  We investigate a suppression mechanism of dark matter and quark scattering
amplitudes in a complex singlet extension of the Standard Model. It has been
pointed out that, in a some variant of the model, the scattering amplitudes
cancel each other in the limit in which two mediator scalars degenerate in
their masses. We study the origin of such the cancellation mechanism and show
that the operators describing the Higgs-singlet scalar mixing play essential
role. We derive sum rules for couplings in the general scalar potential of the
model, which guarantee the cancellation of the scattering amplitudes in the
tree and the 1-loop level.
