Theoretical analysis demonstrates a geometric link between electroweak gauge couplings and the Koide relation, suggesting an algebraic origin for fundamental dimensionless constants.
Dimensionless constants occupy a special place in fundamental physics because their numerical values do not depend on the choice of units. This paper investigates an idealized geometric construction linking the Koide relation for charged leptons to the gauge couplings of the electroweak interaction. It is postulated that the electroweak triplet (g, g′, −e²) satisfies the Koide condition Q = 2/3, while an idealized weak mixing angle θW = 30° imposes g′/g = 1/√3. The requirement e² = g²g′²/(g²+g′²) reduces the construction to a single algebraically fixed constant close to the tabulated value.
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Leonid Vlasenko (2026) studied this question.
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