Total Hadronic Cross Section and the Elastic Slope: An Almost Model-Independent Connection

TL;DR

This paper introduces a nearly model-independent parametrization linking the total hadronic cross section and elastic slope in proton-proton scattering, useful for cosmic-ray physics and air shower studies.

Contribution

It provides an analytical, empirical parametrization of the ratio of total cross section to elastic slope based on data and theoretical limits, aiding high-energy physics applications.

Findings

The parametrization aligns well with existing data above 10 GeV.

It offers a practical tool for cosmic-ray and air shower analysis.

The approach is nearly model-independent and grounded in unitarity and black-disk limit.

Abstract

An almost model-independent parametrization for the ratio of the total cross section to the elastic slope, as function of the center of mass energy, is introduced. The analytical result is based on the approximate relation of this quantity with the ratio $R$ of the elastic to total cross section and empirical fits to the $R$ data from proton-proton scattering above 10 GeV, under the conditions of asymptotic unitarity and the black-disk limit. This parametrization may be useful in studies of extensive air showers and the determination of the proton-proton total cross section from proton-air production cross section in cosmic-ray experiments.