Bremsstrahlung photons from cosmic ray muons of high and ultrahigh energies

The results from calculations for fluxes of bremsstrahlung photons generated at different depths in the atmosphere by cosmic ray muons with energies of up to 10¹⁰ GeV are presented. It is shown that the generation of charmed particles in the atmosphere, along with the generation of J/ψ mesons, must be taken into account in interpretations of experimental data on studying EASes at high and ultrahigh energies.     

Fluxes of high- and ultrahigh-energy cosmic-ray muons

The positive excess of cosmic-ray muons at energies higher than 1 TeV is estimated taking into account the data obtained from accelerator experiments on the production of particle and antiparticles in proton-proton interactions at energies of ～20 TeV. The fluxes of cosmic-ray muons at energies up to ～10¹¹ GeV and the production functions of muon bremsstrahlung photons at different depths in the atmosphere are calculated with due regard for the contribution from the decay of J/ψ mesons. The analysis performed is based on the accelerator data and their extrapolation to higher energies.     

Cosmic ray muons at a depth of 754 hg/cm2 in the Kolar gold Mines

A telescope of area 4 m², consisting of horizontal layers of plastic scintillators, neon flash tubes and absorbers was operated at a depth of 754 hg/cm² in the Kolar Gold Mines. New values for the vertical intensities of muons have been obtained from observations of the angular distribution over the slant depths ∼ 750–2300 hg/cm² and are compared with the existing measurements. From the angular distribution observed, we conclude that muons are produced wholly through the decay of pions and kaons up to energies of the order of 1 TeV. A value of 0.3±0.2 is estimated for theK/π ratio at production, for muon energies around 500 GeV. A decoherence distribution has been obtained for parallel muon events up to distances of the order of 10 m. From this we conclude that the averageP _t of the parents of muons of energy ∼ 250 GeV is of the order of 0.3 GeV/c. From an analysis of rock showers, we obtain the cross section for inelastic interaction of muons of mean energy 100 GeV as (3.8±1.5)×10⁻³⁰ cm²/nucleon.     

Estimating the fraction of gamma quanta in the primary cosmic ray flux with energies of ∼1017 eV from the MSU EAS array data

Using data from the MSU EAS array and model calculations, we search for events with abnormally small fractions of muons with energies above 10 GeV in showers with particle numbers of >2 × 10⁷ and zenith angles of <30 degrees. We confirm with good statistical accuracy that the content of gamma quanta in the primary cosmic ray flux can be as high as 2% at energies of ～10¹⁷ eV.     

Experiments with low-energy muons

Two experiments with low-energy muons are described: the determination of the stopping power of C, Si, Ti and Au for muons at energies down to 2 keV and the measurement of the diffusion times for pµ and dµ atoms in low-pressure (0.25–12 hPa) hydrogen gas. A pronounced Barkas effect was found for muons at the Bragg peak (about 10 keV): the stopping power for µ^– in C, e.g., is about 30% lower than that for µ⁺. The mean kinetic energy of pµ atoms at the end of the cascade in 1 hPa hydrogen gas was determined to be (2.6 ± 0.6) eV (preliminary value).     

Hadron production in 200 GeV μ-copper and μ-carbon deep inelastic interactions

The measurements of the z and p_T² distribution of hadrons produced in the interactions of 200 GeV muons with copper and carbon nuclei are shown in different x_Bj and virtual photon energy intervals. Effects of the jet scattering are seen at the lowest virtual photon energies while for energies above 70 GeV there is no evidence of these effects. Comparison with a theoretical model indicates that at high jet energies the parton fragmentation distance is greater than the nuclear radius and that the parton absorption cross section is less than 10 mb.     

Test of hadron interaction models in the most important energy range of secondary particles in spectra of atmospheric muons

A simple method has been proposed for testing hadron interaction models, which are used to simulate extensive air showers, in observed spectra of atmospheric muons. It has been shown that muon flux intensities in the energy range of 10²–10⁴ GeV that are calculated within the SIBYLL 2.1, QGSJETII-04, and QGSJET01 models exceed the data of the classical experiments L3 + Cosmic, MACRO, and LVD on the spectra of atmospheric muons by a factor of 1.5–2. It has been concluded that these tested models overestimate the generation of secondary particles with the highest energies in elementary events of interaction between hadrons in agreement with the LHCf and TOTEM accelerator experiments.     

