  Strongly modified Higgs-photon-photon and Higgs-gluon-gluon couplings
indicate new electroweak and color mediators, respectively, with a light mass
and a significant coupling to the Higgs boson. We point out the Higgs boson
could have a significant decay width into the mediators and propose uncovering
the hidden new physics through such exotic decays, which can probe the Higgs
coupling with the mediators directly. Focusing on the electroweak mediators, we
study a simplified model using as an example final states with tau leptons and
neutrinos. Because one of the mediators is off-shell and its decay products are
extremely soft, it is challenging to make a discovery at the Large Hadron
Collider. A Higgs factory such as the International Linear Collider, however,
could serve as a discovery machine for the EW mediators even in an early stage.
