The Weinberg angle sin²θ_W = 0.2312 is one of the fundamental parameters of the electroweak theory. It determines the mixing between the electromagnetic and weak forces and fixes the ratio of the W and Z boson masses. In the Standard Model it is measured and inserted.
BFUT Paper 19 derives it from the chirality of the 3+e bifurcation — agreement: 0.01%.
The Physical Origin
In BFUT, the weak mixing angle is the ratio of the electromagnetic coupling mode to the combined electroweak coupling. The 3+e bifurcation produces two structural products with complementary internal circulations — the three-core (proton) and the balancing branch (electron). The chirality of this bifurcation — the degree of asymmetry between the clockwise and counterclockwise circulation modes — determines how the electromagnetic interaction and the weak transformation interact at the electroweak scale.
where g_W is the weak SU(2) coupling and g_Y is the hypercharge U(1) coupling, both derived from the condensation topology and substrate density.
The Three-Way Cross-Check
The Weinberg angle derivation provides a three-way internal consistency check. The BFUT values of α, m_W, m_Z, and sin²θ_W are not independently fitted — they all emerge from the same ρ_s through a single derivation chain. The tree-level relation m_W = m_Z·cos(θ_W) is satisfied within the derivation accuracy. Any improvement in the R₀ precision (shared by both the ħ and α derivations) simultaneously improves all electroweak parameters together.
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