  The Higgs boson may have decay channels that are not predicted by the
Standard Model. We discuss the prospects of probing exotic Higgs decays at the
LHC using the 4-lepton final state. We study two specific scenarios, with new
particles appearing in the intermediate state of the 4-lepton Higgs decay. In
one, Higgs decays to a Z boson and a new massive gauge boson, the so-called
hidden photon. In the other, Higgs decays to an electron or a muon and a new
vector-like fermion. We argue that the upcoming LHC run will be able to explore
a new parameter space of these models that is allowed by current precision
constraints. Employing matrix element methods, we use the full information
contained in the differential distribution of the 4-lepton final state to
extract the signal of exotic decays. We find that, in some cases, the LHC can
be sensitive to new physics even when the correction to the total 4-lepton
Higgs rate is of the order of a percent. In particular, for the simplest
realization of the hidden photon with the mass between 15 and 65 GeV, new
parameter space can be explored in the LHC run-II.
