Investigation of cosmic rays above the knee by means of muon bundles detected in a wide range of zenith angles

The results of investigation of muon bundles at the Earth’s surface in a wide range of zenith angles on the basis of the new phenomenological characteristic of extensive air showers—spectra of local muon density—have been investigated. Features of the local-density spectra are considered within a simple analytical model. The expected distributions of muon density in a wide range of zenith angles and primary energies, calculated on the basis of the CORSIKA code, are compared with the experimental data.     

Cosmic ray sea level muon spectrum at large zenith angle derived from the latest JACEE primary spectrum

The sea level cosmic ray muon spectrum at 89° has been estimated from the primary nucleon spectrum estimated after the latest JACEE measurements. The p-A collision cross section has been considered for hadronic energy moments calculations. The meson atmospheric diffusion equations after Bugaev et al. have been used in this analysis. The calculated large zenith angle muon spectrum is well in accord with the latest MUTRON data for cosmic ray muons arriving at zenith angles 86° to 90°.On leave from Indian Association for the cultivation of Science, Calcutta 700032, India.     

Muon bundles produced by UHE cosmic rays at large zenith angles

The first experimental results on a new EAS observable, the local muon density spectra measured with a large area coordinate detector DECOR in a wide range of zenith angles, are presented. These data correspond to the interval of primary particle energies from 10¹⁵ to 10¹⁸ eV. Some features of local muon density phenomenology are considered on the basis of an analytical model. Expected distributions of the events in the muon density have been calculated by means of the CORSIKA code and compared with experimental data. The text was submitted by the authors in English.     

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.     

Coupling functions for muon hodoscopes

The specific features of calculating the coupling functions for muon hodoscopes are considered. The results of calculating the main coupling functions for three versions of the primary spectra of cosmic rays (CR)—galactic CR, solar CR during proton events, and galactic CR variations during Forbush decreases-are presented. The calculations have been performed based on modeling CR propagation through the Earth’s atmosphere using the CORSIKA code. The mean and median CR energies, contributing to the muon detector counting rate, have been calculated for different zenith angles. It has been shown that muon detectors are sensitive to different energies of primary CRs for different directions.     

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.     

Experimental observation of the effect of the Earth’s magnetic field on the EAS muon component

The dependence of the intensity of muon bundles recorded using the DECOR coordinate track detector on the angle between the directions of bundle arrival and the Earth’s magnetic field has been analyzed for several ranges of zenith angles. It is found that the intensity of muon bundles decreases with an increase in the transverse magnetic field component, in contrast to the results of the calculation performed on the assumption of flux azimuthal symmetry. The effect of coplanarity of particle tracks in the plane formed by the core of an extensive air shower and the Lorentz force vector is also observed.     

Muon content of ultrahigh-energy air showers: Yakutsk data versus simulations

A sample of 33 extensive air showers (EASs) with estimated primary energies above 2 × 10¹⁹ eV and high-quality muon data recorded by the Yakutsk EAS array is analyzed. The observed muon density is compared event-by-event to that expected from CORSIKA simulations for primary protons and iron using SIBYLL and EPOS hadronic interaction models. The study suggests the presence of two distinct hadronic components, “light” and “heavy.” Simulations with EPOS are in good agreement with the expected composition in which the light component corresponds to protons and the heavy component to iron-like nuclei. With SIBYLL, simulated muon densities for iron primaries are a factor of ∼ 1.5 less than those observed for the heavy component for the same electromagnetic signal. Assuming a two-component proton-iron composition and the EPOS model, the fraction of protons with energies E > 10¹⁹ eV is 0.52_−0.20^+0.19 at the 95% C.L. The text was submitted by the authors in English.     

Atmospheric variations in muon intensity for different zenith angles

The barometric and temperature coefficients of muon intensity for a layer of variable mass and the temperature coefficients for mass-weighted mean atmospheric temperature are found by regressions analysis from the results of continuous measurements of muon intensity at different zenith angles and atmospheric parameters. The temperature coefficients of muon intensity are determined for different atmospheric layers. Using the characteristics obtained, the changes in temperature are found for different atmospheric layers from the data on variations in muon intensity. The results obtained are compared with the observed temperature changes.     

Temperature coefficients for muons at different zenith angles

Differential temperature coefficients for a muon flux have been calculated for different threshold energies and zenith angles. Comparison with the results of previous investigations shows only qualitative agreement, whereas the quantitative differences are significant. Possible reasons for such a discrepancy are discussed.     

Measurements of the integrated muon intensity at large zenith angles

Precision measurements of the zenith-angle distributions of muons in the range 61°–89° are performed using the DECOR coordinate detector. The total number of selected events is more than 20 million. The dependence of the integrated muon intensity on the zenith angle is determined for several threshold energies in the range from 1.7 to 7.2. GeV. The experimental results in these ranges of zenith angles and threshold energies are obtained for the first time. It is demonstrated that the dependence of the integrated muon intensity on the zenith angle is adequately described by a simple analytical relationship.     

Investigation of the properties of the flux and interaction of ultrahigh-energy cosmic rays by the method of local-muon-density spectra

A new method for studying extensive air showers is considered. The method is based on the phenomenology of the localmuon density. It is shown that measurement ofmuon-density spectra at various zenith angles makes it possible to obtain information about the energy spectrum, mass composition, and interaction of cosmic rays over a broad range of energies (10¹⁵–10¹⁸ eV) by using a single array of comparatively small size. The results obtained from a comparison of experimental data on muon bundles from the DECOR coordinate detector with the results of simulation performed under various assumptions on the properties of the primary flux and for various hadron-interaction models are presented, and possible versions of the interpretation of these results are discussed.     

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.     

Evidence for changing of cosmic ray composition between 10(17) and 10(18) eV from multicomponent measurements

The average mass composition of cosmic rays with primary energies between 10(17) and 10(18) eV has been studied using a hybrid detector consisting of the High Resolution Fly's Eye (HiRes) prototype and the MIA muon array. Measurements have been made of the change in the depth of shower maximum and the muon density as a function of energy. The results show that the composition is changing from a heavy to lighter mix as the energy increases.     

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.     

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.     

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°.     

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.     

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.     

大天顶角的到达角起伏

基于修正Kolmogorov谱,运用相位结构函数的平方近似,导出了适用于大天顶角传输的到达角起伏方差及其功率谱的解析表达式.研究结果表明,新导出的方差表达式在任意天顶角都是适用的.散射盘尺度和接收孔径对到达角起伏起平滑作用,当接收孔径远大于散射盘尺度时,由于孔径平滑作用,导出的表达式在任意天顶角都可以近似为弱起伏理论给出的结果；当接收孔径小于散射盘尺度时,散射盘尺度的平滑作用明显,接收孔径的平滑作用相对较小,传统的到达角起伏理论仅在小天顶角是适用的,在大天顶角必须用新导出的方差表达式.当接收孔径D<25 cm时,弱起伏理论给出的表达式的适用范围被限制在小于50°~70°的天顶角内.