The limits on the strong Higgs sector parameters in the presence of new vector resonances

In this paper, we investigate how the LHC data limit the Higgs-related couplings in the effective description of a strongly interacting extension of the Standard model. The Higgs boson is introduced as a scalar composite state and it is followed in the mass hierarchy by an $SU(2)$ triplet of vector composites. The limits are calculated from the constraints obtained in the recent ATLAS+CMS combined analysis of the data from 2011 and 2012. We find that the data prefer the scenario where the Higgs couplings to the electroweak gauge bosons differ from its couplings to the vector triplet. We also investigate the unitarity limits of the studied effective model for the experimentally preferred values of the Higgs couplings. We find from the $\pi\pi\rightarrow\pi\pi$ scattering amplitudes that for the vector resonance masses between one and two TeV significant portions of the experimentally allowed regions are well below the unitarity limit. We also evaluate how the existing ATLAS and CMS Run-2 data restrict our model with the upper bounds on the resonance production cross section times its branching ratio for various decay channels. The masses in the range $1\;\mbox{TeV}\leq M_\rho\leq 2\;\mbox{TeV}$ are not excluded in parts or even full parameter space of our theory.