Higgs-Portal Stueckelberg Dark Matter

TL;DR

The paper investigates dark photon DM X with a dark U(1)X, enforcing zero kinetic mixing via a $Z_2$ symmetry and focusing on Higgs-portal interactions up to dimension-6. Mass generation is realized through the Stueckelberg mechanism, which simultaneously introduces a dimension-4 operator $(H^H) X_ X^\u0019$ and additional dimension-6 terms, expanding the EFT for freeze-in production. The authors compute the DM yield from Higgs-pair annihilation in the electroweak-symmetric phase, showing that gauge-invariant dimension-6 operators dominate the production when their coefficients are order one, but Stueckelberg-induced operators can become relevant if those coefficients are suppressed, with interference effects possible. They demonstrate that a wide region of parameter space can reproduce the observed relic density, spanning DM masses from keV to tens of TeV and allowing viable combinations of $\Lambda$ and $T_{\rm reh}$, while ensuring EFT validity and perturbative unitarity.

Abstract

We study dark photon dark matter $X$ associated with a dark $U(1)_X$ gauge symmetry. To evade laboratory and cosmological constraints on kinetic mixing with the Standard Model $U(1)_Y$, we assign a $Z_2$-odd dark parity to $X$ that forbids such mixing. The leading interactions then arise from gauge-invariant dimension-6 Higgs-portal operators, including both parity-even and parity-odd terms. We assume that the dark matter mass is generated via the Stueckelberg mechanism, which also induces a dimension-4 Higgs-portal operator $(H^\dagger H) X_μX^μ$ and additional dimension-6 operators. We investigate freeze-in production of $X$ from Higgs-pair annihilations after reheating, incorporating both gauge-invariant and Stueckelberg-induced operators. First, we consider the case in which the Wilson coefficients of the gauge-invariant dimension-6 operators, $C$ and $\tilde{C}$, are of order unity. We find that, in this case, the Stueckelberg contributions remain subdominant in dark matter production. This result follows from the requirement that the effective scale implied by perturbative unitarity must exceed the cutoff scale of the effective field theory. Next, we explore a more general situation in which $C$ and $\tilde{C}$ are smaller than unity. In this second case, Stueckelberg-induced operators can become comparable and lead to distinctive features in the dark-matter parameter space, including interference effects. For both cases, we show that there exists a wide parameter space consistent with the observed dark matter relic density.

Figures (6)

• Figure 1: Feynman diagrams for DM production from scalar-pair annihilation within the Higgs doublet. Here, $\phi_i\,(i=1,2,3,4)$ denote the four real scalar components of the Higgs doublet, and $X$ represents the real vector DM.
• Figure 2: Parameter space in the $m_X$-$T_{\mathrm{reh}}$ plane consistent with the observed DM relic density for $C = \tilde{C} = 1$. In the left and right panels, we take the cutoff scale to be $\Lambda = 10^{13,14,15,16}~\mathrm{GeV}$ and $\Lambda = 10^{8,10,12}~\mathrm{GeV}$, respectively. The grey regions indicate $T_{\mathrm{reh}} < m_X$, where DM production is Boltzmann suppressed. DM masses below $1~\mathrm{keV}$ are excluded from consideration due to Lyman-$\alpha$ constraints on warm DM Decant:2021mhj. The DM relic density is overproduced in the blue region ($\Omega_X h^2 > 0.12$), whereas the observed value is realized along the boundary.
• Figure 3: Left: Parameter space in the $C$-$\tilde{C}$ plane. We take $m_X = 10~\mathrm{TeV}$ and $100~\mathrm{TeV}$. Right: Parameter space in the $m_X$-$C~(=\tilde{C})$ plane. In all plots, we fix $\Lambda = 10^{16}~\mathrm{GeV}$ and $T_{\mathrm{reh}} = 10^{12}~\mathrm{GeV}$.
• Figure 4: Same as Figure \ref{['fig:RelicD2']}, but with $\Lambda = 10^{12}$ GeV and $T_{\mathrm{reh}} = 10^{8}$ GeV. We choose $m_X = 1~\mathrm{GeV}$ and $10~\mathrm{GeV}$ in the left panel.
• Figure 5: Same as Figure \ref{['fig:RelicD']}, but with a non-zero coupling $\bar{C}_X = 0.1$, whereas the gauge-invariant dimension-6 operators are set to zero, $C = \tilde{C} = 0$. In the left and right panels, we take $\bar{\lambda}_{HX}=5\times10^{-5}$ and $\bar{\lambda}_{HX}=-5\times10^{-5}$, respectively. The cutoff scale is chosen as $\Lambda = 10^{8,10,12,13,14}~\mathrm{GeV}$.