New particles χ that are electrically neutral but couple to the electromagnetic current via higherdimensional operators and that are sufficiently light, at or below the GeV-mass scale, can be produced in pairs in a number of dedicated high-intensity experiments. In this work we consider the production of χ through magnetic-and electric-dipole moments as well as through anapole moment and charge radius interactions in electron beams. We derive new constraints from BaBar, NA64 and mQ and forecast the future sensitivity on the existence of such states, from Belle-II, LDMX and BDX. We present for the first time a detailed treatment of the off-shell production of photons in electron beams with subsequent decay into a χχ pair in a 2-to-4 process. These direct limits are then compared to the effects on SM precision observables, as well as to bounds from flavor physics and high energy colliders. Finally, we consider the possibility that χ is dark matter and study ensuing astrophysical and cosmological constraints. We find that a combination of all considered probes rule out χ particles with mass-dimension five and six photon interactions as dark matter when assuming a standard freeze-out abundance.

Electromagnetically neutral dark sector particles may directly couple to the photon through higher dimensional effective operators. Considering electric and magnetic dipole moment, anapole moment, and charge radius interactions, we derive constraints from stellar energy loss in the Sun, horizontal branch and red giant stars, as well as from cooling of the proto-neutron star of SN1987A. We provide the exact formula for in-medium photon-mediated pair production to leading order in the dark coupling, and compute the energy loss rates explicitly for the most important processes, including a careful discussion on resonances and potential double counting between the processes. Stringent limits for dark states with masses below 3 keV (40 MeV) arise from red giant stars (SN1987A), implying an effective lower mass-scale of approximately 10 9 GeV (10 7 GeV) for mass-dimension five, and 100 GeV (2.5 TeV) for mass-dimension six operators as long as dark states stream freely; for the proto-neutron star, the trapping of dark states is also evaluated. Together with direct limits previously derived by us in Chu et al. (2018), this provides the first comprehensive overview of the viability of effective electromagnetic dark-state interactions below the GeV mass-scale.