We point out the necessity to consider $\beta$-decay observables in resolutions of the $W$-boson anomaly in the Standard Model Effective Field Theory that go beyond pure oblique corrections. We demonstrate that present global analyses that explain the $W$-boson mass anomaly predict a large, percent-level, violation of first-row CKM unitarity. We investigate what solutions to the $W$-boson mass anomaly survive after including $\beta$-decay constraints.
Categories: hep-ph nucl-th