Weinberg Angle sin²θ_W Precision
The weak mixing angle sin²θ_W is one of the most precisely measured parameters in particle physics. The τ-framework derives it at NNLO precision from the e…
Overview
The weak mixing angle sin²θ_W ≈ 0.23122 is one of the most precisely measured parameters in particle physics, governing the strength of the electroweak mixing between the electromagnetic and weak forces. In the τ-framework, sin²θ_W is not a free parameter: it arises from the A–B sector mixing angle (the inter-sector coupling of the holonomy algebra). The LO formula sin²θ_W = ι_τ(1 − ι_τ) gives ≈ 0.2249 from the master constant ι_τ alone.
Detail
At NNLO, the τ-framework derivation (IV.D337) uses Window Universality — the identity W₃(4) = 5 — to generate successive correction terms. The NLO correction (1 − α W₃(4) ι_τ²) and the NNLO correction (1 + α² W₃(3) W₃(4) ι_τ⁴) combine to yield sin²θ_W at −0.7 ppm from the PDG value. This makes sin²θ_W the most precisely derived electroweak parameter in the τ-framework, alongside the W boson mass at −0.5 ppm (IV.T177).
Chapter 27 of Book IV develops the continued-fraction structure of sin²θ_W and cos θ_W, showing that the electroweak mixing angle inherits clean CF structure from ι_τ — evidence that it is a structural consequence of Category τ, not a contingent parameter.
See also: Weinberg Angle NNLO at −0.7 ppm for the full NNLO derivation chain.
Result Statement
IV.D337: sin²θ_W derived at NNLO precision from the electroweak sector, using Window Universality W₃(4) = 5, at −0.7 ppm from the PDG value sin²θ_W = 0.23122. Status: Resolved.