  We investigate string amplitudes by using the partial modular transformation
which we introduced in our previous works. This enables us to extract stringy
threshold corrections from the full string amplitudes and interpret them in
terms of the Wilsonian effective field theory in a natural way. We calculate
mass shifts and wave function renormalizations for massless scalar fields on
brane-antibrane systems. We find that the mass shift can be exponentially small
and negative. We also propose a strategy for realizing a hierarchical mass
spectrum on D-branes.
