Precision of analytical approximations in calculations of atmospheric leptons
2019 July 22
We use the Matrix Cascade Equation code (MCEQ) to evaluate the range of applicability of simple analytic approximations parameterized by spectrum-weighted moments and power-law spectral indices that vary slowly with energy. We compare production spectra of leptons as a function of atmospheric depth, zenith angle and energy. We also compare fluxes obtained with different representations of the primary cosmic-ray spectrum and different models of hadronic interactions. The goal is to quantify the effects of the approximations inherent in the simpler formulas in order to determine their limitations and the conditions under which they may be used. Specifically, the range of phase space for which the errors in the approximate formulas are smaller than the differences from the primary spectrum and the hadronic interaction models. Potential applications include the muon charge ratio, the fraction of prompt leptons from decay of charm and seasonal variations of muons and neutrinos.