The Pitfalls of Dark Crossings

We explore the connection between pair production of dark matter particles at collider experiments and annihilation of dark matter in the early and late universe, with a focus on the correlation between the two time-reversed processes. We consider both a model-independent effective theory framework, where the initial and final states are assumed to not change under time-reversal, and concrete UV-complete models within the framework of supersymmetric extensions to the Standard Model. Even within the effective theory framework (where crossing symmetry is in some sense assumed), we find that the predictions of that symmetry can vary by orders of magnitude depending on the details of the selected effective interaction. Within the supersymmetric models we consider, we find that there is an even wilder variation in the expectations one can derive for collider observables based on cross-symmetric processes such as having a thermal relic or given indirect dark matter detection rates. We also explore additional "pitfalls" where na\"ive crossing symmetry badly fails, including models with very light mediators leading to Sommerfeld enhancements and/or dark matter bound states.