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We present the first lattice QCD study of coupled-channel $D\pi$, $D\eta$ and$D_{s}\bar{K}$ scattering in isospin-1/2 in three partial waves. Usingdistillation, we compute matrices of correlation functions with bases ofoperators capable of resolving both meson and meson-meson contributions to thespectrum. These correlation matrices are analysed using a variational approachto extract the finite-volume energy eigenstates. Utilising L\"uscher's methodand its extensions, we constrain scattering amplitudes in $S$, $P$ and $D$-waveas a function of energy. By analytically continuing the scattering amplitudesto complex energies, we investigate the $S$-matrix singularities. Working at$m_\pi \approx 391$ MeV, we find a pole corresponding to a $J^{P} = 0^{+}$near-threshold bound state with a large coupling to $D\pi$. We also find adeeply bound $J^{P} = 1^{-}$ state, and evidence for a $J^{P} = 2^{+}$ narrowresonance coupled predominantly to $D\pi$. Elastic $D\pi$ scattering in theisospin-$3/2$ channel is studied and we find a weakly repulsive interaction in$S$-wave.

Coupled-Channel $D\pi$, $D\eta$ and $D_{s}\bar{K}$ Scattering from Lattice QCD