The Fermi constant from muon decay versus electroweak fits and CKM unitarity

The Fermi constant <math display="inline"><mrow><msub><mrow><mi>G</mi></mrow><mrow><mi>F</mi></mrow></msub></mrow></math> 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 <math display="inline"><msub><mi>G</mi><mi>F</mi></msub></math>, the constraining power is determined by the precision of the second-best independent determination of <math display="inline"><msub><mi>G</mi><mi>F</mi></msub></math>. The best alternative extractions of <math display="inline"><msub><mi>G</mi><mi>F</mi></msub></math> proceed either via the global electroweak (EW) fit or from superallowed <math display="inline"><mi>β</mi></math> decays in combination with the Cabibbo angle measured in kaon, <math display="inline"><mi>τ</mi></math>, or <math display="inline"><mi>D</mi></math> decays. Both variants display some tension with <math display="inline"><msub><mi>G</mi><mi>F</mi></msub></math> 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 <math display="inline"><msub><mi>G</mi><mi>F</mi></msub></math> into agreement using SM effective field theory and comment on future perspectives.