MUTE: A Program for High-Precision Calculations of Underground and Underwater Muon Intensities

Abstract

High-energy atmospheric muons originating from cosmic ray interactions in Earth's atmosphere have played a vital role in the field of astroparticle physics for nearly a century. Because the properties of the muons reflect the primary cosmic rays that produce them, they serve as a unique probe for understanding the cosmic ray spectrum as well as hadronic interactions at energies beyond the reach of current accelerator experiments. However, these muons also pose a significant challenge in rare event search experiments aiming to detect dark matter and neutrinos. These experiments are typically placed deep underground to escape atmospheric muons, using the rock overburden as natural shielding. However, while travelling through the rock, high-energy muons can induce backgrounds that mimic signals of interest in these detectors. Therefore, large-scale rare event search experiments rely on precise calculations of underground muon fluxes in order to properly characterise their expected backgrounds to develop effective shielding strategies. This work presents a computational code, MUTE (MUon inTensity codE), which calculates forward-predictions for underground and underwater muons by combining the latest computational tools available: MCEq and DAEMONFLUX for surface muon fluxes, and the Monte Carlo code PROPOSAL for transport through matter. The computational scheme is explained, outlining how MUTE achieves a full description of underground and underwater muons up to depths of 14 km.w.e., including calculations for muon intensities, energy spectra, angular distributions, and total fluxes. This method achieves excellent agreement with experimental data from a wide variety of detectors around the world, with precision surpassing previous error estimates. Applications of the MUTE code are also discussed, including its functionality in cross-checking data analyses and its ability to compute high-precision seasonal variations of total underground muon fluxes.