  In this paper we study the reaction $e^+ e^- \to (D^* \bar D^*)^{\pm}
\pi^{\mp}$ in which the BESIII collaboration has claimed the existence of a
$1^+$ resonance, named $Z_c(4025)$, in the $D^*\bar D^*$ invariant mass
spectrum with a mass around 4026 MeV and width close to 26 MeV. We determine
the $D^*\bar D^*$ invariant mass distribution and find that although the
explanation considered by the BESIII collaboration is plausible, there are
others which are equally possible, like a $2^+$ resonance or a bound state.
Even more, we find that the data can be explained without the existence of a
resonance/bound state. In view of the different possible interpretations found
for the BESIII data, we try to devise a strategy which could help in
identifying the origin of the signal reported by the BESIII collaboration. For
this, we study the dependence of the $D^*\bar D^*$ spectrum considering the
different options as a function of the total center of mass energy. We arrive
to the conclusion that increasing the center of mass energy from 4.26 GeV to
4.6 GeV can be useful to distinguish between a resonance, a bound state or just
a pure background as being responsible for the signal found. This information
should be useful for future experiments.
