Fermion masses as mixing parameters in the SM

Flavor transitions via the charged current interactions are parametrized by a three dimensional and unitary transformation. This so called mixing matrix requires of four mixing parameters. Here we show that under the phenomenological observation of hierarchical fermion masses, $m_3 \gg m_2 \gg m_1$, a mixing parametrization can be built with its mixing parameters being the corresponding four independent mass ratios of each fermion sector, i.e., $m_u/m_c$, $m_c/m_t$, $m_d/m_s$, and $m_s/m_b$ and $m_e/m_\mu$, $m_\mu/m_\tau$, $m_{\nu 1}/m_{\nu 2}$, and $m_{\nu 2}/m_{\nu 3}$, for the quark and lepton sector, respectively.