Vector dark matter with non-abelian kinetic mixing

Abstract

An appealing framework for dark matter is provided by light hidden sectors, below the electroweak scale, feebly coupled to the Standard Model via light mediators. We consider a minimal, predictive model where both the dark matter and the mediator are vector bosons, and have the same mass. The portal between the dark sector and the Standard Model is provided by a kinetic mixing between the dark gauge symmetry, $SU(2)_X$, and the hypercharge, $U(1)_Y$, induced by a dimension-six operator. The dark-matter candidates, $X^\pm$, are charged under a custodial symmetry and therefore stable, while the mediator is a massive dark photon, $Z_D$, mixing with the photon and the $Z$. We show how the observed dark-matter abundance can be reproduced via freeze-out or freeze-in, through either the kinetic mixing or the dark gauge interaction. We also analyse dark 3-to-2 annihilations, that can become dominant in model variations with $Z_D$ heavier than $X^\pm$. We confront our relic-density predictions with current and projected experimental, astrophysical and cosmological bounds on the model parameter space, highlighting the correlation between the dark-photon and dark-matter phenomenologies.

Figures (9)

• Figure 1: Feynman diagrams contributing to the number-changing reactions entering the DM Boltzmann equation: (a) kinetic mixing term, corresponding to an $s$-channel diagram mediated by the dark boson $Z_D$, the $Z$ boson, or the photon $\gamma$ ; (b) dark-sector annihilation via contact, $t$-channel, and $u$-channel diagrams; (c)--(e) three distinct SIMP processes: each bubble stands for several possible tree-level topologies, corresponding to different internal propagators. Vertex colours indicate the relevant couplings: green denotes the kinetic mixing parameter $\epsilon$, and purple the dark gauge coupling $g_X$.
• Figure 2: Evolution of the freeze-out DM yield (upper subpanels) and corresponding rates normalized to the Hubble expansion rate (lower subpanels) for four different DM masses: $m_X/{\rm GeV} =$ 0.01 (top left), 10 (top right), 45 (bottom left) and $100$ (bottom right). In each plot, the value of $g_X$ is fixed to reproduce the observed DM relic density, $\Omega_X h^2 = 0.12$Planck:2018vyg, for kinetic mixing $\epsilon \lesssim 10^{-3}$, consistent with experimental limits. The solid blue (dashed gray) lines correspond to the comoving (equilibrium) yield $Y$ ($Y_{\rm eq}$) as a function of $x = m_X/T$. The rates are shown for the five relevant channels, as indicated in the legend.
• Figure 3: Values of the dark gauge coupling $g_X$, as a function of the DM mass $m_X$, which reproduce the observed DM relic abundance, $\Omega_X h^2 = 0.12$Planck:2018vyg. The coloured lines correspond to different values of the kinetic mixing $\epsilon$, as indicated in the legend. The zoomed region near $m_X \simeq 45~\mathrm{GeV}$, corresponding to the $Z$-boson resonance in the $s$-channel, illustrates the enhancement of the kinetic mixing effect. The additional light blue curve in this region represents the case $\epsilon = 10^{-1}$ and is shown only for illustration.
• Figure 4: Diagrams relevant for the $Z_D$ Boltzmann equation: (a) top anti-top annihilation into a dark mediator $Z_D$ and a Higgs doublet $\Phi$ ; (b) $Z_D$ decay into two fermions. Green vertices represent kinetic mixing insertions, while blue stands for the top Yukawa couplings.
• Figure 5: Evolution of the freeze-in DM and $Z_{D}$ yields as a function of $x$ for $m_{Z_D} \simeq m_X = 10~\mathrm{GeV}$. Solid lines represent the DM yield, dot-dashed lines the dark-mediator yield, and gray curves the corresponding equilibrium yields. The colors distinguish between the three different benchmark scenarios defined by fixed $(T_{\rm rh}, g_X, \epsilon)$ values: BP1 = $(v_X,\,3 \times 10^{-6},\,2.5 \times 10^{-15})$ in red, BP2 = $(v,\,3 \times 10^{-6},\,5.4 \times 10^{-9})$ in blue, and BP3 = $(v,\,2 \times 10^{-7},\,8.15 \times 10^{-8})$ in green, all of which reproduce the observed DM relic abundance, $\Omega_X h^2 =0.12$.