  The renormalized one-loop theory is a coarse-grained theory of corrections to
the self-consistent field theory (SCFT) of polymer liquids, and to the random
phase approximation (RPA) theory of composition fluctuations. We present
predictions of corrections to the RPA for the structure function $S(k)$ and to
the random walk model of single-chain statics in binary homopolymer blends. We
consider an apparent interaction parameter $\chi_{a}$ that is defined by
applying the RPA to the small $k$ limit of $S(k)$. The predicted deviation of
$\chi_{a}$ from its long chain limit is proportional to $N^{-1/2}$, where $N$
is chain length. This deviation is positive (i.e., destabilizing) for weakly
non-ideal mixtures, with $\chi_{a} N \alt 1$, but negative (stabilizing) near
the critical point. The positive correction to $\chi_{a}$ for low values of
$\chi_{a} N$ is a result of the fact that monomers in mixtures of shorter
chains are slightly less strongly shielded from intermolecular contacts. The
depression in $\chi_{a}$ near the critical point is a result of long-wavelength
composition fluctuations. The one-loop theory predicts a shift in the critical
temperature of ${\cal O}(N^{-1/2})$, which is much greater than the predicted
${\cal O}(N^{-1})$ width of the Ginzburg region. Chain dimensions deviate
slightly from those of a random walk even in a one-component melt, and contract
slightly with increasing $\chi_{e}$. Predictions for $S(k)$ and single-chain
properties are compared to published lattice Monte Carlo simulations.
