= Electroweak precision test with the W, top and Higgs masses
In an on-shell convention, the <Standard Model> relates the <W boson> <mass> to measured electroweak inputs through
$$
m_W^2\left(1-\frac{m_W^2}{m_Z^2}\right)=\frac{\pi\alpha}{\sqrt2G_F(1-\Delta r)}.
$$
The <radiative corrections> in $\Delta r$ depend on the <top quark> and <Higgs boson> masses. The leading heavy-top contribution to the electroweak rho parameter is $\Delta\rho\simeq3G_Fm_t^2/(8\sqrt2\pi^2)$, reflecting the large mass splitting in the top-bottom weak doublet. The Higgs dependence in the precision corrections is mainly logarithmic over the relevant range. Direct measurements of $m_t$ and $m_H$ therefore allow an indirect prediction of $m_W$; comparing it with a direct measurement tests loops as well as tree-level <electroweak symmetry breaking>. Any tension must include input uncertainties, experimental systematics and higher-order corrections.https://www-cdf.lbl.gov/cdf_ewk/cdf_ewk.html[CDF electroweak physics: relation between W, top and Higgs mass measurements]{ref}
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