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 $10^{19}$ 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 10 GeV will make it possible to distinguish between primary nuclei, protons, and pions; to verify Lorentz invariance for energies above $10^{20}$ eV; and to obtain a new limit on the difference between the maximum possible velocities of muons and pions $(c_{\mu}-c_{\pi})<4\times 10^{-26}$.