Revisit the $Z_c(4025)$ structure observed by BESIII in the $e^+e^- \to (D^*\bar{D}^*)^{\pm,0}\pi^{\mp,0}$ reactions at $\sqrt{s}=4.26$ GeV

Within the framework of the local hidden gauge formalism, we have reanalyzed the hidden-charm vector-vector meson $D^*\bar{D}^*$, $K^*\bar{K}^*$, and $\rho\rho$ interactions with the quantum numbers $I(J^P)=1(1^+)$. The estimation indicates that $D^*\bar{D}^*$ system could form a bound state around 4010 MeV. By comparing our theoretical estimation with the BESIII measurements of the $e^+e^- \to (D^*\bar{D}^*)^{\pm}\pi^{\mp}$ and $e^+e^- \to (D^*\bar{D}^*) ^{0}\pi^{0}$ reactions at $\sqrt{s}=4.26$ GeV , we find that the enhancement structure of the $Z_c(4025)$ in the $D^*\bar{D}^*$ invariant mass distribution observed by BESIII could be interpreted by a shallow $D^*\bar{D}^*$ bound state.