Non-relativistic Effective Interactions of Spin 1 Dark Matter

Abstract

We investigate the non-relativistic reduction of simplified models for spin 1 dark matter (DM) with the aim of identifying features in the phenomenology of DM-quark interactions which are specific to vector DM. In the case of DM-quark interactions mediated by a spin 1 particle, we find two DM-nucleon interaction operators arising from the non-relativistic reduction of simplified models for spin 1 DM that are specific to spin 1 DM, and which were not considered in previous studies. They are quadratic in the momentum transfer, linear in a symmetric combination of polarisation vectors for the DM particle, and arise from simplified models which do not generate momentum transfer independent operators as leading interactions in the non-relativistic expansion of DM-nucleon scattering amplitudes. Within these simplified models, the new operators cannot be neglected when computing DM signals at direct detection experiments. For example, we find that nuclear recoil energy spectra computed by including or neglecting the new operators can differ by up to one order of magnitude for nuclear recoil energies larger than about 20 keV and DM masses below $50$ GeV. Furthermore, the shape of the expected nuclear recoil spectra depends significantly on whether the new operators are taken into account or not. Finally, neglecting the contribution to DM direct detection signals from the new operators leads to inaccurate conclusions when assessing the compatibility of a future direct detection signal with CMB constraints on the DM relic density, especially when the number of signal events is small, e.g. $\mathcal{O}(1)$.