Thermal decoupling of WIMPs from first principles

Abstract

Weakly interacting massive particles (WIMPs) are arguably the most natural dark mattercandidates from a particle physics point of view. After their number density has frozen outin the early universe, thereby setting their relic density today, WIMPs are still kept veryclose to thermal equilibrium by scattering events with standard model particles. Thecomplete decoupling from the thermal bath happens as late as at temperatures of around∼1−10 MeV and provides an important cosmological scale that can directly be translated into asmall scale cut-off of the spectrum of matter density fluctuations. We present here a fullanalytic treatment of the kinetic decoupling process from first principles. This allows anexact determination of the decoupling scale, for arbitrary WIMP candidates and anyscattering amplitude. As an application, we consider the situation of the lightestsupersymmetric particle as well as the lightest Kaluza–Klein particle that arises in theorieswith universal extra dimensions; furthermore, we show that our formalism canalso easily be applied to, e.g., the evolution of the non-relativistic electrons intothe recombination regime. Finally, we comment on the impacts for the smallestgravitationally bound structures and the prospects for the indirect detection of darkmatter.