Composite Higgs Models with a Hidden Sector

We discuss the phenomenology of composite Higgs models that naturally produce a Standard Model-like Higgs boson with a mass of $126$ GeV. The effective theory below the compositeness scale is weakly coupled in these models, and the goldstone sector acts as a portal between the third generation of quarks and a hidden gauge sector. The addition of hidden-sector fermions gives rise to a calculable effective scalar potential with a naturally light scalar resonance. The generic prediction of these theories is the existence of additional pseudo-Nambu Goldstone bosons with electroweak-scale cross sections and masses. In this paper we analyze the collider signatures for some simple concrete realizations of this framework. We find that despite the existence of additional weakly and strongly coupled particles that are kinematically within reach of current experiments, the generic signatures are difficult to resolve at the LHC, and could remain well-hidden in the absence of an $e^+ e^-$ Higgs factory such as the CEPC or a surface detector such as MATHUSLA.