pp Interaction at Very High Energies in Cosmic Ray Experiments

TL;DR

This paper analyzes proton-air cross sections from cosmic ray experiments using a high-precision model of proton-proton scattering, successfully extrapolating accelerator data to ultra-high energies and examining asymptotic behaviors.

Contribution

It introduces a reliable analytical representation of pp scattering amplitudes that accurately describes accelerator data and allows for high-energy extrapolation relevant to cosmic ray interactions.

Findings

Good agreement with cosmic ray data from 1 to 100 TeV

High-energy asymptotic behavior deviates from black disk model

Energy dependence of p-air to pp cross section ratio explained

Abstract

An analysis of p-air cross section data from Extensive Air Shower (EAS) measurements is presented, based on an analytical representation of the pp scattering amplitudes that describes with high precision all available accelerator data at ISR, SPS and LHC energies. The theoretical basis of the representation, together with the very smooth energy dependence of parameters controlled by unitarity and dispersion relations, permits reliable extrapolation to high energy cosmic ray and asymptotic energy ranges. Calculations of the p-air production cross section based on Glauber formalism are made using the input values of the pp forward scattering parameters at high energies, with attention given to the independence of the real and imaginary slope parameters. The influence of contributions of diffractive intermediate states, according to Good-Walker formalism, is examined. The comparison with cosmic ray data is very satisfactory in the whole pp energy interval from 1 to 100 TeV. High energy asymptotic behavior of p-air cross sections is investigated in view of the geometric scaling property of the pp amplitudes. The observed energy dependence of the ratio between p-air and pp cross sections in the data is shown to be related to the nature of the pp cross section at high energies, that does not agree with the black disk image.