  Studies of D and B mesons decays into hadrons have been used to test the
standard model in the last fifteen years. A heavy meson decay involves the
combined effects of a primary weak vertex and subsequent hadronic final state
interactions, which determine the shapes of Dalitz plots. The fact that final
products involve light mesons indicates that the QCD vacuum is an active part
of the problem. This makes the description of these processes rather involved
and, in spite of its importance, phenomenological analyses tend to rely on
crude models. Our group produced, some time ago, a schematic calculation of the
decay $D^+ \to K^- \pi^+ \pi^+$, which provided a reasonable description of
data. Its main assumption was the dominance of the weak vector-current, which
yields a non-factorizable interaction. Here we refine that calculation by
including the correct momentum dependence of the weak vertex and extending the
energy ranges of $\pi\pi$ and $K\pi$ subamplitudes present into the problem.
These new features make the present treatment more realistic and bring theory
closer to data.
