  Dark matter that interacts with the Standard Model by exchanging photons
through higher multipole interactions occurs in a wide range of both strongly
as well as weakly coupled hidden sector models. We study the collider detection
prospects of these candidates, with a focus on Majorana dark matter that
couples through the anapole moment. The study is conducted at the effective
field theory level with the mono-$Z$ signature incorporating varying levels of
systematic uncertainties at the high-luminosity LHC. The projected collider
reach on the anapole moment is then compared to the reach coming from direct
detection experiments like LZ. Finally, the analysis is applied to a weakly
coupled completion with leptophilic dark matter.
