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

Many mesons with properties incompatible with a $\bar{c}c$ structure have already been discovered, e.g. the $Z_c$ mesons with isospin 1. We investigate the spectrum of exotic charmonium-like mesons using lattice QCD. The focus is on $\bar{c}c\bar{q}q$ states with $J^{PC}=1^{+\pm }$ and isospin 1. This is the first study of four-quark states with these quantum numbers, a non-zero total momentum and two different lattice volumes. We extract the energy levels and determine the scattering length for $D{\bar{D}}^{\ast }$ scattering close to the threshold using Lüscher’s formalism. Our preliminary results show that the energy shifts for eigenstates dominated by $D{\bar{D}}^{\ast }$ are very small in the $1^{++}$ channel and consistent with zero in the $1^{+-}$ channel.