Koide's Z_3-symmetric parametrization, quark masses and mixings

TL;DR

This paper explores a Z_3-symmetric parametrization of lepton and quark masses, revealing potential exact phase values and consistency with Koide's formula, offering insights into mass patterns and mixings.

Contribution

It introduces a Z_3-symmetric framework for parametrizing lepton and quark masses, connecting phase parameters with Koide's formula and quark mixing patterns.

Findings

Phase parameters _f take on specific values consistent with experimental data.

The pattern of quark masses aligns with the conjecture that k_{D,U}  1 in the weak basis.

The parametrization supports the validity of Koide's formula at low energies.

Abstract

The sets of charged-lepton (L) and quark (D,U) masses may be parametrized in a Z_3-symmetric language appropriate for the discussion of Koide's formula. Experiment suggests that at the low-energy scale the relevant phase parameters \delta_f take on possibly exact values of \delta_L=3\delta_D/2=3\delta_U=2/9. For k_f (the other parameter relevant for the pattern of masses), a similarly simple expression (k_L=1) is known for charged leptons only. Using the Fritzsch-Xing decomposition of quark-mixing matrices, we show that the suggested pattern of low-energy quark masses is consistent with an earlier conjecture that k_{D,U} \approx 1 in the weak basis.