W-Boson Mass Prediction at −0.5 ppm
The W-boson mass is derived as M_W = (17/5)ι_τ⁻³ m_n [1 + (5/17)αι_τ²] at −0.5 ppm from the PDG value.
Overview
IV.T177 derives the W-boson mass from the τ-framework as M_W = (17/5)ι_τ⁻³ m_n [1 + (5/17)αι_τ²], where m_n is the neutron mass, α is the fine-structure constant, and ι_τ = 2/(π+e). The NLO correction factor (5/17) is governed by Window Universality: W₃(4) = 5 governs all three electroweak NLO corrections. Agreement with the PDG value is at −0.5 ppm — sub-ppm precision with zero free parameters.
Detail
The W-boson mass M_W ≈ 80.377 GeV is one of the most precisely measured quantities in particle physics. Its tree-level value in the Standard Model is determined by the Fermi constant, the fine structure constant, and the Weinberg angle — three measured inputs. Book IV derives M_W from first principles using only ι_τ, α, and the neutron mass. The leading-order formula (17/5)ι_τ⁻³ m_n comes from the A-sector (weak force) coupling at the first enrichment level E₁, where the factor 17 = W₃(5) (fifth windowing number at depth 3) and 5 = W₃(4) (fourth windowing number at depth 3). The NLO correction (5/17)αι_τ² is the electroweak mixing correction, where the same W₃(4) = 5 that governs the LO denominator also governs the NLO numerator — this is Window Universality. The −0.5 ppm agreement makes this one of the most precise zero-parameter predictions in the series.
Result Statement
IV.T177: M_W = (17/5)ι_τ⁻³ m_n [1 + (5/17)αι_τ²] at −0.5 ppm from PDG value. Window Universality: W₃(4) = 5 governs this and all three EW NLO corrections.