Calculation of the flux of atmospheric neutrinos

Atmospheric neutrino fluxes are calculated over the wide energy range from 30 MeV to 3000 GeV for the study of neutrino physics using the data from underground neutrino detectors. In this calculation, a full Monte Carlo method is employed for low energy neutrinos (30 MeV–3 GeV), while a hybrid method is used for high energy neutrinos (1–3000 GeV). At low energies, the ratio (${\nu }_{\mathit{e}}$+ν${\mathrm{¯}}_{\mathit{e}}$)/(${\nu }_{\mathrm{\mu }}$+ν${\mathrm{¯}}_{\mathrm{\mu }}$) agrees well with other calculations and is significantly different from observations. For the high energy neutrino fluxes, the zenith angle dependence of the atmospheric neutrino flux is studied in detail, so that neutrino-oscillation parameters can be calculated for comparison with experimental results. The atmospheric muon flux at high altitude and at sea level is studied to calibrate the neutrino fluxes at low energies and high energies, respectively. The agreement of our calculation with observations is satisfactory. The uncertainty of atmospheric neutrino fluxes is also studied.