Extrapolation of proton-proton cross section to cosmic ray energies using geometrical model

Abstract

We present a new parameterization of the hadronic matter distribution in the geometrical picture of elastic scattering. Our model contains four free energy-dependent parameters that allows us to propose a better description of differential elastic cross section data measured in accelerator experiments from ISR to LHC energies. A simple linear dependence of all parameters on the logarithm of energy above √_s = 300 GeV allows an extrapolation of elastic, inelastic and total proton-proton cross sections to ultra high energies seen in cosmic rays. Results of the extrapolation are in agreement with cross sections presented by ground-based cosmic ray experiments like AUGER or Telescope Array. Our parameterization also shows agreement with “BEL behaviour” of proton.