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Abstract-A set of models for Monte Carlo simulation of production and interaction of high energy muons is developed in the framework of the Geant4 toolkit. It describes the following physics processes: ionization of high energy muons with radiative corrections, bremsstrahlung, electron-positron pair production, muon induced nuclear reactions, gamma annihilation into muon pair, positron annihilation into muon pair, and into pion pair. These processes are essential for the LHC experiments, for the understanding of the background in underground detectors, for the simulation of effects related with high-energy muons in cosmic ray experiments and for the estimation of backgrounds in future colliders. The applicability area of the models extends to 1 PeV. The major use-cases are discussed.Index Terms-Bremsstrahlung, mesons, modeling, Monte Carlo method, positron beam.

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