Abstract:
Cosmic ray particles are observed to $3 10^{20}$ eV, with no sign yet of any cutoff, as would be expected from interaction with the microwave background - of these particles were protons. The various proposals to accont for the partciel energies, their nature, their origin, their spectrum, and the transition from Galactic cosmic rays will be discussed. The most cautious proposal is still that powerful radio galaxies with their hot spots account for all these events. However, the lack of an observed cutoff suggests that at least at the highest energies there may be a transition to a new source population, either through supersymmetric partner particles, or through Big Bang relic decay, or through energetic neutrinos. The transition region in energy to Galactic cosmic ray particles is also under dispute, and there, at about $3 10^{18}$ eV, we may just see heavy nuclei (say, C to Fe) all the way down to the knee, at $3 10^{15}$ eV. From $10^{14}$ eV to $3 10^{20}$ eV there is no general agreement as to the origin of cosmic rays, but there are proposals that may account for all theior properties quite successfully.

Abstract:
A Monte Carlo program, based on GEANT and using GHEISHA at energies below 30 GeV, is developed for simulation of the hadron and muon components of extensive air showers with primary energy 10^12-10^17 eV. Calculations of the characteristics of multi-muon events as observed underground by the LEP detectors are presented and their dependence on the primary cosmic ray composition and some basic assumptions of the hadronic interaction model is discussed.

Abstract:
The review of recent theoretical and experimental results of high energy cosmic ray muon studies is given. Special attention is paid to the problem of the calculation and experimental search of the prompt muon contribution to the sea level muon spectrum and to obtaining physical information about this spectrum from deep underground muon data. Some new author's results in the field of electromagnetic and photonuclear muon interactions are presented

Abstract:
We investigate the relation of the muon charge excess with the nature of the primary, according to isospin conservation and charge exchange mechanism in the earliest interactions. The opportunity to associate a negative charge excess to neutron primaries above 100TeV could be used in astrophysics for close sources, like the Loops or Geminga. The selection of events with zenithal and azimutal incidences favouring the maximal deflection by the geomagnetic field suggests some new criteria to discriminate proton and heavy nuclei in the "knee" region. We explore also the chance to observe in muon target diagram the properties of alignement of UHE events seen in emulsion chambers near 10^7 GeV. At energies larger than the LHC, we present finally some lateral distribution of high energy muons carried out with CORSIKA, using for extrapolation of multiproduction at UHE the Quark Gluon String Model.

R. Engel, T.K. Gaisser, and T. Stanev: "High-energy muon flux and hadronic interaction models"

Abstract:
We discuss muon production in extensive air showers. After giving an outline of the general concept of high-energy muon flux calculations, the role of the hadronic interaction model is investigated. The expected mean muon number and it's fluctuations are presented. Their relation to the primary cosmic ray composition and assumptions on hadronic interactions at high energy are discussed

Abstract:
The Single Source Model of the knee, developed by us on the basis of the world survey of EAS data, makes certain predictions for cosmic rays of lower, sub-PeV energies. This energy region is of special interest for the CosmoLep experiment. The feasibility of the ALEPH detector to study muons in this energy region and prove or disprove our model predictions is discussed. A brief survey is made of relevant muon data from the (few) experiments carried out so far.

Abstract:
The major goal of the Karlsruhe KASCADE experiment is to determine the flux spectrum and the chemical composition of primary cosmic rays around the so called ''knee'', i.e. in the energy range of the primaries of 10^{15} eV to 10^{16} eV. KASCADE is a multi-detector device to observe simultaneously the electromagnetic, muonic and hadronic component of the extended air shower (EAS), created by interactions of the primaries at the atmosphere. A system of large-area position-sensitive multiwire proportional chambers (MWPC) is able to measure the high-energy muon part (E_mu>2 GeV) of the EAS. Different methods of the analysis of the measured muon densities to evaluate primary mass composition and energy spectrum are presented.

Abstract:
CORSIKA is a detailed program to simulate the evolution of extensive air showers initiated by high energy cosmic ray particles. Parameter sets are available to describe the atmosphere at various climatic zones and seasons. Details of the particle tracking are explained. The hadronic interactions at high energies may be simulated by five reaction models alternatively: The VENUS, QGSJET, and DPMJET models are based on Gribov- Regge theory, SIBYLL is a minijet model, and the phenomenological HDPM generator is adjusted to experimental data wherever possible. The influence of those models on observable quantities of air showers are discussed with emphasis to the muonic component.

