Abstract
It has been recently demonstrated that the 125 GeV Higgs boson can mediate a long-range force between TeV-scale particles, that can impact considerably their annihilation due to the Sommerfeld effect, and hence the density of thermal relic dark matter. In the presence of long-range interactions, the formation and decay of particle-antiparticle bound states can also deplete dark matter significantly. We consider the Higgs boson as mediator in the formation of bound states, and compute the effect on the dark matter abundance. To this end, we consider a simplified model in which dark matter co-annihilates with coloured particles that have a sizeable coupling to the Higgs. The Higgs-mediated force affects the dark matter depletion via bound state formation in several ways. It enhances the capture cross-sections due to the attraction it mediates between the incoming particles, it increases the binding energy of the bound states, hence rendering their ionisation inefficient sooner in the early universe, and for large enough couplings, it can overcome the gluon repulsion of certain colour representations and give rise to additional bound states. Because it alters the momentum exchange in the bound states, the Higgs-mediated force also affects the gluon-mediated potential via the running of the strong coupling. We comment on the experimental implications and conclude that the Higgs-mediated potential must be taken into account when circumscribing the viable parameter space of related models.
Highlights
Beyond the TeV regime, and have given impetus to co-annihilation scenarios [1,2,3,4,5], which provide more flexibility in reproducing the observed DM density via freeze-out
We shall consider the simplified model of ref. [42], where DM is assumed to co-annihilate with a coloured scalar that transforms under the fundamental of SU(3)c and possesses a sizeable coupling to the Higgs
This scenario is encountered in the Minimal Supersymmetric SM (MSSM) — with the coloured particle being typically the lightest stop eigenstate — and constitutes one of the last refuges of neutralino DM; as such, it has received a lot of attention recently [2, 43, 44], with the effect of radiative bound-state formation (BSF) due to gluon exchange computed in [38]
Summary
We assume that DM is a Majorana fermion χ with mass mχ, that co-annihilates with a complex scalar X with mass mX. This implies a lower limit on the interconversion cross-section, σ(X + SM ↔ χ + SM) ∼ Γ(X + SM ↔ χ + SM)/neSqM, where neSqM stands for the number density of the SM particles participating in these processes With the latter being relativistic during the DM freeze-out, neSqM ∼ T 3, and H ∼ 17 T 2/MPl, we find the condition σ(X + SM ↔ χ + SM). While σeff vrel in general denotes the effective, thermally averaged cross-section that includes all annihilation and co-annihilation processes, each weighted by the number densities of the interacting species, we assume for the purpose of our study that the NLP self-annihilation is the dominant contribution. It comprises of the direct annihilation channels, and of the BSF processes, whose cross-sections must be weighted by the fraction of bound states that decay rather than being ionised, as we discuss below
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