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

Zbigniew Plebaniak,Tadeusz Wibig,B Pattison

doi:10.1051/epjconf/201714513004

Zbigniew Plebaniak, Tadeusz Wibig + Show 1 more

Open Access

https://doi.org/10.1051/epjconf/201714513004

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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.

Highlights

The hadronic cross section is one of the most important parameter of models dedicated to describing Extensive Air Shower (EAS) development at ultra high energies
We can see an agreement with data over the first dip region which was a weakness of models prepared in past
We have developed a modified simple optical model of protonproton scattering with four model parameters, which allows us to describe the hadronic matter distribution of colliding protons

Summary

Introduction

The hadronic cross section is one of the most important parameter of models dedicated to describing Extensive Air Shower (EAS) development at ultra high energies. Due to QCD nature it is not possible to calculate this parameter from fundamental physical laws This fact forces building complicated phenomenological models, based on accelerator measurements at lower energies, that allow for cross section extrapolations to energies observed in cosmic rays. Such models can give information about the internal structure of colliding particles. In this paper we concentrate on the problem of extrapolating hadronic cross section to cosmic ray energies. For this purpose we developed optical geometrical picture, assume energy dependent parameterization of the hadronic matter distribution in protons. Discussion and physical interpretation are the content of Sect. 5

Scattering amplitudes and their eikonal representation

Results

Discussion