Ultra-high Energy Predictions of Proton-Air Cross Sections from Accelerator Data: an Update

Abstract

At $\sqrt{s}=57\pm 7$ TeV, the Pierre Auger Observatory (PAO) collaboration has recently measured the proton-air inelastic production cross section ${\sigma }_{\mathrm{p}-\mathrm{air}}$. Assuming a helium contamination of 25%, they subtracted 30 mb from their measured value, resulting in a p-air inelastic production cross section, ${\sigma }_{\mathrm{p}-\mathrm{air}}=475\pm 22(stat.){\pm }_{15}^{20}(syst.)$ mb, exclusive of helium contamination. Using this result in a Glauber calculation to obtain the $pp$ inelastic cross section, they found the inelastic $pp$ cross section ${\sigma }_{\mathrm{inel}}=90\pm 7(stat.){\pm }_{11}^9(syst.)\pm 1.5(Glaub.)$ mb. Parameterization of the $\bar{p}p$ and $pp$ cross sections incorporating analyticity constraints and unitarity has allowed us to make accurate extrapolations to ultra-high energies, and using Glauber calculations, accurately predict cosmic ray results for $\spai$. In this update for 57 TeV, we predict i) a $pp$ total cross section, ${\sigma }_{\mathrm{tot}}=133.4\pm 1.6$ mb, using high energy predictions from a saturated Froissart bound parameterization of accelerator data on forward $\bar{p}p$ and $pp$ scattering amplitudes and ii) a p-air inelastic production cross section, ${\sigma }_{\mathrm{p}-\mathrm{air}}=483\pm 3$ mb, by using ${\sigma }_{\mathrm{tot}}$ together with Glauber theory, allowing us to determine independently that the helium contamination was 19%, in reasonable agreement with their estimate of 25%. Our predictions agree with all available cosmic ray extensive air shower measurements, both in magnitude and in energy dependence. By using our value for the $pp$ total cross section at 57 TeV, Block and Halzen \cite{blackdisk} have predicted that the $pp$ inelastic cross section is ${\sigma }_{\mathrm{inel}}=92.9\pm 1.6$ mb, in agreement with the measured POA value.

3 pages, 3 figures

References in corpus (5)

• New evidence for the saturation of the Froissart bound
• Forward hadronic scattering at 7 TeV: predictions for the LHC; an update
• Sifting data in the real world
• Ultra-high Energy Predictions of proton-air Cross Sections from Accelerator Data
• New analyticity constraints on the high energy behavior of hadron-hadron cross sections

Cited by in corpus (10)

• First measurement of the total proton-proton cross section at the LHC energy of {\surd} s =7 TeV
• Connection of the virtual ${\gamma }^{\ast }p$ cross section of $ep$ deep inelastic scattering to real $\gamma p$ scattering, and the implications for $\nu N$ and $ep$ total cross sections
• A comprehensive model of soft interactions in the LHC era
• Measurement of the Proton-Air Cross Section with Telescope Array's Middle Drum Detector and Surface Array in Hybrid Mode
• New experimental evidence that the proton develops asymptotically into a black disk
• Implications of a Froissart bound saturation of ${\gamma }^{\ast }$-$p$ deep inelastic scattering. Part I. Quark distributions at ultra small $x$
• Implications of a Froissart bound saturation of ${\gamma }^{\ast }$-$p$ deep inelastic scattering. Part II. Ultra-high energy neutrino interactions
• Proton-air collisions in a model of soft interactions at high energies
• Analysis of $pp$ and $\bar{p}p$ Elastic Scattering Based on Theoretical Bounds in High-Energy Physics: an Update
• Proton-Air Cross Section and Composition of Ultra High Energy Cosmic Rays Observed by Telescope Array