Indirect detection of dark matter with (pseudo)-scalar interactions

Indirect detection is one of the most powerful methods to search for annihilating dark matter. In this work, we investigate the impact of non-perturbative effects in the indirect detection of dark matter. For this purpose we utilize a minimal model consisting of a fermionic dark matter candidate in the TeV mass range that interacts via scalar- and pseudo-scalar interactions with a massive scalar mediator mixing with the Higgs. The scalar interaction induces an attractive Yukawa potential between dark matter particles, such that annihilations are Sommerfeld enhanced, and bound states can form. These non-perturbative effects are systematically dealt with (potential) non-relativistic effective field theories and we derive the relevant cross sections for dark matter. We discuss their impact on the relic density and indirect detection. Annihilations in dwarf galaxies and the Galactic Center require special care and we derive generalized $J$-factors for these objects that account for the non-trivial velocity dependence of the cross sections in our model. We use limits on the gamma-ray flux based on Fermi-LAT observations and limits on the rate of exotic energy injection from Planck to derive bounds on the parameter space of the model. Finally, we estimate the impact that future limits from the Cherenkov Telescope Array are expected to have on the model.