$W$ boson mass shift and muon magnetic moment in the Zee model

The CDF collaboration at Fermilab has recently reported a new precision measurement of the $W$~boson mass showing a substantial $7\sigma$ deviation from the Standard Model prediction. Moreover, Fermilab has recently confirmed the longstanding tension in the $(g-2)_\mu$ measurement. We propose a unified solution to these deviations within the simplest radiative neutrino mass model: the Zee model. Our analysis establishes non-trivial links between the origin of neutrino mass, the $(g-2)_\mu$ anomaly, and the $W$~boson mass shift while being consistent with lepton flavor violation and all other experimental constraints. We find that the mass spectrum of the physical scalars must be hierarchical to be consistent with the $W$~boson mass shift; remarkably, this is also the key to resolving the $(g-2)_\mu$ tension. Furthermore, this mass splitting offers a unique same-sign dimuon signal through which our model can be tested at the LHC.