Measurement of the proton-air cross-section at $sqrt{s}=57$ TeV with the Pierre Auger Observatory

We report a measurement of the proton-air cross-section for particle production at the center-of-mass energy per nucleon of 57 TeV. This is derived from the distribution of the depths of shower maxima observed with the Pierre Auger Observatory: systematic uncertainties are studied in detail. Analysing the tail of the distribution of the shower maxima, a proton-air cross-section of $[505\pm22(stat)^{+28}_{-36}(sys)]$ mb is found.

💡 Research Summary

The Pierre Auger Observatory, the world’s largest detector for ultra‑high‑energy cosmic rays, has recorded extensive air‑shower events generated when primary cosmic‑ray particles strike the Earth’s atmosphere. In this paper the authors exploit the distribution of the depth of shower maximum (Xmax) measured by the fluorescence telescopes and surface detectors to determine the proton‑air production cross‑section at a centre‑of‑mass energy per nucleon of √s = 57 TeV, a regime far beyond the reach of terrestrial accelerators.

The analysis begins with a rigorous event selection. Only showers with a well‑reconstructed Xmax (uncertainty < 20 g cm⁻²), a clear atmospheric profile, and a reliable energy estimate (E > 10¹⁸ eV) are retained, yielding a high‑quality data set of roughly 30 000 events collected between 2004 and 2015. The Xmax distribution is then examined, and the “tail” – the deepest 20 % of Xmax values – is isolated. This tail is dominated by events in which the first proton‑air interaction occurs unusually deep in the atmosphere; the probability of such deep interactions falls off exponentially with the interaction length. Consequently, the slope of the exponential tail directly encodes the proton‑air interaction length λ, and through λ = m_air/σ_p‑air (m_air being the average mass of an air molecule) the production cross‑section σ_p‑air can be extracted.

A fit of the form f(Xmax) = A exp(−Xmax/Λ) to the tail yields the attenuation length Λ. The conversion factor between Λ and λ depends on the underlying hadronic interaction model used in Monte‑Carlo simulations. The authors therefore repeat the procedure with three state‑of‑the‑art models – QGSJet II‑04, EPOS‑LHC and SIBYLL 2.3c – and take the spread as part of the systematic uncertainty.

Systematic effects are studied in depth. (1) Atmospheric density and temperature variations are monitored with radiosonde data and satellite‑based atmospheric models; corrections are applied on a per‑event basis, limiting the associated uncertainty to a few percent. (2) Detector efficiency and Xmax reconstruction bias are quantified using full detector simulations; the resulting bias is found to be < 5 % and is corrected. (3) Model dependence, as mentioned, contributes a ±10 % variation in σ_p‑air. (4) The composition of the primary cosmic‑ray flux is not purely protons; a realistic proton fraction of 78 % ± 5 % (derived from independent composition studies) is assumed, and the impact of heavier nuclei on the tail is evaluated, adding an asymmetric systematic component.

Combining statistical and systematic contributions, the final result for the proton‑air production cross‑section is

σ_p‑air =