Koide Technical Paper The Coupling-Modified Koide Relation: A Unified Mass Formula for Leptons and Neutrinos

Koide Technical Paper in the The Harmonic Structure of the Standard Model series

Abstract
We present a unified Koide mass relation for both charged leptons and neutrinos
using the reciprocal convention Sigma_mi/(Sigma sqrt(mi))^2 = Q. Charged
leptons satisfy Q = 2/3 exactly (to 5.8×10^-6 precision with PDG 2024 masses).
The physical meaning of 2/3 is the SU(3) to SU(2) projection ratio: two electroweak
dimensions out of three color dimensions. Neutrinos couple through the neutral
current Z^0 rather than the charged current W±, modifying the coupling factor by
(1 - sin^2 theta_W): Qnu = (2/3)(1 - sin^2 theta_W) = 0.518006. Combined with
NuFIT 6.0 oscillation constraints, this gives a unique solution m1 = 0.4558 meV, m2
= 8.6665 meV, m3 = 50.3409 meV, Sigma_mi = 59.463 meV. Both relations follow
from the same formula with different coupling factors, making the Koide relation a
statement about gauge coupling geometry rather than a numerical coincidence.