  We present the first lattice investigation of coupled-channel $D\bar D$ and
$D_s\bar D_s$ scattering in the $J^{PC}=0^{++}$ and $2^{++}$ channels. The
scattering matrix for partial waves $l=0,2$ and isospin zero is determined
using multiple volumes and inertial frames via L\"uscher's formalism. Lattice
QCD ensembles from the CLS consortium with $m_{\pi}\simeq280$ MeV, $a \simeq
0.09 $ fm and $L/a=24,~32$ are utilized. The resulting scattering matrix
suggests the existence of three charmonium-like states with $J^{PC}=0^{++}$ in
the energy region ranging from slightly below $2m_D$ up to 4.13 GeV. We find a
so far unobserved $D\bar D$ bound state just below threshold and a $D\bar D$
resonance likely related to $\chi_{c0}(3860)$, which is believed to be
$\chi_{c0}(2P)$. In addition, there is an indication for a narrow $0^{++}$
resonance just below the $D_s\bar D_s$ threshold with a large coupling to
$D_s\bar D_s$ and a very small coupling to $D\bar D$. This resonance is
possibly related to the narrow $X(3915)$/$\chi_{c0}(3930)$ observed in
experiment also just below $D_s\bar D_s$. The partial wave $l=2$ features a
resonance likely related to $\chi_{c2}(3930)$. We work with several
assumptions, such as the omission of $J/\psi\omega$, $\eta_c\eta$ and
three-particle channels. Only statistical uncertainties are quantified, while
the extrapolations to the physical quark-masses and the continuum limit are
challenges for the future.
