Determination of Higgs self-interactions through the double Higgs production
from gluon fusion is a major goal of current and future collider experiments.
We point out this channel could help disentangle and resolve the nature of
ultraviolet contributions to Higgs couplings to two gluons. Analytic properties
of the double Higgs amplitudes near kinematic threshold are used to study
features resulting from scalar and fermionic loop particles mediating the
interaction. Focusing on the hh invariant mass spectrum, we consider the effect
from anomalous top and bottom Yukawa couplings, as well as from scalar and
fermionic loop particles. In particular, the spectrum at high hh invariant mass
is sensitive to the spin of the particles in the loop.