On the Accuracy of Underground Muon Intensity Calculations

Cosmic ray muons detected by deep underground and underwater detectors have served as an information source on the high-energy cosmic ray spectrum and hadronic interactions in air showers for almost a century. The theoretical interest in underground muons has nearly faded because space-borne experiments probe the cosmic ray spectrum more directly, and accelerators provide precise measurements of hadron yields. However, underground muons probe unique hadron interaction energies and phase space, which are still inaccessible to present accelerator experiments. The cosmic ray nucleon energies reach the hundred-TeV and PeV ranges, which are barely accessible with space-borne experiments. Our new calculation combines two modern computational tools: MCEq, for surface muon fluxes, and PROPOSAL, for underground transport. We demonstrate excellent agreement with measurements of cosmic ray muon intensities underground within estimated errors. Beyond that, the precision of historical data turns out to be significantly smaller than our error estimates. This result shows that the sources of high-energy atmospheric lepton flux uncertainties at the surface or underground can be significantly constrained without taking more data or building new detectors. The reduction of uncertainties can be expected to impact data analyses at large-volume neutrino telescopes and for the design of future ton-scale direct dark matter detectors.