Profiles of energetic muons in the atmosphere

TL;DR

This paper models the production and variation of high-energy atmospheric muons as a function of depth, primary cosmic ray type, and atmospheric conditions, with applications to underground detectors like IceCube, MINOS, and NOvA.

Contribution

It generalizes the Elbert formula to account for meson decay along cosmic-ray trajectories, linking muon rates to atmospheric profiles and primary cosmic ray properties.

Findings

Muon rates vary with atmospheric temperature and primary mass.

The generalized model predicts muon bundle sizes at different depths.

Applications include improved interpretation of data from IceCube, MINOS, and NOvA.

Abstract

The production spectrum of high-energy muons as a function of depth in the atmosphere is relevant for understanding properties of event rates in deep detectors. For a given atmospheric profile, cascades of heavy nuclei develop at higher altitude than proton showers, giving rise to larger separation of muons at depth. For a given type of primary cosmic ray, seasonal variations in muon rates reflect the fact that higher temperatures correspond to lower densities and to a relative increase in the ratio of decay to re-interaction of the parent mesons. In this paper, we present a generalization of the Elbert formula that tracks meson decay to muons along the trajectory of the primary cosmic-ray nucleus. The convolution of the production spectrum with a changing atmospheric profile provides the dependence of event rates and sizes of muon bundles on temperature and primary mass. We consider applications to IceCube and also to multiple muon events in the compact underground detectors of MINOS and the NOvA Near Detector.