The Telescope Array (TA) in Utah and the Pierre Auger Observatory (Auger) in Argentina measure the ultra-high-energy cosmic-ray (UHECR) energy spectrum in the northern and southern hemispheres, respectively. The 16-year TA surface-detector spectrum shows a high-energy cutoff at E≃1019.83 E\simeq10^{19.83}\,eV (6.3 sigma) whose physical origin is undetermined: it may be dominated by propagation energy losses (the Greisen-Zatsepin-Kuzmin photo-pion process for protons, or photodisintegration of nuclei on cosmic photon backgrounds) or by the maximum energy, i.e. maximum magnetic rigidity, that astrophysical sources can reach. A simultaneous fit of a common broken-power-law parent spectrum to the full-aperture TA and Auger spectra yields an approximately 8 sigma north-south spectral difference, while the two spectra agree at 1.8 sigma in the common declination band once localized excess regions (the TA Hotspot and the Perseus-Pisces supercluster excess) and low-exposure edges are removed; whether this difference reflects a genuine hemispheric variation of the UHECR flux or residual instrumental and analysis systematics is actively contested between the two collaborations. The problem is to determine the dominant mechanism behind the flux suppression and to establish the origin of the hemispheric spectral difference, with quantified statistical and systematic uncertainties, consistently with the spectrum, composition, and arrival-direction measurements of both hemispheres. Both questions remain open as of August 2026: composition evidence tilts toward source-related cutoffs in Auger data but remains contested, and the hemispheric difference is variously attributed to genuine flux variation, a nearby bright source, or instrumental effects, with dedicated cross-calibration (Auger@TA) only beginning operation.

Background

Ultra-high-energy cosmic rays (UHECRs) are charged particles - protons or atomic nuclei - reaching Earth with energies above 1018 10^{18}\,eV, the most energetic particles known. Because magnetic deflections are comparatively small at these rigidities and energy losses during intergalactic propagation are severe, their energy spectrum, mass composition, and arrival directions encode where and how they are accelerated. The all-particle differential spectrum above 1018 10^{18}\,eV shows a sequence of features: a hardening called the ankle near 1018.7 10^{18.7}\,eV, a softening often called the instep or shoulder near 1019.110^{19.1}-1019.2 10^{19.2}\,eV, and a strong suppression (the cutoff) beginning near 1019.8 10^{19.8}\,eV.

The suppression has two canonical explanations. Greisen and, independently, Zatsepin and Kuzmin predicted in 1966 that protons above roughly 5×1019 5\times10^{19}\,eV lose energy efficiently by photo-pion production on cosmic microwave background photons, so that sources beyond a few tens of megaparsecs become invisible - a propagation-driven cutoff now called the GZK effect (for nuclei, the analogous propagation process is photodisintegration on cosmic microwave and infrared background photons). Alternatively, the cutoff may reflect a source-limited spectrum: if accelerators have a maximum magnetic rigidity Rmax⁡R_{\max} (energy per unit charge), nuclei of charge ZZ cut off at E≃Z Rmax⁡E\simeq Z\,R_{\max}, a pattern often called a Peters cycle (see M. Stein Muzio et al., arXiv:2309.16518), so that the composition becomes progressively heavier through the suppression. The two pictures predict different composition evolution at the highest energies - protons stay light under a pure GZK cutoff, while a rigidity-limited source population turns heavy - so composition and anisotropy measurements are the main discriminants. The depth of shower maximum, Xmax⁡X_{\max} (the atmospheric slant depth at which the extensive air shower, the particle cascade initiated by the primary cosmic ray, reaches its largest size), is the standard composition-sensitive observable: lighter primaries penetrate deeper on average.

Experimentally, the suppression was first reported by the HiRes experiment in the northern hemisphere and by Auger in the south, and has since been measured precisely by Auger and by TA - the two largest UHECR observatories, one per hemisphere, whose surface detector (SD) arrays use different technologies (Auger: water-Cherenkov tanks; TA: plastic scintillators) and whose energy scales are set by fluorescence telescopes that image shower development calorimetrically, with absolute energy-scale systematic uncertainties of about 14% (Auger) and 21% (TA). A joint Auger-TA spectrum working group operating since 2012 established a relative energy-scale offset of about 9%, conventionally removed by rescaling Auger up and TA down by 4.5%.

