D D ¯ interactions are weak near threshold in QCD

We study near-threshold D 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 channel that is kinematically open is η c η . Using lattice QCD we compute, as a function of varying light-quark mass, the S -matrix for coupled-channel η c η − D 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 χ c 0 ( 1 P ) state and the D s D ¯ s threshold.