Explicit computation of Drinfeld associator in the case of the fundamental representation of gl(N)

We solve the regularized Knizhnik-Zamolodchikov equation and find an explicit expression for the Drinfeld associator. We restrict to the case of the fundamental representation of $gl(N)$. Several tests of the results are presented. It can be explicitly seen that components of this solution for the associator coincide with certain components of WZW conformal block for primary fields. We introduce the symmetrized version of the Drinfeld associator by dropping the odd terms. The symmetrized associator gives the same knot invariants, but has a simpler structure and is fully characterized by one symmetric function which we call the Drinfeld prepotential.Comment: 14 pages, 2 figures; several flaws indicated by referees correcte

Muons with E_th >= 1 Gev and Mass Composition in the Energy Range 10^{18}-10^{20} ev Observed by Yakutsk Eas Array

The ratio of the muon flux density to charged particle flux density at distances of 300 and 600 m from the shower axis (\rhom(300)/\rhos(300) and \rhom(600)/\rhos(600)) is measured. In addition, the energy dependence of \rhom(1000) is analysed for showers with energies above $10^{18}$ eV. A comparison between the experimental data and calculations performed with the QGSJET model is given for the cases of primary proton, iron nucleus and gamma- ray. We conclude that the showers with \E\ge3\times10^{18} eV can be formed by light nuclei with a pronounced fraction of protons and helium nuclei. It is not excluded however that a small part of showers with energies above $10^{19}$ eV could be initiated by primary gamma-rays.Comment: 19th European Cosmic Ray Symposium, Aug 30 - Sep 3 2004, Florence, Italy. 3 pages, 1 figure. Submitted for publication in International Journal of Modern Physics

Influence of Primary Cosmic Radiation Mass Composition on the Estimation of Eas Energy

At the Yakutsk EAS array E_em is determined by using measurements of EAS Cherenkov light flux and charged particle flux. It is known from calculations that these characteristics depend on a sort of primary particle and, therefore, the estimation of E_em depends on a primary particle mass. In the work the dependence of the E_em/E_0 ratio on the energy is given and experimental data are compared with calculations by the QGSJET model. The calculations have been carried out for the primary proton and iron nucleus. The average calculated meaning of the value of E_em/E_0 ratio (between the proton and iron nucleus) within experimental errors is in agreement with experimental data that doesnt contradict to the mixed mass composition of primary cosmic radiation.Comment: 19th European Cosmic Ray Symposium. Aug 30 - Sep 3 2004, Florence, Italy. 3 pages, 1 figure. Subbmitted for publication in International Journal of Modern Physics

Fluctuations of Xmax and Primary Particle Mass Composition in the Range of Energy 5 10^{17} - 3 10^{19} ev by Yakutsk Data

The experimental distributions of \Xmax obtained with the Yakutsk EAS array at fixed energies of $5 \times10^{17}$, $1\times10^{18}$ and $5\times10^{18}$ eV are analysed. A recent version of the QGSJET model is used as a tool of our analysis. In the framework of this model, the most adequate mass composition of primary particles satisfying the experimental data on \Xmax is selected.Comment: 19th European Cosmic Ray Symposium, Aug 30 - Sep 3 2004, Florence, Italy. 3 pages, 1 figure. Submitted for publication in International Journal of Modern Physics

Fluctuations of development maximum depth and nuclear composition of primary cosmic radiation

The extensive air showers (EAS) cascade curves from the Cerenkov light lateral distribution measurements are recovered and the maximum depth fluctuations of the shower development theta x sub m both on the Cerenkov and charged EAS components are defined. At E sub 0 approximates 10 to the 18th power eV the mean content of protons is greater than 85%, and p-air cross section theta sub 0 p-air 750mb

Upper limit on the ultra-high-energy photon flux from AGASA and Yakutsk data

We present the interpretation of the muon and scintillation signals of ultra-high-energy air showers observed by AGASA and Yakutsk extensive air shower array experiments. We consider case-by-case ten highest energy events with known muon content and conclude that at the 95% confidence level (C.L.) none of them was induced by a primary photon. Taking into account statistical fluctuations and differences in the energy estimation of proton and photon primaries, we derive an upper limit of 36% at 95% C.L. on the fraction of primary photons in the cosmic-ray flux above 10^20 eV. This result disfavors the Z-burst and superheavy dark-matter solutions to the GZK-cutoff problem.Comment: revtex, 8 pages, 4 figure

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

We analyse a sample of 33 extensive air showers (EAS) with estimated primary energies above 2\cdot 10^{19} eV and high-quality muon data recorded by the Yakutsk EAS array. We compare, event-by-event, the observed muon density 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 a good agreement with the expected composition in which the light component corresponds to protons and the heavy component to iron-like nuclei. With SYBILL, simulated muon densities for iron primaries are a factor of \sim 1.5 less than those observed for the heavy component, for the same electromagnetic signal. Assuming two-component proton-iron composition and the EPOS model, the fraction of protons with energies E>10^{19} eV is 0.52^{+0.19}_{-0.20} at 95% confidence level.Comment: 8 pages, 3 figures; v2: replaced with journal versio