Pions in primary cosmic rays of ultrahigh energies

In the framework of the Coleman-Glashow hypothesis of an extremely weak violation of Lorentz invariance, neutral and charged pions can be stable for energies above 10¹⁹ eV and enter into the composition of primary cosmic rays of ultrahigh energies. The kinematic exclusion of reactions of pions with relic photons is particularly important, because it allows the Greisen-Zatsepin-Kuzmin paradox to be resolved. The parameters of extensive air showers induced by primary pions calculated within the model of quark-gluon strings with allowance for the Landau-Pomeranchuk-Migdal effect and interactions of neutral pions of ultrahigh energies are not contradictory to the available data of observations. It has been shown that observations of production heights of muons with energies above 10GeV will make it possible to distinguish between primary nuclei, protons, and pions; to verify Lorentz invariance for energies above 10²⁰ eV; and to obtain a new limit on the difference between the maximum possible velocities of muons and pions (c_µ?c_π)<4×10^?26.     

Properties of giant air showers and the problem of estimating the primary-particle energy

The main errors in energy estimation in individual events detected at the Yakutsk EAS array are analyzed. The data on the fraction of muons are considered. For inclined showers with energies exceeding 10¹⁹ eV, it is much larger than the value given by approximation at lower energies. This difference may be due to new processes arising upon interaction between particles with such energies, which leads to a significant increase in the muon component in the total primary-particle energy.     

Studying the muon and hadron components of extensive air showers with the Carpet-2 array

The method of separating muons and hadrons recorded by the Muon Detector of the Carpet-2 air shower array of Baksan Neutrino Observatory (Institute for Nuclear Research, Russian Academy of Sciences) is described. The results of studying characteristics of the muon and hadron components of extensive air showers (EAS) with N _e ≥ 10⁵ are presented. For the range of distances 40–55 m from shower axes the numbers of hadrons with energies higher than 30 GeV and muons with energies above 1 GeV are obtained as functions of the shower size N _e .     

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.     

Interaction of high energy muons in association with EAS,with rock and lead

An investigation on the interaction of high energy muons, associated with EAS and having energies greater than several hundred GeV, has been carried out at Kolar Gold Fields. A visual detector consisting of neon flash tube hodoscope has been used together with a scintillator detector to observe the muons and accompanying showers at the underground level. It has been found that nearly 90% of the showers observed at the underground level are generated in course of pure electromagnetic interactions of the muons with the matter traversed by them. The observed number of the showers is found to be consistent with the expected number calculated using the cross-sections for knock-on, bremsstrahlung and direct pair production processes. Rest of the observed showers do not appear to fit in the pure electromagnetic interaction scheme. Various possible production processes for these events have been discussed. Considering these events to be due to photonuclear interaction of muons in the rock, the observed number leads to a production cross-sectionσ _μ (?25 GeV) ?(1.6±0.75)10^?29 cm²/nucl.     

Low energy muons as probes of thin films and surfaces

Polarized muons with kinetic energies of a few eV (epithermal μ⁺) can be generated by slowing down energetic muons in appropriate moderators consisting of a thin layer of a van der Waals gas frozen on a substrate. The availability of polarized muons with kinetic energies in the eV to several keV range opens the possibility to extend the μSR technique to the study of thin films and surfaces (low energy μSR, LE-μSR). We summarize the characteristics of the very slow polarized muons and of a low energy beam based on the moderation technique. We discuss the implantation of muons in thin film samples and the potential and limitations of LE-μSR. As an example first results obtained by implanting slow μ⁺ in a sample consisting of a Ni film deposited on Ag are presented.     

First μ+SR studies on thin films with a new beam of low energy positive muons at energies below 20 keV

At the Paul Scherrer Institute slow positive muons (μ⁺) with nearly 100% polarization and an energy of about 10 eV are generated by moderation of an intense secondary beam of surface muons in an appropriate condensed gas layer. These epithermal muons are used as a source of a tertiary beam of tunable energy between 10 eV and 20 keV. The range of these muons in solids is up to 100 nm which allows the extension of the μ⁺SR techniques (muon spin rotation, relaxation, resonance) to the study of thin films. A basic requirement for the proper interpretation of μ⁺SR results on thin films and multi-layers is the knowledge of the depth distribution of muons in matter. To date, no data are available concerning this topic. Therefore, we investigated the penetration depth of μ⁺ with energies between 8 keV and 16 keV in Cu/SiO₂ samples. The experimental data are in agreement with simulated predictions. Additionally, we present two examples of first applications of low energy μ⁺ in μ⁺SR investigations. We measured the magnetic field distribution inside a 500-nm thin High-T_C superconductor (YBa₂Cu₃O_7-δ), as well as the depth dependence of the field distribution near the surface. In another experiment a 500-nm thin sample of Fe-nanoclusters (diameter 2.4(4) nm), embedded in an Ag matrix with a volume concentration of 0.1%, was investigated with transverse field μ⁺SR. This revised version was published online in August 2006 with corrections to the Cover Date.     

