The complementary of CTAO, direct detection and collider searches for dark matter in Effective Field Theories and Simplified Models

Abstract This paper explores the sensitivity of the Cherenkov Telescope Array Observatory to dark matter annihilation in the Galactic Center, within the frameworks of Effective Field Theory and Simplified Models. We present sensitivity forecasts, utilizing an up-to-date instrument configuration and incorporating the latest models for Galactic Diffuse Emission. A key aspect of our work is the inclusion of updated dark matter density profiles, J-factors, and velocity dispersion distributions derived from the FIRE-2 cosmological hydrodynamical simulations, which significantly impact the expected indirect detection signals. Furthermore, we update the constraints from direct detection experiments (Xenon1T and LZ) taking into account the astrophysical uncertainties informed by the FIRE-2 simulations, and also investigate limits coming from collider searches (ATLAS and CMS). Our analysis reveals improved constraints on the effective suppression scale ( M * ) in the Effective Field Theory framework and on the mediator mass ( M med ) in Simplified Models compared to previous studies, highlighting the complementarity of the Cherenkov Telescope Array Observatory with direct and collider searches in probing a wide range of dark matter scenarios. We discuss the implications of these results for various dark matter interaction types, including scalar, pseudoscalar, vector, and axial-vector mediators, and emphasize the importance of considering realistic astrophysical inputs in interpreting dark matter search results across different experimental fronts.