The OPERA detector, designed to search for $ u_{mu} to u_{tau}$ oscillations in the CNGS beam, is located in the underground Gran Sasso laboratory, a privileged location to study TeV-scale cosmic rays. For the analysis here presented, the detector was used to measure the atmospheric muon charge ratio in the TeV region. OPERA collected charge-separated cosmic ray data between 2008 and 2012. More than 3 million atmospheric muon events were detected and reconstructed, among which about 110000 multiple muon bundles. The charge ratio $R_{mu} equiv N_{mu^+}/N_{mu^-}$ was measured separately for single and for multiple muon events. The analysis exploited the inversion of the magnet polarity which was performed on purpose during the 2012 Run. The combination of the two data sets with opposite magnet polarities allowed minimizing systematic uncertainties and reaching an accurate determination of the muon charge ratio. Data were fitted to obtain relevant parameters on the composition of primary cosmic rays and the associated kaon production in the forward fragmentation region. In the surface energy range 1-20 TeV investigated by OPERA, $R_{mu}$ is well described by a parametric model including only pion and kaon contributions to the muon flux, showing no significant contribution of the prompt component. The energy independence supports the validity of Feynman scaling in the fragmentation region up to $200$ TeV/nucleon primary energy.
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