Pion Production Cross-section Measurements in p+C Collisions at the CERN SPS for Understanding Extensive Air Showers

An important approach to studying high-energy cosmic rays is the investigation of the properties of extensive air showers; however, the lateral distribution of particles in simulations of such showers strongly depends on the applied model of low-energy hadronic interactions. It has been shown that many constraints to be applied to these models can be obtained by studying identified-particle spectra from accelerator collisions, in the energy range of the CERN Super Proton Synchrotron. Here we present measurements of the pion production cross-section obtained by the NA61/SHINE experiment at the SPS, in proton-carbon collisions at the beam energy of 31 GeV from the year 2007. Further analyses of identified-particle yields in SHINE, in particular with a pion beam, are in preparation.

💡 Research Summary

The paper reports the first measurements of charged‑pion production cross‑sections in proton‑carbon (p + C) collisions at a beam momentum of 31 GeV, performed by the NA61/SHINE experiment at the CERN Super Proton Synchrotron. The motivation stems from the need to improve the modelling of low‑energy hadronic interactions in extensive air‑shower (EAS) simulations, which are crucial for interpreting data from cosmic‑ray observatories such as KASCADE, KASCADE‑Grande and the Pierre Auger Observatory. Current hadronic interaction models (GHEISHA, FLUKA, UrQMD) exhibit significant discrepancies when compared with air‑shower observables, especially in the predicted muon content at ground level. Accelerator data in the SPS energy range are therefore essential for tuning these models.

NA61/SHINE utilizes an upgraded NA49 spectrometer equipped with five Time‑Projection Chambers for tracking, momentum, charge and dE/dx measurement, three Time‑of‑Flight walls for additional particle identification, and a downstream Projectile Spectator Detector. The detector offers a large acceptance (≈ 50 % for p_T ≤ 2.5 GeV/c), high momentum resolution (σ(p)/p ≈ 10⁻⁴ (GeV/c)⁻¹), tracking efficiency above 95 %, dE/dx resolution of about 4 % and ToF resolution of 100 ps.

The analysis is based on 0.6 million p + C events recorded during the 2007 pilot run. Three independent methods were employed to extract the π⁺ and π⁻ spectra:

1. h‑method – assumes all negatively charged hadrons are pions and corrects for non‑pion contributions using Monte‑Carlo simulations. This method provides high statistics but is model‑dependent and cannot be applied to positive pions.
2. dE/dx identification – uses the specific energy loss in the TPCs to identify pions in momentum regions where Bethe‑Bloch curves for different species do not overlap. It offers explicit identification with good statistics but is limited to certain momentum intervals.
3. dE/dx + ToF identification – combines energy‑loss and time‑of‑flight information, extending explicit pion identification over a broader momentum range at the cost of reduced acceptance.

For each method, particles passing quality cuts were binned in total momentum (p) and polar angle (θ) to account for varying detector response. The resulting production cross‑sections (σ_prod = σ_inel − σ_qel) were compared with CORSIKA‑based air‑shower simulations employing the three interaction models. The comparison shows that FLUKA reproduces the measured spectra well for polar angles below 180 mrad, while UrQMD provides a better description at larger angles. GHEISHA shows systematic deviations in both regions, indicating the need for further refinement.

Systematic uncertainties are presently at the level of 20 % or less, dominated by tracking efficiency, particle‑identification boundaries, and the model‑dependent corrections in the h‑method. Ongoing work aims to reduce these uncertainties below 10 % by exploiting the larger data sets collected in 2009 (≈ 5 million p + C events and several million π + C events at higher beam energies) and by improving calibration procedures.

The authors conclude that the NA61/SHINE pion spectra constitute a valuable benchmark for low‑energy hadronic interaction models used in EAS simulations. The demonstrated agreement with FLUKA at small angles and with UrQMD at larger angles provides guidance for model developers and will help to reduce the systematic uncertainties in cosmic‑ray composition and energy reconstruction derived from air‑shower measurements. Future publications will present the finalized results and extend the analysis to the high‑statistics π + C data, further strengthening the experimental constraints on hadronic interaction models relevant to astroparticle physics.