Negative muon capture in very light atoms

The transition rates for unbound muons to be captured into atomic bound states are calculated as functions of (1) incident muon center-of-mass energy, (2) muon principal quantum number n, and (3) muon (final) angular momentum l, for the hydrogen, helium, and lithium atoms. These rates reflect differences in electron binding energies. At muon energies of several hundred electron volts, lithium K-shell electrons are more likely to be ejected than the L-shell electron, while this behavior is reversed for energies ? 10 eV. However, in each case when the capture rate is folded with a muon stopping power function, the result is that more than half of the unbound muons are absorbed above 75 eV. Implications for experiments which look at muon transfer processes are noted.     

Muons in extensive air showers of energies E 0=1016.6–1019.8 eV

Data on muons with the threshold energy E _μ≈1.0×secθ GeV in extensive air showers of energies E ₀≥4×10¹⁶ eV measured on the Yakutsk and Akeno arrays are jointly analyzed. The results are compared with the calculations by the quark-gluon-string model with jets. It is shown that this model does not contradict the data measured for energies E ₀≤10¹⁸ eV on both arrays under the assumption that the primary particle composition differs from the composition where heavy nuclei dominate over protons. Experimental data for energies E ₀≥3×10¹⁸ eV indicate that the shower development differs from that predicted by the quark-gluon-string model with jets.     

Electrons and muons in extensive air showers of energies E 0≥3×1017 eV: Yakutsk array data and QGSJET model

The results obtained from an analysis of the 1974–1998 Yakutsk array data on muons with threshold energy E _μ ≈ 1.0 × secθ GeV and on all charged particles (electrons and muons) in extensive air showers (EAS) are reported and compared with the results of calculations based on the model of quark-gluon strings with jets. For energies of E ₀≤3×10¹⁸ eV and zenith angles of θ≤45°, the results of the model calculations are consistent with the measured properties of the showers, while, for higher energy EASs, there are considerable discrepancies, which are probably due to the change in the development of the shower cascade in the region E ₀≥3×10¹⁸ eV.     

Mass Composition of Cosmic Rays with Energies above 1017 eV According to the Data from the Muon Detectors of the Yakutsk EAS Array

The lateral distribution of muons in extensive air showers with energies above 1017 eV detected by underground scintillation detectors with a threshold of 1.0 GeV at the Yakutsk array in 1986–2016 has been analyzed. The experimental data on the muon flux density at a distance of 300 m from the shower axis have been compared to the calculations within various models of hadron interactions at ultrahigh energies. The experimental data are in the best agreement with the QGSJet01 and QGSJet II-04 models. The mass composition of cosmic rays in the energy range of (1–30) × 10¹⁷ eV changes from middle nuclei to a purely proton composition.

     

Methodological Issues of Gamma-Ray and Neutrino Searches at the Yakutsk Array

The method used to perform searches for extensive air showers (EAS) generated by neutral particles, such as high-energy gamma rays and astrophysical neutrinos, and the results of such searches are presented. A comprehensive analysis of relevant data, including those on EAS electrons, muons, and Cherenkov light and their time responses in scintillation and Cherenkov detectors, is performed for this purpose. An upper limit on the gamma-ray flux at the energies of 3 × 10¹⁸, 10¹⁹, and 3 × 10¹⁹ eV is set. A multivariate analysis of EAS properties of neutrino-induced air showers does not reveal neutrino-induced showers.     

Estimate of the fraction of primary photons in the cosmic-ray flux at energies ∼1017 eV from the EAS-MSU experiment data

We reanalyze archival EAS-MSU data in order to search for events with an anomalously low content of muons with energies E _μ > 10 GeV in extensive air showers with the number of particles N _e ? 2 × 10⁷. We confirm the first evidence for a nonzero flux of primary cosmic gamma rays at energies E ～ 10¹⁷ eV. The estimated fraction of primary gamma rays in the flux of cosmic particles with energies E ? 5.4 × 10¹⁶ eV is ε_γ = (0.43 _?0.11 ^+0.12 )%, which corresponds to the intensity I _γ = (1.2 _?0.3 ^+0.4 ) × 10^?16 cm^?2 s^?1 sr^?1. The study of arrival directions does not favor any particular mechanism of the origin of the photon-like events.