Oblique corrections to the $W$ width

The lowest-order expression for the partial $W$ width to $e\nu$, $\Gamma (W\to e\nu )=\frac{G_{\mu }{M}_W^3}{\left(6\mathrm{}\pi \sqrt{2}\right)}$, has no oblique radiative corrections from new physics if the measured $W$ mass is used. Here $G_{\mu }=(1.166\mathrm{}39\pm 0.00002)\times {10}^{-5\mathrm{}}$ GeV/${\mathit{c}}^2$ is the muon decay constant. For the present value of $M_W=(80.14\mathrm{}\pm 0.27)$ GeV/${\mathit{c}}^2$, and with $m_t=140\mathrm{}$ GeV/${\mathit{c}}^2$, one expects $\Gamma (W\to e\nu )=(224.4\mathrm{}\pm 2.3)$ MeV. The total width ${\Gamma }_{\mathrm{tot}}\mathrm{}\left(W\right)\mathrm{}$ is also expected to lack oblique corrections from new physics, so that $\frac{{\Gamma }_{\mathrm{tot}}\mathrm{}\left(W\right)\mathrm{}}{\Gamma (W\to e\nu )}=3+6[1+\{\frac{{\alpha }_s\left(M_W\right)}{\pi }\left\} \right]$. Present data are consistent with this prediction.