the knee reflects a rigidity-dependent cutoff of supernova-shock-accelerated nuclei, where the magnetic rigidity R=pc/ZeR = pc/Ze measures how easily a particle of momentum pp and charge ZeZe is deflected; whether the cutoff rigidity is ≈3 PV\approx 3\,\mathrm{PV} (a proton knee) or ≈0.1 PV\approx 0.1\,\mathrm{PV} (an iron-group knee) is itself contested, and a further class of models attributes the knee to a dominant contribution from a single nearby source.

The highest-energy secondary hadrons of a shower are concentrated in the EAS core, the small region around the shower axis, historically studied with X-ray emulsion chambers — stacks of lead plates and photographic emulsions that image the electromagnetic cascades from neutral-pion decay with about 100 μm spatial resolution. Emulsion-chamber experiments at the high-altitude observatories of Pamir, Chacaltaya and Tien Shan have reported a set of correlated anomalies in the knee region: violation of Feynman scaling (the expectation that secondary-hadron spectra keep their shape as energy grows) above 3 PeV; an excess of muons in showers accompanied by gamma-ray families; 'halos', diffuse electromagnetic spots with anomalously deep penetrating power; 'alignment', the collinear arrangement of energy clusters in the shower core; Centauro-type events, hadron-rich and pion-poor cascades first observed at Chacaltaya; and 'delayed fronts', shower signals separated by hundreds of nanoseconds up to microseconds, studied at the Tien Shan Horizon-T array. Collider measurements of forward particle production — from the LHCf and RHICf forward-collision detectors at the Large Hadron Collider (LHC) and the Relativistic Heavy-Ion Collider (RHIC) — at equivalent laboratory energies of 1–100 PeV show that hadron production scales normally, which rules out new nuclear physics as the cause and points back to the primary composition.

Strange quark matter (SQM) is the hypothesis, due to Bodmer (1971) and Witten (1984), that matter with roughly equal densities of up, down and strange quarks could be stable or metastable at large baryon number, possibly the true ground state of the strong interaction. Small charged lumps of SQM — strangelets, with baryon numbers A≈102A \approx 10^{2}–10810^{8} and electric charges Z≈30Z \approx 30–10001000 — would behave as superheavy quasi-nuclei; at A≈1052A \approx 10^{52} such an object is a strange quark star. Bjorken and McLerran (1979) invoked strangelets to explain Centauro events, since strangelet breakup should produce hyperons (baryons containing strange quarks) rather than pions.

Shaulov et al. (JETP Letters 116, 1 (2022)) synthesized the EAS-core data into what they call the CORE model: the ordinary nuclear component of Galactic cosmic rays cuts off at a rigidity Rmax⁡≈0.1 PVR_{\max} \approx 0.1\,\mathrm{PV}, while the knee itself and the spectrum up to about 100 PeV are formed by strangelets, which are shock-accelerated alongside nuclei like quasi-nuclei and, being far heavier, extend the Galactic spectrum up to the extragalactic component. The model's acknowledged central weakness is quantitative: calculations of strangelet interactions with air nuclei within QCD are absent, so its ingredients — geometric cross sections σ≈A2/3\sigma \approx A^{2/3} of order 1 to 10310^{3} barns, a tiny inelasticity (the fraction of the projectile's energy lost per collision) of order 10−310^{-3}, and interaction lengths of order 0.01 g/cm20.01\,\mathrm{g/cm^2} — are order-of-magnitude estimates, and every explanation of the anomalies remains qualitative. The paper states that a final resolution of whether strange quark matter exists in nature will require large-aperture instruments in open space, which do not yet exist.

Problem Statement

Provide a quantitative description of the interaction of strangelets with air nuclei — inelastic cross section, inelasticity, the evolution of baryon number and electric charge (abrasion, fusion, fission, and decay at the stability boundary), and secondary-particle production, all as functions of baryon number and energy — anchored in QCD where possible (for example, calibrated to heavy-ion collision data and constrained by the SQM stability window, the range of baryon numbers and charges for which strange quark matter is stable or metastable) and otherwise in controlled, QCD-consistent effective modeling; incorporate this description into air-shower simulations; and use it to determine whether a nonnuclear strangelet component of cosmic rays can quantitatively reproduce the observed 3 PeV knee together with the anomalous EAS-core observables (scaling violation in secondary-hadron spectra, muon excess, halos, alignment, Centauro-type events, and delayed shower fronts). The outcome must make the SQM/CORE model of the knee falsifiable against existing data — either demonstrating quantitative compatibility with the anomalies and specifying what measurements, ground-based or on the high-luminosity open-space instruments the source calls for, would confirm or exclude strange quark matter in nature, or demonstrating quantitative incompatibility and thereby excluding the strangelet interpretation of the knee-region anomalies. Two further threads acknowledged by the source — the cooling and evaporation rate of strange quark stars, which sets the strangelet source term, and the possible contribution of relic quark stars to dark matter — are related open questions but are not part of this problem's completion boundary, and the ultimate empirical confirmation of strange quark matter in nature rests on future experiments.

References

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