Parameterization of muon bundle energy loss in deep ice

When a high-energy cosmic ray particle interacts in the atmosphere, it creates a cascades of secondary particles, including electrons, positrons, photons and mesons. These mesons will decay into muons, muon neutrinos and other particles. These high energy muons are collectively referred to as a muon bundle. The energy and number of these muons in a bundle are related to the primary energy and mass of the cosmic ray particle. The parameterization takes into account the primary energy and zenith angle of the cosmic ray particle. We also consider the spatial separation between muons in the bundle as they propagate through the ice. This allows us to add new parameters to the muon bundle energy loss. We present the energy loss of muon bundles generated by cosmic ray particles with primary energies from 500 TeV to 500 PeV.