Cosmic muon flux at shallow depths underground

The cosmic muon background has been calculated for facilities placed at shallow depths. A relatively simple formula has been proposed for the muon spectrum at sea level that ensures the calculation of the depth dependences of the vertical muon intensity and integral muon flux. Calculations show that the zenith-angle distribution of the muon flux density is almost unchanged for depths from 10 to 100 m of solid rock. The muon angular distributions are presented for all three possible cases of the arrangement of the instruments in measurements carried out on the ground and at shallow depths. It has been shown that, to eliminate the cosmic muon background, it is necessary to install an active cosmic ray shielding “umbrella” covering a zenith angle ? of no less than 80°.     

Sea level muon spectra at large zenith angles derived from the latest JACEE primary nucleon spectrum

Summary Sea level muon energy spectra at large zenith angles have been derived from the latest JACEE primary spectrum using the Fermilab Single-Arm Spectrometer data on charged-meson production. The role of increasing total cross-section on the final result for the energy spectra has been investigated here with special emphasis. The inclusion of the rising total cross-section at cosmic range of energies, it is seen, has come into much use in explaining the observed data at very high energies. The autors of this paper have agreed not to receive the proofs for correction.     

Estimation of the Sea Level Muon Spectra at Different Zenith Angles below 10 TeV Energy

The moderate energy primary cosmic ray nucleon spectrum has been calculated from the direct measurements of Webber et al., Seo et al., and Menn et al. along with the other results surveyed by Swordy. Using these directly measured primary mass composition results all particle primary nucleon energy spectrum has been constructed using superposition model to estimate the energy spectra of muons from the decay of the cosmic ray non-prompt and prompt mesons in the atmosphere. The Z-factors have been estimated from the CERN LEBC-EHS on the Lorentz invariant cross section results on pp ^±X and pp K^±X inclusive reactions and FNAL data on ^±p ^±X reactions, and duly corrected for A--A collisions. Using these Z-factors the meson energy spectra in the atmosphere have been calculated. The sea level muon energy spectra at zenith angles 0°, 45°, 72°, and 75° have been derived from the decay of non-prompt mesons by adopting standard diffusion equation of hadronic cascades. The contribution of charmed mesons to muon spectrum has also been accounted by adapting the conventional procedure. The derived differential sea level muon energy spectra for energies 10 TeV have been found to follow the power law fits of the form N (E) const. E ^-. Our estimated muon energy spectra at zenith angles 75° have been found comparable with the global spectrograph muon flux results of MARS, DEIS, and MSU groups.     

Cosmic prompt-muon spectrum at super high energies estimated from the JACEE primary spectrum using recent charmed-particle production cross-sections

Summary The prompt-muon flux generated directly from the decay of short-lived particles like D-mesons and Λ_c-hyperons produced during primary cosmic proton-air collisions has been estimated. The inclusive production cross-sections of charmed particles based on the recombination of quark parton model developed by Bugaevet al. and the primary-nucleon spectrum based on the latest JACEE balloon flight data have been used in this investigation. The derived direct muon spectrum has been compared with the earlier results of Elbertet al., Inazawaet al. Bugaevet al. and Allkofer and Bhattacharyya.     

Local Muon Density Spectra at Various Zenith Angles Measured with NEVOD-DECOR

Data on cosmic ray muon bundles accumulated at the NEVOD-DECOR complex over the period from May 2012 to December 2018 have been analyzed. Local muon density spectra at various zenith angles have been reconstructed and compared with CORSIKA-based simulations. At large zenith angles and high muon multiplicities corresponding to primary particle energies more than about 3 × 1017 eV an excess of multi-muon events compared to simulations is clearly seen. Present data are compatible with the expectation for recent LHC-adjusted hadron interaction models only under assumption of extremely heavy (iron group nuclei) primary composition. The assumption of a heavy composition is however in contradiction with other EAS observables, such as maximum depth and its fluctuations.     

Super-high-energy neutrino spectra in the atmosphere derived from the latest JACEE, MSU, SOKOL and CRN primary spectrum usingZ-factors for p-air collisions estimated from Fermi national accelerator data

Summary The absolute spectra of atmospheric neutrinos in the vertical direction and at large zenith angle have been estimated directly from the primary cosmic-ray nucleon spectrum based on the latest JACEE, MSU, SOKOL and CRN data surveyed by Swordy. The Fermi National Accelerator Laboratory results for pp→K^±X, pp→K^±X and pp→pX inclusive reactions have been used for theZ-factor calculations for meson production and these were modified for p-air and A-A collisions. The derived muon and electron neutrino spectra at 0° and 89° from non-prompt meson decay are found comparable with the results of Volkova and Zatsepin, and Butkevichet al. An estimate of the prompt muon neutrino spectra at 0° and 89° fromtthe charmed-meson decay has been given along with the earlier results of different authors. The present result for muon neutrino spectra at zenith angles 0° and 89° is found in approximate agreement with the EAS-TOP results of the Gran Sasso group.     

