Muon multiplicity at high energy proton-nuclei collisions

Estimation of multiplicity of muons and pions production at high energy proton-nuclei collisions is given. Both QED and QCD contributions are considered for peripheral kinematics of muon pair and $\sigma$-meson production, keeping in mind it's final conversion to muons. An attempt to explain the excess of positive charged muons compared to negative one in cosmic muon showers is given. We derive the dependence of cross-section of $n$ pairs as a function of $n$ at large n as $d^n(n!n^2)^{-1}$.