Fermi constants and “new physics”

Abstract

Various precision determinations of the Fermi constant are compared. Included are muon and (leptonic) tau decays as well as indirect prescriptions employing \ensuremath{\alpha}, ${m}_{Z},$ ${m}_{W},$ ${\mathrm{sin}}^{2}{\ensuremath{\theta}}_{W}{(m}_{Z}{)}_{\overline{\mathrm{MS}}},$ $\ensuremath{\Gamma}(\stackrel{\ensuremath{\rightarrow}}{Z}{l}^{+}{l}^{\ensuremath{-}}),$ and $\ensuremath{\Gamma}(\stackrel{\ensuremath{\rightarrow}}{Z}\ensuremath{\nu}\overline{\ensuremath{\nu}})$ as input. Their good agreement tests the standard model at the \ifmmode\pm\else\textpm\fi{}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 ${W}^{*\ifmmode\pm\else\textpm\fi{}}$ bosons (Kaluza-Klein excitations). For the last of those examples, ${m}_{{W}^{*}}\ensuremath{\gtrsim}2.9\mathrm{TeV}$ is found.