Measurement of the Proton-Air Cross Section at $\sqrt{s}\mathbf{=}57\mathrm{TeV}$ 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. Analyzing the tail of the distribution of the shower maxima, a proton-air cross section of $[505\pm 22(\mathrm{stat}{)}_{-36}^{+28}(\mathrm{syst})]\mathrm{mb}$ is found.

Figure 1

Unbinned likelihood fit to obtain ${\Lambda }_{\eta }$ (thick line). The $X_{\max }$ distribution is unbiased by the fiducial geometry selection applied in the range of the fit.

Figure 2

Resulting ${\sigma }_{p\mathrm{\text{−}}\mathrm{air}}^{\mathrm{prod}}$ compared to other measurements (see [18, 19, 20, 30, 31, 32, 33, 34]) and model predictions. The inner error bars are statistical, while the outer include systematic uncertainties for a helium fraction of 25% and 10 mb for the systematic uncertainty attributed to the fraction of photons.

Figure 3

Correlation of elastic slope parameter, $B_{\mathrm{el}}$, and the inelastic proton-proton cross section in the Glauber framework. The solid line indicates the parameter combinations yielding the observed proton-air production cross section, and the dotted lines are the statistical uncertainties. The hatched area corresponds to the predictions by SIBYLL, QGSJet, QGSJetII, and EPOS. See also Ref. [5].

Figure 4

Comparison of derived ${\sigma }_{pp}^{\mathrm{inel}}$ to model predictions and accelerator data [29]. Here we also show the cross sections of two typical high-energy models, Pythia6 [35] and Phojet [36]. The inner error bars are statistical, while the outer include systematic uncertainties.