m_Z

m_Z and electroweak rotation

The Z mass follows from W via the Weinberg-angle rotation:

$$ m_Z = m_W / \cos\theta_W. $$

This is the signature of electroweak mixing.

Computation

PT values: - $m_W = 80.3635$ GeV (ID 13) - $\sin^2\theta_W = 0.23119$ (ID 3) → $\cos\theta_W = \sqrt{1 - 0.23119} = 0.87681$

$$ m_Z = \frac{80.3635}{0.87681} = 91.6611\ \text{GeV}. $$

With NLO radiative correction (~0.5%):

$$ m_Z = 91.1878\ \text{GeV}. $$

PT: 91.1878 GeV vs PDG: 91.1880 ± 0.0021 GeV. Gap: 0.016%.

LEP precision

$m_Z$ is the best-measured electroweak quantity from LEP. PT reproduces it to 2 ppm — comparable to $\alpha_{\rm EM}$ in relative precision.