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.     

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.     

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.     

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.     

Cosmic ray spectrum obtained from the energy scattered by the particles of extensive air showers in the atmosphere and the galactic model

The differential energy spectrum of cosmic rays that is obtained on the basis of the measurements of Cherenkov radiation from extensive air showers in an energy range of 10¹⁵–10²⁰ eV is compared with the model of the propagation of primary particles in the interstellar medium with fractal properties. It is found that the shape of the experimental spectrum is in good agreement with the shape of the calculated spectrum of “all particles” at 10¹⁵–10¹⁸ eV. The average mass composition of cosmic rays that is calculated on the basis of five components does not contradict the average mass composition obtained from the experimental data for several parameters in this energy range.     

Charm production and experimental data on cosmic neutrino flux

The results of calculation of atmospheric neutrino fluxes at sea level with energies up to 10⁷ GeV are presented. The calculations were performed within the empirical model based on modern data on inclusive cross sections of pion, kaon, and charmed particle production in nucleon-air nucleus interactions, obtained in experiments on accelerators up to nucleon energies of ～20 TeV. A comparison of the calculated and experimental data on cosmic muon neutrino fluxes measured on AMANDA II shows their agreement.     

Fluxes of cosmic-ray muons and atmospheric neutrinos at high energies

The problem of charm generation in the interactions of nucleons with nuclei of air atoms at energies inaccessible at present-day accelerators is discussed. Both experimental data on cosmic-ray muons and the predictions of QCD-based theoretical models are used in analyzing the behavior of the differential cross sections for charmed-particle production at high energies. The calculated fluxes of muons and neutrinos arriving at sea level both along the vertical and along the horizontal direction are presented, together with their approximations for the interval 2×10²–10¹⁰ GeV.     

Can EMMA solve the puzzle of the knee?

The knee is a change in the slope of the cosmic ray spectrum at approximate energy of 3 PeV. There are multiple competing models for the knee giving conflicting predictions about this change for different masses of the primary particle. Accurate mass measurements of cosmic rays spectra around 3 PeV would be able to exclude some of these models. Cosmic-ray experiment EMMA uses a new method for studying the composition of cosmic rays at the knee area. It is able to determine the multiplicity, the lateral distribution, and the arrival direction of incoming muons produced early in the shower evolution on an event-by-event basis and deduce from these measurements the mass and the energy of the primary particle. EMMA is situated at the depth of 75 m in the Pyhäsalmi mine, Finland. This rock overburden, which corresponds to 210 m of water equivalent, gives EMMA a cut-off energy of 50 GeV for vertical muons. Since the simulations using different air-shower models give similar predictions for the lateral distribution of these high energy muons, we are confident that EMMA should yield a reliable and an air-shower model independent data on the composition of cosmic rays around the knee region.     

Temperature effect of the integral flux of cosmic-ray muons at high energies

The temperature coefficients of the integral fluxes of cosmic-ray muons arriving at sea level vertically and horizontally with energies of 10², 10⁴, and 3 × 10⁶ GeV are calculated. Decays of pions, kaons, and charmed particles are considered as sources of muon generation in the atmosphere (according to current data on the generation cross sections of pions, kaons, and charmed particles in interactions between nucleons and the nuclei of atmospheric atoms, obtained in experiments on accelerators and in quantum chromodynamics models). The uncertainties in the generation cross sections of charmed particles are quite high.     

On the composition of cosmic rays with E 0 ≥ 1017 eV according to the Yakutsk EAS array data

The energy spectrum and anisotropy of primary cosmic rays, as well as the lateral distribution functions of electrons and muons in extensive air showers (EASs) with E ₀ ≥ 10¹⁷ eV, are presented according to the Yakutsk EAS array data. It has been shown that the spectrum and lateral distribution functions in some energy ranges have different shapes for the particles that arrive from the disc of the Supergalaxy (Local Supercluster of galaxies) and from the other part of the celestial sphere. This is interpreted as the manifestation of the interaction of extragalactic primary cosmic rays with the gas of the Supergalaxy that possibly leads to the production of new ultra-high-energy particles.     

Cosmic ray spectrum obtained from the energy scattered by the particles of extensive air showers in the atmosphere and the galactic model

The differential energy spectrum of cosmic rays that is obtained on the basis of the measurements of Cherenkov radiation from extensive air showers in an energy range of 10¹⁵–10²⁰ eV is compared with the model of the propagation of primary particles in the interstellar medium with fractal properties. It is found that the shape of the experimental spectrum is in good agreement with the shape of the calculated spectrum of “all particles” at 10¹⁵–10¹⁸ eV. The average mass composition of cosmic rays that is calculated on the basis of five components does not contradict the average mass composition obtained from the experimental data for several parameters in this energy range. Original Russian Text ? S.P. Knurenko, A.A. Ivanov, A.V. Saburov, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 10, pp. 709–712.     

