Ultra-high Energy Predictions of proton-air Cross Sections from Accelerator Data

TL;DR

This paper predicts proton-air inelastic cross sections at ultra-high energies using a Froissart bound parameterization of accelerator data, Glauber theory, and constraints from analyticity and unitarity, aligning well with cosmic ray measurements.

Contribution

It introduces a novel extrapolation method for proton-air cross sections at energies up to 100,000 TeV based on a saturated Froissart bound model and Glauber theory, incorporating fundamental physics constraints.

Findings

Predicted cross sections agree with cosmic ray data.

Extrapolation remains accurate up to 10^5 TeV.

Model respects analyticity and unitarity constraints.

Abstract

We predict $\sigma_{p{-}\rm air}^{\rm prod}$, the proton--air inelastic production cross section, at $pp$ center-of-mass energies $2\le\sqrt s \le 100000$ TeV, using high energy predictions from a saturated Froissart bound parameterization of accelerator data on forward $\bar pp$ and $pp$ scattering amplitudes, together with Glauber theory. The parameterization of the $\bar pp$ and $pp$ cross sections incorporates analyticity constraints and unitarity, allowing accurate extrapolations to ultra-high energies. Our predictions are in excellent agreement with cosmic ray extensive air shower measurements, both in magnitude and in energy dependence