Light top partners and precision physics

We analyze the corrections to the precision EW observables in minimal composite Higgs models by using a general effective parametrization that also includes the lightest fermionic resonances. A new, possibly large, logarithmically divergent contribution to (S) over cap is identified, which comes purely from the strong dynamics. It can be interpreted as a running of (S) over cap induced by the non-renormalizable Higgs interactions due to the non-linear sigma-model structure. As expected, the corrections to the (T) over cap parameter coming from fermion loops are finite and dominated by the contributions of the lightest composite states. The fit of the oblique parameters suggests a rather stringent lower bound on the sigma-model scale f greater than or similar to 750 GeV. The corrections to the Z (b) over bar (L)b(L) vertex coming from the lowest-order operators in the effective Lagrangian are finite and somewhat correlated to the corrections to (T) over cap. Large additional contributions are generated by contact interactions with 4 composite fermions. In this case a logarithmic divergence can be generated and the correlation with (T) over cap is removed. We also analyze the tree-level corrections to the top couplings, which are expected to be large due to the sizable degree of compositeness of the third generation quarks. We find that for a moderate amount of tuning the deviation in V-tb can be of order 5% while the distortion of the Z (t) over bar (L)t(L) vertex can be 10%.