Spectrum of cosmic-ray nucleons and the atmospheric muon charge ratio

Interpretation of measurements of the muon charge ratio in the TeV range depends on the spectra of protons and neutrons in the primary cosmic radiation and on the inclusive cross sections for production of ${\pi }^{\pm }$ and $K^{\pm }$ in the atmosphere. Recent measurements of the spectra of cosmic-ray nuclei are used here to estimate separately the energy spectra of protons and neutrons and hence to calculate the charge separated hadronic cascade in the atmosphere. From the corresponding production spectra of ${\mu }^{+}$ and ${\mu }^{-}$ the ${\mu }^{+}\mathrm{/}{\mu }^{-}$ ratio is calculated and compared to recent measurements. The comparison leads to a determination of the relative contribution of kaons and pions. Implications for the spectra of ${\nu }_{\mu }$ and ${\bar{\nu }}_{\mu }$ are discussed.