  We address a general problem in the evaluation of triangle loops stemming
from the consideration of the range of the interaction involved in some of the
vertices, as well as the energy dependence of the width of some unstable
particles in the loop. We find sizeable corrections from both effects. We apply
that to a loop relevant to the $D_s^+ \to \pi^+ \pi^0 \eta $ decay, and find
reductions of about a factor of $4$ in the mass distribution of invariant mass
of the $\pi \eta$ in the region of the $a_0(980)$. The method used is based on
the explicit analytical evaluation of the $q^0$ integration in the $d^4q$ loop
integration, using Cauchy's residues method, which at the same time offers an
insight on the convergence of the integrals and the effect of form factors and
cutoffs.