Abstract:
The history of energetic cosmic ray muon studies is reviewed, and the unique potentials of the LEP detectors in this field are identified. Some of the outstanding issues relevant to muon studies are noted in the context of current research initiatives. Single muon studies are relevant to atmospheric neutrino flux calculations, while multimuon events not only shed light on primary composition but may also be sensitive to new physics. Other exploratory studies, such as CosmoLep, are also noted.

Abstract:
Composition measurements with KASCADE with particular emphasis placed on uncertainties induced by HE interaction models and on what EAS data can do for testing and improving the models.

Abstract:
Possibility of high energy muon measurements deep underground in the LEP experiments will be discussed. we are able to measure muon coincidences up to about 100 m, due to the high energy threshold. Possible observations of muon coincidences for the detectors which are placed at the distance up to several kilometers will be discussed.

Jens Kremer: "Observation of ground level muons with the CAPRICE97 experiment"

Abstract:
A measurement of ground level muons was performed with the NMSU-WIZARD/CAPRICE magnet spectrometer in Fort Sumner, New Mexico, USA in Spring 1997. The spectrometer was equipped with a superconducting magnet, a time-of-flight system, an electromagnetic calorimeter and a Ring Imaging Cherenkov detector with a gaseous C_4 F_10 radiator. Positive and negative muon spectra and the mu^+ to mu^- ratio are presented in the momentum range from 200 MeV/c to 120 GeV/c. The results are compared with results obtained with a similar experiment at a different geomagnetic location. The data show latitude dependent geomagnetic effects.

B.A. Khrenov: "Results of the measurements in the MSU underground laboratory"

Abstract:
In period of 1958-1989 the Moscow State University group made measurements of the Cosmic Ray penetrating component at the depth of 40 mwe underground. Above the underground room the EAS array operated in conjunction with the underground detectors. In that period various underground detectors were in operation: EAS muon flux detector of area 37 sq. m (muon threshold energy 10 GeV), magnetic muon spectrometer (MDM 500 GeV/c), secondary shower detectors. EAS muon detectors proved to be very useful in study of EAS physics (the invariance of scaling model was approved, the knee in the primary spectrum was confirmed, the changing of primary composition in the knee region is indicated). In measurements of "single" particle interactions underground the disageement with the expected secondary shower size spectrum from muon component was found. This disagreement was interpreted in the MSU original papers as an indication of the existence of unknown penetrating primary component. In the present talk this data are discussed in view of a recent suggestion of new SUSY particles (G. Farrar).

Abstract:
At a depth of > 1450m of rock only muon- and neutrino -events are observed. The muons have a mean energy of 300 GeV and generate dominantly electromagnetic events, pair production, bremsstrahlung and elastic electron scattering. At a smaller rate also hadronic events are produced, by virtuell photons at very small Q*2. Multimuons occur with a few % rate and some muons range out in the detector. The muon event characteristics will be described in detail. Since the muon energy spectrum is rather independent of depth similar muon events are expected at detectors much nearer to the surface, like at LEP. In addition a brief account of neutrino events will be given.

Abstract:
The region of the "knee" of the primary spectrum is studied by EAS-TOP (2000 m a.s.l., Gran Sasso Laboratories) in the e.m. (Ne) and muon components at Emu > 1 GeV (Nmu/GeV) at the surface and Emu > 1.3 TeV (Nmu/TeV) in correlation with the detectors operating in the underground Gran Sasso laboratories (LVD, MACRO). The status of the analysis and the main results are discussed.

Abstract:
Cosmic-ray exotic event, called Centauro, is characterised by the multiple particle production without (appreciable) production of gamma-rays (and electrons). We have several candidate events of Centauro-type by a series of emulsion chamber experiment at Mt. Chacaltaya (5,200 m, Bolivia). Recently we found another candidate event of small multiplicity. Experimental data of these candidate events are summarized and a discussion is made on the origin of Centauro events.

