  In this letter we study a novel effect of a hidden sector coupling to the
standard model Higgs boson: an enhancement of the Higgs pair production cross
section near threshold due to bound state effects. After summing the ladder
contributions of the hidden sector to the effective $ggHH$ coupling, we find
the amplitude for gluon-gluon scattering via a Higgs loop. We relate this
amplitude to the double Higgs production cross section via the optical theorem.
We find that enhancements of the order of 100 for the partonic cross section
near the threshold region can be obtained for a hidden sector strongly coupled
to the Higgs boson. The corresponding cross section at the LHC can be as large
as a factor of 10 times the SM result for extreme values of the coupling. The
detection of such an effect could in principle lead to important information
about the hidden sector.
