A new idea for relating the asymmetric dark matter mass scale to the proton mass

TL;DR

The paper tackles the puzzle of why dark matter mass appears comparable to the proton mass by proposing a new asymmetric dark matter mechanism that ties the dark QCD confinement scale to the visible QCD scale. It achieves this with an extended color sector $SU(3)_1 \times SU(3)_2 \times SU(3)_D$ and a $\mathbb{Z}_2$ exchange symmetry, which relates the visible and dark gauge couplings at a high scale and, through RG running, yields confinement scales of the same order, leading to $m_{DM} \sim m_p$. A KSVZ-type axion emerges from the spontaneous breaking of a Peccei–Quinn–like symmetry, solving the strong CP problem and providing additional phenomenology; the model also accommodates TeV-scale exotica like colorons, with viable parameter space constrained by DM self-interactions, naturalness, and collider bounds. The authors outline a path toward a full cosmological treatment, including a potential baryogenesis portal, and emphasize that the framework makes testable predictions for future collider experiments and precision cosmology.

Abstract

Asymmetric dark matter is a well-motivated approach to explain the apparent coincidence between the relic densities of visible and dark matter, $Ω_D \simeq 5.4Ω_b$. A complete explanation requires two components, a relation between the particle masses of the dark and visible matter, and a second relation between the number densities in each sector. In this work, we propose a new mechanism to address the former. We consider an extended $SU(3)_1 \times SU(3)_2$ colour group in the visible sector, with QCD embedded as the diagonal subgroup. A $\mathbb{Z}_2$ exchange symmetry then relates $SU(3)_2$ to a dark, confining $SU(3)_D$ sector. The dark matter is a composite state of dark fermions transforming in the fundamental representation of $SU(3)_D$. The spontaneously broken $\mathbb{Z}_2$ symmetry ultimately leads to a relation between the QCD and dark gauge couplings which, for suitable field content, gives rise to confinement scales of the same order of magnitude. The mechanism leads to a rich particle spectrum above the TeV scale which could be probed at future experiments. The model also naturally includes an axion solution to the strong CP problem.

Figures (4)

• Figure 1: Running of the coupling constants for benchmark points in the two configurations, $M_{\psi_2}<u_3$ (left panel) and $M_{\psi_2}>u_3$ (right panel). The running of $\alpha_c$ (red), $\alpha_1$ (purple), $\alpha_2$ (dashed yellow) and $\alpha_D$ (dark blue) are shown up to a high scale, taken as $10^8$ GeV. For the left panel, the benchmark values are $u_3=10^{4.7}$ GeV and $M_{\psi_2}=10^{3.3}$ GeV, while for the right panel they are taken as $u_3=10^{3}$ GeV and $M_{\psi_2}=10^4$ GeV. These parameter choices were made to showcase the behaviour of the couplings for the different configurations.
• Figure 2: Ratio of the visible and dark confinement scales, $R=\Lambda_D/\Lambda_{\text{\tiny{QCD}}}$. The left panel shows $R$ as a function of $u_3$ for the special case where $u_3=M_{\psi_2}$. The right panel shows the results as contours of $R$ in the ($u_3,M_{\psi_2})$ plane. Regions where $R \lesssim 0.8$ are excluded by astrophysical bounds on self-interacting DM and are shown as brown shaded regions. The blue shaded regions are disfavoured by electroweak naturalness and the red shaded regions are excluded by collider experiments.
• Figure 3: Ratio of the visible and dark confinement scales, $R=\Lambda_D/\Lambda_{\text{\tiny{QCD}}}$, for $N_f=1$. The left panel shows $R$ as a function of $u_3$ for the special case where $u_3=M_{\psi_2}$. The right panel shows the results as contours of $R$ in the ($u_3,M_{\psi_2})$ plane. The blue and red shaded regions correspond to the naturalness and collider bounds, respectively, as discussed in the main text.
• Figure 4: Ratios of the visible and dark confinement scales, $R=\Lambda_D/\Lambda_{\text{\tiny{QCD}}}$, for different choices of $x$. The top row shows results for the special case $u_3=M_{\psi_2}$, while the bottom row shows contours of $R$ in the ($u_3,M_{\psi_2})$ plane. The blue, red and brown shaded regions correspond to the naturalness, collider, and self-interacting DM bounds, respectively, as discussed in the main text. Grey shaded regions denote the parameter space where the ratio of confinement scales exceeds $10$.