Γ_t

Γ_t — top decay width

The top quark decay width is:

$$ \Gamma_t = \frac{G_F m_t^3}{8\pi\sqrt{2}} \cdot |V_{tb}|^2 \cdot \left(1 - \frac{m_W^2}{m_t^2}\right)^2 \left(1 + 2\frac{m_W^2}{m_t^2}\right) \cdot K_{\rm QCD}. $$

Computation

PT values: - $G_F = 1.166\,38 \times 10^{-5}$ GeV⁻² (ID 4) - $m_t = 172.698$ GeV (ID 12) - $|V_{tb}|^2 = 0.998\,431$ (ID 24) - $m_W = 80.3635$ GeV (ID 13) - $K_{\rm QCD} \approx 0.890$ (NLO QCD correction)

$m_W^2/m_t^2 = 0.2167$

$$ \Gamma_t = \frac{1.166 \times 10^{-5} \cdot (172.7)^3}{8\pi\sqrt{2}} \cdot 0.9984 \cdot (0.7833)^2 \cdot (1.4334) \cdot 0.890 = 1.3060\ \text{GeV}. $$

PT: 1.3060 GeV vs PDG: 1.42 ± 0.19 GeV. Gap: 8% (but at 0.6σ — within error bar).

Tension to watch

The 8% gap is apparent but stays within the experimental margin (13%). As LHC refines the measurement, either the value converges to 1.3 (PT validated) or stays at 1.4 (PT in ~3σ tension).