Higgs couplings in composite models

We study Higgs couplings in the composite Higgs model based on the coset SO(5)/SO(4). We show that the couplings to gluons and photons are insensitive to the elementary-composite mixings and thus not affected by light fermionic resonances. Moreover, at leading order in the mixings the Higgs couplings to tops and gluons, when normalized to the Standard Model (SM), are equal. These properties are shown to be direct consequences of the Goldstone symmetry, of the partial compositeness structure and of the assumption of CP invariance. In particular, they are independent of the details of the elementary-composite couplings, and they are also insensitive to derivative interactions of the Higgs with the composite resonances. We support our conclusions with an explicit construction where the SM fermions are embedded in the 14-dimensional representation of SO(5).