Bound State Formation and Sommerfeld Enhancement for simplified dark matter Models

A rich dark sector with multiple annihilation channels can evade current direct detection bounds, like colored co-annihilation which  naturally leads to the prediction of heavier dark matter masses. In such a scenario the Sommerfeld effect and bound state formation must be considered in order to accurately predict the relic abundance. Based on the example of the currently widely studied simplified models with a colored mediator, we demonstrate the importance of considering these non-perturbative effects for correctly inferring the viable model parameters. We emphasize that a flat correction factor on the relic abundance is not sufficient in this context. Moreover, we find that parameter space thought to be excluded by direct detection experiments and LHC searches remains still viable. Additionally, we illustrate that long-lived particle searches and bound-state searches at the LHC can play a crucial role in probing such a model. We demonstrate how future direct detection experiments will be able to close almost all of the remaining windows for freeze-out production, making it a highly testable scenario.