  Attempts to use coarse-grained molecular theories to calculate corrections to
the random-phase approximation (RPA) for correlations in polymer mixtures have
been plagued by an unwanted sensitivity to the value of an arbitrary cutoff
length, {\it i.e.}, by an ultraviolet (UV) divergence. We analyze the UV
divergence of the inverse structure factor $S^{-1}(k)$ predicted by a
`one-loop' approximation similar to that used in several previous studies. We
consider both miscible homopolymer blends and disordered diblock copolymer
melts. We show, in both cases, that all UV divergent contributions can be
absorbed into a renormalization of the values of the phenomenological
parameters of a generalized self-consistent field theory (SCFT). This
observation allows the construction of a UV convergent theory of corrections to
SCFT phenomenology. The UV-divergent one-loop contribution to $S^{-1}(k)$ are
shown to be the sum of: (i) a $k$-independent contribution that arises from a
renormalization of the effective $\chi$ parameter, (ii) a $k$-dependent
contribution that arises from a renormalization of monomer statistical segment
lengths, (iii) a contribution proportional to $k^{2}$ that arises from a
square-gradient contribution to the one-loop fluctuation free energy, and (iv)
a $k$-dependent contribution that is inversely proportional to the degree of
polymerization, which arises from local perturbations in fluid structure near
chain ends and near junctions between blocks in block copolymers.
