Abstract
The formation of stable or meta-stable bound states can dramatically affect the phenomenology of dark matter (DM). Although the capture into bound states via emission of a vector is known to be significant, the capture via scalar emission suffers from cancellations that render it important only within narrow parameter space. While this is true for neutral scalar mediators, here we show that bound-state formation via emission of a charged scalar can be extremely significant. To this end, we consider DM charged under a dark U(1) force and coupled also to a light complex scalar that is charged under the same gauge symmetry. We compute the cross-sections for bound-state formation via emission of the charged scalar, and show that they can exceed those for capture via vector emission, as well as annihilation, by orders of magnitude. This holds even for very small values of the DM coupling to the charged scalar, and remains true in the limit of global symmetry. We then compute the DM thermal freeze-out, and find that the capture into meta-stable bound states via emission of a charged scalar can cause a late period of significant DM depletion. Our results include analytical expressions in the Coulomb limit, and are readily generalisable to non-Abelian interactions. We expect them to have implications for Higgs-portal scenarios of multi-TeV WIMP DM, as well as scenarios that feature dark Higgses or (darkly-)charged inert scalars, including models of self-interacting DM.
Highlights
The capture into bound states via emission of a vector is known to be significant, the capture via scalar emission suffers from cancellations that render it important only within narrow parameter space. While this is true for neutral scalar mediators, here we show that bound-state formation via emission of a charged scalar can be extremely significant
Scalar force mediators have been invoked in a variety of theories, including self-interacting dark matter (DM) and Higgs portal models residing in the multi-TeV regime
We computed the cross-sections for the radiative capture of non-relativistic particles into bound states via emission of a scalar that is charged under either a local or global symmetry
Summary
We assume that DM consists of a complex scalar field X that couples to a dark Abelian gauge force U(1)D with V being the gauge boson, as well as to a light complex scalar Φ that is doubly charged under the same force. The quartic terms stabilize the scalar potential at large field values. We do not attempt a detailed phenomenological study of the model, but instead focus on computing the radiative capture into bound states via emission of a charged scalar, and showcasing its implications. Seen from a high-energy perspective, this amounts to a near cancellation between the high-energy value of the running Φ mass and the running contribution. While this may be fine-tuned, the value of the running Φ mass at high energies does not affect our computations. Eq (2.1) can be viewed as an effective theory valid below ∼ mX, that is potentially stabilised by additional physics at higher scales, such as supersymmetry
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