  We extend previous calculations of the non-local form factors of
semiclassical gravity in $4D$ to include the Einstein-Hilbert term. The
quantized fields are massive scalar, fermion and vector fields. The non-local
form factor in this case can be seen as the sum of a power series of total
derivatives, but it enables us to derive the beta function of Newton's constant
and formally evaluate the decoupling law in the new sector, which turns out to
be the standard quadratic one.
