Rapid Bound State Formation of Dark Matter in the Early Universe

Abstract

The thermal decoupling description of dark matter (DM) and co-annihilating partners is reconsidered. If DM is realized at around the TeV-mass region or above, even the heaviest electroweak force carriers could act as long-range forces, leading to the existence of meta-stable DM bound states. The formation and subsequent decay of the latter further deplete the relic density during the freeze-out process on top of the Sommerfeld enhancement, allowing for larger DM masses. While so far the bound-state formation was described via the emission of an on-shell mediator (W ± , Z, H, g, photon or exotic), we point out that this particular process does not have to be the dominant scattering-bound state conversion channel in general. If the mediator is coupled in a direct way to any relativistic species present in the Early Universe, the bound-state formation can efficiently occur through particle scattering, where a mediator is exchanged virtually. To demonstrate that such a virtually stimulated conversion process can dominate the on-shell emission even for all temperatures, we analyze a simplified model where DM is coupled to only one relativistic species in the primordial plasma through an electroweak-scale mediator. We find that the bound-state formation cross section via particle scattering can exceed the on-shell emission by up to several orders of magnitude.

Dark matter bound-state formation at higher order: a non-equilibrium quantum field theory approach

“…So far, the formation of dark matter bound states via the emission of an on-shell mediator was considered as the dominant process. However, it was pointed out recently that this does not necessarily have to be the dominant BSF channel during the thermal dark matter freeze-out [63]. The conversion between scattering and bound states in the radiation dominated epoch can also efficiently take place via bath-particle scattering, where a mediator is exchanged virtually between a DM two-body pair and a relativistic primordial plasma particle.…”

“…While in ref. [63], a mediator with a mass larger than the binding energy was investigated, we consider massless or lighter mediators in the present work. The masses of SM force-carries is temperature dependent during the electroweak cross over, which motivates to investigate these cases more carefully.…”

“…The problem is that the bound-state formation amplitudes diverge for massless mediators in the forward scattering direction of the in-and out-going bath particles in figure 1 (see also ref. [63]). Since these processes are temperature dependent, the Kinoshita-Lee-Nauenberg (KLN) theorem [65,66] is not directly applicable.…”

Dark matter bound state formation via emission of a charged scalar

“…Importantly, our results can be recast to compute BSF via scattering on a bath of relativistic particles, through exchange of a charged scalar, according to the recent analysis of ref. [24]. This can be particularly important for the chemical decoupling of multi-TeV WIMP DM coupled to the 125 GeV Higgs [35]; in this regime the Higgs can indeed act as a light mediator [1,2], even if its on-shell emission in capture processes is not kinematically allowed.…”

“…Reference [24] found that the rate of capture via scattering factorises into the radiative crosssection (albeit without any phase-space suppression due to the mass of the emitted scalar), times a part that includes the kinematics and dynamics of the bath particles. The cross-sections (2.25) can then be recast to calculate BSF via off-shell exchange of a charged scalar.…”