On the sensitivity of CTA to gamma-ray boxes from multi-TeV dark matter

Collider, direct and indirect searches for dark matter have typically little or no sensitivity to weakly interacting massive particles (WIMPs) with masses above a few TeV. This rather unexplored regime can however be probed through the search for distinctive gamma-ray spectral features produced by the annihilation of WIMPs at very high energies. Here we present a dedicated search for gamma-ray boxes -- sharp spectral features that cannot be mimicked by astrophysical sources -- with the upcoming Cherenkov Telescope Array (CTA). Using realistic projections for the instrument performance and detailed background modelling, a profile likelihood analysis is implemented to derive the expected upper limits and sensitivity reach after 100 h of observations towards a $2^\circ\times2^\circ$ region around the Galactic centre. Our results show that CTA will be able to probe gamma-ray boxes down to annihilation cross sections of $10^{-27}-10^{-26}\,\text{cm}^3\text{/s}$ up to tens of TeV. We also identify a number of concrete particle physics models providing thermal dark matter candidates that can be used as target benchmarks in future search campaigns. This constitutes a golden opportunity for CTA to either discover or rule out multi-TeV thermal dark matter in a corner of parameter space where all other experimental efforts are basically insensitive.