Remark on Koide's Z3-symmetric parametrization of quark masses

TL;DR

This paper examines Koide's Z3-symmetric parametrization of quark masses, suggesting specific phase values for up and down quarks that align with experimental data, extending a framework previously applied to charged leptons.

Contribution

It extends Koide's Z3-symmetric parametrization to quark masses and proposes specific phase values for up and down quarks based on data analysis.

Findings

Phase parameter _L is approximately 2/9.

Suggested low-energy phase values: _U=2/27, _D=4/27.

Data supports Z3-symmetric parametrization for quarks.

Abstract

The charged lepton masses may be parametrized in a Z3-symmetric language appropriate to the discussions of Koide's formula. The phase parameter \delta_L appearing in this parametrization is experimentally indistinguishable from 2/9. We analyse Koide's parametrization for the up (U) and down (D) quarks and argue that the data are suggestive of the low-energy values \delta_U=\delta_L/3=2/27 and \delta_D=2\delta_L/3=4/27.