Experimentally guided Monte Carlo calculations of the atmospheric muon and neutrino flux

The WILLI detector upgraded with the possibility to detect muons from different zenith and azimuthal angles of incidence is used to measure the charge ratio of low energy atmospheric muons, in particular the East -West effect. The results of Monte Carlo simulations with the CORSIKA code can be fairly well understood if the solar modulation, the geomagnetic cut-off and the local magnetic field are taken into account by the simulations. The data can be used to scrutinize the high-energy hadronic interaction models used as generators in the Monte Carlo program CORSIKA, and they shed some light on the models DPMJET, VENUS, UrQMD, currently in vogue. Via this procedure, having refined and calibrated the ingredients of the CORSIKA code, atmospheric muon and neutrino fluxes have been calculated and compared with recent measurements of the atmospheric muon flux and other calculations of the neutrino flux for various sites of different geomagnetic coordinates. Additionally, based on our simulations of the muon flux with CORSIKA, semi-analytical approximations used to calculate the muon flux for different applications, can be checked.