Several charged charmonium-like hadrons called $Z_c$ have been recently discovered by different experiments. In contrast to conventional hadrons these contain at least two valence quarks and antiquarks ($bar{c}cbar{d}u$). We perform a lattice QCD simulation of the $I^G(J^{PC})=1^+(1^{+-})$ channel including all relevant two-meson operators under 4.3 GeV: $J/psi pi$, $psi_{2S}pi$, $psi_{1D}pi$, $D bar{D}^*$, $D^* bar{D}^*$, $eta_c rho$ as well as additional diquark anti-diquark operators. In our $N_f = 2$ simulation with pion mass at 266 MeV we are able to identify all two-meson levels within the energy region of interest. However we find no additional level identifiable as a candidate for $Z_c$.
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