Effective field theories for dark matter pairs in the early universe: Debye mass effects

In some scenarios for the early universe, non-relativistic thermal dark matter chemically decouples from the thermal environment once the temperature drops well below the dark matter mass. The value at which the energy density freezes out depends on the underlying model. In a simple setting, we provide a comprehensive study of heavy fermionic dark matter interacting with the light degrees of freedom of a dark thermal sector whose temperature T decreases from an initial value close to the freeze-out temperature. Different temperatures imply different hierarchies of energy scales. By exploiting the methods of non-relativistic effective field theories at finite T, we systematically determine the thermal and in-vacuum interaction rates. In particular, we address the impact of the Debye mass on the bound-state formation cross section and the bound-state dissociation and transition widths, and ultimately on the dark matter relic abundance. We numerically compare the corrections to the present energy density originating from the resummation of Debye mass effects with the corrections coming from a next-to-leading order treatment of the bath-particle interactions. We observe that the fixed-order calculation of the inelastic heavy-light scattering at high temperatures provides a larger dark matter depletion, and hence an undersized yield for given benchmark points in the parameter space, with respect to the calculation where Debye mass effects are resummed.