Recent cosmic-ray measurements are challenging our models of propagation in the Galaxy. A good characterization of the secondary cosmic rays (B, Be, Li and sub-iron species) is crucial to constrain these models and exploit the precision of modern CR experiments. In this work, a Markov chain Monte Carlo analysis has been implemented to fit the experimental flux ratios between B, Be and Li and their flux ratios to the primary nuclei C and O. We have fitted the data using two different parametrizations for the spallation cross sections. The uncertainties in the evaluation of the spectra of these secondary cosmic rays, due to spallation cross sections, have been considered by introducing scale factors as nuisance parameters. We have also tested two different formulations for the diffusion coefficient, which differ in the origin of the high energy hardening of cosmic rays. Additionally, two different approaches are used to scale the cross sections, one based on a combined analysis of all the species (combined analysis) and the other reproducing the high energy spectra of the secondary-to-secondary flux ratios of Be/B, Li/B, Li/Be (scaled analysis). This allows us to make a better comparison between the propagation parameters inferred from the cross sections parametrizations tested in this work. This novel analysis has been successfully implemented using the numerical code DRAGON2 to reproduce the cosmic-ray nuclei data up to $Z=14$ from the AMS-02 experiment. It is found that the ratios of Li favor a harder spectral index of the diffusion coefficient, but compatible with the other ratios inside the observed $2sigma$ uncertainties. In addition, it is shown that, including these scale factors, the secondary-to-primary flux ratios can be simultaneously reproduced.
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