Fermion masses as mixing parameters in the SM

Abstract

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.

Comments: 8 pages; to be published in Journal of Physics Conference Series (IOP). Joint Proceedings of the XV Mexican Workshop on Particles and Fields & the XXX Annual Meeting of the Division of Particles and Fields of the Mexican Physical Society