High-energy neutrino fluxes and flavor ratio in the Earth's atmosphere

We calculate the atmospheric neutrino fluxes in the energy range $100$ GeV -- $10$ PeV with the use of several known hadronic models and a few parametrizations of the cosmic ray spectra which take into account the knee. The calculations are compared with the atmospheric neutrino measurements by Frejus, AMANDA, IceCube and ANTARES. An analytic description is presented for the conventional ($\nu_\mu+\bar\nu_\mu$) and ($\nu_e+\bar\nu_e$) energy spectra, averaged over zenith angles, which can be used to obtain test data of the neutrino event reconstruction in neutrino telescopes. The sum of the calculated atmospheric $\nu_\mu$ flux and the IceCube best-fit astrophysical flux gives the evidently higher flux as compared to the IceCube59 data, giving rise the question concerning the hypothesis of the equal flavor composition of the high-energy astrophysical neutrino flux. Calculations show that the transition from the atmospheric electron neutrino flux to the predominance of the astrophysical neutrinos occurs at $30-100$ TeV if the prompt neutrino component is taken into consideration. The neutrino flavor ratio, extracted from the IceCube data, does not reveal the trend to increase with the energy as is expected for the conventional neutrino flux in the energy range $100$ GeV - $30$ TeV. A depression of the ratio $R_{\nu_\mu/\nu_e}$ possibly indicates that the atmospheric electron neutrino flux obtained in the IceCube experiment contains an admixture of the astrophysical neutrinos in the range $10-50$ TeV.