Freeze-in Production of Non-Abelian Millicharged Vector Dark Matter

Abstract

We present the first predictive realization of vector freeze-in dark matter from a hidden non-Abelian gauge sector, spontaneously broken to a residual $U(1)$ with a massless dark photon mediator. A massive dark vector particle-antiparticle pair acquires small millicharges via a dimension-five kinetic mixing operator that induces a dimension-four mixing term with effective coefficient $ε$, and interacts through the hidden gauge coupling $g_D$, linking it weakly to the Standard Model. Solving the relic abundance with a two-temperature Boltzmann evolution including plasmon decays, we find that $ε, g_D \sim 10^{-7}$ reproduce the observed density while satisfying astrophysical and cosmological bounds. This minimal framework links non-Abelian vector dynamics, long-range dark forces, and dark matter, and can be testable with upcoming sub-GeV dark matter direct-detection experiments.

Figures (7)

• Figure 1: Evolution of the dark sector for benchmark point BM1, defined by $m_{Z^\prime} = 0~\text{GeV}$, $m_{W^\prime} = 0.01~\text{GeV}$, $m_{h_D} = m_{W^\prime}/3$, $g_D = 10^{-7}, \epsilon = 3.8 \times 10^{-7}$, and $\sin\beta = 0$. Top left: Temperature ratio $\xi = T_h/T$ between the dark and visible sectors. Top right: Comoving number densities of dark matter (solid red), dark photons (solid blue), and dark Higgs bosons (solid green). Bottom panels: Interaction rates (per unit volume per unit time) for various processes: $f\bar{f} \to W^p W^m$ (red dashed), $Z$-boson decay (purple dashed), plasmon decay (orange dashed), dark matter pair annihilation into $Z^\prime Z^\prime$ (blue dashed) and $h_D h_D$ (green dashed), and the inverse process $h_D h_D \to W^p W^m$ (magenta dashed).
• Figure 2: Parameter space yielding the correct freeze-in dark matter abundance with reheating temperatures $T_{\rm RH} = 0.1~\text{GeV}, 10~\text{GeV}$, and $1~\text{TeV}$ represented by solid black, blue, and red curves, respectively. Left: Projection onto the $(m_{W^\prime},\epsilon)$ plane with $g_D = 10^{-7}$. Right: Projection onto $(m_{W^\prime}, g_D)$ plane with $\epsilon = 0.5\times10^{-7}$. All remaining parameters follow benchmark BM1, and we fix $\xi_0 = 0.01$. The purple shaded region is excluded by halo-shape (ellipticity) constraints described in (\ref{['eq:ellipticity']}). The gray region is excluded by current DM direct detection searches from SENSEI SENSEI:2020dpa, DAMIC DAMIC-M:2023gxo, EDELWEISS EDELWEISS:2020fxc, SuperCDMS SuperCDMS:2018mne, CDEX CDEX:2022kcd, DarkSide-50 DarkSide:2022knj, XENONnT XENON:2024znc, and PandaX-II PandaX-II:2021nsg. The dashed magenta and orange lines show the projected reach of OSCURA Oscura:2022vmiOscura:2023qik and aluminum-based superconducting detectors Hochberg:2021pktKnapen:2021run, respectively. The dotted black, blue, and red lines indicate the parameter space where dark-sector annihilations significantly deplete the freeze-in abundance with reheating temperatures $T_{\rm RH} = 0.1~\text{GeV}, 10~\text{GeV}$, and $1~\text{TeV}$, respectively.
• Figure 3: Effective number of relativistic species, $\Delta N_{\rm eff} (T_{\rm BBN})$ evaluated at the BBN, and dark matter relic density (indicated by the color scale) as functions of the initial temperature ratio $\xi_0 = (T_{h0}/T_0)_{\rm RH}$ with $T_0 = T_{\rm RH} =1$ TeV. All other parameters are fixed to the values of benchmark point BM1. The region above the red dashed line corresponds to $\Delta N_{\rm eff} > 0.18$, which is excluded by combined BBN and CMB constraints Yeh:2022heq. Points highlighted with red circles indicate parameter choices that reproduce the observed dark matter relic density within the $2\sigma$ range.
• Figure 4: Feynman diagrams for the process of dark matter annihilation into a pair of the SM fermions.
• Figure 5: Feynman diagrams for the process of dark matter annihilation into di-$Z'$ bosons.