Profiles of energetic muons in the atmosphere

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.