  In a scalar-coupled-gravity model, the quadratically divergent counter term
appearing in the mass renormalization of the scalar fields must inherit
corrections arising out of gravitational interactions. In this work we have
explicitly demonstrated that there are no such corrections of gravitational
origin to the quadratic divergences in the mass counter terms. This statement
holds true irrespective of the nature of the gravitational interaction, i.e.,
whether gravity is described by general relativity or f(R) theory.
Interestingly, it also turns out that the one loop effective action of
scalar-coupled-gravity system will be well-behaved \emph{if and only if} the
$f(R)$ theory is free from ghosts. In particular, the results derived in the
context of f(R) theory are shown to be in exact agreement with the
corresponding results derived from the equivalent scalar-tensor representation.
Our analysis suggests the tantalizing possibility that the masses of the scalar
fields can be consistently kept smaller than some Ultra Violet (UV) cutoff
scale and is independent of the nature of the gravity theory, which may involve
higher curvature corrections. All these will be true provided the matter fields
and the gravity theory can be embedded consistently into a UV complete theory
at the Planck scale.
