Abstract
As the Higgs boson properties settle, the constraints on the Standard Model extensions tighten. We consider all possible new fermions that can couple to the Higgs, inspecting sets of up to four chiral multiplets. We confront them with direct collider searches, electroweak precision tests, and current knowledge of the Higgs couplings. The focus is on scenarios that may depart from the decoupling limit of very large masses and vanishing mixing, as they offer the best prospects for detection. We identify exotic chiral families that may receive a mass from the Higgs only, still in agreement with the $h\gamma\gamma$ signal strength. A mixing $\theta$ between the Standard Model and non-chiral fermions induces order $\theta^2$ deviations in the Higgs couplings. The mixing can be as large as $\theta\sim 0.5$ in case of custodial protection of the $Z$ couplings or accidental cancellation in the oblique parameters. We also notice some intriguing effects for much smaller values of $\theta$, especially in the lepton sector. Our survey includes a number of unconventional pairs of vector-like and Majorana fermions coupled through the Higgs, that may induce order one corrections to the Higgs radiative couplings. We single out the regions of parameters where $h\gamma\gamma$ and $hgg$ are unaffected, while the $h\gamma Z$ signal strength is significantly modified, turning a few times larger than in the Standard Model in two cases. The second run of the LHC will effectively test most of these scenarios.