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 throughThe 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 $\Delta \rho \simeq 3G_F{m}_t^2/(8\sqrt{2}{\pi }^2)$, 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.^[ref]