Electroweak precision tests of composite Higgs models

We study constraints on Composite Higgs models with fermion partial compositeness from electroweak precision measurements, including the 2022 $W$-boson mass result from the CDF collaboration. We focus on models where the Composite Higgs sector arises from underlying four-dimensional strongly interacting gauge theories with fermions, and where the SM fermions obtain their mass via linear mixing terms between the fermions and the composite sector -- the so-called fermion partial compositeness scenario. In general, the Composite Higgs sector leads to a small and positive $S$ parameter, and a negative $T$ parameter, but the fermion partial compositeness sector results in an overall positive $T$ parameter in a large part of parameter space. We, therefore, find good agreement between the full composite models and the current electroweak precision measurement bounds on $S$ and $T$ from LEP and CDF, including the offset and correlation of $S,T$ with respect to the SM predictions.