  In order to explore the spectrum of hidden-charm scalar and tensor
resonances, we study meson-meson scattering with $J^{PC}=0^{++}, 2^{++}$ in the
charmonium energy region using lattice QCD. Employing a light-quark mass
corresponding to $m_\pi \approx 391$ MeV, we determine coupled-channel
scattering amplitudes up to around 4100 MeV considering all kinematically
relevant channels consisting of a pair of open-charm mesons or a charmonium
meson with a light meson. A single isolated scalar resonance near 4000 MeV is
found with large couplings to $D\bar{D}$, $D_s \bar{D}_s$ and the kinematically
closed $D^* \bar{D}^*$ channel. A single tensor resonance at a similar mass
couples strongly to $D\bar{D}$, $D\bar{D}^*$ and $D^* \bar{D}^*$. We compare
the extracted resonances to contemporary experimental candidate states,
previous lattice results and theoretical modeling. In contrast to several other
studies, we do not find any significant feature in the scalar amplitudes
between the ground state $\chi_{c0}(1P)$ and the resonance found around 4000
MeV.
