Cosmic-rays with energies up to 3 Γ10 20 eV have been observed. The nuclear composition of these cosmic rays is unknown but if the incident nuclei are protons then the corresponding center of mass energy is β s nn = 700 TeV. High energy muons can be used to probe the composition of these incident nuclei. The energy spectra of high-energy (> 1 TeV) cosmic ray induced muons have been measured with deep underground or under-ice detectors. These muons come from pion and kaon decays and from charm production in the atmosphere.
Terrestrial experiments are most sensitive to far-forward muons so the production rates are sensitive to high-x partons in the incident nucleus and low-x partons in the nitrogen/oxygen targets. Muon measurements can complement the central-particle data collected at colliders. This paper will review muon production data and discuss some non-perturbative (soft) models that have been used to interpret the data. I will show measurements of TeV muon transverse momentum (p T ) spectra in cosmic-ray air showers from MACRO, and describe how the IceCube neutrino observatory and the proposed Km3Net detector will extend these measurements to a higher p T region where perturbative QCD should apply. With a 1 km 2 surface area, the full IceCube detector should observe hundreds of muons/year with p T in the pQCD regime. Nuclear Physics A 830 (2009) 869c-872c