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The standard approach of calculating the relic density of thermally produceddark matter based on the assumption of kinetic equilibrium is known to fail forforbidden dark matter models since only the high momentum tail of the darkmatter phase space distribution function contributes significantly to darkmatter annihilations. Furthermore, it is known that the computationally lessexpensive Fokker-Planck approximation for the collision term describing elasticscattering processes between non-relativistic dark matter particles and theStandard Model thermal bath breaks down if both scattering partners are closein mass. This, however, is the defining feature of the forbidden dark matterparadigm. In this paper, we therefore include the full elastic collision termin the full momentum-dependent Boltzmann equation as well as in a set of fluidequations that couple the evolution of the number density and dark mattertemperature for a simplified model featuring forbidden dark matterannihilations into muon or tau leptons through a scalar mediator. On thetechnical side, we perform all angular integrals in the full collision termanalytically and take into account the effect of dark matter self-interactionson the relic density. The overall phenomenological outcome is that the updatedrelic density calculation results in a significant reduction of theexperimentally allowed parameter space compared to the traditional approach,which solves only for the abundance. In addition, almost the entire currentlyviable parameter space can be probed with CMB-S4, next-generation beam-dumpexperiments or at a future high-luminosity electron-position collider, exceptfor the resonant region where the mediator corresponds to approximately twicethe muon or tau mass.

Forbidden dark matter annihilation into leptons with full collision terms