Cosmic-rays with energies up to 3x1020 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 sqrt snn = 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 aresensitive 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 (pT) spectra in cosmic-ray air showers fromMACRO, and describe how the IceCube neutrino observatory and the proposed Km3Net detector will extend these measurements to a higher pT region where perturbative QCD should apply. With a 1 km2 surface area, the full IceCube detector should observe hundreds of muons/year with pT in the pQCD regime.