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

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.