  We consider, in more details than it was done previously, the effective
low-energy behavior in the quantum theory of a light scalar field coupled to
another scalar with much larger mass. The main target of our work is an IR
decoupling of heavy degrees of freedom, including in the diagrams with mixed
light-heavy contents in the loops. It is shown that the one-loop diagrams with
mixed internal lines produce an IR non-local contributions which are exactly
the same as the ones in the theory of the light scalar alone, with the
effective self-interaction which can be obtained by the functional integration
of the heavy scalar, almost neglecting its kinetic term. The same effect takes
place in curved space, regardless of a larger amount of non-localities which
show up in the effective model.
