Ultra-high Energy Predictions of Proton-Air Cross Sections from Accelerator Data: an UpdateReport as inadecuate



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


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At $\sqrt s = 57\pm 7$ TeV, the Pierre Auger Observatory PAO collaboration has recently measured the proton-air inelastic production cross section $\sigma { m p-air}$. Assuming a helium contamination of 25%, they subtracted 30 mb from their measured value, resulting in a p-air inelastic production cross section, $\sigma { m p-air}=475 \pm 22\ { m stat.}\pm^{20} {15} \ { m syst.}$ 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 $\sigma { m inel}= 90\pm 7\ { m stat.} \pm^9 {11} { m syst.} \pm 1.5 { m \ Glaub.}$ mb. Parameterization of the $\bar pp$ 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, $\sigma { m tot}=133.4\pm 1.6$ mb, using high energy predictions from a saturated Froissart bound parameterization of accelerator data on forward $\bar pp$ and $pp$ scattering amplitudes and ii a p-air inelastic production cross section, $\sigma { m p-air}=483\pm 3 $ mb, by using $\sigma { m tot}$ 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 $\sigma { m inel}= 92.9\pm 1.6$ mb, in agreement with the measured POA value.



Author: M. M. Block

Source: https://archive.org/







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