Uncertanties of atmospheric high-energy muon fluxes and spectrum of primary cosmic rays

New results of calculations of nucleon, π-and K-meson, and muon fluxes generated during high energy cosmic ray interactions with the Earth’s atmosphere are presented. The calculations are based on the method of solving the nuclear cascade equations with allowance for non-scaling behavior of inclusive hadron production cross sections, increase of cross sections of inelastic hadron-nucleus collisions with energy, and non-power-law character of primary spectrum. The hadron and muon fluxes are calculated at different atmospheric altitude levels for several spectral models and compositions of primary cosmic rays. Results of calculations are compared with recent measurements using the L3+Cosmic and CosmoALEPH facilities. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 41–46, September, 2007.     

Muon Spectra at Different Altitudes Derived from Bose-Type Model

The spectra of cosmic pions and kaons produced at the top of the atmosphere have been derived from the primary cosmic ray spectrum of GRIGOROV et al. by using the Bose-type model. With the help of pion and kaon atmospheric diffusion equations the muon spectra at different atmospheric depths viz., 690, 535 and 1033 g cm^?2 have been estimated. The results are in accord with the magnetic spectrograph data of KOCHARIAN et al. and ALLKOFER et al.     

Energy spectrum of cosmic ray muons above 10 TeV according to BUST data

The energy spectrum of cosmic ray muons in the range of several TeV to PeV obtained through the analysis of multiple interactions of muons (the pair meter technique) in the Baksan Underground Scintillation Telescope (BUST) is presented. Results are compared with prior BUST data on the muon energy spectrum measurements and data of other experiments, along with calculations for different muon spectrum models.     

Investigation of the Energy Loss of Muon Bundles in the Cherenkov Water Calorimeter

Investigations of the energy loss of muon bundles are being conducted at the Experimental complex NEVOD. Such investigations are directed to detailed study of “muon puzzle” (the excess of multi-muon events observed in several cosmic ray experiments at ultra-high energies). Results of measurements of the muon bundle energy deposit during a long period of observations in primary cosmic ray energy range 10–1000 PeV have been obtained and have been compared with simulations performed on the basis of the CORSIKA code.     

The extensive air shower muon number spectrum beyond the knee in the cosmic-ray energy spectrum

The extensive air shower (EAS) muon number spectrum is obtained with increased statistics using the central muon detector of the EAS MSU array, which records muons with energies above 10 GeV. The dependence of the mass composition of primary cosmic rays on the energy is considered. The conclusion is confirmed that for energies from 3 × 10¹⁵ eV (the primary energy spectrum knee) up to 10¹⁷ eV a change in the composition associated with an increase in the proportion of heavy nuclei occurs; however, after the energy of 10¹⁷ eV, the proportion of heavy nuclei begins to decrease and the composition becomes lighter. A comparison with similar data from other experiments is conducted. The existence of an additional component of cosmic rays is confirmed; earlier an indication of its presence was derived from data on the EAS electron number spectrum.     

THE VERTICAL DIFFERENTIAL MOMENTUM SPECTRUM OF THE MUON AT 3200M ABOVE SEA-LEVEL

The vertical differential momentum spectrum and the charge ratio of the cosmic ray muon, in the range(0.4—250GeV/c), has been measured by means of the magnetic spectrometer and the range-spectrometer in Yunnan station at 3200 m above the sea level. The present spectrum is in agreement with the differential spectrum of muons, measured by others at the same mountain altitude. In the 15—250GeV/c momentum range, the spectrum obtained from the present experiment is also in good agreement with the differential spectrum of the muon which has been determined by O.C. Allkofer et al. at the sea level. The charge ratio of the muon is almost constant in the range (5—100GeV/c). The average value is 1.30±0.06.     

Derivation of muon spectrum at high energies from the recent JACEE primary cosmic-ray spectrum using Fermilab data on meson production

Summary The energy spectrum of sea level muons in the range (10²÷10⁴) GeV has been calculated from the latest directly measured JACEE primary spectrum using Fermilab results on pp→π^± X and pp→K^± X inclusive reactions. The conventional pion atmospheric diffusion equation after Bugaevet al. has been used in this analysis to account the flux of muons emerged from the multiple generation of mesons in air. The derived muon spectrum has been compared with the earlier magnetic spectrograph data of Durham and Kiel groups. The latest BAKSAN scintillator telescope data is well in agreement with the calculated integral spectrum originated from the meson decays in the range (1÷10⁴) GeV.     

