  The presence of colored particles can affect both the single and the pair
Higgs productions substantially. For scalar particles, this happens if their
portal couplings to the Standard Model Higgs are large and their masses are not
too high. In the present work these processes are studied in the case of
several leptoquarks which may appear in many beyond Standard Model theories. It
is found that the constraints on the portal couplings from the single Higgs
production and the decays to various channels measured by the LHC experiments
still allow increased Higgs pair production rate. For the masses in the range
from 180 GeV to 300 GeV, depending on the strength of such portal couplings,
the Higgs pair production may reach an order to several hundred in magnitude
larger rate than the Standard Model case for the 8 TeV run. Therefore, combined
with the on going searches for leptoquarks by both the CMS and ATLAS, this is
one of the possible scenarios to be probed directly by the current data. The
current study demonstrates that if colored scalars modify scalar potentials
through portal couplings, which has been studied for variety of motivations
such as playing a potentially important role in electroweak phase transition,
composite models or radiative neutrino masses, this fact may appear as the
modified Higgs pair production.
