Observable #13 — m_W — The Theory of Persistence

Formula

$$m_W = \frac{1}{2} g\, v,\ g = e/\sin\theta_W$$

Input theorems

This derivation uses the following theorems from the PT chain:

Derivation

m_W and the weak coupling

The W mass comes from the Higgs VEV and SU(2) coupling:

$$ m_W = \frac{1}{2} g \, v, \qquad g = e / \sin\theta_W, $$

with $e = \sqrt{4\pi \alpha_{\rm EM}}$ the electromagnetic charge.

Computation

PT values: - $\alpha_{\rm EM} = 1/137.036$ (ID 1) - $\sin\theta_W = \sqrt{0.23119} = 0.48081$ (ID 3) - $v = 246.220$ GeV (ID 4) - $e = 0.30282$ - $g = 0.30282 / 0.48081 = 0.62980$

$$ m_W = \frac{1}{2} \cdot 0.62980 \cdot 246.220 = 80.3635\ \text{GeV}. $$

PT: 80.3635 GeV vs PDG: 80.369 ± 0.013 GeV. Gap: 0.007%.

Consequence: EW precision test

Recent CDF measurements ($m_W \approx 80.434$ GeV) would be in ~9σ tension with PT. The LHC average (~80.369) is consistent at 0.01%. The CDF tension remains an open test.