Weak mixing angle sin²θ_W
The weak mixing angle sin²θ_W (Weinberg angle) is, in the τ-framework, the τ-effective dimensionless coupling of the electroweak crossing — derived as sin²θ_W = ι_τ (1 − ι_τ). It is a Layer-1 dimensionless readout of the master constant; the τ-prediction agrees with PDG to ∼2.7%.
τ-Definition
The weak mixing angle sin²θ_W (Weinberg angle) is, in the τ-framework, the τ-effective dimensionless coupling of the electroweak crossing — derived as sin²θ_W = ι_τ (1 − ι_τ). It is a Layer-1 dimensionless readout of the master constant; the τ-prediction agrees with PDG to ∼2.7%.
Categorical invariant. sin²θ_W = ι_τ (1 − ι_τ) — the EW-crossing readout, the product of the κ(A) and κ(D) sector couplings.
Primary registry anchor:
IV.D130
τ-Derivation Chain
SI Translation
Numerical value: 0.22489 ± 0.00060 dimensionless
Calibration anchor: PG-P01-neutron
Calibration chain:
- Layer 0: ι_τ = 2/(π + e_math) ≈ 0.341
- Layer 1: sin²θ_W = ι_τ (1 − ι_τ) = κ(A) · κ(D) ≈ 0.2249
- PDG value: sin²θ_W ≈ 0.23121(4) (on-shell scheme); deviation ∼2.7%
- Conjectural sector — refinement expected at higher cascade depth
Manuscript reference: manuscript-sources/book-05/part07-closure/ch-closure-constants.tex
Lean Coverage
See Also
Related glossary entries
Referenced by
Cross-domain bridges
This glossary term sits on the boundary between domains. The τ-framework's cross-domain pivots are the structural junctions where physics, life, and metaphysics readouts meet.