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 which also includes the lightest fermionic resonances. A new, possibly large, logarithmically divergent contribution to S is identified, which comes purely from the strong dynamics. It can be interpreted as a running of S induced by the non-renormalizable Higgs interactions due to the non-linear sigma-model structure. As expected, the corrections to the T 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 > 750GeV. The corrections to the Z bL bL vertex coming from the lowest-order operators in the effective Lagrangian are finite and somewhat correlated to the corrections to T. 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 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 Vtb can be of order 5% while the distortion of the Z tL tL vertex can be 10%.