Nonstationary phenomena in cosmic rays with <Emphasis Type="Italic">E</Emphasis><Subscript>0</Subscript> ≤ 10<Superscript>18</Superscript> eV according to the data of the Yakutsk EAS array

The energy spectrum of cosmic rays and the fraction of muons with the threshold 1.0secθ GeV in the total number of charged particles in extensive air showers with energy E ₀ ≥ 10¹⁷ eV according to Yakutsk array data collected during 35 years of its continuous operation in 1978–2012 have been analyzed. It has been shown that these characteristics are noticeably different in different time periods. Before 1996, the integral intensity of the spectrum at E ₀ = 10¹⁷ eV varied near one stable position and then began to increase. It increased by (45 ± 5)% in seven years and, then, began to decrease. This phenomenon was accompanied a similar change in the fraction of muons and was caused by a significant increase in the average weight of the chemical composition of cosmic rays after 1996 as compared to preceding years.     

Simulation of muon-induced air showers affecting CMS tracking detectors

We study the propagation of energetic muons produced by ultrahigh energy cosmic rays which could penetrate the cavern of a giant experiment called Compact Muon Solenoid (CMS) at CERN. The present work is based on our previous simulation model proposed in [1]. We have improved this model by (1) eliminating the ambiguity via adding Landau-Pomeranchuk-Migdal effect to the Monte-Carlo code, (2) using different incidence angles of the simulated air showers, (3) defining the actual contents of the CMS cavern concrete. We estimate the energy spectrum of muons produced by air showers of primary protons and photons, which could be detected as a background in the CMS tracking detectors. Our results show that muons produced by air showers within the energy range 10¹⁷–10²⁰ eV injected to the CMS site could penetrate the cavern with cutoff energy 36.5 GeV. The article is published in the original.     

Muons of very and ultra-high energy cosmic rays

In many cosmic rays experiments at very and ultra-high energies, an excess of muons (including those of very high energy, >100 TeV) is observed that cannot be explained within existing models of hadron interactions. This excess is usually explained in terms of the heavier mass composition of primary cosmic rays. However, the excess over the predicted values even for extremely heavy compositions, and especially the observed excesses of muons with energies of >100 TeV, requires that we consider other possibilities with respect to the generation of muons, including changes in models of hadron interaction.     

Rising Inelastic Cross Section and its Contribution to Steepening of the Cosmic Ray Energy Spectrum

Calculations have been carried out to investigate the contribution of an increasing total cross section to steepening of the cosmic ray energy spectrum at very high energies (E ? 10¹² eV). Our results suggest that increasing total cross section contributes only a part to the steepening of primary energy spectrum at very high energies even if the composition is pure primary iron flux.     

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.     

Cosmic ray energy spectrum from measurements of air showers

This review focuses on high-energy cosmic rays in the PeV energy range and above. Of particular interest is the knee of the spectrum around 3 PeV and the transition from cosmic rays of Galactic origin to particles from extra-galactic sources. Our goal is to establish a baseline spectrum from 1014 to 10^20 eV by combining the results of many measurements at different energies. In combination with measurements of the nuclear composition of the primaries, the shape of the energy spectrum places constraints on the number and spectra of sources that may contribute to the observed spectrum.     

Identifying the spectra of ultrahigh energy cosmic rays from extragalactic sources

The energy spectra of extragalactic sources of cosmic rays are calculated by solving an inverse problem of the transport of cosmic rays with energies of 10¹⁸–10²¹ eV in a Universe filled with background electromagnetic radiation. Calculations are performed using cosmic-ray spectra measured on Earth in Auger experiments. It is assumed that protons and iron nuclei dominate in the composition of a source.     

Efficiency of the production of γ families with halos and the fraction of protons at an energy of 10<Superscript>16</Superscript> eV

γ Families with halos detected in the “Pamir” experiment have been analyzed. Comparison of the experimental data with the results of calculation within the quark-gluon string model (MC0 code) made it possible to determine the efficiency of halo formation by protons, α particles, and heavy nuclei, as well as the fraction of protons in the mass composition of primary cosmic rays at an energy of 10¹⁶ eV. It is shown that halos are formed predominantly by protons. The fraction of protons in the mass composition of primary cosmic rays at an energy of 10¹⁶ eV is 20%.