  We investigate the Schmid theorem, which states that if one has a tree level
mechanism with a particle decaying to two particles and one of them decaying
posteriorly to two other particles, the possible triangle singularity developed
by the mechanism of elastic rescattering of two of the three decay particles
does not change the cross section provided by the tree level. We investigate
the process in terms of the width of the unstable particle produced in the
first decay and determine the limits of validity and violation of the theorem.
One of the conclusions is that the theorem holds in the strict limit of zero
width of that resonance, in which case the strength of the triangle diagram
becomes negligible compared to the tree level. Another conclusion, on the
practical side, is that for realistic values of the width, the triangle
singularity can provide a strength comparable or even bigger than the tree
level, which indicates that invoking the Schmid theorem to neglect the triangle
diagram stemming from elastic rescattering of the tree level should not be
done. Even then, we observe that the realistic case keeps some memory of the
Schmid theorem, which is visible in a peculiar interference pattern with the
tree level.