W. Rhode: "Possibilities and Limitations of the Measurement of the Muon Flux Deep Under Ground "

Abstract:
Using the measurements of the muon flux with the Frejus detector as example the existing measurements of the depth dependence and the energy spectrum at the detector location, and their limitations due to systematic uncertainties (muon cross section, rock overburden, angular dependence, etc.) are discussed. Especially the search for the contribution of prompt muons, the boundary conditions for the determination of the primary chemical composition, and the consequences for large (km3) neutrino telescopes are discussed.

Abstract:
The talk will focus on the CosmoAleph setup and the results obtained since 1995. Coincidence rates observed between different stations are compared to Monte Carlo simulations, with emphasis on the sensitivity to the muon lateral distribution in extended air showers and the chemical composition of primary particles.

Abstract:
Extensive air showers (EAS) are the only way to study cosmic rays above a few hundred TeV primary energy. The properties of EAS are briefly reviewed, with emphasis on observables which depend on primary mass such as the muon-to-electron ratio and longitudinal development. Then the problems encountered by EAS measurements are discussed: - insufficient knowledge of strong interactions at high energies; - large fluctuations, especially of proton induced showers; - the limited sensitivity of EAS observables to primary mass. It is then outlined how the design of the KASCADE experiment tries to overcome these problems.

Abstract:
Underground muon events detected by the MACRO experiment at Gran Sasso have been studied for different purposes. The studies include the vertical muon intensity measurement, the multiplicity distribution, the lateral and angular muon distribution and searches for jet substructures inside muon bundles. These analyses have contributed to bring new insights in cosmic ray physics. Moreover, this activity allows the testing and tuning of Monte Carlo simulations, in particular for aspects associated with models of hadronic interactions and muon propagation through the rock.

Abstract:
Experimental data obtained by emulsion chambers at Pamir and Chacaltaya are compared with simulation calculations using CORSIKA program employing several models for high energy hadronic interactions. Although those models are considered to be based on modern theory and are widely-accepted as standard simulation codes, it is shown no models can explain many of characteristics, hadron-gamma correlation, shower-clusters of small spread, penetrating cascades and so on, observed in the experiments.

Abstract:
Review of various ideas for putative phenomena in forward physics which may be relevant for high energy cosmic ray muon experiments

Abstract:
The sensitivity of the muon component for measurement of the composition of primary cosmic ray flux at ultra-high energies, $10^{14}-10^{16}$, has been known for a long time. Several experiments have attempted to determine composition using small or moderate size detectors for muons. Unfortunately, these experiments have yielded ambiguous results. During the past few years, we have attempted to study the muon component in air showers with very large area detectors, for example, a 200 $m^2$ area detector in the GRAPES II experiment and a 560 $m^2$ area detector in the GRAPES III experiment at the Institute's mountain altitude (800 $g.cm^{-2}$) laboratory at Ooty in southern India. The details of these two experiments and preliminary results obtained from them would be presented at the meeting.

Abstract:
High precision muon chambers of the L3 detector permit the measurement of the energy spectrum of muons over a large momentum range, 50-2000 GeV/c, for single and multiple muons with a very large solid angle area exposure factor. Interpretation of these observations in terms of high energy cosmic ray astrophysics would be greatly facilitated if energies of primary cosmic rays which have generated the observed muons through their interaction in the atmosphere could be measured with reasonable accuracy. We present plans of the L3+Cosmics group to install a mini-air shower array above the L3 detector to observe associated showers and estimate the primary energy for about $\sim 20\%$ of the multiple muon events observed with the L3 detector.

Abstract:
The CUPP project (Centre for Underground Physics in Pyhäsalmi) aims at establishing underground physics experiments in the Pyhäsalmi zinc/copper mine. The mine is presently 1220 metres deep and mining will go on until at least year 2012. The first proposed large underground experiment is a multimuon experiment at only 50 metres consisting of seven 100m$2$ detector elements arranged in a hexagonal array with one in the centre. The detector is especially designed for the composition study of the knee region $10^{15}-10^{16}$eV. The model dependence of the Monte Carlo simulations is discussed.

Abstract:
The L3 detector contains a high resolution muon spectrometer. The L3+Cosmics experiment aims at using this detector to measure atmospheric muons. Our first goal is to record the muon momentum spectrum at a 1% precision in the range 20-2000 GeV/c, the charge ratio and it's angular dependence. Also subjects like muon multiplicity distributions, upward going muons, muon astronomy and searches for new physics will be studied with this instrument.