Muon energy-loss distribution and its applications to muon energy determination

For measurements of the cosmic-ray muon spectrum at energies above 100 TeV and for observations of high-energy astronomical neutrinos a big detector is necessary. In both cases, information on the muon energy plays an important role. The method for estimating the muon energy from the energy loss should yield accurate values with a big detector. To evaluate the method we measured the muon energy-loss distribution in the MUTRON detector and applied the results to a big detector proposed for deployment in the ocean. When estimating the muon energy we divided the muon track into several segments and discarded the segment with the maximum energy loss. If a detector with a volume of ${\mathrm{}\left(500\mathrm{m}\right)\mathrm{}}^3$ is constructed in the ocean using strings of detectors with 50-m spacing between adjacent strings, and 10-m spacing between detectors on a string, muon energies could be measured with a relative error of about 30%. For muons produced by the charged-current interaction (${\nu }_{\mu }+N\to \nu +X$), the neutrino direction can be determined with an error less than 1° for muon energies above 1 TeV.