Kneelike structure in the spectrum of the heavy component of cosmic rays observed with KASCADE-Grande

We report the observation of a steepening in the cosmic ray energy spectrum of heavy primary particles at about 8×10(16) eV. This structure is also seen in the all-particle energy spectrum, but is less significant. Whereas the "knee" of the cosmic ray spectrum at 3-5×10(15) eV was assigned to light primary masses by the KASCADE experiment, the new structure found by the KASCADE-Grande experiment is caused by heavy primaries. The result is obtained by independent measurements of the charged particle and muon components of the secondary particles of extensive air showers in the primary energy range of 10(16) to 10(18) eV. The data are analyzed on a single-event basis taking into account also the correlation of the two observables.     

Investigation of the zenith angle dependence of cosmic-ray muons at sea level

Angular distribution of cosmic-ray muons at sea level has been investigated using the Geant4 simulation package. The model used in the simulations was tested by comparing the simulation results with the measurements made using the Berkeley Lab cosmic ray detector. Primary particles’ energy and fluxes were obtained from the experimental measurements. Simulations were run at each zenith angle starting from θ?=?0° up to θ?=?70° with 5° increment. The angular distribution of muons at sea level has been estimated to be in the form I(θ)?=?I(0°) cos ⁿ (θ), where I(0°) is the muon intensity at 0° and n is a function of the muon momentum. The exponent n?=?1.95±0.08 for muons with energies above 1 GeV is in good agreement, within error, with the values reported in the literature.     

High-energy cosmic ray muons in the Earth’s atmosphere

We present the calculations of the atmospheric muon fluxes at energies 10–10⁷ GeV based on a numerical-analytical method for solving the hadron-nucleus cascade equations. It allows the non-power-law behavior of the primary cosmic ray (PCR) spectrum, the violation of Feynman scaling, and the growth of the total inelastic cross sections for hadron-nucleus collisions with increasing energy to be taken into account. The calculations have been performed for a wide class of hadron-nucleus interaction models using directly the PCR measurements made in the ATIC-2 and GAMMA experiments and the parameterizations of the primary spectrum based on a set of experiments. We study the dependence of atmospheric muon flux characteristics on the hadronic interaction model and the influence of uncertainties in the PCR spectrum and composition on the muon flux at sea level. Comparison of the calculated muon energy spectra at sea level with the data from a large number of experiments shows that the cross sections for hadron-nucleus interactions introduce the greatest uncertainty in the energy region that does not include the knee in the primary spectrum.     

Discovery of atmospheric neutrino oscillations**

Atmospheric neutrinos are produced by cosmic ray interactions in the atmosphere. The zenith‐angle and energy dependence of the muon‐ and electron‐ neutrino events are observed in atmospheric neutrino experiments. Through these studies neutrino oscillations were discovered. In this article, studies of atmospheric neutrinos in the Kamiokande and Super‐Kamiokande experiments are described.     

Expected Spectra of Muon-Induced Cascades in IceCube

The neutrino telescope IceCube is capable to reconstruct the energy spectrum of muons in very high energy region by means of measurements of muon-induced cascades. To compare with experimental data, the expected spectra of cascades were theoretically estimated. Calculations were performed for two variants of muon spectrum on the ice surface: a simple power-law energy spectrum with a differential slope index −3.7, and a composite spectrum combined of two power spectra with differential indexes −3.7 and −2.7. The differential spectra of cascades for different zenith angles and integral cascade spectra calculated for two variants of muon spectra are discussed.     

Energy release of inclined muon groups in the nevod water Cherenkov detector

The results of the analysis of the first experimental data on the energy release of inclined muon groups of cosmic rays in the water Cherenkov detector, obtained at the NEVOD-DECOR complex, are presented. It was found that the average specific energy release in the Cherenkov calorimeter (normalized to the muon densitymeasured by the data of the coordinate detector)weakly depends on the muon density; however, the significant dependence on the zenith angle is observed, which indicates an increase in the average muon energy in groups with an increase in the zenith angle.     

Energy spectrum and mass composition of primary cosmic rays at energies 10<Superscript>15</Superscript>–10<Superscript>18</Superscript> eV

Data on muon and electron components of extensive air showers (EAS) (obtained with the EAS MSU array) were used to derive the primary cosmic ray (PCR) mass composition. It is shown that for energies beyond the knee at energy 3 × 10¹⁵ eV the abundance of heavy nuclei increases with energy. But at energies above 10¹⁷ eV the abundance of light nuclei starts to grow. The primary cosmic ray spectrum in the range 10¹⁵–10¹⁸ eV is analyzed. It is shown that at energies above 10¹⁷ eV the additional component appears and it differs from the bulk of Galactic cosmic rays generated by shocks in SN remnants.