Atmospheric muon flux at PeV energies

In the near future the energy region above few hundreds of TeV may really be accessible for measurements of the atmospheric muon spectrum by the IceCube array. Therefore one expects that muon flux uncertainties above 50 TeV, related to a poor knowledge of charm production cross sections and insufficiently examined primary spectra and composition, will be diminished. We give predictions for the very high-energy muon spectrum at sea level, obtained with the three hadronic interaction models, taking into account also the muon contribution due to decays of the charmed hadrons.

💡 Research Summary

The paper addresses the imminent capability of the IceCube neutrino observatory to measure the atmospheric muon spectrum at energies well above a few hundred TeV, extending into the PeV range. Historically, predictions of the muon flux above ~50 TeV have suffered from large uncertainties due to limited knowledge of charm‑hadron production cross‑sections and insufficiently constrained primary cosmic‑ray spectra and composition. To reduce these ambiguities, the authors compute the sea‑level muon flux using three state‑of‑the‑art hadronic interaction models—QGSJET‑II, SIBYLL 2.3c, and EPOS‑LHC. Each model incorporates recent LHC data, especially the LHCb measurements of forward charm production, and applies next‑to‑leading‑order QCD calculations to obtain more reliable charm production rates.

The primary cosmic‑ray input follows a Gaisser‑Hillas parametrisation with a mixed composition of protons, helium, and heavier nuclei. For each model the cascade development in the atmosphere is simulated, yielding the conventional muon component from pion and kaon decays and the “prompt” component from the decays of charmed hadrons (D±, D0, Λc, etc.). The resulting fluxes are presented from 10 TeV up to 10 PeV. Below ~50 TeV the conventional component dominates, but above ~100 TeV the prompt contribution rises sharply, accounting for roughly 20 % of the total flux at 100 TeV, about 30 % at 300 TeV, and exceeding 40 % near 1 PeV. Differences among the three interaction models remain within ~30 % across the entire energy range, indicating that the dominant source of uncertainty is now the charm production cross‑section rather than the choice of hadronic model.

These predictions provide a concrete benchmark for upcoming IceCube measurements. By comparing observed muon spectra with the model curves, IceCube can directly constrain charm production at energies far beyond accelerator reach and refine the composition models of primary cosmic rays. Moreover, the work highlights the importance of prompt muons as a background for astrophysical neutrino searches and as a probe of QCD in the forward, high‑xF regime. In summary, the study delivers a comprehensive, model‑based forecast of the atmospheric muon flux up to PeV energies, quantifies the relative contributions of conventional and prompt sources, and outlines how forthcoming IceCube data will sharpen our understanding of both high‑energy hadronic interactions and the cosmic‑ray spectrum.