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The CDF collaboration at Fermilab has recently reported a new precisionmeasurement of the $W$~boson mass showing a substantial $7\sigma$ deviationfrom the Standard Model prediction. Moreover, Fermilab has recently confirmedthe longstanding tension in the $(g-2)_\mu$ measurement. We propose a unifiedsolution to these deviations within the simplest radiative neutrino mass model:the Zee model. Our analysis establishes non-trivial links between the origin ofneutrino mass, the $(g-2)_\mu$ anomaly, and the $W$~boson mass shift whilebeing consistent with lepton flavor violation and all other experimentalconstraints. We find that the mass spectrum of the physical scalars must behierarchical to be consistent with the $W$~boson mass shift; remarkably, thisis also the key to resolving the $(g-2)_\mu$ tension. Furthermore, this masssplitting offers a unique same-sign dimuon signal through which our model canbe tested at the LHC.

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