Fermion masses as mixing parameters in the SM

TL;DR

This paper proposes a novel way to parametrize the fermion mixing matrix in the Standard Model using the hierarchical fermion mass ratios, linking mass hierarchies directly to mixing parameters.

Contribution

It introduces a new parametrization of the mixing matrix based on fermion mass ratios, connecting mass hierarchies with mixing parameters in the SM.

Findings

Mixing parameters can be expressed as mass ratios in hierarchical fermion sectors.

The parametrization applies to both quark and lepton sectors.

Provides a phenomenological link between fermion masses and mixing angles.

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.