The vertical sea-level muon spectrum at energies above 1 GeV and the muon intensities at depths up to 18 km w.e. in different rocks and in water are calculated. The results are particularly collated with a great body of the ground-level, underground, and underwater muon data. In the hadron-cascade calculations, we take into account the logarithmic growth with energy of inelastic cross sections and pion, kaon, and nucleon generation in pion-nucleus collisions. For evaluating the prompt muon contribution to the muon flux, we apply the two phenomenological approaches to the charm production problem: the recombination quark-parton model and the quark-gluon string model. We give simple fitting formulas describing our numerical results. To solve the muon transport equation at large depths of a homogeneous medium, we use a semianalytical method, which allows the inclusion of an arbitrary (decreasing) muon spectrum at the medium boundary and real energy dependence of muon energy losses. Our analysis shows that at the depths up to 6-7 km w.e., essentially all underground data on the muon flux correlate with each other and with the predicted one for conventional (π, K)-muons, to within 10 %. However, the high-energy sea-level muon data as well as the data at high depths are contradictory and cannot be quantitatively described by a single nuclear-cascade model.

A new calculation of the atmospheric fluxes of cosmic-ray hadrons and muons in the energy range 10-10 5 GeV has been performed for the set of hadron production models, EPOS 1.6, QGSJET II-03, SIBYLL 2.1, and others that are of interest to cosmic ray physicists. The fluxes of secondary cosmic rays at several levels in the atmosphere are computed using directly data of the ATIC-2, GAMMA experiments, and the model proposed recently by Zatsepin and Sokolskaya as well as the parameterization of the primary cosmic ray spectrum by Gaisser and Honda. The calculated energy spectra of the hadrons and muon flux as a function of zenith angle are compared with measurements as well as other calculations. The effect of uncertainties both in the primary cosmic ray flux and hadronic model predictions on the spectra of atmospheric hadrons and muons is considered.

We present high energy spectra and zenith-angle distributions of the atmospheric muons computed for the depths of the locations of the underwater neutrino telescopes. We compare the calculations with the data obtained in the Baikal and the AMANDA muon experiments. The prompt muon contribution to the muon flux underwater due to recent perturbative QCD-based models of the charm production is expected to be observable at depths of the large underwater neutrino telescopes. This appears to be probable even at rather shallow depths (1-2 km), provided that the energy threshold for muon detection is raised above $\sim 100$ TeV.Comment: 7 pages, RevTeX, 7 eps figures, final version to be published in Phys.Rev.D; a few changes made in the text and the figures, an approximation formula for muon spectra at the sea level, the muon zenith-angle distribution table data and references adde

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 (νµ +νµ) and (νe +νe) 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 νµ 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 νµ/νe 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.PACS numbers: 13.85. Tp, 95.85.Ry, 95.55.Vj

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