Fermi constants and “new physics”

Various precision determinations of the Fermi constant are compared. Included are muon and (leptonic) tau decays as well as indirect prescriptions employing α, $m_Z,$ $m_W,$ ${\sin }^2{\theta }_W{(m}_Z{)}_{\overline{\mathrm{MS}}},$ $\Gamma \left(\overrightarrow{Z}{l}^{+}{l}^{-}\right),$ and $\Gamma \left(\overrightarrow{Z}\nu \overline{\nu }\right)$ as input. Their good agreement tests the standard model at the ±0.1% level and provides stringent constraints on new physics. That utility is illustrated for heavy neutrino mixing, two-Higgs-doublet models, S, T, and U parameters, and excited $W^{*\pm }$ bosons (Kaluza-Klein excitations). For the last of those examples, $m_{W^{*}}\gtrsim 2.9\mathrm{TeV}$ is found.