Analytical description of the distributions of primary and secondary cosmogenic particles

TL;DR

This paper develops analytical models for the energy and angular distributions of primary and secondary cosmogenic particles, including muons and neutrinos, effectively describing their behavior across different energies, altitudes, and angles.

Contribution

It introduces a unified analytical framework for describing cosmogenic particle distributions, incorporating physical effects like energy loss and decay, applicable to various particle types and conditions.

Findings

Analytical functions accurately fit muon momentum data at different altitudes.

The model describes neutrino and electron-type distributions across sites.

Zenith angle distribution follows a cos^{n-1}θ dependence, unaffected by decay.

Abstract

In this work, we present an analytical description of the energy distributions of primary and secondary cosmogenic particles on Earth in terms of parameters having clear physical meaning. A modified power law is assumed for energy distributions, incorporating terms such as energy loss/decay, which are effective at low energies, and a source term, which is dominant at high energies. The parametrizations of the momentum distribution of primary protons and helium have been obtained including energy loss term. For muons, both the energy loss and decay terms have been included. It is shown analytically that zenith angle distributions is given by $\cos^{n-1}\theta$ in terms of energy index $n$ and the presence of decay term does not affect it. The analytical function describes the muon momentum distribution data at different altitudes and zenith angles. The same form is also applied to describe the atmospheric muon and electron-type neutrino distributions simulated at various sites. The presented analytical functions provide an excellent description of all kinds of cosmogenic particles.