Energy and angular distributions of atmospheric muons at the Earth

TL;DR

This paper develops and tests analytical models for the energy and angular distributions of atmospheric muons at Earth, improving the description of muon data across energy ranges and angles.

Contribution

It introduces a modified power law for muon energy distribution and derives new analytical forms for zenith angle distributions, including a model without flat Earth assumptions.

Findings

The modified power law fits cosmic muon data well across energy regimes.

New analytical zenith angle distributions accurately describe data at all angles.

Parameters can characterize muon data as functions of energy, angle, and altitude.

Abstract

A fair knowledge of the atmospheric muon distributions at Earth is a prerequisite for the simulations of cosmic ray setups and rare event search detectors. A modified power law is proposed for atmospheric muon energy distribution which gives a good description of the cosmic muon data in low as well as high energy regime. Using this distribution, analytical forms for zenith angle ($\theta$) distribution are obtained. Assuming a flat Earth, it leads to the $\cos^{n-1}\theta$ form where it is shown that the parameter $n$ is nothing but the power of the energy distribution. Exact analytical function is obtained for inclined trajectory of muon. A new closed form for zenith angle distribution is obtained without assuming a flat Earth and which gives an improved description of the data at all angles even above $70^o$. These distributions are tested with the available atmospheric muon data of energy and angular distributions. The parameters of these distributions can be used to characterize the cosmic muon data as a function of energy, angle and altitude.