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We show that it is essential to include renormalisation group (RG) effectsfor determining the SMEFT parameter space consistent with the CDF W-massanomaly at the matching scale. This is because operators that are only weaklyconstrained--for instance those probed by diboson and Higgs data--can have acontribution to the W-boson mass via one-loop RG effects, that is comparable tothe tree-level contribution of the much more strongly constrained operatorsrelated to electroweak precision observables. We RG evolve the low energy SMEFTparameter space consistent with the anomaly to the matching scale and find amuch larger allowed region. In particular we find that it is possible to have avanishing or even negative T -parameter at the matching scale. This willhopefully lead to a larger set of UV completions that can explain the anomaly.For the one-loop contributions to be important a relatively low new physicsscale around 800 GeV is required. This enhances the possibility of probing thisnew physics in direct and indirect searches in the recent future.

Running away from the T-parameter solution to the W mass anomaly