  We provide an updated assessment of the power of the Cherenkov Telescope
Array (CTA) to search for thermally produced dark matter at the TeV scale, via
the associated gamma-ray signal from pair-annihilating dark matter particles in
the region around the Galactic centre. We find that CTA will open a new window
of discovery potential, significantly extending the range of robustly testable
models given a standard cuspy profile of the dark matter density distribution.
Importantly, even for a cored profile, the projected sensitivity of CTA will be
sufficient to probe various well-motivated models of thermally produced dark
matter at the TeV scale. This is due to CTA's unprecedented sensitivity,
angular and energy resolutions, and the planned observational strategy. The
survey of the inner Galaxy will cover a much larger region than corresponding
previous observational campaigns with imaging atmospheric Cherenkov telescopes.
CTA will map with unprecedented precision the large-scale diffuse emission in
high-energy gamma rays, constituting a background for dark matter searches for
which we adopt state-of-the-art models based on current data. Throughout our
analysis, we use up-to-date event reconstruction Monte Carlo tools developed by
the CTA consortium, and pay special attention to quantifying the level of
instrumental systematic uncertainties, as well as background template
systematic errors, required to probe thermally produced dark matter at these
energies.
  "Full likelihood tables complementing our analysis are provided here [
https://doi.org/10.5281/zenodo.4057987 ]"
