Composition from high $p_\mathrm{T}$ muons in IceCube

Cosmic rays with energies up to $10^{11}\,\mathrm{GeV}$ enter the atmosphere and produce showers of secondary particles. Inside these showers muons with high transverse momentum ($p_\mathrm{T} \gtrsim 2\,\mathrm{GeV}$) are produced from the decay of heavy hadrons, or from high $p_\mathrm{T}$ pions and kaons very early in the shower development. These isolated muons can have large transverse separations from the shower core up to several hundred meters, together with the muon bundle forming a double or triple track signature in IceCube. The separation from the core is a measure of the transverse momentum of the muon's parent particle. Assuming the validity of perturbative quantum chromodynamics (pQCD) the muon lateral distribution depends on the composition of the incident nuclei, thus the composition of high energy cosmic rays can be determined from muon separation measurements. Vice versa these muons can help to understand uncertainties due to phenomenological models as well as test pQCD predictions of high energy interactions involving heavy nuclei. After introducing the physics scenario of high $p_\mathrm{T}$ muons in kilometer-scale neutrino telescopes we will review results from IceCube in its 59-string configuration as starting point and discuss recent studies on composition using laterally separated muons in the final detector configuration.