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Many mesons with properties incompatible with a $\bar cc$ structure havealready been discovered, e.g. the $Z_c$ mesons with isospin 1. We investigatethe spectrum of exotic charmonium-like mesons using lattice QCD. The focus ison $\bar cc \bar qq$ states with $J^{PC}=1^{+\pm}$ and isospin 1. This is thefirst study of four-quark states with these quantum numbers, a non-zero totalmomentum and two different lattice volumes. We extract the energy levels anddetermine the scattering length for $D\bar D^*$ scattering close to thethreshold using L\"uscher's formalism. Our preliminary results show that theenergy shifts for eigenstates dominated by $D\bar{D}^*$ are very small in the$1^{++}$ channel and consistent with zero in the $1^{+-}$ channel.

Charmonium-like states with $J^{P}=1^{+}$ and isospin 1