The Fermi constant from muon decay versus electroweak fits and CKM 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). However, to search for physics beyond the SM (BSM), it is the precision of the second-best independent determination of $G_F$ that defines the sensitivity. The best alternative extractions of $G_F$ proceed via the global electroweak (EW) fit or from superallowed $\beta$ decays in combination with the Cabibbo angle measured in kaon, $\tau$, 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 CKM 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.