Measurement of the proton-air cross-section with the Pierre Auger Observatory

Abstract

We present the procedure to measure the proton-air cross-section at a center-of-mass energy per nucleon of 57TeV developed by the Pierre Auger Collaboration. The conversion from proton-air to inelastic proton-proton cross-section with an extended Glauber calculation is discussed. The systematic uncertainties of the analysis are summarized and the final result compared to accelerator data and model predictions. The growth of hadronic cross-sections towards ultra-high energies reflects changes in the internal structure of the colliding particles. Due to the nature of QCD it is still not possible to calculate hadronic cross-sections at ultra-high energies from first principles. It is thus of paramount importance to measure hadronic cross-sections in order to guide the development of phenomenological models needed to describe secondary multiparticle production at ultra-high energies. Such models are crucial, for example, for a detailed interpretation of available cosmic-ray air-shower data in terms of the primary mass composition. Without a better understanding of the cosmic-ray mass composition it will be very difficult to distinguish between different scenarios of cosmic-ray acceleration and propagation. We present the measurement of the proton-air cross-section with data of the Pierre Auger Observatory (1). The Pierre Auger Observatory is located close to the town of Malargue in Argentina. It consist of about 1660 water Cherenkov particle detector spread over a surface area of 3000km 2 .D uring clear and moonless nights the atmosphere on top of the surface array is overlooked by 27 fluorescence telescopes. This analysis is based on the observation of the longitudinal air-shower development with the telescopes. By combining the timing data of the surface detectors with that of the fluorescence telescopes a very precise reconstruction of the geometry is achieved (2). This technique is called hybrid reconstruction. It allows us a very accurate measurement of Xmax, the position at which an air-shower deposits the maximum energy per unit of mass of atmosphere traversed (3). With the precise observation of longitudinal air-shower fluctuations it is possible to achieve high sensitivity to the mean free path of the primary cosmic-ray particles and thus to the cross-section. This technique is well known and has been first applied by the Fly's Eye experiment (4). We also discuss systematic uncertainties and limitations of the cross-section measurement. In a last step, the proton-air cross-section measurement is converted into a proton-proton cross-section. This conversion makes use of a Glauber calculation, which has been extended to account for inelastic screening effects.