Constraints of hadronic interaction models from the cosmic muon observations

Abstract

A simple method of the vertical muon energy spectrum simulations has been suggested. These calculations have been carried out in terms of various models of hadronic interactions. The most energetic π ± -mesons and K ± -mesons produced in hadron interactions contribute mainly to this energy spectrum of muons due to the very steep energy spectrum of the primary particles. So, some constraints on the hadronic interaction models may be set from a comparison of calculated results with cosmic data on the vertical muon energy spectrum. This comparison showed that the most energetic secondary particles production is too high in the case of the QGSJET II-04 model and rather low in the case of the QGSJET II-03 model. These conclusion have been supported by the LHC data. The longitudinal development of extensive air showers (EAS), in particular, the depth Xmax of its maximum, is determined by the rate of fragmentation of energy E0 of the primary particle. This rate depends on the interaction cross sections of shower particles, and on the energy spectra of secondary particles are generated in interactions. Obviously, if the probability of particle production with energies close to the energy of the incident particle is high then the development of the cascade slows down. Conversely, in the case of rapid fragmentation of the incident energy cascades develop rather rapidly. The depth Xmax of shower maximum in many studies is the main parameter for determining the composition of primary cosmic radiation (PCR) at ultra-high energies. It should also be noted that in the case of the slow rate of development cascade and hence large values of depth Xmax the lateral distribution of the shower particles at the observation level becomes narrower. Therefore, the values of signals in the surface and underground detectors located at large distances from the shower core are decreased. It must be taken into account when determining the density of muons at large distances from the shower core and the composition of the PCR found from the muon lateral distribution. Studies of the composition and characteristics of the energy spectrum of the PCR are important components of theories of the origin of cosmic rays at ultra-high energies. Interpretation of experimental data on the depth of the shower maximum Xmax and the observed fraction of muons at a fixed distance from the shower core are carried out in terms of different hadronic