Abstract
We introduce DRAKE, a numerical precision tool for predicting the dark matter relic abundance also in situations where the standard assumption of kinetic equilibrium during the freeze-out process may not be satisfied. DRAKE comes with a set of three dedicated Boltzmann equation solvers that implement, respectively, the traditionally adopted equation for the dark matter number density, fluid-like equations that couple the evolution of number density and velocity dispersion, and a full numerical evolution of the phase-space distribution. We review the general motivation for these approaches and, for illustration, highlight three concrete classes of models where kinetic and chemical decoupling are intertwined in a way that quantitatively impacts the relic density: (i) dark matter annihilation via a narrow resonance, (ii) Sommerfeld-enhanced annihilation and (iii) ‘forbidden’ annihilation to final states that are kinematically inaccessible at threshold. We discuss all these cases in some detail, demonstrating that the commonly adopted, traditional treatment can result in an estimate of the relic density that is wrong by up to an order of magnitude. The public release of DRAKE, along with several examples of how to calculate the relic density in concrete models, is provided at drake.hepforge.org
Highlights
Precision calculations are necessary in order to match the percent-level observational accuracy
We introduce DRAKE, a numerical precision tool for predicting the dark matter relic abundance in situations where the standard assumption of kinetic equilibrium during the freeze-out process may not be satisfied
We review the general motivation for these approaches and, for illustration, highlight three concrete classes of models where kinetic and chemical decoupling are intertwined in a way that quantitatively impacts the relic density: (i) dark matter annihilation via a narrow resonance, (ii) Sommerfeld-enhanced annihilation and (iii) ‘forbidden’ annihilation to final states that are kinematically inaccessible at threshold
Summary
We will consider situations where DM interactions with the SM heat bath, through elastic scattering and annihilation processes, are initially strong enough to establish both chemical and kinetic equilibrium. Describes the effect of two-body annihilations, and the collision term for elastic scattering processes is given by. Robertson-Walker universe, such that fχ only depends on the absolute value of the DM momentum, p = |p|. Both collision terms and the squared amplitudes |M|2 for the respective process are implicitly summed over all heat bath particles f , and final and initial state internal degrees of freedom, respectively. The phase-space distribution of the heat bath particles is given by the usual g±(ω) = 1/ exp(ω/T ) ± 1. For further highly non-relativistic version of Eq (5), and given by (see details about Eq (1), see Refs. [33,34]
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