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.     

Meson cascade in the atmosphere,uncertainties in calculating the fluxes of high-energy muons,and data of direct measurements

A new calculation of the atmospheric fluxes of cosmic-ray hadrons and muons in the energy range 10–10⁴ GeV is performed on the basis of the method for solving nuclear-cascade equations with allowance for a nonscaling behavior of inclusive hadron-production cross sections, the growth of cross sections for inelastic hadron-nucleus collisions with increasing energy, and a non-power-law character of the primary spectrum. The fluxes of secondary cosmic rays at various levels in the atmosphere are calculated for three models of the spectrum and composition of primary cosmic rays. The effect of uncertainties in the spectrumand composition of primary cosmic rays on the flux of atmosphericmuons and their charge ratio at sea level is investigated. The calculated energy spectra of muons at sea level are compared with the results of previous experiments and the results of recent measurements performed by means of the L3 + Cosmic and CosmoALEPH spectrometers, as well as with the results of other calculations.     

Intensity of muon bundles at large zenith angles and hadron interaction models at energy of 1018 eV

Characteristics of muon bundles detected with the DECOR detector are compared to predictions based on different hadron interaction models and various assumptions as to the spectrum and mass composition of primary cosmic rays. The intensity of primary cosmic rays derived from the muon bundle data is considerably higher than that measured by means of the fluorescence technique. Either changes in the hadron interaction characteristics at ultrahigh energies or a revision of the energy calibration in the fluorescence technique of measuring EAS energy is required to explain these results.     

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.     

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.     

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.     

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.     

Atmospheric neutrino flux supported by recent muon experiments

We present a new one-dimensional calculation of low and intermediate energy atmospheric muon and neutrino fluxes, using up-to-date data on primary cosmic rays and hadronic interactions. We study several sources of uncertainties relevant to our calculations. A comparison with the muon fluxes and charge ratios measured in several modern balloon-borne experiments suggests that the atmospheric neutrino flux is essentially lower than one used for the standard analyses of the sub-GeV and multi-GeV neutrino induced events in underground detectors.     

Muon–hadron detector of the carpet-2 array

The 1-GeV muon–hadron detector of the Carpet-2 multipurpose shower array at the Baksan Neutrino Observatory, Institute for Nuclear Research, Russian Academy of Sciences (INR, Moscow, Russia) is able to record simultaneously muons and hadrons. The procedure developed for this device makes it possible to separate the muon and hadron components to a high degree of precision. The spatial and energy features of the muon and hadron extensive-air-shower components are presented. Experimental data from the Carpet-2 array are contrasted against data from the EAS-TOP and KASCADE arrays and against the results of the calculations based on the CORSIKA (GHEISHA + QGSJET01) code package and performed for primary protons and iron nuclei.     

Deficit of the calculated muon flux at sea level for E µ ≳ 100 GeV: Analysis of possible reasons

The reasons why a deficit of the calculated muon flux for E _μ ≳ 100 GeV arises if use is made of data from direct measurements of the spectra of primary cosmic rays and present-day nuclear-interaction models are considered. It is shown that this problem may stem from significantly underestimating the primary-nucleon flux in balloon-borne experiments employing the technique of emulsion chambers. This procedure relies on an extrapolation of accelerator data; therefore, it is necessary to estimate, on the basis of various Reggeon models of hadron interactions, the systematic error introduced by this circumstance in the results of the measurements. Such an analysis would make it possible to refine the behavior of the spectra of primary cosmic rays, to reduce the methodological part of the error in the calculation of the fluxes of secondary cosmic rays in the atmosphere, and to draw more precise conclusions on the flaws in present-day interaction models without invoking new accelerator data. Original Russian Text ? A.A. Lagutin, A. G. Tyumentsev, A. V. Yushkov, 2006, published in Yadernaya Fizika, 2006, Vol 69, No. 2, pp. 293–302.     

Neutrons and antiprotons in ultrahigh-energy cosmic rays

The neutron fraction in the very high-energy cosmic rays near the Greisen-Zatsepin-Kuzmin (GZK) cutoff energy is analyzed by taking into account the time dilation effect of the neutron decays and also the pion photoproduction behaviors above the GZK cutoff. We predict a non-trivial neutron fraction above the GZK cutoff and a negligibly small neutron fraction below. However, there should be a large antiproton fraction in the high-energy cosmic rays below the GZK cutoff in several existing models for the observed cosmic-ray events above and near the GZK cutoff. Such a large antiproton fraction can manifest itself by the muon charge ratio μ⁺/μ^- in the collisions of the primary nucleon cosmic rays with the atmosphere, if there is no neutron contribution. We suggest to use the muon charge ratio as one of the information to detect the composition of the primary cosmic rays near or below the GZK cutoff.     

