Fermi Constant from Muon Decay Versus Electroweak Fits and Cabibbo-Kobayashi-Maskawa Unitarity.

The Fermi constant G_{F} is extremely well measured through the muon lifetime, defining one of the key fundamental parameters in the standard model (SM). Therefore, to search for physics beyond the SM (BSM) via G_{F}, the constraining power is determined by the precision of the second-best independent determination of G_{F}. The best alternative extractions of G_{F} proceed either via the global electroweak (EW) fit or from superallowed β decays in combination with the Cabibbo angle measured in kaon, τ, or D decays. Both variants display some tension with G_{F} from muon decay, albeit in opposite directions, reflecting the known tensions within the EW fit and hints for the apparent violation of Cabibbo-Kobayashi-Maskawa unitarity, respectively. We investigate how BSM physics could bring the three determinations of G_{F} into agreement using SM effective field theory and comment on future perspectives.