Recent measurements of the Higgs-muon coupling are directly probing muon mass generation for the first time. We classify minimal models with a one-loop radiative mass mechanism and show that benchmark models are consistent with current experimental results. We find that these models are best probed by measurements of $(g-2)_mu$, even when taking into account the precision of Higgs measurements expected at future colliders. The current $(g-2)_mu$ anomaly, if confirmed, could therefore be a first hint that the muon mass has a radiative origin.
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