Study of the quarkonium polarization in the muon channel at ALICE

The study of quarkonium polarization at hadron colliders represents an important test of the production models. Recent results, obtained at CDF, are in striking disagreement with NRQCD predictions, although such a model correctly reproduces the production cross sections. Furthermore, in nucleus-nucleus collisions, the observed degree of polarization may be related to the characteristics of deconfined matter. Because of these interesting features, quarkonium polarization will surely represent an interesting observable at LHC energies. In ALICE, the polarization of the Ω and Γ states can be measured in the dilepton channel, both in the central barrel and in the forward (2.5<y<4) muon arm. We present the results of a feasibility study, relative to the muon channel, concerning p-p and Pb-Pb collisions, showing the expected performance for the measurement of J/Ω and Γ polarization, both as a function of transverse momentum and centrality.     

Portion of muons with a threshold energy above 1 GeV in extensive air showers with ultra-high energies,according to the Yakutsk EAS array data

Characteristics of the muon component in extensive air showers and the fluctuations of muons are considered. In this work, we compare experimental data with computations performed for various models of the hadron interactions of protons and iron nuclei. The aim of this analysis is to obtain information on the mass composition of cosmic rays in an ultra-high energy region.     

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.

     

Cross section dependence of event rates at neutrino telescopes

We examine the dependence of event rates at neutrino telescopes on the neutrino-nucleon cross section for neutrinos with energy above 1 PeV, and contrast the results with those for cosmic ray experiments. Scaling of the standard model cross sections leaves the rate of upward events essentially unchanged. Details, such as detector depth and cross section inelasticity, can influence rates. Numerical estimates of upward shower, muon, and tau event rates in the IceCube detector confirm these results.     

Uncertainties in underground muon flux calculations

Influence of various theoretical and experimental uncertainties on results of underground muon flux calculations is estimated on the basis of a semi-analytical solution of muon spectrum transport equation. Status and accuracies of theoretical formulae for muon interaction cross sections and energy loss rate are discussed. A brief review of recent improvements in theoretical treatment of muon interactions is given. A necessity of a comprehensive verification of different muon transport codes is stressed.     

Heavy fragment production cross sections from 1.05 GeV/nucleon 56Fe in C, Al, Cu, Pb, and CH2 targets

We have obtained charge-changing cross sections and partial cross sections for fragmentation of 1.05 GeV/nucleon Fe projectiles incident on H, C, Al, Cu, and Pb nuclei. The energy region covered by this experiment is critical for an understanding of galactic cosmic ray propagation and space radiation biophysics. Surviving primary beam particles and fragments with charges from 12 to 25 produced within a forward cone of half-angle 61 mrad were detected using a silicon detector telescope to identify their charge and the cross sections were calculated after correction of the measured yields for finite target thickness effects. The cross sections are compared to model calculations and to previous measurements. Cross sections for the production of fragments with even-numbered nuclear charges are seen to be enhanced in almost all cases.     

Investigation of the PCR energy spectrum shape by the means of the local EAS muon density technique

The results of studying the primary cosmic radiation (PCR) flux in the energy range 10¹⁵–10¹⁸ eV at the NEVOD-DECOR experimental array using local muon density spectra are reported. The experimental distributions and the spectra obtained by simulation of EAS muon LDF using the CORSIKA code are compared. Possibilities of using a new method for analysis of muon bundle events on the basis of the primary energy estimator are discussed.     

Emission of muonic tritium into vacuum: An atomic beam for muon experiments

The emission of muonic tritium atoms from a thin film of hydrogen isotopes into vacuum was observed. The time and position of the muon decays were measured by tracking the decay electron trajectory. The observations are useful both for testing the theoretical cross sections for muonic atomic interactions, and producing an atomic beam of slow μ^-t with a controllable energy. This revised version was published online in August 2006 with corrections to the Cover Date.     

Diffusion radius of muonic hydrogen atoms in H-D gas

The diffusion radius of the 1S muonic hydrogen atoms in gaseous H₂ targets with various deuterium admixtures has been determined for temperatures T=30 and 300 K. The Monte Carlo calculations have been performed using the partial differential cross sections for pμ and dμ atom scattering from the molecules H₂, HD and D₂. These cross sections include hyperfine transitions in the muonic atoms, the muon exchange between the nuclei p and d, and rotational-vibrational transitions in the target molecules. The Monte Carlo results have been used for preparing the time-projection chamber for the high-precision measurement of the nuclear μ^- capture in the ground-state pμ atom, which is now underway at the Paul Scherrer Institute.