Higgs boson coupling to a new strongly interacting sector

In the framework of strongly interacting dynamics for electroweak symmetry breaking, heavy composite particles may arise and cause observable effects, as they should couple strongly to the resulting Higgs boson and affect the signals that appear at one loop level. Here we study this expected behavior, contrasting it with current experimental knowledge. We work in a simple and generic scenario where the lowest lying composite states are the Higgs scalar doublet and a massive vector triplet. We use an effective chiral Lagrangian to describe the theory below the compositeness scale $\Lambda$, assumed to be $4\pi v \simeq~3$ TeV. The effective theory contains the Standard Model spectrum and the extra composites. We determine the constraints on this scenario imposed by our current knowledge of the $Zb\bar{b}$ vertex, the $T$ and $S$ oblique parameters, and the recently measured Higgs mass and its diphoton decay rate. We found that the $T$ and $S$ parameters as well as the Higgs diphoton decay do not provide important constraints on the model. In contrast, the constraints arising from the $Zb\bar{b}$ vertex and from the Higgs mass at $126$ GeV are fulfilled only if the heavy vector resonances do not couple strongly with quarks, and at the same time the Higgs boson has a moderate but not too strong coupling to the heavy composite resonances.