We investigate a recently proposed UV-complete composite Higgs scenario in the light of the first LHC runs. The model is based on a $SU(4)$ gauge group with global flavour symmetry breaking $SU(5) to SO(5)$, giving rise to pseudo Nambu-Goldstone bosons in addition to the Higgs doublet. This includes a real and a complex electroweak triplet with exotic electric charges. Including these, as well as constraints on other exotic states, we show that LHC measurements are not yet sensitive enough to significantly constrain the models low energy constants. The Higgs potential is described by two parameters which are on the one hand constrained by the LHC measurement of the Higgs mass and Higgs decay channels and on the other hand can be computed from correlation functions in the UV-complete theory. Hence to exclude the model at least one constant needs to be determined and to validate the Higgs potential both constants need to be reproduced by the UV-theory. Due to its UV-formulation, a certain number of low energy constants can be computed from first principle numerical simulations of the theory formulated on a lattice, which can help in establishing the validity of this model. We assess the potential impact of lattice calculations for phenomenological studies, as a preliminary step towards Monte Carlo simulations.
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