Systematic analysis of fermionic masses and flavor mixings: a model-independent approach

In a model-independent context, we perform a systematic and detailed study of the fermion flavor masses and mixings. In this analysis, we present a most general parameterization form of the $3 \times 3$ mass matrix, as well as the Pontecorvo-Maki-Nakagawa-Sakata flavor mixing matrix, in terms of the fermionic masses and some free parameters. A likelihood test using the $\chi^2$ statistic is implemented to evaluate whether the theoretical expressions for the leptonic flavor mixing angles also reproduce the experimental data. The results of the $\chi^2$ fit show that the theoretical expressions obtained for the Pontecorvo-Maki-Nakagawa-Sakata mixing matrix correctly reproduce the actual experimental data on neutrino oscillations.