Non-Abelian dark matter and dark radiation

We propose a new class of dark matter models with unusual phenomenology. What is ordinary about our models is that dark matter particles are weakly interacting massive particles; they are weakly coupled to the standard model and have weak scale masses. What is unusual is that they come in multiplets of a new dark non-Abelian gauge group with milliweak coupling. The massless dark gluons of this dark gauge group contribute to the energy density of the Universe as a form of weakly self-interacting dark radiation. In this paper we explore the consequences of having (i) dark matter in multiplets, (ii) self-interacting dark radiation, and (iii) dark matter which is weakly coupled to dark radiation. We find that (i) dark matter cross sections are modified by multiplicity factors which have significant consequences for collider searches and indirect detection, and (ii) dark gluons have thermal abundances which affect the cosmic microwave background (CMB) as dark radiation. Unlike additional massless neutrino species the dark gluons are interacting and have vanishing viscosity and (iii) the coupling of dark radiation to dark matter represents a new mechanism for damping the large scale structure power spectrum. A combination of additional radiation and slightly damped structure is interesting because it can remove tensions between global $\mathrm{\Lambda }\mathrm{CDM}$ fits from the CMB and direct measurements of the Hubble expansion rate ($H_0$) and large scale structure (${\sigma }_8$).

Figure 1

Annihilation of dark matter into $SU(2{)}_{\text{weak}}$ gauge bosons or SM fermions. Since the mass splitting between members of $SU(2{)}_{\text{weak}}$ multiplets is small compared with energy transfer in the annihilation diagrams (i.e. twice the $\chi$ mass) we compute the coannihilation of full $SU(2{)}_{\text{weak}}$ multiplets and ignore the mass splittings.

Figure 2

Color factors for the different types of DM search experiments. The different multiplicity factors can be easily understood from the color flow in the figure. For direct detection the color of the incoming dark matter is the same as of the outgoing and so there is no multiplicity factor. For indirect detection it is an annihilation diagram, so just as for the thermal relic calculation there is a $1/2N$ suppression because a DM particle can only annihilate if it finds the antiparticle with the right antidark color. For colliders there is a $2N$ enhancement because any of the different N colors can be created and an extra two from Dirac vs Majorana.

Figure 3

Indirect detection constraints from gamma ray line searches from H.E.S.S. (blue region) and projected sensitivity for gamma ray lines at CTA (gray region) assuming an Navarro-Frenk-White profile for the dark matter distribution in the Galactic center, both taken from [34]. The red dots are the cross sections for dark matter annihilation into gamma rays in our models for $N=2$ up to $N=10$, which were obtained by appropriately rescaling the next-to-leading-log cross section with Sommerfeld enhancement from [34]. For comparison we plotted in black the cross section for the annihilation cross section to photons in the standard wino model as a function of mass, also from [34].

Figure 4

Expected significance of missing energy (MET) searches for DM at the LHC and a future 100 TeV collider. The solid black lines in each plot correspond to the sensitivity of the collider to winolike DM, an $SU(2{)}_{\text{weak}}$ triplet Majorana fermion. The colored dots labeled by different $N$ values correspond to our models in which the DM is a Dirac fermion with multiplicity $N$ and mass chosen to yield the correct abundance from thermal freeze-out.

Figure 5

The process through which dark gluons maintain equilibrium with the DM and the SM plasma for small ${\alpha }_d$.

Figure 6

t-channel scattering of dark matter with dark gluons.

Figure 7

Dark sector temperatures as a function of scale factor $a$. Shown are the dark gluon temperature (black dashed), and DM temperatures for three representative values of ${\alpha }_d={10}^{-8}$ (upper, blue), ${\alpha }_d={10}^{-9}$ (middle, red), and ${\alpha }_d={10}^{-10}$ (lower, green).

Figure 8

Power spectrum including the DM-DR interactions normalized by the power spectrum with interactions turned off. The black dotted curve corresponds to ${\alpha }_d={10}^{-8}$, the green dashed curve corresponds to ${\alpha }_d={10}^{-8.5}$, and the red line corresponds to ${\alpha }_d={10}^{-9}$. The power spectra are defined proportional to ${\delta }_{\mathrm{DM}}^2$ at $a={10}^{-3}$. The vertical yellow band labeled $k_{\mathrm{eq}}$ indicates modes which enter the horizon at matter-radiation equality; modes which enter the horizon earlier are to the right (larger $k$). The blue band labeled ${\sigma }_8$ indicates modes which the observable ${\sigma }_8$ is most sensitive to.