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In this work we study the $D^* \bar{D}^*$ current with QCD sum rules. Wewrite the correlation function using the general current corresponding to the$D^* \bar{D}^*$ system and then use spin projectors to obtain the correlationfunction in the $0^+, 1^+$ and $2^+$ spin-parity configurations. The purpose ofthe present work is to investigate the possibility of explaining the recentlyreported $Z_c(4025)$ as a $D^* \bar{D}^*$ moleculelike state. As a result wefind a state for each spin case with a very similar mass: $M^{S=0} = \left(3943\pm 104\right)$ MeV, $M^{S=1} = \left(3950 \pm 105\right)$ MeV, $M^{S=2} =\left(3946 \pm 104 \right)$ MeV. We discuss that our mass results, within errorbars, for $1^+$ or $2^+$ are both compatible with $Z_c(4025)$. However, ourresults are also compatible with a possible $D^* \bar{D}^*$ bound state, inagreement with predictions of some previous works. We have also calculated thecurrent-state coupling which turns out to be larger in the $2^+$ case.

Relating $D^* \bar{D}^*$ currents with $J^\pi= 0^+,1^+$ and $2^+$ to $Z_c$ states