  We prove to all orders of renormalized perturbative polymer field theory the
existence of a short chain expansion applying to polymer solutions of long and
short chains. For a general polymer network with long and short chains we show
factorization of its partition sum by a short chain factor and a long chain
factor in the short chain limit. This corresponds to an expansion for short
distance along the fractal perimeter of the polymer chains connecting the
vertices and is related to a large mass expansion of field theory.
  The scaling of the second virial coefficient for bimodal solutions is
explained. Our method also applies to the correlations of the multifractal
measure of harmonic diffusion onto an absorbing polymer. We give a result for
expanding these correlations for short distance along the fractal carrier of
the measure.
