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 key fundamental parameters in Standard Model (SM). Therefore, to search for physics beyond SM (BSM) via $G_F$, constraining power determined by precision second-best independent determination $G_F$. best alternative extractions $G_F$ proceed either global electroweak (EW) fit or from superallowed $\beta$ decays combination with Cabibbo angle kaon, $\tau$, $D$ decays. Both variants display some tension decay, albeit opposite directions, reflecting known tensions within EW and hints apparent violation CKM unitarity, respectively. We investigate how BSM could bring three determinations into agreement using effective field theory comment on future perspectives.