Partial compositeness under precision scrutiny

We revisit the impact of top partial compositeness on electroweak precision observables in the misaligned vacuum basis. We identify a new source for $S$ in the singlet mixing case, and for $S$-$T$ in the bi-doublet mixing, stemming from misalignment in the gauge couplings of the top partners. Hence, a positive shift in $T$ can be obtained in both cases, as preferred by the recent CDF measurement of the $W$ mass. These results, obtained for the minimal fundamental coset SU(4)/Sp(4), apply to any composite Higgs model with top partial compositeness.
Comment: 33 pages and 2 figures; Accepted by JHEP, v2 appendix updated