Constraints on vector resonances from a strong Higgs sector

We consider a scenario of a composite Higgs arising from a strong sector. We assume that the lowest lying composite states are the Higgs scalar doublet and a massive vector triplet, whose dynamics below the compositeness scale are described in terms of an effective Lagrangian. Electroweak symmetry breaking takes place through a vacuum expectation value just as in the Standard Model, but with the vector resonances strongly coupled to the Higgs field. We determine the constraints on this scenario imposed by (i) the Higgs diphoton decay rate, (ii) the electroweak precision tests and (iii) searches of heavy resonances at the LHC in the final states $l^+l^-$ and $l\nu_l$ ($l=e,\mu$), $\tau^+\tau^-$, $jj$, $t\bar{t}$, $WZ$, $WW$, $WH$ and $ZH$. We find that the heavy vector resonances should have masses that are constrained to be in the range $2.1$ - $3$ TeV. On the other hand, the mixing of the heavy vectors with the Standard Model gauge bosons is constrained to be in the range $\tan\vartheta\sim 0.1 - 0.3$, which is consistent with the assumption that the Higgs couples weakly to the Standard sector, even though it couples strongly to the heavy vector resonances.