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We reexamine the consequences of perturbative unitarity on dark matterfreeze-out when both Sommerfeld enhancement and bound state formation affectdark matter annihilations. At leading order (LO) the annihilation cross-sectionis infrared dominated and the connection between the unitarity bound and theupper bound on the dark matter mass depends only on how the different partialwaves are populated. We compute how this picture is modified at next-to-leadingorder (NLO) with the goal of assigning a reliable theory uncertainty to thefreeze-out predictions. We explicitly compute NLO corrections in a simple modelwith abelian gauge interactions and provide an estimate of the theoreticaluncertainty for the thermal masses of heavy electroweak $n$-plets. Along theway, we clarify the regularization and matching procedure necessary to dealwith singular potentials in quantum mechanics with a calculable, relativisticUV completion.

The Sommerfeld enhancement at NLO and the dark matter unitarity bound