The 16-year TA SD spectrum measures the ankle at 1018.70 10^{18.70}\,eV, the shoulder at 1019.15 10^{19.15}\,eV, and the cutoff at 1019.83 10^{19.83}\,eV. Beyond the cutoff-interpretation problem, a second finding complicates the picture. A simultaneous fit of a common broken-power-law parent spectrum to the two full-aperture spectra yields an 8.0−2.4+2.0σ8.0^{+2.0}_{-2.4}\sigma north-south difference (TA sees a more intense flux and a higher cutoff energy than Auger), which drops to 1.8 sigma in the common declination band once the regions hosting TA's two known medium-scale anisotropies - localized excesses in the arrival-direction distribution on angular scales of tens of degrees - namely the Hotspot toward Ursa Major (an excess of events above 5.7×1019 5.7\times10^{19}\,eV, i.e. 57 EeV) and an excess toward the Perseus-Pisces supercluster above 1019.4 10^{19.4}\,eV - plus a low-exposure edge are excluded. TA interprets this as a genuine hemispheric flux variation driven largely by those anisotropic excesses; the updated joint working-group comparison instead finds a significant energy-dependent difference, equivalent to an energy shift of 16-20% per decade, already within the common sky, and concludes that the main source of the discrepancy may lie in instrumental and analysis-method differences between the two experiments (for example composition-dependent energy calibration). Composition measurements sharpen rather than settle the cutoff question: Auger's 17-year fluorescence Xmax⁡X_{\max} data show the mean primary mass increasing and the composition becoming less diverse above 1018.4 10^{18.4}\,eV - strong evidence against a predominantly proton composition at the cutoff, favoring source-related cutoffs in Auger-focused interpretations - while TA's northern-hemisphere Xmax⁡X_{\max} distributions remain compatible with proton primaries, and an independent 2026 analysis of the isotropy of arrival directions still argues for a light composition. The dominant mechanism behind the cutoff, and the origin of the hemispheric spectral difference, are therefore both open.

Problem Statement

Determine the physical origin of the high-energy suppression of the ultra-high-energy cosmic-ray spectrum and of the north-south spectral difference between the Telescope Array and Pierre Auger Observatory measurements. (1) Dominant mechanism of the cutoff: identify, with quantified statistical confidence and controlled systematic uncertainties, whether the flux suppression observed near E≃1019.8 E\simeq10^{19.8}\,eV is dominated by propagation energy losses (photo-pion production of protons on the cosmic microwave background, the GZK mechanism, and/or photodisintegration of nuclei on cosmic photon backgrounds) or by the maximum energy, i.e. maximum rigidity, attainable at the astrophysical sources, or by a specified combination of these effects; the determination must be consistent with the measured spectra, composition-sensitive observables such as Xmax⁡X_{\max}, and arrival-direction distributions in both hemispheres. (2) Origin of the hemispheric spectral difference: establish whether the approximately 8 sigma difference between the full-aperture TA and Auger spectra (which becomes a 1.8 sigma agreement in the common declination band after removing localized excess regions and low-exposure edges) is (a) a genuine astrophysical variation of the UHECR flux between the northern and southern skies, arising from the source distribution or local large-scale structure, from medium-scale anisotropies such as the TA Hotspot and the Perseus-Pisces supercluster excess, or from a nearby dominant source, or (b) a residual instrumental or analysis systematic such as an energy-scale drift with energy, composition- and hadronic-model-dependent reconstruction, or aperture and coverage differences; the answer must reconcile the full-aperture and common-sky comparisons and the currently divergent interpretations of the two collaborations. These two questions are linked and jointly define the problem: if the hemispheric difference is astrophysical, the cutoff position and shape differ between hemispheres and directly constrain the suppression mechanism, while if it is instrumental, cutoff inferences from any single-hemisphere spectrum must be revised before a mechanism can be identified. An accepted answer resolves both at the generality of the source question.

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