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

TL;DR

This paper compares different methods of determining the Fermi constant, highlighting tensions among them and exploring how new physics could reconcile these differences within the Standard Model framework.

Contribution

It analyzes the discrepancies between muon decay, electroweak fits, and CKM unitarity in determining $G_F$, proposing effective field theory solutions.

Findings

Tensions exist between muon decay and other $G_F$ determinations.

Effective field theory can potentially reconcile these differences.

Implications for new physics scenarios are discussed.

Abstract

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 $\beta$ 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.