$D\bar{D}$ interactions are weak near threshold in QCD

We study near-threshold $D\bar{D}$ scattering in $S$ and $D$-wave to determine whether or not resonances or bound states are present. Working in the approximation where charm-annihilation is forbidden, with two degenerate light-quark flavors and a heavier strange quark, isospin is a good quantum number, and the only other other channel that is kinematically open is ${\eta }_c\eta$. Using lattice QCD we compute, as a function of varying light-quark mass, the $S$-matrix for coupled-channel ${\eta }_c\eta -D\bar{D}$ scattering and find only weakly interacting meson pairs. In contrast to several other studies, we find no evidence for any bound-state or resonance singularity in the energy region between the deeply-bound ${\chi }_{c0}(1P)$ state and the $D_s{\bar{D}}_s$ threshold.