Systematic investigation on vector dark matter-nucleus scattering in effective field theories

In this paper, we systematically investigate the general spin-1 dark matter–nucleus interactions within the framework of effective field theories (EFTs). We consider both the nonrelativistic (NR) and the relativistic EFT descriptions of the DM interactions with nucleons and quarks. In the NREFT framework, we present a complete list of NR operators for spin-1 DM coupling to nucleons and compute their contributions to the DM response functions. Next, we consider all possible leading-order relativistic EFT operators between DM and light quarks and the photon, and we perform NR reductions to match them onto the NREFT. We then derive the nuclear scattering rate from these interactions and employ recent DM direct detection data (from both the nuclear recoil and the Migdal effect) to constrain all these EFT operators and DM electromagnetic properties. We find that the elastic nuclear recoil data (from PandaX-4T, XENONnT, LZ, and DarkSide-50) set stringent bounds on the EFT coefficients for a DM mass above a few GeV, while the Migdal-effect datasets (from PandaX-4T, XENONnT, and DarkSide-50) can probe a DM mass region as small as 20 MeV. Lastly, we construct a UV-complete model that can provide a complex spin-1 DM candidate, and at the same time generate DM-quark/photon operators discussed in this work.