Dark matter and dark radiation from chiral $U(1)$ gauge symmetry

TL;DR

This paper presents a minimal chiral $U(1)_X$ dark sector in which anomaly cancellation requires five chiral fermions, some acquiring mass via a dark Higgs and others remaining massless as dark radiation. The model yields two DM candidates (a Dirac and a Majorana fermion) and predicts a dark photon that kinetically mixes with SM hypercharge, enabling SM–DS interactions and thermal histories that can place the DS in or out of equilibrium with the SM. Cosmological constraints on $ extstyle \\Delta N_{ m eff}$ favor a two-component DM with limited massless DS states and tightly constrain the kinetic mixing: for a Dirac-dominated DM, $\epsilon\sim 10^{-6}$ is required to satisfy direct detection bounds (LZ), while a Majorana-dominated scenario allows larger $\epsilon$ but still faces direct-detection limits due to a Dirac subcomponent. The paper also explores collider tests of the invisible dark photon, showing that $e^+e^- \to \gamma Z'$ searches at future lepton colliders can probe $\epsilon \gtrsim 4\times 10^{-4}$ for $m_{Z'}\sim 30$ GeV, with cosmological constraints disfavoring very light $Z'$; overall, the work links DM phenomenology with dark radiation and collider signatures in a testable framework.

Abstract

We consider a simple model of a dark sector with a chiral $U(1)$ gauge symmetry. The anomaly-free condition requires at least five chiral fermions. Some of the fermions acquire masses through a vacuum expectation value of a Higgs field, and they are stable due to an accidental symmetry. This makes them dark matter candidates. If the dark sector was once in thermal equilibrium with the Standard Model and dark radiation constraints are included, two-component dark matter may be needed since the number of massless fermions is restricted. When the Dirac fermion is the main component of dark matter, the kinetic mixing should be around $10^{-6}$: a larger value is restricted by direct detection limits, while a smaller value prevents thermal freeze-out. If the main dark matter component is a Majorana fermion, the kinetic mixing can be larger. Still, a sub-component of Dirac fermion could produce a detectable signal in future direct detection experiments. We also discuss the possibility of testing an invisible dark photon at future lepton collider experiments, taking into account cosmological constraints.

Figures (6)

• Figure 1: The black solid lines are the interaction rates in Eq. \ref{['eq:thermalization']} and the blue dashed lines are the Hubble rates. In the regions above the blue dashed lines and below the black solid lines, the dark sector is thermalized.
• Figure 2: The spin-independent cross section in units of pb (red dashed) for the Dirac dark matter. The black solid lines show $\Omega h^2 = 0.12$. The dark Higgs mass is taken as 70 GeV.
• Figure 3: The spin-dependent cross section in units of pb (blue dotted) for the Majorana dark matter.
• Figure 4: The relic densities of the dark matter particles and the Dirac fermion (left), and the effective spin-independent cross section (right), $\sigma_{\rm SI,eff}$, in units of pb; $\sigma_{\rm SI,eff} = \sigma_{\rm SI,p} \times \Omega_{\rm Dirac} h^2/0.12$. The mass for the Dirac fermion is set as $M_D=M_Z'/2-0.1 =14.9\,{\rm GeV}$. The observed value of dark matter density and the (approximate) LZ limit are shown as the blue-dotted and black dotted lines, respectively.
• Figure 5: The same figure as Fig. \ref{['fig:si_eff']} but for different values of $M_{Z'}$ and $\epsilon$. The mass for the Dirac fermion is set as $M_D=M_Z'/2-0.1 =2.4\,{\rm GeV}$.