Interpreting electroweak precision data including the $W$-mass CDF anomaly

We perform a global fit of electroweak data, finding that the anomaly in the W mass claimed by the CDF collaboration can be reproduced as a universal new-physics correction to the T parameter or vertical bar H-dagger D-mu H vertical bar(2) operator. Contributions at tree-level from multi-TeV new physics can fit the anomaly compatibly with collider bounds: we explore which scalar vacuum expectation values (such as a triplet with zero hypercharge), Z' vectors (such as a Z' coupled to the Higgs only), little-Higgs models or higher-dimensional geometries provide good global fits. On the other hand, new physics that contributes at loop-level must be around the weak scale to fit the anomaly. Thereby it generically conflicts with collider bounds, that can be bypassed assuming special kinematics like quasi-degenerate particles that decay into Dark Matter (such as an inert Higgs doublet or appropriate supersymmetric particles).